Università degli Studi di Torino Scuola di Dottorato in Scienza e Alta Tecnologia

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1 Università degli Studi di Torino Scuola di Dottorato in Scienza e Alta Tecnologia Università degli Studi di Torino Scuola di Dottorato in Scienza e Alta Tecnologia Tesi di Dottorato di Ricerca in Scienza e Alta Tecnologia. Indirzzo:Fisica e Astrofisica Tesi di Dottorato di Ricerca in Scienza e Alta Tecnologia. Indirizzo: Nome dell indirizzo COUPLING LAND SURFACE PROCESS MODEL WITH THE WEATHER RESEARCH FORECAST MODELING SYSTEM Zhang Ying Tutor: Prof. Claudio Cassardo XXII Ciclo, Gennaio 2010.

2 Università degli Studi di Torino Scuola di Dottorato in Scienza e Alta Tecnologia Coupling Land Surface Process Model with the Weather Research Forecast Modeling System Zhang Ying

3 Acknowledgements First of all, I really appreciate to my academic supervisor, Prof. Claudio Cassardo. I learnt from him not only way to research but also way to live. I also appreciate Prof. Arnaldo Longhetto for not only valuable discussions about my work but also many advices. Also I would like to thank my colleagues of GRUPPO GEOFIT who helped to make my time as a PhD student particularly enjoyable. I would like to thank my family and my friends who encouraged me in my work. I especially appreciate the support of Jiangxi Provincial Meteorological Administration. Finally I acknowledge financial support for my studies from the University of Turin.

4 Abstract Over the past 20 years, the land surface processes (LSPs) made a rapid progress in developing climate model and general circulation models (GCMs) as well as regional and mesoscale atmospheric models. The LSP is one of elementary physical and biochemistry process which affects the atmospheric circulation and climate change. The climate system is influenced by the land surface at a variety of time and spatial scales. Between the atmosphere and surface, exchange of energy, momentum and transportation of radiation are included. As a source, the atmosphere is heated by the surface by sensible heat energy, as well as surface provides moisture to the atmosphere as a sink via evaporation. Many studies (Rowntree 1983; Mahfouf et al. 1991; Chen and Avissar 1994a, b,) showed that the LSPs play an important role in climate model and general circulation models (GCMS) but also in mesoscale numerical weather prediction models. In this thesis, a hydro-thermodynamic soil vegetation scheme called land surface process model (LSPM, Cassardo et al., 1995) has been introduced into the Weather Research and Forecasting (WRF) model. The land surface process model is a soil vegetation atmosphere transfer (SVAT) model which developed at University of Turin. It is a typical one-dimensional model of energy, momentum and water exchanges between the atmosphere and land. The LSPM has various degrees of sophistication in dealing with thermal and moisture fluxes in multiple layers of the soil and may also handle vegetation, root, and canopy effects and surface snow-cover prediction. It was tested in different climatic conditions. The WRF model is a numerical weather prediction (NWP) and atmospheric I

5 simulation system designed for both research and operational applications. Now three land surface schemes are available included in WRF model; they are the 5-layer thermal diffusion, the NOAH LSM and the Rapid Update Cycle (RUC) LSM. In the past, the LSPM was always used to simulate different climatic regions as a individual model or was coupled to RAMS. In this work the two-way coupled WRF-LSPM has been realized successfully. In WRF-LSPM, the WRF model provides the air temperature, the atmospheric pressure, the specific humidity, the total cloudiness, the X component wind velocity U, the Y component wind velocity V, the precipitation rate (rain + snow), the low cloudiness, the solar global incoming radiation and the relative humidity, initial soil moisture and temperature to LSPM. The fluxes calculated by LSPM, as well as soil temperature and moisture, canopy temperature and many other surface variables, provided as a lower boundary condition for the vertical transport done in the planetary boundary layer (PBL) schemes of WRF. The LSPM does not provide tendencies, but updates the land s state variables including the ground (skin) temperature, soil temperature profile, soil moisture profile, snow cover, and canopy properties. To verify the effect of the WRF-LSPM, a set of experiments have done, which include heat wave event in Piedmont region, Italy, 2003 and a mesocale typhoon Sepat event in China, II

6 Contents Abstract Contents I IV 1 General introduction of the land surface process 1 2 General introduction of land surface parameterization scheme Physical processes in soil The thermodynamic properties Soil hydrology Physical processes of surface by snow The energy equation The mass balance equation Physical processes in canopy Interception Aerodynamical resistances Drag coefficients Similarity theory at near ground boundary layer Neutral layer Non-neutral layer The introduction of land surface process model Introduction of LSPM The structure of LSPM The physical processes in LSPM III

7 3.3.1 Radiative fluxes Energy balance Heat Transfer in Soil The vegetation temperature Hydrological processes Soil Vegetation Surface and underground runoff The snow parameterization Definitions Melting processes of snow Snow energy balance Snow albedo Thermal balance in the snow pack Snow compaction and density Snow coverage Summary The introduction of WRF The main features of WRF model WRF software framework Dynamical equations Time integration scheme Lateral boundary conditions Nesting Physical processes Technical information on source code compilation Coupling the LSPM model with the WRF model Introduction Brief description of the LSPM...61 IV

8 5.3 Dataset for vegetation classification and soil texture in WRF and LSPM Vegetation classification Soil texture The physical interface of WRF Initialization of soil moisture Preliminary comparison of LSPM, NOAH and RUC schemes Summary A landfall typhoon simulation by WRF-LSPM Introduction Setting of the experiment Meteorological analysis of the event The sensitivity experiments Analysis of Control run Validation of the WRF-LSPM Comparison of NOAH, RUC and LSPM Analysis of sensitivity experiments results Sensitivity experiments on initial soil moisture Summary The 2003 heat wave analysis in Piedmont region, Italy Introduction The Piedmontese station data Setting of the experiments Model results Temperature Precipitation Wind speed Brief comparison of surface energy and water budget Dry and wet sensitivity experiments LSPM offline simulation V

9 7.8 Summary Conclusion 121 Appendix A: How to compile and run WRF version 3.1 in a Linux workstation 126 Appendix B: How to implement the LSPM into WRF 131 Bibliography 142 VI

10 Chapter 1 General Introduction of the land surface processes Although the importance of the land surface processes (LSPs) was evidenced since the first model of Deardorff (1978), their impact of land surface on weather and climate was only recently recognized. The atmospheric general circulation (AGC) models used for climate simulation and weather forecasting require the fluxes of radiation, heat, water vapor, and momentum across the land-atmosphere interface to be specified. These fluxes are calculated by land surface parameterizations. Early efforts to introduce parameterizations of land surface processes into global climate models were driven by the understanding that the development of the atmospheric planetary boundary layer (PBL, including clouds and precipitation) is strongly affected by the redistribution of incoming radiative energy at the land surface into sensible and latent heat fluxes. In numerical prediction model (NPM), the land surface models (LSMs) use atmospheric information from the surface layer scheme, radiative forcing from the radiation scheme, and precipitation forcing from the microphysics and convective schemes, together with internal information on the land s state variables and land-surface properties, to provide heat and moisture fluxes over land points and sea-ice points. These fluxes provide a lower boundary condition for the vertical transport in the PBL schemes. Budyko (1956) put forward a simple so-called Bucket scheme in which he presumed the surface to act as a single layer like a bucket, in order to obtain the amount of evaporation and runoff. Manabe (1969) firstly adopted this scheme to evaluate hydrological budget between land surface and atmosphere in general circulation model (GCM). His scheme predicted the water vapor in the atmosphere, 1

11 the soil moisture and snow cover without taking into account the soil and vegetation categories. Charney (1975) was one of the first researchers to study the sensitivity of LSP in GCM. In his research, he took into account the biosphere, and eventual feedback mechanisms able to conceivably lead to instabilities or met stabilities in desert border regions. In fact, a reduction of vegetation, with a consequent increase in albedo in the Sahel region at the southern margin of the Sahara would cause vertical sinking motion, and then additional drying. Carson (1981) gave a summary on the earliest LSP parameterization schemes as follows: in LSMs the vegetation would lead two key issues that are of paramount importance for LSPs. Firstly, and foremost, the accurate description of land surface characteristics, including the surface albedo, roughness, etc, were assigned simply too generically, not considering the effects of different soil textures and vegetation categories; in this way, the model could not present the physical realism of the surface-atmosphere interaction. Secondly, in the Bucket scheme, the soil was only considered as a single layer, like a bucket, with the result that the moisture diffusion in the soil was ignored, causing a calculation bias of the surface temperature and soil moisture content. Thirdly, the bucket model only use one layer in the soil (a single soil reservoir) and does not allow a quick response to precipitation events. For vegetated areas, the bucket model fails to recognized the impact of the canopy resistance on evaporation. For that reason, hereafter, the action of vegetation cover was took into account on the LSPs, which were called soil vegetation atmosphere transfer schemes (SVATs), in the GCMs. The first generation of SVATs evolved from the simplest bucket schemes focused only on the soil water availability (Manabe, 1969), through the schemes of Deardorff (1978), to the biosphere-atmosphere transfer scheme (BATS) of Dickinson et al. (1986) and to the simple biosphere (SiB) model of Sellers et al. (1986). Most studies focused on the global change of the interactions between the hydrosphere, biosphere, and atmosphere attracted extensive attention, and more and more international investigations recognized the importance of including the heterogeneities 2

12 typical of the hydrological processes (e.g., the features of soil texture, precipitation, and topography) into the land surface schemes (Famiglietti and Wood 1994; Peters-Lidard et al. 1998). Following the recognition of the importance of LSPs in climate modeling systems, there have been significant efforts to attempt to represent more accurately the land atmosphere interactions. As a result of this pursuit, a wide spectrum of LSMs were developed in the last 30 years. One important work along with this idea is the introduction of a foliage layer (represented by a single) into a soil model proposed by Deardorff (1978). This idea and the conception and equations of force-restore on heat exchange that were adopted as the main base conception in many subsequent LSPs. Dickinson et al. (1984, 1993) firstly introduced the treatment of the vegetation in the BATS model through empirical relationships between leaf stomatal controls of transpiration and environmental parameters such as temperature and light levels. BATS as subsequently included into the National Center for Atmospheric Research (NCAR) community climate model. BATS uses three soil layers. All layers have homogeneous soil characteristics. Vegetated areas and non vegetated bare soil areas are assumed to be distributed evenly. Vegetation and soil parameters are usually a function of vegetation and soil type, respectively. Roots can occur unequally in both the surface and the root zone-surface layers. Sellers et al. (1986) developed a SiB to calculate the transfer of energy, mass and momentum between the atmosphere and the vegetated surface. The SiB model is a one-dimensional soil-vegetation-atmosphere model to be used in GCMs. The basic processes in SiB model are conceptually similar to those in BATS, however the vegetation, in the model grid was divided into two layers. The upper layer represents the canopy of trees or shrubs, while the lower layer represents the annual cover of grass or other herbaceous plants (Fig. 1.1). The soil was divided into three layers including: the surface layer, the root layer and the bottom layer, respectively. The governing equations were used for calculating nine prognostic physical variables: four temperatures (the canopy temperature and the three soil surface temperatures), two interception water stores (one for the canopy and the other for the ground cover) and 3

13 the three layers soil moistures. Xue et al. (1991) developed a simplified version of SiB (SSiB) in response to criticism from the atmospheric modeling community that the original model was computationally expensive and more complex than truly was necessary for GCM applications. Fig. 1.1: Vegetation morphology represented in the SiB, (derived from Sellers, 1986) Subsequent, more than twenty LSPs (e.g, Mccumber et al. 1981; Pan et al. 1987; Noilhan et al. 1989; Wood et al.1992; Cassardo et al ), which are more modest or complex with respect to SiB, were developed by different research projects. The complex models employ a comprehensive treatment of biophysical and radiative interactions between soil surface, vegetation, and the atmosphere. The SVATs include the physical treatment of the atmosphere-biosphere complicated exchanges of momentum, water and energy. Basing on the land surface parameters, the actual physiological processes (e.g., transpiration) and radiative processes were described and improved in detail. The SVATs made a great progress compared with the bulk models. Koster et al. (2000) described a catchment-based approach for modeling land-surface processes: the use the hydrological catchments as the fundamental land unit, rather than the regular grid adopted in atmospheric models. He emphasized, using the World Climate Research Programme Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) results, that both evaporation and runoff control the annual total evaporation. The less accurate of these formulations determines the evaporation error. He emphasized also the need to improve the treatment of subgrid-scale soil moisture heterogeneity and its effects on runoff generation. His preliminary results illustrate the key role of spatial 4

14 heterogeneity in determining soil moisture and, hence, runoff. The results show that the individual land-surface schemes participating to PILPS capture specific aspects of the complex system with reasonable accuracy but no one scheme captures the whole system satisfactorily and consistently. Global climate and the global carbon cycle are controlled by exchanges of water, carbon and energy between the terrestrial biosphere and atmosphere. So-called third generation LSMs developed rapidly (e.g., Collatz et al. 1991; Bonan 1995; Sellers et al. 1996; Foley et al. 1996; Dickinson et al. 1998) including a treatment of photosynthesis to describe the stomatal controls on evaporation and transpiration (e. g., Sellers et al. 1996). This third generation of LSMs include the explicit representation of the role of carbon and nitrogen in modulating energy and water fluxes. Collatz et al. (1991) utilized an energy balance and mass transport sub-model to couple the physiological processes via a variable boundary layer to the ambient environment. The combined models were used to simulate the responses of latent heat flux and stomatal conductance for a soybean canopy in the course of an idealized summer day, using the big-leaf approximation. The simulations illustrate the possible significance of the boundary layer in mediating feedback loops which affect the regulation of stomatal conductance and latent heat. Plants transpiration is considered as a by-product of the above mentioned requirements for leaves to assimilate carbon. In the third generation LSMs, a key parameter is the leaf's capacity for photosynthesis, identified by the maximum carboxylation rate (V cmax ), which is known to have a strong association with leaf nitrogen content. Increase in productivity of a plant canopy may result from increasing its Leaf Area Index (LAI, total leaf area per unit ground area) as well as from increasing the photosynthetic activity of leaves. Cox et al. (1998) pointed out that observed leaf level relationships between stomatal conductance and net photosynthesis suggest an alternative approach. They gave an appropriate algorithm for scaling these values up to canopy level, such relationships allow canopy conductance values to be derived from (comparatively) well validated models of leaf photosynthesis. This approach is likely to become especially attractive as land surface schemes are extended to simulate CO 2 fluxes. 5

15 Niyogi et al. (2009) pointed out that current land surface schemes used for mesoscale weather forecast models use the Jarvis-type stomatal resistance formulations for representing the vegetation transpiration processes. The authors developed and coupled a photosynthesis, gas exchange-based surface evapotranspiration model as a land surface scheme for mesoscale weather forecasting model applications. The coupling system was validated over different natural surfaces including temperate C4 vegetation (prairie grass and corn field) and C3 vegetation (soybean, fallow, and hardwood forest) under contrasting surface conditions (such as different soil moisture and leaf area index). Their results indicated that the coupled model was able to realistically simulate the surface fluxes and the boundary layer characteristics over different landscapes. Most of the current LSMs are used for representing the soil-vegetation-atmosphere transfers. But it is important, in the future, that a model not only need to be focused on the interactions among atmosphere, vegetation, and soils that impact seasonal-to-centennial climate predictions, but also that it is based on developmental and biophysical properties of plants. Such hybrid model must operate on a diurnal cycle at any spatial resolution, combining dynamically general plant types, photosynthesis, respiration, plant competition, nitrogen uptake, energy balance and transpiration, soil organic matter decomposition, and soil mineral N availability. This thesis includes eight chapters, organized as follow: - In chapter 1, a general development introduction of three generation land surface processes schemes. - In chapter 2, the land surface physical parameterization schemes are discussed from a general point of view. - In chapter 3, the land surface process model (LSPM) is presented, and its parameterization schemes are illustrated. - In chapter 4, the Weather Research and Forecasting Model (WRF) is presented, and its control equations, method of integration schemes are illustrated. - In chapter 5, a number of issues related to the coupled WRF-LSPM are presented. 6

16 - In chapter 6, a set of simulation experiments focused on the sensible heat flux, latent heat flux and moisture flux fields have been performed by WRF-LSPM in order to investigate the typhoon Sepat. - In chapter 7, the energy and water budget reproduced by the three land schemes (LSPM, NOAH and RUC) coupled with WRF are simulated in Piedmont region during the summer of A quantitative model results comparison is performed and discussed. - In chapter 8, the general conclusions are outlined. 7

17 Chapter 2 General introduction of land surface parameterization scheme As mentioned in the chapter 1, the LSPs play an important role between atmosphere and surface. The current LSPs include the energy, momentum and water exchanges at the interface between the atmosphere and surface. The incident shortwave radiation absorbed by surface depends on the land surface properties. The partitioning of the available energy at the surface into latent and sensible heat fluxes depends on the net solar radiation, which in turn is defined as the sum of the radiative fluxes, latent and sensible heat flux. The latent and sensible heat fluxes play different roles for the atmosphere. Sensible heat means energy immediately available for the atmosphere, while the latent heat flux is related to the evaporation flux which provides moisture to the boundary layer. The soil layer regulates, through its water content, the redistribution of rainfall in evaporation, soil storage, groundwater recharge, and runoff. Vegetated covered surfaces have the ability to extract water from soil root layer. Numerical weather prediction at large scale is generally performed by a numerical integration of the hydrodynamic equations governing atmospheric motions. The differential equations taking a grid-point model, for example, are approximated by finite difference equations applied to a grid of finite volumes. The microscale processes in the form of heat and moisture fluxes over land and sea are the driving forces for the large-scale circulation systems of the earth. The balance of energy fluxes at the surface is crucial for the understanding of the interaction between land surface and the atmosphere. Hence, the LSP scheme should be able to provide adequate feedback mechanism for PBL and other physical processes. The LSP schemes used in GCMs range from simple bucket models to complex models with more realistic and detailed description of vegetation and soil processes. Therefore parameterization of LSPs is one of the most important components of the atmospheric 8

18 modeling. In the following section, the land surface physical parameterization schemes are discussed from a general point of view. 2.1 Physical processes in soil The thermodynamic properties The soil is characterized by its texture, structure, composition, and water content. The soil can be considered a three phase heterogeneous system, where the solid phase is called the soil matrix, the liquid phase is the soil water and the gaseous phase is the moist air trapped in its pores (Hillel 1982). The soil temperature is determined by the heating absorption (or release), but among different type soils there are different thermal variations, because both the heat storage and conduct are also different. Heat variations in the atmosphere and land surface are determined mainly by the incoming solar radiation. The solar radiation is the main heat source affecting the soil thermal processes. By neglecting small energy components, the energy balance on a surface can be expressed using the following equation: Rn GH LE (2.1) where R n is net radiation, G is the soil heat flux, H is the sensible heat flux, and LE is the latent heat flux. All fluxes have units of W m -2 ; R n is positive downwards, while H and LE are defined as positive when directed from soil to atmosphere, and G possible from surface to deep soil. The thermodynamic properties of the soil are mainly decided by the following four physical parameters: C V : Volumetric heat capacity (J m -3 K -1 ). λ: Thermal conductivity (W m -1 K -1 ). k: Thermal diffusivity (m 2 s -1 ). T: Soil temperature (K) Volumetric heat capacity 9

19 Volumetric heat capacity c V is the amount of heat required to raise the temperature of a unit volume by 1 K. It depends on the mineral, organic matter, and water content of soil. C V can be written as: cv cj (2.2) where ρ is the density of some material, and c j is the corresponding mass specific heat. Table 2.1 gives the heat capacities of different materials. Material Mass specific heat capacity (J g -1 K -1 ) Volumetric heat capacity (J cm -3 K -1 ) Quartz Kaolinite Calcium Soil air Water Table 2.1: Heat capacity of some materials in soil The amount of energy (Q) needed to raise or lower the temperature of a known volume (V) of soil from T i to T j is given by: Q c ( T T) V (2.3) V j i Thermal diffusivity Thermal diffusivity is the ratio of the thermal conductivity to the volumetric heat capacity. It measures how fast the temperature of a soil layer changes. k (2.4) c Therefore, it is useful to determine the rate of temperature variation for a soil layer. V Thermal conductivity It is difficult to evaluate the soil thermal conductivity, and there are many empirical formulas to calculate the soil thermal conductivity. One of the most precise is the scheme of Johansen (1975), reported in Peter-Lidard et al. (1998) : ( ) (2.5) e sat dry dry 10

20 where λ e is Kersten number (λ e, known as the Kersten number); λ sat and λ dry are the soil thermal conductivity in the case of saturated and dry soil, respectively. The latter is given by: dry d d (2.6) Where γ d is the dry density in kg m -3. The dry density may be obtained from the porosity n assuming the same solids unit weight as: (1 n)2700 (2.7) d Soil temperature The classical one dimension heat conduct equation is gave as: c V T F z t z (2.8) where T is soil temperature (K), c V is the volumetric soil heat capacity (J m -3 K -1 ), z is the vertical coordinate in m, positive downwards), and F z is heat flux. F z can be written as: F z k T T z (2.9) where k T is the thermal conductivity. Combing equation (2.9) with (2.8) gives the classical heat conduction equation: T t 2 T k 2 z (2.10) where k k c T is the soil thermal diffusivity. Typical values for k are ( m 2 V s -1 ) for snow, to for farms, and for water. The volumetric heat capacity and the thermal conductivity depend on the soil type and its water content. In practice, for the integration of Eq. (2.8) and Eq. (2.9), one needs to discretize both equations in space and time. Discretization in space means choosing soil layers of a given depth; each layer will be characterized by its thermal 11

21 inertia, thus the upper layers will change their temperature more rapidly than the lower layers (Dickinson, 1988). For a soil with uniform thermal diffusivity with depth, the boundary condition often used are: (1) periodic temperature variation at the surface, and (2) no temperature change at great depths. The solution is periodic temperature variation that decreases in amplitude with depth. If the period of the cycle is, the amplitude wave changes with depth as (Stull, 1988): T of the Then 1/2 T( z) Tsurface expz (2.11) k T(,) z t T T() z (2.12) where k is a constant, D is the depth of top layer, and 1 year (annual cycle) or 1 day (day cycle). For more realistic nonperiodic forcings or nonuniform soil properties, Eq. (2.10) can be solved with a variety of numerical schemes, analytical serie expansions or Fourier decompositions Soil hydrology The conservation of soil moisture in vertical requires: t Q z (2.13) where η is the volumetric soil moisture content (m 3 m -3 ), t is the time (s), z is the vertical coordinate (positive downwards), Q is the soil water flux (m s -1 ), positive upward. In agreement with the Darcy law, it can be written: Q K( x, y, z) (2.14) where K is the hydraulic conductivity (m s -1 ) and ѱ is the moisture potential (m). Richardson (1922) and Richards (1931) extended the Darcy's law to the flow of water in the unsaturated case, expressing the water flux in terms of a gradient of the 12

22 hydraulic conductivity: Q w K( ) K( ) z (2.15) where ρ w is the density of water (kg m -3 ). In most LSPs, the calculation of hydraulic conductivity (K) and moisture potential (ѱ) are made using the empirical functions of volumetric soil moisture content (η) evaluated by Clapp and Hornberger (1978): ( ) b (2.16) s s K K s 2 3 ( ) b s (2.17) where ѱ s and K s are the saturated moisture potential and the saturated hydraulic conductivity, respectively, and b is a non-dimensional coefficient, called the Clapp and Hornberger exponent. In the hydrologic models, the prognostic equation for the volumetric soil moisture content (η) can be written as: K ( ) t z z z (2.18) where both the soil water diffusivity λ and hydraulic conductivity K are functions of η. Fig. 2.1: Hydraulic conductivity as function of volumetric soil moisture for four soil types: sand, silt, loam, and clay (Derived form Chen and Jimy Dudhia, 2001). This diffusive form of Richard s equation is derived from the Darcy s law under the assumption of a rigid, isotropic, homogeneous, and one-dimensional vertical flow 13

23 domain (Hanks and Ashcroft, 1986). The relationship between the volumetric soil moisture content η and the thermal conductivity is illustrated in Fig The hydraulic conductivity, K, as well as the diffusivity, λ, are highly nonlinearly dependent on the soil moisture, as shown in Fig. 2.1 A complete theory of heat and moisture transfer must describe the moisture transfer under the combined influence of gradients of temperature and moisture content, and the heat transfer under the influence of temperature gradients and mass flow of moisture. 2.2 Physical processes of surface by snow The processes on a surface covered by snow are important both for climate change studies and in the evaluation of the hydrological cycle. The skin temperature of snow cover has a great influence on the energy variations between snow cover and atmosphere. The status of snow cover is not only related to the energy transportation from its inner, but has also an important impact on the underlying bare soil. However, despite the importance of snow cover in climate studies, the snow processes are over-simplified in many GCMs. Some very important processes, which are crucial for correctly predicting the snow-atmosphere-soil interactions, are neglected. The snow sublimation, accumulation, and snow-melting are based only on the surface temperature and surface energy budget. However, many complex and physically based snow schemes (e.g., Jordan, 1991, Loth and Graf, 1993) have been developed in order to describe in detail the three-phase changes, the movement of water inside snow, the snow compaction, the snow particle growth, and so on. In this subsection, the mass balance and energy budget equations will be presented The energy equation The energy variation in the snow cover is affected by the solar radiation, the sensible and latent heat fluxes between the snow pack and the atmosphere, the heat fluxes between the snow and the land surface, the heat conductance within the snowpack and 14

24 the energy released from phase change. Considering the snow pack subdivided into many layers, the enthalpy budget equation for each snow layer is, H T t z z ( K s R ( z)) (2.19) where K (W m -1 K -1 ) is the effective heat conductivity and H the volumetric specific enthalpy of water (J m -3 ). Within snow cover, the short wave radiation flux (W m -2 ) R s is given by the Beer law, R ( z) R (0)(1 )exp( z) (2.20) s where α is surface albedo. The temperature of each sublayer of snow can be calculated through the following relation: s H C ( T ) f LW (2.21) v i i li l where L li (J kg -1 ) is the latent heat of fusion for ice, ρ l (kg m -3 ) is the liquid water intrinsic density, and W is the volumetric snow water equivalent. The value of f i is the dry snow mass fraction of the i-th sublayer and assumes values ranging 0 (melt water) and 1 (dry snow). C v (J m -3 K -1 ) is the mean snow volumetric specific heat capacity and can be principally calculated from the fractional mass and its heat capacity of each phase. In some complex and physically based snow models, the vapor phase change, the vapor diffusive term and its contribution to both mass and energy balances are considered in the balance equations The mass balance equation The mass balance equation describes the changes of the total water equivalent, which is the sum of the liquid water and the ice grain mass. In this balance, snowfall and rainfall, snow melting, runoff, and evaporation at the snow surface are be taken into account to evaluate mass balance changes. The equation to predict the change of total water equivalent in the surface layer 15

25 (i=1) is: ( WD i zi) PIF0 IF1RF1E t 0 (2.22) where D zi is the thickness of the i-th sublayer, W j is the i-th volumetric snow water equivalent. E 0 (m s -1 ) is the evaporation rate occurring at the snow surface; RF 1 (m s -1 ) is the runoff, IF 1 (m s -1 ) is the actual liquid water infiltration flux output for the layer, P is the snowfall and IF 0 is the infiltrated liquid water into this layer. There are some very important parameters characterizing the snow: in addition to the effective thermal conductivity and heat capacity, also snow size, albedo and holding capacity are very important, and are parameterized in many literatures. The snow model is a highly nonlinear dynamic system, with no analytical solution. To obtain numerical solutions, it is better to consider a layered the snowpack, especially when snow depth is large. Researches have shown that the multiplayer snow model and the layering methodology are both crucial in simulating snow processes. 2.3 Canopy processes The canopy is an important factor for determining the surface energy budget. The vegetation reflection and scatter to solar radiation affect the surface albedo directly. Deardorff (1978) developed a simple parameterization scheme for a vegetation layer. In this scheme it involved an abbreviated energy balance equation to obtain temperature of a representative foliage element and diagnosis of mean air temperature and humidity within the vegetation layer. Sellers et al. (1986) developed a SiB model which includes three soil layers and two vegetation layers. The model provided a more accurate diurnally varying description of the surface energy partition into sensible heat and latent heat. Dickinson and Henderson-Seller (1988) carried out some experiments to investigate Amazon deforestation by using a simple model of biosphere. The results show that the surface warming is due to deforestation or desertification. In vegetation canopy processes include the resistances to evapotranspiration, 16

26 aerodynamical resistances and the effect on the interception. It is very important to make reasonable parameterization for these processes Interception Vegetation canopy can store water and intercept precipitation on the leaf surface. These behaviors reduce precipitation into soil. The bulk representation of vegetation have been incorporated into many land surface parameterization schemes. The interception equation can be written as, t Wc P I P Dr E (2.23) P 0, while W c W fmax Dr P 0, while W c W fmax Dr where W c is water stored on leaf (m), P I is rate of precipitation (m s -1 ), P Dr is water drainage rate (m s -1 ), which the drainage usually can be separate into dripping from the canopy and stem flow. E is rate of evaporation (m s -1 ). W fmax is the maximum water content which depends on the types and properties of plants. Wf max LAI( mm) (2.24) where LAI is the leaf index Aerodynamical resistances The turbulent transport of momentum and other quantities between the surface and atmosphere is a complex process. The resistance network is represented in Fig Fig. 2.2: The resistance network 17

27 According to the studies of Dai and Zeng (1997), the aerodynamic resistances over canopy r ah, r am and r av, are calculated as: r ah 1 C U ; DFH a r am 1 C U ; DFM a r av 1 C U (2.25) DFV a where C DFM, C DFH and C DFV are drag coefficients for momentum, heat and water vapor (see section 2.3.3). The aerodynamic resistance beneath canopy r d can be calculated according to the Bonan (1996) formulation: z0 fh z0gh df h 3(1 ) 3(1 ) f za za rd e e (2.26) 3 ku* ( hf d f ) Resistance to water evaporation from bare soil r soil is calculated according to Sellers et al. (1992) as: rsoil q e s (2.27) Laminar leaf resistance beneath canopy r b is calculated as: r b LAI d u 0 (2.28) af Canopy resistance is calculated, according to Dickinson (1984), as the combination of 4 terms depending on solar radiation, soil moisture, atmospheric humidity (air moisture deficit) and atmospheric temperature in the following way: 1 r rf MIN s LAI F F F F min (,5000 / m ) (2.29) where the functions F 1, F 2, F 3, F 4 account for the dependence on solar radiation R sd, soil moisture in the root zone q s, atmospheric water vapor deficit q sat (T a )-q a and air temperature T a (Dingman, 1994), respectively. Over snow, two additional resistances are used; they are the resistances corresponding to r d and r soil, and are respectively given by: z z 0 0 gh d sn f h 3(1 ) 3(1 ) f za za rdsn e e (2.30.a) 3 ku* ( hf d f ) r s 1 soilsn 150( m ) (2.30.b) 18

28 2.3.3 Drag coefficients According to the Garratt (1994) formulation, the neutral drag coefficients for momentum (C DFM ) N, for heat (C DFH ) N and for water vapor (C DFV ) N are calculated as: ( C ) DFM N 2 k za d f 2 ; (ln ) z 0 fm ( C ) DFH N 2 k za d f za d ln ln f ; z z 0 fm 0 fh ( C ) DFV N 2 k za d f za d f (2.31) ln ln z z 0 fm 0 fv where z 0fm, z 0fh, z 0fv are the roughness lengths. The non-neutral drag coefficients using the Louis (1979) formulations, are respectively given by: C ( C ) f ( R ); C ( C ) f ( R ); C ( C ) f ( R) (2.32) DFM DFM N m i DFH DFH N h i DFV DFV N v i where R i is Richardson number and the f(r i ) are the stability functions. 2.4 Similarity theory at near ground boundary layer The PBL is the layer of atmosphere in which the motion is strongly affected by the interaction with the earth's surface. The molecular viscosity is effective only over distances of few millimeters, but has the important effect of reset the horizontal wind speed at the soil surface. The transport of quantities such as moisture, heat, momentum, and pollutants is dominated in the horizontal by the mean wind, and in the vertical by turbulence. The PBL includes the surface layer and outer layer, much of turbulence is generated by surface forcing: solar heating causes thermals, frictional drag causes wind shears, obstacles deflect flow causing turbulent wakes, etc. In this section, the transport of turbulence of BL is introduced by the similarity theory. Similarity theory may explain the statistical averages of the meteorological elements and turbulence. It is an useful tool to describe the framework of BL near surface. Similarity theory starts with the identification of the relevant physical parameters, then dimensionless groups are formed from the these parameters, and finally experimental data is used to find 19

29 functional relations between dimensionless groups Neutral layer Under the neutral condition, the potential temperature does not change with a height varying. The thermal factor can be ignored. Monin and Obukhov (1954) hypothesized that any dimensionless characteristic of the turbulence can depend only upon the parameters: friction velocity u *, height z. The average wind speed gradient along the horizontal direction can be written as: u z u * kz (2.33) where k is Von Karman constant. And to integrate the Eq. (2.33), the wind profile can be written as: u u z ln( ) kz z * (2.34) where z 0m is the roughness length. This equation is the typical form of wind velocity profile under the neutral condition. z 0m is related to the surface roughness status depending on the surface roughness factors. Chamberlain (1983) evaluated z 0m of sea surface, sand and snow by using the following empirical equation: 0m z 0m 2 au c * (2.35) g where a c is the parameter related to the surface. The roughness lengths are often derived from land-use maps with an extra contribution from the variance of the sub-grid topography (see Table 2.2). Ground cover Roughness length (m) Water or ice (smooth) 10-4 Mown grass 10-2 Long grass, rocky ground 0.05 Pasture land 0.20 Suburban housing 0.6 Forest, cities 1-5 Table 2.2: Typical roughness lengths (Wieringa 1986) 20

30 If the displacement distance d (m) is considered, the Eq. (2.34) can be given as: u u z d kz z * ln( ) (2.36) 0m Non-neutral layer In the non-neutral condition, the thermal factor and the kinematic factor all are considered. If the potential temperature and specific humidity are considered, also the kinematic fluxes of heat ( w' ') and moisture ( wq ' ') are needed. Since the non-neutral surface layer has two relevant length scales (z and L ). All dimensionless quantities are written as function of z/l as: u u* z m( ) z kz L * z H ( ) z kz L (2.37a) (2.37b) where q q* z H ( ) z kz L (2.37c) 3 u* L kg( ' ') 0 (Obukhov length) (2.38a) ( ' ') 0 * (turbulence temperature scale) (2.38b) u* q ( ' q ') 0 * (turbulence humidity scale) (2.38c) u* z The Obukhov L was proposed firstly by Obukhov (1946). The m( ) and L ( z ) H are dimensionless functions proposed by many empirical forms. Panofsky L and McCormick (1960) combined the π theory and experiment data to proposed a form as: 21

31 4 15z 3 m m 1 (2.39) L Fig. 2.3: The dimensionless gradient ϕ m and ϕ H Businger et al. (1971) and Dyer (1974) used the data from the Kansas experiment and revised the Eq. (2.39) as: m m z z 14.7, 0 L L z z L L 1/4 (1 15 ), 0 (2.40a) z z H , 0 L L z 1/2 z m 0.47(1 9 ), 0 L L (2.40b) Fig. 2.3 shows the range of the dimensionless gradient ϕ m and ϕ H (Stull 1991). 22

32 Chapter 3 The introduction of Land Surface Process Model 3.1 Introduction of LSPM The land surface process is a critical component for the study of the weather and climate through its partitioning of solar radiation into sensible and latent heat fluxes, its redistribution of precipitation into evaporation, soil storage, groundwater recharge, or runoff, and its regulation of biogeochemical cycles with processes such as photosynthesis and respiration. These water and energy exchanges between the atmosphere and the land surface are known to significantly impact weather and climate, which has motivated significant advancement in the understanding of the physical processes governing these exchanges. These studies have resulted in the development of the land surface process model (LSPM). The LSPM is a soil-vegetation-atmosphere transfer (SVAT) scheme developed at the Turin University and subsequently improved (Cassardo et al. 1998; Mutinelli 1998) and tested (Cassardo et al. 1997; Ruti et al. 1997). The LSPM is able to represent the physical processes at the interface between the atmospheric surface layer, the vegetation, and soil. LSPM, which can be classified in the category of the so-called big leaf models, uses multi-layer schemes for soil temperature and moisture calculation, and calculates the turbulent fluxes using the electric-analogue scheme. 3.2 The structure of LSPM The LSPM is a one-dimensional model which analyzes the energy, momentum and water exchanges between the atmosphere and land. The LSPs in LSPM are described in terms of physical fluxes and hydrological state of the land. Its domain can be schematized into three main zones: atmosphere, vegetation and soil. The vegetation is considered as an uniform layer (big-leaf approximation). The variables in the canopy 23

33 layer (temperature, humidity, wind, fluxes, etc) are calculated as weighted averages between the atmospheric, canopy and (eventual) snow components, which are evaluated individually by means of budget equations. Turbulent fluxes are calculated by using the analogue electric scheme, where the resistances are evaluated separately for each layer. Soil moisture and temperature are calculated using multi-layer schemes, in which the user can selected a variable number of soil layers and its depths. In this way, the LSPM can evaluate the thermal and hydrological budget in soil, canopy, snow and surface atmospheric layer. Fig. 3.1: Scheme of the physical and hydrological processes in the LSPM The main component processes and their interactions are illustrated in Fig The LSPM can run offline as a single model, and can be coupled with numerical weather or climate prediction model. Its main parameterizations include: (1) the calculations for soil and snow temperatures, according to their corresponding surface energy 24

34 balances, (2) the calculations for soil moisture, evaporation, on surface and underground runoff, (3) the calculations for surface albedo according to soil moisture, land cover and evaluated snow cover, (4) the calculation of vegetation water budget (including leaf water storage, precipitation intercepted by leaves and stems, and the stomatal resistance and their limiting conditions due to dry soil or atmospheric humidity), (5) the calculation of the surface drag coefficients and their dependence power stabilities determined by the Richardson number, and (6) the calculation for canopy temperature according to energy balance, including the air heat and moisture fluxes. The following sections will describe in detail the above mentioned processes. 3.3 The physical processes in LSPM The physical processes include radiative fluxes, momentum flux, sensible and latent heat fluxes, the partitioning of latent heat into canopy evaporation, soil evaporation and transpiration, and the heat transfer in a multi-layer soil or in a lake Radiative fluxes The radiative fluxes include absorption, reflection and transmittance of solar radiation and absorption and emission of longwave radiation. Momentum flux, and sensible and latent heat fluxes in the surface layer are based on the Monin-Obukhov similarity theory. They have different formulations over the bare and vegetated soil Shortwave radiation From Fig. 3.2, R sd and R su are the solar downward and upward fluxes, respectively. R sd is partitioned between the vegetated flux R svd and the bare soil flux R sgd, as well as the solar upward flux R su is partitioned between the vegetated flux R svu and the bare soil flux R sgu. Therefore: Rsd Rsvd Rs gd (3.1.a) R R R (3.1.b) sn svu sgn 25

35 Fig. 3.2: Scheme of solar radiation Then the net radiation NR s can be described as: NR R R (3.2) s sd su All these components are parameterized as: Rsd G r (3.3.a) R R (3.3.b) svd sd v R R (1 ) (3.3.c) sgd sd v Rsvu Rsvdv (3.3.d) Rsgu Rsgd g (3.3.e) where G r is the global incoming solar radiation, v is the vegetation coverage, and and g are the albedo of vegetated surface and ground surface The incoming (solar) shortwave radiation The global solar radiation on a specified site, in absence of observations, is calculated taking into account the period of the year and the observed cloudiness (Page 1986). The following variables are used: the Julian day J, the latitude φ, the longitude λ (section ), the summer time code Cleg, the pressure p, the coefficient R, the low (C nl ) and total (C n ) cloud cover. The complete of equations of shortwave radiation can be read in the document of LSPM 2006 (Cassardo 2006). When LSPM is coupled 26

36 with a NWP model, as for instance WRF, the shortwave radiation can be derived from the initial and boundary conditions of reanalyze The calculation solar angle The solar angle γ (degrees) is calculated by LSPM using the current date, the latitude φ and the longitude λ of the site, the summer time code Cleg and the site inclination angles (the azimuth β and the zenith ). The first operation is the correction for a tilted surface, performed using the concept of equivalent plan (Dingman, 1994): the solar incident angle over a plan tilted at a latitude φ 0 and a longitude 0 with azimuth β and zenith is equivalent to that over a horizontal plan in a point of the great circle perpendicular to the inclined plan of the slope angle Calculation of surface albedo The parameterization of the surface albedo in LSPM is carried out using the mean vegetation albedo α ffh, the dry soil albedo α sdmax, the water albedo α w (0.14), the saturation ratio of the first soil layer q 1, the actual time t, the latitude φ and the longitude λ of the location. The soil albedo is given by the sum of these components: the first (α fh ) depends on the relative humidity q 1 and on its temperature T 1 of the first soil layer, while the second ( α fz ), used for all albedoes during daytime, is function of the solar angle (γ). fh if q and T 1 > 0 C (3.4.a) w fh = sdmax q 1 otherwise (3.4.b) fz exp[ (90 ) ) 1] (3.4.c) The vegetation albedo α f is given by: f ffh fz 0.03(3.5) where the factor 0.03 represents a rough estimate of the daily mean value of fz. The snow albedo sn is calculated only in presence of snow. This value varies 27

37 between a maximum threshold α snmax =0.85 (fresh snow) and a minimum threshold α snmin =0.50 (for old or dirty snow): sn = sn_min sn sn_min exp( f t/ 1 ) if T sn < 0 (3.6.a) sn = sn - ( α α/ 1 ) if T sn = 0 (3.6.b) where the parameters are τ α =0.008, τ f =0,24 and τ 1 =86400s (Douville et al., 1995). The total albedo is the weighted average of the bare soil, vegetation and snow albedoes according with the expression: Longwave radiation sn snsn (1 sn) f f (1 f ) g (3.7) Fig. 3.3: Scheme of longwave radiation Fig. 3.3 shows the scheme of longwave radiation. R ld and R lu are the downward and upward longwave fluxes, respectively. R lu includes the flux from the top of vegetation (R lvtu ) and the flux from the ground (R lgu ). R R R (3.8.a) lu lvtu lgu R T (1 ) R 4 lvtu v v v v lvtd (3.8.b) R 4 (1 ) T (1 ) R (3.8.c) lgu g v l g where R lvtd and R lgd are the downward longwave flux from the top of the vege tation and that to the ground surface, is the Stefan-Boltzmann constant ( W m -2 K -4 ), ε α, ε ν and ε g are the emissivities of atmosphere, vegetation an lg d 28

38 d ground, respectively, and T α, T ν and T l are the temperatures of atmosphere, v egetation and ground surface, respectively. R ld, R lvtd, R lgd are parameterized as: R ld T (3.9.a) a 4 a R R (3.9.b) lvtd ld v Rlg d Rld(1 v) (3.9.c) The atmospheric emissivity ε a is given by: C 0.22 (1 C ) h 0.67 (1670 qa) a n n f (3.10) where h f is a specific function accounting for the presence of haze introduced by Cassardo et al. (1995) to obviate the too low values of net radiation predicted by the model in hazy conditions. The haze event is parameterized on the basis of the values assumed by the following three variables: the relative humidity RH (%), horizontal wind speed v (m s -1 ) and the solar global radiation Gr (W m -2 ). a. Relative humidity (RH) if RH < 85 %, F1 = 0 b. Horizontal wind speed (v): if v v max, F 2 = 0 if RH 85 %, F1 = ( 85 RH ) 15 (3.11.a) if v min < v < v max F 2 =0.5 v v vmax v min 1 cos 180 if v v min F 2 = 1 (3.11.b) where v min = 2 m/s and v max = 5 m/s depend on the observational site; c. Solar global radiation (Gr): if Gr 40 Wm -2 F 3 = 0 If Gr 0 Wm -2 F 3 = 1 min If 0 < Gr < 40 Wm -2 Gr Gr min F 3 =0.5 1 cos 180 Grmin (3.11.c) The probability that haze can form is then evaluated as (0 h f 1 ): 29

39 h f = (F1 F2 F3) (3.11.d) Net radiation Net radiation at the surface is the sum of the net solar and longwave radiation (according to Deardorff, 1978, and McCumber, 1980): R ( R R ) ( R R ) (3.12.a) n sd su ld lu R ( R R ) ( R R ) (3.12.b) nf sfd sfu lfd lfu R ( R R ) ( R R ) (3.12.c) ng sgd sgu lg d lgu R ( R R ) ( R R ) (3.12.d) nsn ssnd ssnu lsnd lsnu Energy balance In LSPM, the evaluation of momentum, sensible and latent heat fluxes, and evaporation fluxes between the atmosphere at the reference height and the surface are derived from the Monin-Obukhov similarity theory applied to the surface layer (constant flux layer) Sensible and Latent Heat fluxes for Non-Vegetated Surface For a non-vegetated surface, sensible heat flux(h) is defined as: The latent heat flux is defined as: H C ( ) s (3.13) a p atm 1 ah E ( q q )/ r r a atm surf aw srf (3.14) where C p is the heat capacity of air and is a constant (1003 J Kg -1 K -1 ), θ atm is the air potential temperature (K), θ 1 is the potential temperature of the surface (K) and, q atm is the specific humidity (g Kg -1 ) at the height z a, qsurf fhqs ( T1 ) where q s (T 1 ) is the saturated specific humidity of the soil surface, f h is the soil surface relative humidity, r aw and r ah 1 s ah are the aerodynamic resistance (s m -1 ) for water vapor and heat momentum, respectively. r srf is the resistance to evaporation from bare soil. 30

40 Sensible heat fluxes and evaporation fluxes in case of vegetated surfaces In the case in which the soil surface is covered by vegetation, H and λe are partitioned into vegetation and soil fluxes depending on vegetation T f and soil T 1 temperatures and on vegetation q s (T f ) and soil f h q s (T 1 ) specific humidities. In the case of absence of snow: In the case of presence of snow: H H H (3.15) f H H f Hg H f, sn Hg, sn g (3.16) Also for the evaporation flux E, in the layer between the surface at height z 0h +d and the atmosphere at the height z atm it is possible to write a similar budget equation: E Ef Eg Ef, sn Eg, sn (3.17) Latent heat fluxes for vegetated surfaces The latent heat fluxes are expressed by multiplying all evaporation fluxes, by the latent heat of evaporation λ(t) as: F ( T) E (3.18) Momentum fluxes The momentum flux parameterization evaluates firstly the friction velocity u * : * 2 2 u uw ' ' vw ' ', 0.01 m/ s (3.19) The vertical scale velocity w * is calculated in function of the ratio z/l in neutral and non-neutral version: z z w 0.27MAX 10, u L L 20 2 * N * (3.20) and ѱ N is the stream function, defined as: N z/ L z z (3.21) L L 31

41 Interface heat fluxes Soil and vegetation conductive heat fluxes at the border with the atmosphere are given by (respectively): QG Rng Hg Fg Q g, rain (3.22.a) Qf Rnf H f Ff Q f, rain (3.22.b) where the direct conductive heat flux produced by the rainfall can be evaluated as: Qf, rain CswPf w( Ta Tf ) (3.23.a) Q C P T T) 1 (3.23.b) grain, sw g w( a In these formulations, C sw =4186 J m -3 K -1 is the water heat capacity, P f and P g are the rainfall rates over vegetation and bare soil, respectively, and ρ w =1000 Kg m -3 is the water density Resistances and Drag coefficients The parameterization of the resistances and drag coefficients refer to the section and Roughness Lengths The roughness lengths are defined differently according with the surface type. At beginning, the zero displacement level d f is evaluated as: d f 0.67h (3.24) f f where d f is the vegetation height and f the vegetation cover. Over land, the momentum roughness length for bare soil z 0gm (m) is calculated as: z0gm (3.25.a) and the corresponding values for heat and water vapor are evaluated as: z0gh z0gv z0 gm /7.4 (3.25.b) while the momentum roughness length for vegetated soil is assumed as: z0 fm 0.13hf (3.25.c) 32

42 In case of snow, the momentum roughness length for snow is defined as (Dingman 1994): z 0sn 2 v u* u* exp ( ) u* g 0.10 (3.26) where ν is the air kinematic viscosity, given by: v ( Ta ) (3.27) and T a the air temperature. The average roughness length for momentum is evaluated as: z z z (3.28) 0m (1 fsn) f 0 fm (1 f )(1 gsn) 0gm snz 0sn where fsn is the fraction of vegetation covered by snow, gsn the fraction of bare soil covered by snow and sn the fraction of soil surface covered by snow. Averaged roughness lengths for heat and water vapor are evaluated as: z0h z0v z0 m /7.4 (3.29) The canopy-air interface temperature and specific humidity T af and q af could be solved as: T af q af Ts s(1 ) T s T (1 ) s (1 ) T T sah f sb (1 fsn) sd fsn (1 f ) sd a ah f b fsn f d fsn sn f d gsn 1 gsn sn (1 ) q s q s (1 ) s (1 ) q s q q s sah f sf (1 fsn) sd fsn (1 f )( ss (1 gsn) sdgsn) f fsn sf f fsn ssn d f s gsn sgfh d gsn ssn a ah (3.30) (3.31) Heat Transfer in Soil By Combing Eq. (2.8) and Eq. (2.9), the one dimensional energy conservation requires T Fz T c kt (3.32) z z z z where ρc is the volumetric soil heat capacity (J m -3 K -1 ), T is the soil temperature (K) and k T is the thermal conductivity (W m -1 K -1 ). The above equation, in order to be solved, must be discretized. LSPM uses the Crank- Nicholson method. 33

43 The energy balance for the i-th layer can thus written as : z t i n1 n ( c) i ( Ti Ti ) Fz, i1 Fz, i (3.33) where the superscripts n and n+1 indicate the values at the beginning and end of the time step, respectively, and Δt is the time step (seconds). This equation is solved by using the Crank-Nicholson method, which combines the explicit method, with fluxes evaluated at n, and the implicit method, with fluxes evaluated at n+1: z 1 ( c) ( T T ) ( F F F F t 2 i n1 n n1 n1 n n i i i z, i1 z, i z, i 1 z, i) (3.34) resulting in a tridiagonal system of equations d at bt ct 1 (3.35) n1 n1 n i i i1 i i i i1 For the first soil layer (i=1), F z,i-1 =F z,0 = -Q G, where Q G is the heat flux into the soil (positive into the soil). The resulting equations are: a 0 (3.36a) i b i k t z z ( c) izi Ti, i i1 (3.36b) c i k z (3.36c) i Ti, zi 1 ( c) z k d T Q ( T T ) (3.36d) i i n Ti, n i i G i t zi zi 1 The boundary condition at the bottom of the soil column (i=m) is F z,i = -QGBOT, while QGBOT is evaluated adapting the analytical formulation for the heat transfer into soil. The formulation is: zbot zbot 180 QGBOT QG exp( )sin( t 45 ) (3.37) D D where ωt = 180 t/12 90 (t is the daily angle), z bot is the depth of the lowest boundary. n i The vegetation temperature 34

44 The equation regulating the energy budget in the vegetation is: T f t Q C f f (3.38) where T f is the vegetation (or canopy) temperature, Q f is the net input of energy (in W m -2 ) and C f the integrated heat capacity of vegetation (in J m -2 K -1 ). The C f can be parameterized as: C C LAI P (3.39) 6 f fw mf The value C fw derives from the assumption that vegetation possesses the same heat capacity of 0.55 mm of water (Garratt, 1994). T f can be solved using the following numeric scheme: T f PT f Q f C f t (3.40) which is different from the one used for soil temperature, due to the high value of C f which could cause numeric instability 3.4 Hydrological processes The hydrological processes include snow accumulation and melt, rainfall, interception, infiltration and runoff, soil hydrology, including water transfer in a multi-layer soil Soil In the atmospheric domain, soil moisture is a lower boundary condition that rules the partitioning of energy in terms of sensible and latent heat fluxes (Dirmeyer et al. 2000). Wrong estimations of soil moisture could have a deep effect on the model predictions, leading to the wrong simulation of the surface layer evolution, and hence forecasts of cloud cover and precipitations, in both medium and short ranges, could be consequently affected (Dirmeyer et al. 2000). Soil water is calculated from the conservation equation Eq. (2.13). The flux of water Q (m s -1 ) can be divided into: Q Ql Q v (3.41) 35

45 where Q l is the liquid water flux and Q v is the water vapor flux. According to the Fig. 3.4, the vertical water flow at the depth z is: Q ( D D ) K D z z l v vt The one-dimensional water conservation requires that: T z (3.42) K T [( Dl Dv ) ] [ DvT ] t z z z z z (3.43) Fig. 3.4: Schematic diagram of the multi-layer soil profile for moisture where D lη is the liquid water diffusivity due to the soil water content gradient, D vt is the liquid water diffusivity due to the temperature gradient, D vη is the water vapor diffusivity due to the soil water content gradient, and K is the hydraulic conductivity. Using also in this case the Crank- Nicholson method to discretize the equation in the several soil layers, the water balance for the i-th layer is: z t i n1 n ( i i ) Qi 1 Qi e i (3.44) where e i account for the transpiration and surface evaporation Similarly to the soil temperature case, even the volumetric soil moisture η is defined at the centre of each layer, while the hydraulic conductivity and the diffusivities are defined at the interfaces. 36

46 3.4.2 Vegetation Leaf moisture: rainfall, interception, infiltration and runoff Precipitation is either intercepted by the canopy or falls to the ground as throughfall and stemflow. The maximum water amount M fmax which given by equation (Garratt, 1994): M LAI (3.45) 4 f max 210 is used to evaluate the drainage from vegetation according with the formula: f d d f f M f M f max t if 0 if M M f f M M f max f max (3.46) where M f is canopy (leaf) water content. If d f is positive, thus M f = M fmax. The interception should be smaller than I max, where: I m ax M f max t M f (3.47) Canopy water is evaluated using a mass balance equation in which the components are: interception, dew and evaporation, respectively, and all terms are expressed in rates (m s -1 ): M t f q q q int er cdew ceva (3.48) The wet fraction of canopy (or leaf wetness) R f is defined as: R f M M f f max 2/3 1 (3.49) The quantity of water (rain, snow, dew or frost) intercepted by the vegetation p f is calculated as: P p (1 ) (3.50) f f a fsn The quantity of water above vegetation M f (m) is evaluated as: E fw M f t( pf ) (3.51) where E fw is the evaporation from the wet portion of canopy (if positive) or the fw 37

47 condensation of water vapor above leaves (if negative). The water not intercepted by the vegetation and the fraction drained reach the ground and compose the precipitation rate reaching the soil p g, defined as: p ( p p d )(1 ) (3.52) g a f f gsn In the case in which the temperature of the T f vegetation is smaller than 0, the eventual water present on the vegetation is added to the snow content and M f is set equal to zero. Thus the frost is considered like the snow. Finally, in the case in which it is snowing, the entire precipitation p a is assumed as snow (p sn, PRECSN, in m s -1 ). In the case in which there is snow at the ground, the water balance of snow must include also the rainfall over snow p gonsnow (m s -1 ), given by: p ( p p d ) 0 (3.53) gonsnow a f f gsn Evapotranspiration from roots As far as the roots, two coefficients have been introduced in order to account of their geometrical distribution. For the calculation of the soil mean temperature and moisture in the roots layer, the volume of soil in which there are roots is compared to the total soil volume, assuming an uniform distribution. Expressing such volumes for unit of surface area, the percentage of occupation of soil by roots dd(i) in every layer second depends on the layer depth z(i) and on the roots depth d R according to the formula: i zi () dd( i) if z( j) d d i R z( j) d j1 R i j1 () () if ( ) dd i DEP i z j d d R j1 R R (3.54) For the calculation of the contribution of every layer to the transpiration and the heat capacity, it has been assumed that the roots are uniformly distributed in a cone of height d R and base radius d R (it can be demonstrated that the base area does not influence the calculations under the assumption of uniform distribution). The total volume occupied by the roots is therefore: 38

48 V RADTOT 3 dr (3.55) 3 thus, for each i-th layer of soil, the volume occupied by roots is given by the difference between the volume of the cone of height and base radius: z( j), and the volume of the cone of height and base radius: z( j). This is equivalent to express: i j1 3 3 i 1 i Vrad ( i) z( j) z( j) 3 j1 j1 while the total volume of the i-th layer is given by: i1 j1 (3.56) V i d z i (3.57) 2 TOT () R () The percentage in volume of the i-th layer occupied by roots is thus: Vrad () i DP root ( i) V () i (3.58) while the percentage of roots in the i-th layer with respect to the total volume of roots (useful to establish the contribution of i-th layer to the total evapotranspiration) is: DD root TOT KV R rad() i () i f V () i (3.59) RADTOT where K R is an experimental constant, assumed equal to 0.05, and where the coefficient f takes into account the quantity of vegetation Surface and underground runoff While the previous versions of LSPM parameterized the maximum soil infiltration capacity (P infiltrmax ) using the formula of Boone and Wetzel (1995), the recent versions have adopted a new scheme, for which P infiltrmax is given by: P K 1 b(1 s1 w1 inf iltr max s d1 s1 i1 ) (3.60) The effective infiltration is then evaluated as the minimum value between the actual 39

49 precipitation P in and P infiltrmax. Note that all precipitation are volume rates per unit of surface and are measured in m/s. The eventual excess water is considered as surface runoff R s1 (m): R t( P P ) (3.61) s1 infiltr max geff The saturation runoff can occur at each soil level interface in the case in which in that layer the soil moisture content exceed the porosity, and is calculated as R s2 (m) level per level: Rs2 sidi( q i 1) (3.62) The total surface runoff R s is now calculated as: R (1) s Rs1 Rs2 (3.63) while the underground runoff R u, which includes both drainage and intermediate runoff, is given by: N R R () i Q ( N ) (3.64) u s2 out i2 where Q out (N) is the water drainage from the N-th, and the last layer, evaluated by: where C dren is the drainage parameter. Q ( N) C K t (3.65) out dren 3.5 The snow parameterization Definitions The water equivalent of the snow pack is defined as the ratio between of the volume of liquid water (V w ) and ice (V i ) present in the snow pack and the base area A (Fig. 3.5): h h h V A m m i w (3.66) where V m = V w + V i is the water and ice volume expressed in terms of volume of equivalent water. h w is the liquid water content, h i the ice content. 40

50 Fig. 3.5: The structure of the snow pack Melting processes of snow In LSPM, the melting process is considered and subdivided into three phases (Dingman 1994): the warming phase, the snow pack temperature increases from the initial value T s <0 to the melting point T m =0. the ripening phase, the snow pack is heated at a constant temperature of T s =0. In this case, part of the snow melts but the resulting water remains in the snow pack pores, retained by the surface tension forces. the melting phase In addition, the snow pack was considered as a homogeneous layer of snow Snow energy balance The energy balance of the entire snow pack can be written (Cox et al., 1999) by summing the net radiation, the conductive heat flux coming from soil, canopy and eventual rainfall (all considered positive when entering in the snow), and of the sensible and latent heat fluxes (considered positive when leaving the snow). The resulting equation is: Q ( R H Q Q Q Q ) t (3.67) av N sn sn Esn Gsn F sn rain where R Nsn is the net radiation relative to the snowy surface, H sn and Q Esn are the sensible and latent heat fluxes, Q Gsn, Q Fsn are the heat fluxes transmitted to the snow from both canopy and bare soil by conduction. Q rain is the heat fluxes transmitted to 41

51 the snow pack by the rainfall Net Radiation over Snowy Surfaces Net radiation relative to the snowy surface can be expressed as: RNsn Rswsnd Rswsnu Rlwsnd Rlwsnu (3.68) The downward and upward short-wave radiations are respectively given by: R (1 ) R R (3.69a) swsnd f gsn swd f fsn swd R (1 ) R R (3.69b) swsnu f gsn sn swd f fsn sn swd where R swd is the solar global radiation and the two components in the above equations respectively account for bare soil and vegetation. Likewise, the downward and upward long-wave radiations are respectively given by: R (1 ) R R (3.70a) lwsnd f gsn lwd f fsn lwd Rlwsnu (1 f ) gsnr lw, snow f fsnrlw, snow (3.70b) where R lwd is the downward long-wave radiation, and R lw,snow is the upward long-wave radiation emitted by the snow surface and given by: R 4 lw, snow snts (1 sn) Rlwd (3.71) Surface temperature and moisture over snowy surfaces The temperature and specific humidity for canopy and soil surfaces are defined as weighted averages between the snow and snow-free fractions in the following way: T T (1 ) T (3.72a) canopy fsn sn fsn f T T (1 ) T (3.72b) surf gsn sn gsn 1 q q ( T ) (1 ) q ( T ) (3.72c) canopy fsn sat sn fsn sat f q q ( T ) (1 ) f q ( T) (3.72d) surf gsn sat sn gsn h sat where f h is the relative humidity at the soil surface, q sat denotes the saturated specific humidity, and T 1, T sn and T f are the soil, snow and vegetation surface temperatures, 1 42

52 respectively Conductive fluxes in the snow pack Heat fluxes can be transmitted to the snow from both the canopy and the bare soil by conduction. According to Fourier s law, these contributions have been parameterized as: Q 2K T T h sn f Fsn f, sn fsn hs f Q K T T sn 1 Gsn 2 g, sn fsn hs d 1 (3.73a) (3.73b) for vegetation and bare soil, respectively. K f,sn and K g,sn are the thermal conductivities between the surface and the snow Snow albedo The snow albedo is assumed to vary with time between the thresholds α snmin =0.50 and α snmax =0.85. Based on Robinson and Kukla (1984) and Verseghy (1991), the rate of decay of albedo has been assumed to obey to the following expression: 1 ( tt) ( t). e (3.74) f t sn sn snmin sn min where τ f =0.24 is an empirical parameter and t 1 =86400 s = 1 day (Verseghy, 1991). The above equation show an exponential decay of albedo, and the time needed for albedo to change from the maximum value α sn =α snmax to the minimum value α sn = α snmin, in absence of snowfalls and other phenomena, is about 10 days. In case of fresh snow, it is assumed that if the fresh snowfall (P sn t) exceeds the empirical threshold h snwhite =10-5 m, the snow albedo is completely refreshed and set to its maximum value while, if P sn t< h snwhite, the albedo is calculated as the weighted average of fresh and old snow albedoes, according to the equation: sn snmax snwhite sn sn ( sn ) new hsnwhite ( P t) ( h P t) (3.75) where the fresh snow is assumed to have the albedo snmax (Dingman, 1994). The 43

53 values calculated using the above equation represent the daily mean albedo and during daytime it is also considered the contribution due to the solar elevation (McCumber, 1980). The total surface albedo is finally evaluated as the weighted averages of the bare soil (or water), vegetation and snow albedoes according to the equation: tot snsn (1 sn) f f (1 f ) g (3.76) Thermal balance in the snow pack The behavior of the snow pack temperature T sn depends on the energy balance. If there is not any liquid water inside snow pack, the snow pack temperature would increase by: T Q av sn (3.77) whc m i Where ΔQ av is the available energy. If the available energy is negative (ΔQ av <0) and its absolute value is larger than the energy required to refreeze all liquid water inside snow pack (Q solid ), the energy deficit is used to cool the snow pack by the quantity: Q Q av soild Tsn (3.78) whc m i Hydrological balance in the snow pack If the available energy ΔQ av is positive, the (excess) energy ΔQ av =ΔQ av - Q warm will be considered. The following three possibilities arise: ΔQ av < Q ripe, the available energy is lower than required for saturating completely the snow pack. The water equivalent h m is kept constant, while the liquid water content h w increases by: ' Qav hw (3.79a) Q ripe < Q av < Q melt,tot, The water equivalent decreases by the quantity: w f 44

54 Q Q ' av ripe hm (3.79b) w f while the liquid water content in the snow pack is forced to approach the riped value (h w =h wret ). The exceeding water equivalent is considered as runoff. Q av > Q melt,tot, In this case the whole snow pack will melt. If the available energy is negative, the water equivalent h m does not change, thus there is not runoff. Two possibilities arise, according to the value of ΔQ av compared with Q solid. ΔQ av < Qs olid, The available energy is not sufficient to refreeze all liquid water, if any. The liquid water content decreases by the quantity: Q ΔQ av Q solid, All liquid water solidifies and h w =0. av hw (3.79c) w f When new snow is precipitating at the rate P sn, the water equivalent is incremented by the quantity: ( h ) h P t (3.79d) m new m sn When it rains over the snow pack at the rate P gonsnow, the liquid water content hw of snow pack is incremented up to the value h wret, the remainder of water being expelled as runoff: h P t ( h h ) (3.79e) w gonsnow wret w In this case, also the water equivalent content is incremented by the same value: h (3.79f) m Finally, in the case in which the water equivalent content decreases, the runoff can be calculated as: hw R h ( h ) 0 m m new (3.79g) and the contribution coming by eventual rainfall exceeding ripe snow should to be added: R P t( h h ) 0 (3.80) gonsnow wret w 45

55 3.5.6 Snow compaction and density Since the snow height h s is used in the LSPM to evaluate some parameters (such as the roughness length), it is important to obtain an accurate physical description of h s. It is evident that h s is strongly related to the value of the snow density ρ s. The snow compaction is a complex process because it depends not only from the actual values of some snow parameters (height, temperature, liquid water content, etc.), but also from the history of the snow pack. Several parameterizations used in literature have been compared in this study. According to Anderson (1976), the change of snow density due to compaction can be expressed as: 1 ds ( z) Ch 1 m( z)exp CT 2 sn( z) C3s( z) (3.81) ( z) dt s where C 1 is the fractional increase in snow density per unit water equivalent of load per unit time at the temperature T s (z)=0 and density ρ s (z)=0, while C 2 and C 3 are the observational constants. If a short integration time (LSPM usually uses D t <60 s) is considered, the r.h.s. of the above equation can be supposed constant and snow density can be integrated over time. The average snow density of the snow pack, composed by a single snow layer, can be expressed by the integration of the previously obtained solution over the snow depth h s, giving: Since new snowfalls also affect snow density and depth, snow density is assumed to vary during snowfall according to the following expression (Koren et al., 1999): s() thm snewpsn t s( t t) MAX smin, MIN smax, (3.82) hm Psnt where the density of the new snowfall ρ snew is estimated on the basis of the air temperature T a as (Gottib, 1980): 1.5 snew MIN s max, MAX s min, s min 17( Ta C1 ) (3.83) with C 1 =15 K, and the snow density is always assumed to vary between a minimum value ρ smin =50 Kg m -3 and a maximum value ρ smax =400 Kg m -3 (Dingman 1994; Koren et al. 1999). 46

56 3.5.7 Snow coverage The snow coverage is one of the most important physical parameters in the snow scheme. A small error in the evaluation of the snow coverage can produce significant errors in the evaluation of the snow pack despite other sophisticated snow processes parameterizations. As starting point, a crude linear regression to the observed snow depth hs and the observed coverage sn gathered in 6 Siberian stations (Ruswet experiment, Robock et al. 1995, where surface vegetation is short grass) has been applied. By considering only the values of sn when sn <100% (see Fig. 3.6) and searching a regression line of kind Y=AX), the following expression has been obtained: (3.84) sn Ch 1 s with C 1 =8.34 m -1, while the following expression has been derived when searching a regression line of kind Y=AX+B: with C 2 =3.78 m -1 and with C 3 =0.44 m -1. (3.85) sn Ch 2 s C 3 Fig. 3.6: Regression lines between (non-fully) snow coverage and snow heights in the Russian stations of RUSWET dataset. Many models evaluate too simply snow coverage, not taking into account the type of surface covered by snow. In LSPM, the dependence of the surface type is included. A good way to include the surface characteristics is obtained by including the surface roughness length z 0 in the formulation for sn. It can be written as: 47

57 0.26h h 2 s s 0 sn for h 2 s z 0 z z (3.86) where the numerical coefficients are dimensionless, and the roughness length is related to the type of surface (bare soil, vegetation). 3.6 Summary LSPM was tested in different climatic conditions. Ruti et al. (1997) used the LSPM to evaluate the energy budget in the Po valley, Italy, and the predictions were compared with those of another land surface model. The results show that LSPM seemed to produce a better estimate of the entire energy budget with respect to BATS and BMOD schemes. Cassardo el al. (1998) performed some sensitivity experiments on some vegetation and soil parameters. In this LSPM, the parameterizations of the radiation terms and of turbulent heat fluxes were modified furthermore, also a parameterization of runoff has also been developed, in order to close the hydrologic balance. The results of the simulation show that LSPM can reproduce well the energy, heat and water budgets and their behaviors with varying the selected parameters. Qian et al. (2001) added an underground water vapor flux into the soil moisture prognostic equation. The improved LSPM was applied over desert areas. The simulation results seem to compare better with the observed behavior of soil moisture and turbulent heat fluxes than those overlooking the water vapor flux. Cassardo and Loglisci (2005) simulated the components of the energy and hydrologic budgets in four European synoptic stations. Cassardo et al. (2007) simulated the daily mean solar global radiation, precipitation cumulated, mean sensible heat flux to estimate the summer 2003 heat wave in Piedmont region, Italy. 48

58 Chapter 4 The introduction of Weather Research and Forecasting Model (WRF) The WRF model was developed by the National Center for Atmospheric Research (NCAR), the National Oceanic and Atmospheric Administration (NOAA), the National Centers for Environmental Prediction (NCEP) and the Forecast Systems Laboratory (FSL), the Air Force Weather Agency (AFWA), the Naval Research Laboratory (NRL), the University of Oklahoma, and the Federal Aviation Administration (FAA). The WRF model is well suited for a wide range of applications, from idealized research simulations to operational forecasting, and has the flexibility to accommodate future. It can be made a significant use in advancing research objectives in a number of areas, such as convection-resolving NWP, hurricane forecasting, regional climate studies, and air chemistry/quality research. In this section, a brief description of the Advanced Research WRF (ARW) is provided here. The detailed WRF introduction is reported in Skamarock et al (2008), available in the WRF web site ( 4.1 The main features of WRF model The WRF is an Euler non-hydrostatic with a run-time, fully compressible model with mass coordinate system, designed as the next NWP model and data-assimilation system. The horizontal grid of WRF is the Arakawa C-grid (Arakawa and Lamb, 1977), in which u and y grid points are each offset from mass points to improve the numerical accuracy. In time integration, a 2nd- or 3rd-order Runge-Kutta scheme was used for treating acoustic and gravity-wave modes. WRF main feature includes (Skamarock et al, 2008): Time integration: Time-split integration using a 2nd- or 3rd- order Runge-Kutta 49

59 scheme with smaller time step for acoustic and gravity-wave modes. Initial conditions: Three dimensional for real-data, and one-, two- and three-dimensional for idealized data. Digital filtering initialization (DFI) capability available (real-data cases). Nesting: One-way interactive, two-way interactive, and moving nests. Multiple levels and integer ratios. Nudging: Grid (analysis) and observation nudging capabilities available. 4.2 WRF software framework Technically, the WRF model code does not allow the use of common blocks, and therefore all variables must be transferred into the subroutines through argument lists. The use of modules (a feature of FORTRAN 90) makes easier the design of interface. The main features are the following: Highly modular, single-source code for maintainability. Support for multiple dynamics solvers and physics modules. Input/Output Application Program Interface (API) enabling various external packages to be installed with WRF, thus allowing WRF to easily support various data formats. Model coupling API enabling WRF to be coupled with other models such as ocean, and land models, etc. 4.3 Dynamical equations The WRF equations are formulated using a terrain-following hydrostatic-pressure vertical coordinate (Fig. 4.1, Laprise 1992) denoted by η and defined as: ( p p )/ (4.1) h where phs pht, p h is the hydrostatic component of the pressure, and p hs and p ht are values referring the surface and top boundaries, respectively. ht 50

60 Fig. 4.1: The η coordinates (derived from the web site of WRF at In WRF, the momentum equations adopted are: Fu U m Uu Vu u p p p ' t x x( ) y( ) ( ) ( d x ' d' x ) ( / d)( d x' ' x d x ) (4.2) Fv V m Uv Vv m m v p p p ' t y x( ) y( ) ( y / x) ( ) ( d y ' d' y ) ( / d)( d y' ' y d y ) (4.3) 1 1 ' FwtW ( mxmy / m ) y x( Uw) y( Vw) ( w) my g( / d) p' d ( qv qc qr) my dg (4.4) The governing equations using perturbation variables to reduce truncation errors in the horizontal pressure gradient calculations in the discrete solver and machine rounding errors in the vertical pressure gradient and buoyancy calculations. 4.4 Time integration scheme In the WRF, a third-order Runge-Kutta (RK3, Wicker and Skamarock (2002)) time integration scheme was used for a time-split integration. It consists of two primary loops: an outer loop for the large-time-step Runge-Kutta integration, and an inner loop for the acoustic mode integration. In the RK3 scheme, physics can be integrated within the RK3 time integration. 51

61 The WRF model is typically integrated with a fixed time step, that is chosen to produce a stable integration. During any time in the integration, the maximum stable time step is likely to be larger than the fixed time step. The adaptively-chosen time step is usually larger than the typical fixed time step, hence the dynamics integrates faster and physics module is called less often, thus the time-to-completion of the simulation can be substantially reduced. The time step can be increased and the new time step is computed as: Cr t t (4.5) target current min(1 fi, ). previous Crdomain where a typical value for the regulated increase is f i = 5%. In a simulation which uses nests, the fine-grid domain must maintain an integer number of time steps within a single model integration step from the parent one. 4.5 Lateral boundary conditions Several lateral boundary conditions are available for idealized flows, and can be specified for real-data simulations in WRF Periodic lateral boundary conditions Lateral boundary conditions in the WRF can be specified as periodic in x (west-east), y (south-north), or in both (x, y). The periodic boundary conditions constrain the solutions to be periodic Open lateral boundary conditions Open lateral boundary conditions, also referred to as gravity-wave radiating boundary conditions, can be specified for the West, East, North, or South boundary, or for any combination of these Symmetric lateral boundary conditions Symmetry lateral boundary conditions can be specified for the West, East, North, or South boundary, or for any combination thereof. The symmetry boundaries are located 52

62 on the normal-velocity planes at the lateral edges of the grids Specified lateral boundary conditions For real case-study simulation, the specified boundary condition are used for the outer-most coarse grid. The specified lateral boundary conditions for the nest are automatically selected for all fine grids. The coarse grid specified lateral boundary is comprised of both a specified and a relaxation zone. The specified zone is determined entirely by the temporal interpolation of an external forecast or analysis. The specified lateral boundary condition for the coarse grid requires an external file, generated as the initial condition file during the pre-processing phase. According with the studies of Davies and Turner (1977), the following function is used: F F ) (4.6) 2 t n 1( LS ) 2 ( LS where n is the number of grid points from the outer row or column along the boundary, and ѱ LS is the large-scale value obtained by spatial and temporal interpolation from the external analysis. F 1 and F 2 are the weighting function coefficients. On the coarse grid, the specified boundary condition applies to the horizontal wind components, potential temperature, ',, and water vapor. The ' d lateral boundary file must contain enough information to update the boundary zone values throughout the entire simulation period. 4.6 Nesting The nesting implementation in WRF is similar to the implementations in other mesoscale and cloud scale models (e.g. MM5, ARPS). The major improvement in the WRF nesting infrastructure, compared with the analogous techniques used in other models, is the ability to compute nested simulations efficiently on parallel distributed-memory computer systems. Nested grid simulations can be produced using either 1-way nesting or 2-way nesting. When using concurrent 1-way and 2-way 53

63 nesting, several options for initializing the fine grid are provided. All fine grid variables can be interpolated from the coarse grid. All fine grid variables can be read as input from an external file whose information for both meteorological and the terrestrial fields. The fine grid can have some of the variables initialized with a higher-resolution external data set. For a moving nest, an external orography file may be used to update the fine grid terrain elevation. 4.7 Physical processes The WRF physics contain several categories, each of them possessing several associated choices. The physics categories are: Microphysics Cumulus parameterization Planetary boundary layer (PBL) Land-surface model Radiation. All options of different processes in WRF are listed in Table 4.1. The next section outlines mainly the land surface physics options available in the WRF layer thermal diffusion This simple LSM is based on the MM5 5-layer soil temperature model. Layers are 1, 2, 4, 8, and 16 cm thick, respectively from top to bottom. Below these layers, the temperature is fixed at a deep-layer average. The energy budget includes radiation, sensible, and latent heat flux. It also allows for a snow-cover flag, but the snow cover is fixed in time. Soil moisture is also fixed with a landuse- and season- dependent constant value, and there are no explicit effects of the vegetation NOAH LSM The NOAH LSM was originally created by Pan and Mahrt (1987), then extended by 54

64 Chen et al. (1996), including the modestly complex canopy resistance approach of Microphysics options Kessler scheme Purdue Lin scheme WRF Single-Moment 3-class (WSM3) scheme WSM5 scheme WSM6 scheme Eta Grid-scale Cloud and Precipitation scheme Thompson et al. scheme Goddard Cumulus Ensemble Model scheme Morrison et al. scheme Cumulus parameterization options Kain-Fritsch Betts-Miller-Janjic Grell-Devenyi ensemble Surface layer options Similarity theory (MM5) Similarity theory (Eta) Similarity theory (PX) Land surface model options 5-layer thermal diffusion NOAH LSM Rapid Update Cycle (RUC) Model LSM Pleim-Xiu LSM Urban Canopy Model Planetary boundary layer options Medium Range Forecast Model (MRF) PBL Yonsei University (YSU) PBL Mellor-Yamada-Janjic (MYJ) PBL Asymmetrical Convective Model version 2 (ACM2) PBL Atmospheric radiation options Rapid Radiative Transfer Model (RRTM) Longwave Eta Geophysical Fluid Dynamics Laboratory (GFDL) Longwave NCAR Community Atmosphere Model Longwave Eta Geophysical Fluid Dynamics Laboratory (GFDL) Shortwave MM5 (Dudhia) Shortwave Goddard Shortwave NCAR Community Atmosphere Model Shortwave Table 4.1: The physical options of different processes in WRF. Noilhan and Planton (1989) and Jacquemin and Noilhan (1990). This is a 4-layer soil temperature and moisture model with explicit prediction of canopy moisture and snow 55

65 cover. The soil layer thickness are 10, 30, 60 and 100 cm from top to bottom. Hydrological processes include root zone evapotranspiration, soil drainage, and runoff, taking into account vegetation categories, monthly vegetation fraction, and soil texture Energy budget According to the introduction of NOAH scheme coupling with MM5 model of Chen and Dudhia (2001), the surface skin temperature is determined, following Mahrt and Ek (1984), by applying a single linearized surface energy balance equation representing the combined soil vegetation surface. The soil heat flux is controlled by the usual diffusion equation for soil temperature (T): ( T) T CQ ( ) Kt ( Q) () t z z (4.7) Where the volumetric heat capacity, C v (J m -3 K -1 ), and the thermal conductivity, K t (W m -1 K -1 ), are formulated as functions of the volumetric soil water content, Q Hydrological budget The prognostic equation for the volumetric soil moisture content (Q) is: Q Q K ( D ) FQ t z z z (4.8) where both soil water diffusivity D and hydraulic conductivity K are functions of Q, and where F Q represents sources and sinks (i.e., precipitation, evaporation, and runoff ) of soil water Snow and sea-ice model The snow model has only one layer of snow cover and simulates the snow accumulation, sublimation, melting, and heat exchange at snow atmosphere and snow soil interfaces. The heat flux between the soil and the snow is estimated as: G K T T s soil snow (4.9) Dsnow 56

66 where T s is the skin temperature, T soil the temperature in the first soil layer, and D snow the physical snow depth. K snow is the thermal diffusivity for snow. In NOAH model, regarding vegetation classification, the 1-km resolution U.S. Geological Survey s (USGS) SiB model vegetation categorization is utilized. This land cover dataset is derived from the 1-km satellite Advanced Very High Resolution Radiometer (AVHRR) data RUC LSM The RUC (Rapid Update Cycle, Smirnova et al. 1997, 2000) contains a multilevel soil model, the treatment of vegetation, and a two-layer snow model. It solves heat and moisture transfer equations for six soil layers, and the energy and moisture budget equations at the ground surface is solved, using an implicit scheme for the computation of the surface fluxes (Benjamin et al. 2004). Smirnova et al. (1997, 2000) explained in detail the configurations of RUC model for the forecast of heat and moisture exchanges between the soil and atmosphere. The soil model solves heat diffusion and Richards moisture transfer equations, and in the cold season takes into account the phase changes of the soil water Energy budget The heat conduction equation can be written as: T T ( t z c z ) s s (4.10) where ν, c s, and ρ s, are the thermal conductivity, specific heat capacity, and soil density, respectively. The volumetric heat capacity of soil ρ s c s which is calculated as the weighted contribution of the dry soil and the liquid water. The heat budget equation for the interface-spanning layer with average temperature T g is written as: Tg c ( R H Lv EG t z ) (4.11) where R n is the net radiation, H the sensible heat flux, L ν E the latent heat flux, and G 57

67 the soil heat flux Hydrological budget The formulation of a moisture balance equation is given as g w t ( Ws I E1 ) z (4.12) where η g is the average volumetric water content in the surface soil layer, I is the infiltration rate, E 1 is the total moisture flux to the atmosphere, and W s the soil moisture flux. The RUC contains also a multi-layer snow routine with variable snow density, the treatment of the liquid water percolation through the snow pack, the evolution of the snow depth, temperature and albedo; the hydrological budget is evaluated considering both snow-atmosphere and snow-soil interfaces, and a simple parameterization of fractional snow cover is included. Finally the model considers the possibility that the grid averaged skin temperature could decrease above the freezing point. 4.8 Technical information on source code compilation The WRF modeling system has been installed on a Linux PC. The package is mostly self-consistent, i.e. The WRF model do not requires external libraries. On the contrary, the WPS package, separated from the WRF source code, has additional external libraries that must be installed. One of the external packages required by each component of the system is the netcdf library, which is one of the supported I/O API packages. Specifically, there are three tar files for the WRF modeling system code. The first one contains the WRF model (including the real and ideal pre-processors), the second one is the WRF-VAR code and the third one the WRF chemistry (Fig. 4.2). For the specific installation process, please refer to the Appendix A. 58

68 Fig. 4.2: The WRF system components (derived from the web site of WRF at 59

69 Chapter 5 Coupling the LSPM model with the WRF model 5.1 Introduction In the past few decades, LSPs and their modeling play important roles, not only in large-scale atmospheric models including GCMs (e.g., Rowntree and Bolton 1983, Mintz 1984; etc.), but also in regional and mesoscale atmospheric models (e.g., Avissar and Pielke 1989; Chen and Avissar 1994a, b, etc.). LSMs have long been important components in global scale climate models (GSCMs) because of their more complete representation of the surface energy and hydrological budgets, as well as for their ability to represent and respond to changing climatic conditions and changing ecosystems. For mesoscale meteorology modelings (MMMs) such long-term changes are not important; however, seasonal changes in vegetation characteristic and synoptic changes in surface moisture conditions have important effects even on short term meteorological simulations. Land surface processes, such as radiative exchanges and evapotranspiration, govern the partitioning of net radiation into sensible, latent, and soil heat fluxes, which in turn strongly influence ground level air temperature and humidity as well as the PBL development. Heat and moisture exchanges between the soil surface and the atmosphere are frequently dominant driving mechanisms for atmospheric circulation. These surface processes are included in physics of GCMs and MMMs by specifying different lower boundary conditions, depending on surface characteristics. In particular, the prediction of the soil surface temperature and moisture content is critical for obtaining successful forecasts of heat and moisture exchange between the surface and the atmosphere (Smirnova, et al., 1997). More accurate and reliable calculation of surface soil fluxes requires a detailed knowledge of soil temperature and moisture profiles 60

70 (Chen et al. 1996). During the last decades, the development of the coupling of LSMs with MMMs made a rapid progress. For example, the LSMs s key elements include soil moisture based on the Interaction Soil Biosphere Atmosphere (ISBA) model (Noilhan and Planton, 1989), surface fluxes including parameterization of vegetation, and a non-local closure PBL model developed by Pleim and Chang (1992). Pleim and Xiu (1995) describe the development and initial testing of a land surface and PBL model for use in mesoscale models. Because they provide the surface boundary condition to the atmosphere, LSPs play critical roles in affecting the PBL structure. In addition, due to the development of MMMs with higher spatial and temporal resolutions, it is very important to obtain the land surface forcings at small scale (e.g. soil moisture, soil temperature, vegetation type, soil characteristics). Therefore, much attention is devoted to the parameterization of the PBL in GCMs and MMMs (Pielke 1974; Tapp and White 1976; Anthes and Warner 1978; Deardorff 1978). The WRF model is a non-hydrostatic, compressible model with mass coordinate system, designed as the next generation NWP model and data-assimilation system. It is well suited for a wide range of applications, from idealized research simulations to operational forecasting. It can be made a significant use in advancing research objectives in a number of areas, such as convection-resolving NWP, hurricane forecasting, regional climate studies, and air chemistry/quality research. The RUC and NOAH LSMs are the first two land surface schemes introduced in WRF. They have been described in and 4.7.3, respectively. In this study, the multilayer soil model LSPM has been coupled with WRF in order to calculate soil fluxes on the basis of time-dependent solutions for temperature and moisture. In this way, a new two-way model (this version will be hereafter references as WRF-LSPM) is fulfilled. Moreover, the coupling allows the calculation of the surface physical fluxes and of many relevant hydrological variables. 5.2 Brief description of the LSPM 61

71 A brief description of the soil thermodynamics and soil hydrology in the LSPM is provided here. The detailed LSPM parameterizations are reported in 3. In the following, only the parts relevant for this study will be outlined. The LSPM consider only one canopy layer (big leaf approximation) and diagnose the following variables: soil moisture and temperature in the soil layers, water stored on the canopy, and snow stored on the soil and vegetation. In this study I have used six soil layers, and the thickness of each layer from the soil surface to the bottom have been set at 5, 10, 20, 40, 160 and 300 cm, respectively. The root depth d R variable with the vegetation type is calculated in the following way: hf dr hf 0.20m (5.1a) 2 where h f is the vegetation height (m). d 0.10 h 0.2m (5.1b) R f Energy budget Soil temperature is predicted by the following equation: T Fz T c kt (5.2) z z z z where ρc is the volumetric soil heat capacity (J m -3 K -1 ), T is the soil temperature (K) and k T is the thermal conductivity (W m -1 K -1 ). The above equation is discretized numerically and solved using the Crank-Nicholson method. The heat flux F z,i, at the interface between i-th and (i+1)-th soil layers is evaluated as: F k zi, Ti, Ti Ti 1 zi zi 1 (5.3) 2 For the first soil layer (i=1), F z,i-1 =F z, 0 = -Q G, where Q G is the heat flux into the soil (positive when entering into the soil). The resulting equation for the first layer is: ( c) z T T T T n1 n1 n n i i n1 n i i1 i i ( Ti Ti ) QG kt, i( 1 ) t zi zi 1 zi zi 1 (5.4) 62

72 The boundary condition at the bottom of the soil column (i=m) is F z,i = -Q GBOT. Where this last quantity represents the soil heat flux exchanged with the bottom layers not considered by LSPM. The resulting equations is: ( c) z T T T T n1 n1 n n i i n1 n i1 i i1 i ( Ti Ti ) QGBOT kt, i ( t zi 1 zi zi 1zi ) (5.5) For a generic soil layer, with m-1 i 2, ( c) z T T T T T T T T n1 n1 n n n1 n1 n n i i n1 n i1 i i1 i i i1 i i1 ( Ti Ti ) kti, 1 ( ) kti, ( t zi 1 zi zi 1 zi zi zi 1 zi zi 1 ) (5.6) Hydrologic budget The water flux Q (m s -1 ) is partitioned into the liquid water flux Q l and the water vapor flux Q v. The volumetric soil water content ƞ (m 3 m -3 ) is predicted by the following equation: K T [( Dl Dv ) ] [ DvT ] t z z z z z (5.7) where D l is the liquid water diffusivity due to soil water content, and D v and D vt (m 2 s -1 K -1 ) are, respectively, the analogous one for the water vapor diffusivity. K (m s -1 ) is the hydraulic conductivity. Hydraulic conductivity and water diffusivity are highly nonlinearly dependent on the soil moisture and it can span over several orders of magnitude even for a small variation in soil moisture, particularly when the soil is relatively dry (Chen and Dudhia 2001). Also Eq. (5.7) is discretized numerically and solved using the Crank-Nicholson method. The water flux from layer i-th to layer (i+1)-th is: i i 1 Ti Ti 1 Qi ( Dl i Dv i) ki ( DvT) i zi zi 1 zi zi 1 (5.8) 2 2 The water balance for the i-th layer is: z t i n1 n ( i i ) Qi 1 Qi e i (5.9) 63

73 where e i account for the transpiration and (for i=1 only) for the surface evaporation. Also this scheme is integrated using the Crank-Nicholson method. For the first soil layer i=1, Q Q (5.10) i1 infl ei Qseva ( Q tran) i (5.11) where Q infl is the infiltration, Q seva is the surface evaporation, and Q tran is the transpiration from the root zone. The result for the first layer is: z t n1 n1 i n1 n i i1 ( i i ) Qinf l Qseva Qtran ( Dl Dv ) i zi zi 1 ( D D ) K ( D ) n n n n i i1 i i1 l v i 1 vt i z z i z i 1 i z i1 T T 2 (5.12) For the bottom layer, i=m, Q i =-K i, e i = (Q tran ) i and zi ( ) ( ) t n1 n1 n1 n i1 i i i Qtran Dl Dv i1 zi 1 zi ( D D ) K K ( D ) n n n n i1 i i1 i l v i1 i i1 vt i1 z z i 1 z i i1 z i T T 2 (5.13) For all other layers, m-1 I 2, e i = (Q tran ) i and z t z z n1 n1 n1 n1 i n1 n i1 i i i1 ( i i ) ( Dl Dv ) i1 ( Dl Dv ) i i1 i zi z i 1 ( D D ) ( D D ) K K n n n n i1 i i i1 l v i1 li vi i i i1 zi 1zi zi zi 1 n n n n Ti 1 Ti Ti Ti 1 ( Qtran) i ( DvT ) i1 ( DvT ) i1 zi 1 zi zi zi The maximum soil infiltration capacity is calculated according with the formulation of NCAR model. This parameterization has been preferred to that of Boone and Wetzel (1996), originally used in LSPM, as the infiltration values seem more reasonable, especially in case of dry soil. The maximum infiltration, P infiltrmax is formulated as (5.14) 64

74 P K 1 b(1 s1 w1 inf iltr max s d1 s1 i1 ) (5.15) The effective infiltration is then evaluated as: P p f P (5.16) in gef inf iltr max and the eventual excess water is considered as surface runoff R s1 (m): R t( P P ) (5.17) s1 infiltr max geff The saturation runoff can occur at each soil level interface in the case in which soil moisture content exceed the porosity, and is calculated as R s2 (m) level per level: Rs2 sidi( q i 1) (5.18) Total surface runoff R s is now calculated as: R (1) s Rs 1 Rs2 (5.19) while underground runoff R u, which includes both drainage and intermediate runoff, is given by: m R R () i Q ( m ) (5.20) u s2 out i2 The evaporation flux E in the layer between the surface at height z 0h +d and the atmosphere at the height z atm, it can be expressed using a budget equation: E = Ef + Eg + Ef,sn + Eg,sn (5.21) where the suffix f refer to vegetated snow-free soil, the suffix g to snow-free bare soil, and the suffices f,sn and g,sn to the portions of vegetated and bare soil covered by snow, respectively Snow parameterization In LSPM a simple snow model is included for dealing with various surface characteristics. A generic snow pack is characterized by a snow depth h s, a volume V s and a base area A. The snow parameterization scheme has only one layer of snow cover and simulates the snow melting, and heat exchange at snow atmosphere and snow soil interfaces. The energy balance of the entire snow pack can be written (Cox 65

75 et al., 1999) by summing the net radiation, the conductive heat flux coming from soil, canopy and eventual rainfall (all considered positive when entering in the snow), and of sensible and latent heat fluxes (considered positive when leaving the snow). The resulting equation is: Q ( R H Q Q Q Q ) t (5.22) av N sn sn Esn Gsn F sn rain where R Nsn is the net radiation relative to the snowy surface, H sn and Q Esn are the sensible and latent heat fluxes, Q Gsn and Q Fsn are the heat fluxes transmitted to the snow from the canopy and the bare soil by conduction and Q rain is the heat fluxes transmitted to the snow pack by rainfall. The snow albedo is assumed to vary with the time between the thresholds α snmin =0.50 and α snmax =0.85. Based on Robinson and Kukla (1984) and Verseghy (1991), the rate of decay of albedo has been assumed to obey to the following expression: 1 f t ( tt) ( t) e (5.23) sn sn snmin snmin where τ f =0.24 is an empirical parameter and t 1 =86400 s = 1 day (Verseghy, 1991). The above equation show an exponential decay of albedo, and the time needed for albedo to change from the maximum value α sn =α snmax to the minimum value α sn = α snmin, in absence of snowfalls and other phenomena, is about 10 days. 5.3 Dataset for vegetation classification and soil texture in WRF and LSPM The vegetation type and the soil texture are the primary variables to decide the land surface land surface characteristic fields. In the NOAH scheme of WRF, the 1-km resolution U.S. Geological Survey s (USGS) SiB model vegetation categorization, which has 24 land cover classes, is used. However, the user may select an alternative set of land use categories based on the MODIS land-cover classification of the International Geosphere-Biosphere Programme and modified for the NOAH LSM. These categories are not a subset of the 24 USGS categories. The 20-category MODIS-based land use data can be selected instead of the USGS data in the WRF 66

76 Preprocessing System (WPS). WHS Vegetation type f (lw) f (sw) h f R gl r min d f fsum f LAI m LA 1 Crop/mixed farming Short grass Evergreen needle leaf tree Deciduous needle leaf tree Deciduous broadleaf tree Evergreen broadleaf tree Tall grass Desert Tundra Irrigated crop Semi-desert Ice cap/glacier Bog or marsh Inland water Ocean Evergreen shrub Deciduous shrub Mixed woodland Settlement Dense settlement Po Valley (SPC) Piedmont vineyards Siberia glan field TABLE 5.1: Vegetation types characteristics. WHS column from 1 to 18 indicates codes taken from Wilson and Henderson-Sellers (1985), from 19 to 23 codes taken from Cassardo (2006). Second column lists the vegetation cover associated to column 1. f is the albedo (lw stands for longwave and sw for shortwave), h f the vegetation height (m), R gl the Noilhan parameter for the dependence of canopy stomatal resistance from solar radiation, r min the minimum stomatal resistance (s m -1 ), d f the 2 nd leaf dimension (m), fsum the base vegetation cover, f its seasonal variation, LAI min the winter value of leaf area index and LAI its annual excursion. (Derived from Cassardo et al. 2009) Vegetation classification in 67

77 Traditionally, the LSPM can initialize the vegetation parameters in the following three ways: giving the specific values for each parameter; taking the values from an extension (Cassardo 2006) of the global dataset of Wilson and Henderson-Sellers (1985) -- in this case, only the vegetation code is required; taking the values from the ECOCLIMAP database (Masson et al. 2003). For this study, the values of the extended global dataset of Wilson and Henderson-Sellers (1985) have been used; this dataset has 23 land cover classes (see Table 5.1). The land cover dataset is derived from the MODIS land-cover classification initialized by the WRF Preprocessing System. The dominant vegetation type in each grid box has been selected in order to represent the grid vegetation characteristics. As this categorization is slightly different from the LSPM dataset, then in the WRF-LSPM coupled model, I have matched the MODIS land-cover classification with the global dataset of Wilson and Henderson-Sellers to apply in WRF-LSPM scheme. January April July October Fig. 5.1: The seasonal variation of MODIS 1KM green vegetation fraction in Italy (2008). 68

78 Fig. 5.1 shows the 1km grids green vegetation fraction in different season in Italy Soil texture Landuse type is one of the most important parameters in the LSMs to describe the exchange processes of heat, moisture, and momentum in between land and atmosphere. In the WRF model, vegetation fraction, albedo, roughness, and emissivity are parameterized according to the landuse type. Therefore, the landuse type in the model plays an important role to improve the interaction of land surface with the PBL. Soil parameters are taken from an extension of the Clapp and Hornberger (1978) table; the parameters are classified by soil type code, an index which needs to be specified externally. Concerning the soil types (Table 5.2), LSPM considers 14 types of soils: the values of the parameters for the first 12 types are taken from the original table of Clapp and Hornberger (1978), while the last two were added in Cassardo (2006). The first 11 types of soil are determined from the percentages of sand, silt and clay furnished by ECOCLIMAP database through the USDA-NCRS (1997) soil triangle (Fig. 5.2). Fig. 5.2: The USDA-NCRS (1997) soil textural database. 69

79 Code Soil type B K s s wi s c 1 Sand Loamy sand 3 Sandy loam Silt loam Loam Sandy clay loam 7 Silty clay loam Clay loam Sandy clay Silty clay Clay Peat Ice Very pure sand TABLE 5.2: Soil type characteristics. Column 1 and 2 are the soil codes and types, respectively, as indicated by Clapp and Hornberger (1978) for codes from 1 to 12, and by Cassardo (2006) for codes 13 and 14. List of the correspondences between soil type codes and soil types. b is a coefficient, K s is the saturated hydraulic conductivity (in dm 2 s -1 ), s the porosity (in units of volumetric soil moisture), wi the wilting point (in units of volumetric soil moisture), s the saturated moisture potential (in cm), and c the dry soil heat capacity (J m -3 K -1 ). (Derived from Cassardo et al. 2009). 5.4 The physical interface of WRF The WRF model does not allow to use the common blocks, and it requires that all variables have to be passed into subroutines through argument lists. In addition, the use of the modules (a feature of FORTRAN 90) makes easier the design of physics interface. For the physics interface, a three-level structure (solver, driver, and individual scheme) similar to those of the other LSM coupled with WRF (Fig. 5.3) has been constructed. The idea of three-level structure is so that users can easily 70

80 implement their schemes into the WRF with little need to understand other parts of WRF code Level 1 - Solver The first level, solver (solve_eh.f for height model and solve_em.f for mass model), is the main subroutine for calling dynamics and physics. The solver is a bridge, connecting dynamics and physics. In addition, the parallel processes regarding Fig. 5.3: The schematic diagram of physical interface (derived from the model part, such as multi threading and message passing, are also dealt with in this subroutine Level 2 - Driver Instead of calling directly the different physics schemes, the solver calls the physics drivers, which are the interfaces between the solver and the individual physics schemes, and are shared by the two dynamic cores. The mechanism that allows different dynamic cores to use the same physics driver is the physics preparation calls in each solver (phy_prep and moist_physics_prep). This subroutine calculates the variables used in all physics routines. Except subgrid eddy diffusion, every physics component has its own driver, such as the microphysics_driver, cumulus_driver, 71

81 pbl_driver, and radiation_driver. The pbl_driver includes the surface layer, land/sub-surface, and the boundary layer, while the radiation_driver includes long wave and short wave radiations calculation. In each driver, CASE SELECT statements are used to branch to the choice of scheme. The flags for choosing different physics schemes are located in the namelist.input file. The design of the driver interface has been made in order to provide a plug-compatible environment for users to plug in their own physics packages Level 3 - Individual physics scheme. The prohibition of using common blocks separates users' codes from the WRF code quite well, and allows users to easily implement their packages into WRF, though some minor changes of the WRF code might be required. One module comes with each physics scheme, and all subroutines related to the scheme should be included into this module. For the detailed introduction of the implement LSPM into WRF, please refer to Appendix B. 5.5 Initialization of soil moisture For short-term forecasts, soil moisture, and especially its surface value, may play an important role in modulating the regional scale circulation and the convective weather systems. The level of soil saturation determines the availability of water, as well as the hydraulic properties of the soil, and for this reason soil saturation exerts a significant control on the rates of exfiltration and subsequent evaporation (e.g., Brubaker et al. 1996; Eltahir 1998). The soil moisture is a very important component of LSM, and it would not make much sense to implement a sophisticated LSM in mesoscale models without a proper soil moisture initialization procedure (Chen and Dudhia 2001). In WRF-LSPM, the initial soil moisture can be obtained from reanalysis systems, e.g. the NCEP Final Analysis (FNL from GFS) database. But the reanalysis tends to have very wet soil moisture, due to a model positive precipitation bias (e.g., Chen and Mitchell 1999, Chen and Dudhia 2001). Thus, to decrease the bias, it is necessary to adjust the soil moisture in the initialization procedure, when using NCEP-NCAR 72

82 reanalysis soil moisture fields to initialize the WRF model. It is also well known that the vertical gradients of the soil moisture are able to drive the soil moisture and the heat fluxes. For a soil in which the moisture diffusivity is uniform with the depth and for a site being in not arid conditions, it is possible (Cassardo et al. 2006) to suppose that the soil moisture will approach the field capacity at increasing depths. A vertical profile of the initial soil moisture was thus introduced into the WRF-LSPM according with the following relation: qk ( ) q ( q q ) e FC GFS FC z/ H P g H (5.24) where g is the thermal diffusivity (assumed equal to 10-6 m 2 s -1 ), q the initial soil moisture (in units of saturation ratio, e.g. in m 3 m -3 ), P the daily cycle (P = 1 day = s), Z the soil depth and q FC the field capacity (Stull 1998); in units of saturation ratio as variables. To demonstrate the sensitivity of the coupled WRF-LSPM model to the initial soil moisture fields, a set of 48 h sensitivity experiments were performed by changing (increasing and decreasing) 0.1 (in terms of moisture volumetric content). All experiments refer to simulations carried out starting from 00 UTC of 2 nd August, 2003, over the Piedmont region in NW Italy. The initial soil moisture and temperature conditions for the WRF-LSPM has been obtained from the NCEP Final Analysis (FNL from GFS) database. The reanalysis volumetric soil moisture fields refer to four soil layers: 0-10 cm, cm, cm, cm. The initial soil moisture, used in these sensitivity experiments have been interpolated from the GFS at the six soil layers, 0-5 cm, 5-10 cm, cm, cm, cm, and cm. Fig. 5.4 shows the surface heat fluxes response to the different initial soil moistures in the grid-point near to the center of Turin ( E, N), from 00 UTC of 2 nd to 4 th August, The initial surface soil moisture according with GFS was m 3 m -3. An increment of 0.1 in the initial soil moisture causes a reduction of about 150 W m -2 of sensible heat flux (almost the half) and a shift of 3 h of the maximum, and an opposite behavior for the latent heat flux. On the contrary, a reduction of 0.1 in the initial soil moisture causes a smaller change of about W 73

83 m -2 in both fluxes. Hence a perturbation in initial soil moisture seems able to affect the surface energy balance, in some cases dramatically. a b Fig. 5.4: Sensitivity of surface heat fluxes (a: sensible heat flux; b: latent heat flux) to the initial soil moisture at the point near to the center of Turin ( E, N) from 00 UTC of 2 nd to 4 th August, Despite the sensitivity of short-medium weather forecasts and climate prediction to the initial soil-water conditions, at present very few methods are available to define the soil-water content in data-assimilation systems. One reason is that there are no routine observations of high-resolution soil moisture at large scales. Even if there has been an effort in recent years to provide satellite-based estimates of soil-water content (Schmugge and Becker 1991), this method could provide only estimates for the water contents in the top few centimeters of the soil. An effective methodology that can be applied in a forecast/data-assimilation system is that based on the ideas of Mahfouf (1991). He described two possible methods: a variational algorithm where a cost function is minimized over a sequential assimilation scheme consisting in a set of 74

84 predictions and in static corrections of soil moisture. Basing on his research, some assimilation schemes were developed. In the current study, the initial soil moisture and soil temperature used by LSPM are normally obtained from NCEP Global Data Assimilation System (GDAS) and the NCEP-NCAR reanalysis system. 5.6 Preliminary comparison of LSPM, NOAH and RUC schemes To compare the results of three land surface schemes (LSPM, NOAH and RUC) coupled with WRF, several short-term numerical simulations were performed from 00 UTC of 2 nd to 9 th August, This period has been chosen because of the existence of clear-sky conditions over Piedmont region, Italy, which allows a better assessment of the land surface processes. Fig. 5.5 shows a comparison of solar downward radiation, soil temperature at 10 cm deep, and surface heat fluxes produced by three simulations. All the model results are plotted at 3 h time intervals. The point chosen for the comparison also is located at the city center of Turin ( E, N). The downward solar radiation simulated by the three schemes are similar. The predicted soil temperature of WRF-LSPM and WRF-NOAH are similar, and the difference between the two schemes fall within the range of 2 K, whereas the predicted result of RUC is higher than the others. Fig. 5.5c shows the corresponding surface sensible heat flux comparison. The predicted sensible heat flux by WRF-RUC scheme is significantly higher than the other two schemes, with a maximum difference about 250 W m -2 at the local noontime. The WRF-LSPM result is similar to that of WRF-NOAH, but the peak values are slightly higher than those of WRF-NOAH. Also in Fig. 5.5d the predicted latent heat flux by WRF-RUC scheme is significantly lower than that of the other two schemes. The initial soil moisture in the WRF-RUC scheme may be responsible for such above difference. In WRF-NOAH and WRF-LSPM scheme the periodic variation of vegetation takes into account the initial soil moisture, whereas in WRF-RUC scheme the periodic variation of vegetation is ignored, which lead to smaller initial soil moisture. Hence utilizing only the surface moisture to determine the evaporation rate in the WRF-RUC model cannot correctly represent the influence of environmental conditions and that 75

85 of deep root zone soil moisture on the canopy resistance. a b c d Fig. 5.5: Comparison of (a) net radiation flux (W m -2 ), (b): soil temperature (k) at 10cm deep, (c) sensible heat flux (W m -2 ), and (d) latent heat flux (W m -2 ) simulated by three land surface schemes (LSPM, NOAH and RUC) at the point near to the center of Turin ( E, N) from 00 UTC of 2 nd to 9 th August, Summary The work reported in this section constitutes the implementation of the LSPM scheme coupled with the WRF. A new two-way model (WRF-LSPM) is fulfilled. Moreover, the coupling allows the calculation of the surface physical fluxes and of many relevant hydrological variables. The aim is to provide an efficiently executed for weather forecast and hydrologic applications at different scales. In this work, the 1-km resolution U.S. Geological Survey s (USGS) model vegetation categorization, which has 24 land cover classes, is used. The vegetation and soil properties are determined by the spatial distribution of vegetation and soil types. In addition, a vertical profile of the initial soil moisture has been introduced into the WRF-LSPM. To demonstrate the sensitivity of the coupled WRF-LSPM model to the initial soil moisture fields, a sensitivity test was performed to determine the impact of 76

86 land-surface characteristics and soil moisture initialization. The result shows that this perturbation in initial soil moisture seems to primarily affect the surface energy balance in simulated area. The change of 0.1 in the initial soil moisture in terms of its volumetric value can cause a change of surface heat flux. In addition, several short-term numerical experiments were conducted to evaluate the WRF model coupled with NOAH, LSPM and RUC schemes. The performance of three schemes is briefly documented. All schemes seem able to capture fairly well the downward radiation at the surface. The predicted by the WRF-LSPM and WRF-NOAH models has the similar results, whereas those of the WRF-RUC model is significantly different from them. The preliminary results show that WRF-LSPM is able to provide the energy and water fluxes at the boundary atmosphere required by WRF. Further simulations including evaluations are needed for other synoptic conditions will be introduced in the next chapters. 77

87 Chapter 6 Experiments 1: A landfall typhoon simulation by WRF-LSPM 6.1 Introduction It is well know that the tropical cyclones (TCs), in Asian countries called typhoons, are one of the major responsible of natural disasters. Over the past several decades, the performances of the TCs numerical modeling has made great improvements. The results of many researches show that the latent heat flux, the moisture flux and the sensible heat flux play important roles in modeling the intensity and the track of the TCs (e.g., Ooyama 1969; Tuleya and Kurihara 1982; Rotunno and Emanuel 1987). A detailed diagnosis of the energy budget of the simulated tropical cyclone was carried out by changing the coefficient of air surface energy exchange in early tropical cyclone research (Ooyama 1969). The results showed that the model was capable of simulating the typical life cycle of tropical cyclones, including the mature hurricane stage, with a remarkable degree of reality. Rosenthal (1971) performed a set of experiments to test the intensity of TCs in relation with heat, moisture and momentum fluxes by using a seven-layer asymmetric, hydrostatic primitive equation model. He suggested that, by increasing the heat and moisture transfer coefficients, also the maximum wind speed during the mature phase of the storm was increased. The model-attained hurricane intensity was also found to be well correlated with the maximum surface evaporation and the large-scale environmental convective available potential energy (Shen et al. 2000). As known, TCs derive energy primarily from evaporation by the ocean and from the associated condensation in convective clouds concentrated near their centre (Holland 1993). In a TC before making landfalling, the sea surface provides enough energy, used in the moisture, heat, and momentum fluxes, to sustain the TCs 78

88 movement, rotation, and intensifying. But in the case of a landfalling TC, it decays rapidly because of the irregular terrain and the cut off energy from sea. The land surface processes and the rainfall feedback play an important role for a landfall typhoon sustaining (Chen et al. 2004). The properties of surface and topography are interacting with the typhoon, that decides the decay and the growth of energy and momentum. Several studies concluded that the reduction of surface evaporation is critical for the TCs decay after the landfall (e.g., Miller 1958; Fett 1966; Tuleya 1994). Tuleya (1994), using the Geophysical Fluid Dynamics Laboratory (GFDL) hurricane model, found that the moist land surface coupling, similar to the ocean coupling, tends to reduce the hurricane intensity through local surface cooling. model.zhang et a1.(1994) studied the effect of ocean boundary layer fluxes on mature typhoon, and the result shows that the vertical transfer of TC boundary layer fluxes has a small effect on TC tracks, but it is very important for TC sustaining. Li et al. (2007) pointed out that the vertical transfer of fluxes in the boundary layer over saturated wetland has significant influence on the intensity, structure, and rainfall of the landfalling Typhoon Nina (197503). All these studies are focused on the important effect of TC boundary layer processes on development of TCs. In this simulation, the effects of different land surface schemes on precipitation, heat and vapor flux fields have been investigated. In addition to the schemes already included into WRF package, also the LSPM has been coupled with the WRF Model. A set of sensitivity experiments focused on the sensible heat flux, latent flux and moisture flux fields has been performed, and the variations on the landfalling typhoon track have been investigated. In addition, also the impact of the soil moisture initialization (not only the surface values, but also its vertical profiles) on the typhoon precipitation has been investigated with the help of the WRF-LSPM model. 6.2 Setting of the experiment Choice of the WRF parameterizations 79

89 The WRF simulations have been carried out in this study by choosing the following parameterizations: the YSU PBL scheme; the surface layer schemes RUC, NOAH and the LSPM; the RRTM longwave radiation scheme; the Dudhia shortwave radiation scheme, the Kain-Fritsch (new Eta) Cumulus Parameterization scheme; the WSM 3-class simple ice scheme Model domain and resolution In these simulations, two-nested domains with two different horizontal grid sizes have been used: 30 km (DM1) and 15 km (DM2), both centered over the Hunan province, China Vegetation cover, soil and land-use data The vegetation fraction, all the soil and land use data, the field capacity and the permanent wilting point have been assigned as described by Chen and Dudhia (2000). A 10m global USGS 24-category landuse map has been used in order to choose the type of surface. The numbers of soil layers used in the simulations of WRF-LSPM and WRF-RUC have been set to 6, and their depths have been set to (top to bottom): 5, 10, 40, 80, 160 and 300 cm, respectively, while that of the 4 standard layers in WRF-NOAH has been set to 10, 30, 60, and 100 cm Initial and boundary conditions, and simulation time These simulations were run from 19 August 2007, 00 UTC, to 25 August 2007, 00 UTC. As initial and lateral boundary conditions for DM1, the NCEP Final Analysis (FNL from GFS) database with resolution of 1 6-HOURLY with 24 vertical levels (1000 mb, 975 mb, 925 mb, 900 mb, 85 0mb, 800 mb, 700 mb, 650 mb, 600 mb, 550 mb, 500 mb, 450 mb, 400 mb, 350 mb, 300 mb, 250 mb, 200 mb,150 mb, 100 mb, 70 mb, 50 mb, 30 mb, 20 mb, and 10 mb) in latitude and longitude, and 6 h in time, was selected. A set of soil moisture sensitivity experiments in DM2 was performed in the period August 2007, the coarser domain DM1 provides boundary values for the nest DM2. Finally, the nest needs its calculation back to the coarser domain. 80

90 6.3 Meteorological analysis of the event The typhoon Sepat made landfall in Huian city, Fujian province at the 18 UTC 18 August 2007 and soon after weakened into a tropical low pressure which passed Hujian province, Jiangxi Province and Hunan Province. In Fujian province Sepat moved quickly but in Jiangxi province the speed of TC Sepat decreased, and it did not move towards but turned to left. Looking at the 500 hpa map (Fig. 6.1), at the north of TC Sepat was blocked by a strong continental high-pressure, while surrounded by the eastern subtropical high and the southern low-latitude equatorial high-pressure circulation which lead to a slow-moving. The North continental high pressure system blocked the forward of typhoon, and the subtropical high pressure continued to grow westward, and leading to an westward turn. In addition, the jet stream from Indian Ocean continued to maintain or strengthen. It compensated the loss of momentum caused by the surface friction, at the same time the vapor channel was strengthened at the east side. Fig. 6.1: 500hPa geopotential field at the 00 UTC of August 20 th, 2007 (m). Image provided by the NOAA/ESRL Physical Sciences Division, Boulder Colorado from their Web site at After making a landfall, the strong tropical storm Sepat caused a continuous heavy rainfall event over China mainland. Especially the cyclone low pressure persisting in Hunan province for 60 h produced a severe flood event. During this period, 67 (28, 15, 10, 3) meteorological stations measured an accumulated rainfall greater than 50 (100, 81

91 200, 300, 400) mm. The maxima of precipitation (516.1 mm) was recorded at Zixing (25.99 N, E), a city located at the South-east of the Hunan province. According to small-scale automatic monitoring network statistics data, during the above-mentioned period, for a total cumulative rainfall 300 mm observed in 93 rain gauge stations (these stations which located in different points according to the topography of Hunan Province are be as the additional observation for above mentioned meteorological stations), 500 mm observed in 9 rain gauge stations. Due to the concentration, high intensity, broad range and longer lasting time, resulting in flash floods, mudslides, landslides have occurred. The rainfall event was defined a comprehensive assessment of the special large weather disasters. Ye et al. (2007) performed some simulations of the typhoon Sepat using the mesoscale numerical model AREM, and the results showed that there was a strong vapor flux over the heavy rainfall area. In particular, two vapor tongues were present: one was the southerly current related to the South-western monsoon, and the other northerly current related to the typhoon low pressure circulation, respectively. Both of them provided large quantities of vapor moisture. 6.4 The sensitivity experiments The four sensitivity experiments performed in this work have been designed as follows. In the control run, all surface fluxes have been transferred to the boundary layer. In the nolhf run, the surface latent heat flux has not been transferred to the boundary layer and has been set equal to zero. In the noshf run, the sensible heat flux has not been transferred to the boundary layer and has been set equal to zero. In the noshflhf run, the sensible heat flux and the latent heat flux have not been transferred to the boundary layer and has been set equal to zero Analysis of Control run Fig. 6.2 shows that the control run gives a good estimate of the track of typhoon Sepat after its landfall. To compare the result of the control run with the observed and the NCEP data, the 700 hpa wind field has been selected, because the boundary layer 82

92 heights during the typhoon passage were at about 2500 m. The first part of the two typhoon tracks (simulated and observed), before entering into the Jiangxi province, Fig. 6.2: Observed (solid line) and simulated in the control run (dashed line), tracks of the typhoon Sepat after its landfall. are almost overlapped. After entering into the Jiangxi province, the simulated track is slightly different from the observed one. About the typhoon left turning, two reasons can be explained. From one hand, the circulation of the typhoon following the subtropical high rightward extending. From the other hand, it may be considered the effect of Poyang lake, which is the largest inner deep-water lake located in the northern Jiangxi province in China. Shen et al. (2002) pointed out that the local surface cooling over a water-covered land causes a reduction in the potential evaporation, thereby considerably reducing hurricane intensity during landfall. This reduction of intensity may produce a rightward turning when the storm is driven by the subtropical high pressure, as in this case. In the whole simulated area, the observational precipitation cumulated during the passage of the typhoon Sepat and simulated in the control run (Fig. 6.3) appears to be in agreement with the observations, although the rainfall amount in the zone of the observed maximum is underestimated by mm (but the location of this maximum is well captured), and there is another area of intense rainfall in the SE part of the domain predicted but not observed. The heavy rainfall observed in Hunan province has been predicted exactly when it occurred, i.e. when the Sepat typhoon passed on the Jiangxi Province. Also, as can be seen from the panels in Fig. 6.4, heavy 83

93 precipitation produced an area of run-off and soil moisture increase that followed the rainfall pattern. For this reason, despite the underestimation of the rainfall, the good match of timing and localization of the intense rainfall makes WRF-LSPM a very useful tool to simulate such kind of events. a b Fig. 6.3: a): Precipitation cumulated observed and b): precipitation cumulated simulated in the control run, expressed in mm, from the 00 UTC of August 19 th to the 00 UTC of August 25 th, a b c d Fig. 6.4: a): Top-layer soil moisture (m 3 m -3 ) at 00 UTC August 21, 2007, b): top-layer soil moisture (m 3 m -3 ) at 00 UTC August 22, c): rainfall total (mm) between 00 UTC August 21, and 00 UTC August 22, and d): runoff total (mm) in same period for WRF simulation with LSPM. The white cycle in top two figures that present the Poyang Lake which is the biggest lake in China. 84

94 6.4.2 Validation of the WRF-LSPM In order to get quantitative information, a statistical analysis has been carried out on the comparison between the simulated precipitation and observed data from 00 UTC of 19 th to 00 UTC of 25 th. In this rainfall event caused by TC Sepat, the main rainfall appeared in the first three days. In most stations, the cumulated precipitation values appear to be underestimated in comparison with observations. In the first day, the LSPM scheme underestimates the observed rainfall; in the second day, the predicted of rainfall are in agreement with the observed rainfall; in the third day, the LSPM scheme overestimate slightly the observations. In the last two days, the precipitation significantly decreased because of the weakening of the TC. As shown in Table 6.1, the absolute value of bias is lower than 10 mm in 19% of stations, and lies in the range between 10 mm and 30 mm in 69% of stations, while larger than 30 mm only in 12% of stations. The bias shows that the WRF-LSPM can capture the main rainfall events. BIAS classes Percentages BIAS 10 mm mm < BIAS 20 mm mm < BIAS 30 mm 41 BIAS > 30 mm 12 TABLE 6.1. Percentages of cumulated precipitation BIAS (in mm) between the WRF-LSPM simulated and observed in 88 stations of Hunan province Comparison of NOAH, RUC and LSPM (control run) All these models dynamically predict water and energy fluxes and states at the land surface, although their parameterizations and/or structures representing various processes are different. For example, the LSPM scheme has a number of layers which can be selected by the user, and in this study has been set to 6-layers (depths are 5, 10, 20, 40, 160 and 300 cm), while the NOAH scheme has 4-layers (depths are 10, 30, 60 85

95 and 100 cm) and the RUC scheme has 6-layers (5, 10, 20, 40, 160 and 300 cm). In this thesis, the hourly precipitation and runoff, the soil moisture (at 10 cm deep) and the surface soil temperature ( at 10 cm deep) of these three land surface schemes above mentioned have been compared in order to verify the simulation effects in the station of Zixing (25.99 N, E), in which the maximum of precipitation values has been observed. Note that, for the LSPM and RUC schemes, the second layer corresponds to the depth of 10 cm, while in NOAH scheme the first layer corresponds to the depth of 10 cm. Hourly precipitation and runoff Fig. 6.5 shows the hourly rainfall and runoff from 00 UTC of 19 th to 00 UTC of 25 th (August 2007). From the cumulated rainfall, both NOAH and LSPM schemes, coupled with WRF, underestimate the observed rainfall. The cumulated rainfall of WRF-NOAH scheme is closer to observations. In the first day, both WRF-NOAH and WRF-LSPM underestimate the observed rainfall; in the second day, the predicted rainfall is in accordance with the observed one; in the third day, the WRF-NOAH scheme overestimates the observations, while the WRF-LSPM scheme overestimate slightly the observations. The error of the first day may be caused by the spin-up problem of both WRF and LSPM or NOAH, which forbids realistic precipitation rate predictions at the beginning of the forecast period. As regards as the precipitation peak rate, the observed peak rate is about 29 mm h -1, while the maximum precipitation rate predicted by the WRF-NOAH scheme is 46 mm h -1 and that of WRF-LSPM scheme is about 28 mm h -1, closer to the observations. The runoff output evaluated during the whole precipitation event by the two land surface schemes matches with the precipitation pattern. The cumulated runoff evaluated by WRF-NOAH is about 327 mm and that of WRF-LSPM about mm. WRF-LSPM predicted a significant runoff during the whole precipitation event, while that predicted by WRF- NOAH seems concentrated in the only two days, the 21 st and the 22 nd, related to the intense precipitation periods. 86

96 Rainfall Cumulated mm LSPM NOAH Observations Days (August 2007) a Cumulated mm Runoff LSPM NOAH Days (August 2007) b Fig. 6.5: a): Hourly precipitation (mm) observed and simulated (NOAH and LSPM schemes) at Zixing station (25.99 N, E) from 00 UTC of 19 th to 00 UTC of 25 th (August 2007), b): hourly runoff (mm) observed and simulated (NOAH and LSPM schemes) at Zixing station from 00 UTC of 19 th to 00 UTC of 25 th. Soil moisture The soil moisture here shown is the volumetric soil moisture, i.e. the volume of soil water per unit of volume of soil (m 3 m -3 ), and the value corresponding to the saturation, or porosity, for these kind of soil is in the range m 3 m -3. Fig. 6.6a shows that the soil moisture evaluated by the three schemes were consistent with the rainfall pattern (Fig. 6.5a) in Zixing station. From 19 th to 23 rd the values of soil moisture present a rising tendency, due to the typhoon precipitation. At the 21 UTC of 22 nd, the soil moisture reached its maximum. After the 23 rd, the soil moisture is subject to a downward trend caused by the absence of rainfall. But the soil moisture 87

97 predicted by WRF-RUC scheme is always lower than that of the other two schemes. The soil moisture predicted by WRF-LSPM scheme is in agreement with that of WRF-NOAH scheme, although it is slightly higher. In the WRF-LSPM and WRF-NOAH schemes simulation, from the 22 nd to the 23 rd the soil moisture continues to increase, reaching values close to the saturation and a maximum value at the 21 UTC of 22 nd, with values ranging in the interval m 3 m -3. a Fig. 6.6: a): Soil moisture (m 3 m -3 ) at 10 cm deep simulated (NOAH, LSPM and RUC schemes) at Zixing station from 00 UTC of 19 th to 00 UTC of 25 th (August 2007); b): soil temperature (K) at 10 cm deep simulated (NOAH, LSPM and RUC schemes) at Zixing station from 00 UTC of 19 th to 00 UTC of 25 th (August 2007). b Soil temperature Fig. 6.6b shows that the variation of soil temperatures show the same fluctuation. Except for the first day, the WRF-LSPM scheme is in agreement with the WRF-NOAH scheme. In the first and the last day, it is evident a strong increase of 88

98 soil temperature, perhaps related to the sunshine after the rainfall. During the heavy rainfall period, the soil temperatures show a decrease, reaching the minimum values (about K) during the 22 nd of August. The WRF-RUC soil temperatures are higher than those (1-2K) of the other schemes. This difference may be caused, perhaps, to the different depths of the soil in the three schemes. As a conclusion, both WRF-NOAH and WRF-LSPM schemes seem able to capture the main features of this landfalling typhoon Analysis of sensitivity experiments results Sensitivity on surface heat fluxes: effects on the Wind field at 700 hpa The experiments nolhf, noshf and nolhfshf allowed to estimate the importance of latent and sensible heat flux transfers from the surface to the boundary layer during the typhoon movement. Fig. 6.7 shows the streamlines of the wind speed fields at 700hPa, which evidence the position and the intensity of the typhoon center. Compared to the control run, the position of typhoon eye in the noshf run is located in the northwestern Jiangxi province, and in the nolhf run is located in the border zone of the northern Jiangxi province, while in the nolhfshf run is almost in accordance with the nolhf run, as well as the streamlines does not differ too much. By comparing the nolhf run and the noshflhf with the Control run, it can be noticed that the anticyclonic circulation and the divergence in the upper layer of the typhoon area are significantly weakened. In the noshf run the position of typhoon eye is changed, but the TC center s intensity is almost consistent with that of the Control run. Therefore, the removal of the effects of sensible heating flux is also unfavorable for long lasting sustention of typhoon circulation (Li et al. 2007). The latent and sensible heat fluxes are the main energy transportation processes from the boundary of the TCs to the mainland. It can be concluded that both latent heat flux and sensible heat flux had provided the energy necessary to sustain the typhoon after its landfall. Looking at the shifts in the eye positions and intensity, these experiments seem suggest that the latent flux has played, as expected, a more 89

99 important role than the sensible heat flux on the intensity and track of this typhoon: the energy derived from the evaporation from the surface layer has thus been used to sustain the landfalling typhoon. In addition, the vapor convergence and the lift in the boundary layer has also provided energy, due to the condensation energy release of the latent heat action when vapor was lifted from surface to the boundary layer. a b c d Fig. 6.7: The stream field (m s -1 ) of the wind at 700 hpa level in a): the control run, b): the noshf run, c): the nolhf run, and d): the nolhfshf run at the 00 UTC of August 21 st, Sensitivity on surface heat fluxes: effects on the vorticity Fig. 6.8 shows the latitudinal cross sections of the vertical vorticity and of the relative humidity over a direction passing through the typhoon center at the 00 UTC of August 21 st, From the control run, at the typhoon center (about E of longitude) there was an upward gradient increase from the lowest levels to the highest levels, and the maximum vorticity center of s -1 appeared in the middle levels. Such distribution of vorticity corresponds to the unstable stratification and the rising movement of the air around the typhoon eyewall. The relative humidity distribution shows, as expected, a moist-tongue expanding from the lowest levels to the highest 90

100 ones. Gray (1975) summarized the physical parameters most relevant in favoring the cyclogenesis in the typhoons. He founded that the genesis of a tropical cyclone is related to six environmental factors; one of them is the presence of large values of relative humidity in the lower and middle troposphere. The configuration of water vapor presents a distinct asymmetric feature: the convection is triggered in relatively humid conditions, but is inhibited with lower humidity. The result is the presence of a very wet layer below the 500 hpa level, while above 200 hpa there is a dry area. Fig. 6.8a presents the warm-cored structure and the moist character of the Sepat typhoon center. It is clearly visible the strong upward convective area in correspondences of a very wet area in the lowest layers around the cyclone. a b c d Fig. 6.8 Latitudinal cross sections of the vertical vorticity (10-5 s -1 ), and the relative humidity in a): the control run, b): the noshf run, c): the nolhf run, and d): the noshflhf run referring at the latitude of 28.5 E and at the 00 UTC of August 21 st, By comparing the noshf, nolhf and noshflhf runs with the control run, the vorticity gradients in the formers are significantly weaker than in the latter. Especially in the case of the noshflhf run, the anticyclonic circulation and the divergence in the whole layer of the typhoon area are weakened significantly. The vertical relative 91

101 humidity gradients are much smaller in the nolhf and noshflhf runs than in the control run, suggesting the conclusion that the lack of the latent heat flux and/or of the moisture flux decreases the intensity of the landfalling typhoon because they inhibit the transfer of moisture from the surface layer to the uppest layers. In addition, the absence of latent heat flux and/or of moisture flux caused a large transfer of sensible heat flux from the surface to the boundary layer, while the moist static energy was low in the atmospheric boundary layer. In the noshf run and noshflhf, the relative humidity presented the feature of being low both in the lowest and in the highest layers, but high in the intermediate layer. Under wet soil moisture conditions, cooling of surface temperature is associated with small sensible heat flux (Eltahir 1998), which causes relatively small boundary layer depths and a cooling center. When the mesoscale circulation is well developed, the mesoscale latent heat flux is stronger than the sensible heat flux (Chen et al. 1994), thus the lack of latent heat flux inhibits the convective development and the sustaining of the typhoon. In conclusion, all parameters involved in the sensitivity experiment, e.g. the latent heat flux and the sensible heat flux, influence the intensity of the typhoon Sepat, but the latent heat flux seems to play the most important role. Sensitivity on surface heat fluxes: effects on the precipitation Fig. 6.9 shows the precipitation cumulated from the 00 UTC of August 19 th to the 00 UTC of August 25 th, 2007, in the four different experiments. In control run the result show the presence of a rainfall center which position is in accordance with the observations. The pattern of the other runs (nolhf, noshf and noshflhf) show the absence of significant relative maxima over the South-eastern Hunan province. The formation of heavy rainfall observed there can be associated with the ascent motion connected with the cyclone low pressure. Moreover, because the Southeastern Hunan province is a mountainous area, the large-scale atmospheric forcings provided by the orographic lifting lead to the formation of heavy rainfalls. 92

102 a b c d Fig. 6.9: The precipitation accumulated (mm) over Hunan and Jiangxi provinces in a): the control run, b): the noshf run, c): the nolhf run, and d): the noshflhf run from the 00 UTC of August 19 th to the 00 UTC of August 25 th, In addition, at the South-western side of the Sepat typhoon, the interaction of its circulation with the special orography of the South-eastern area caused a convergence which favored the vertical transport of the latent heat flux, contributing to enhance the production of mesocale vortices and of low pressure areas. These factors favored the sustaining of the typhoon, as well as the increment in the amplitude of the heavy rainfall event. The comparison of the distribution of the accumulated precipitation in the sensitivity experiments show that, in the nolhf run and noshflhf run, due to the latent heat flux lack, the intensity and range of precipitation are weakened significantly, although the nolhf run captured the precipitation center location. The precipitation predicted covered the southern area of the Jiangxi province and the South-eastern one of the Hunan province. Maxima predicted were about 200 mm, a value much lower than the mm observed in Zixing. The results of the noshf run are spatially not similar to those of the control run. The maxima in the 93

103 South-eastern Hunan province are absent, and the rain area as a whole shifted further northwards, so that the maximum precipitation was located in the North of the Jiangxi province. Also these data show that the latent heat flux played a role most important than that of the sensible heat flux on distribution and magnitude of heavy rainfall. Also concerning the impacts on the rainfall amounts, the influence of the latent heat flux is far greater than that of the sensible heat flux: the lack of the former caused a direct reduction of the rainfall intensity and a shift of its location, while the lack of the latter only influenced the drop areas. 6.5 Sensitivity experiments on initial soil moisture Most studies on the soil precipitation feedbacks focus on the role of soil moisture. The level of soil saturation determines the availability of water, as well as the hydraulic properties of the soil, and for this reason soil saturation exerts a significant control on the rates of exfiltration and subsequent evaporation (Eltahir 1998; Brubaker et al. 1996). For short-term forecasts, soil moisture, and particularly its surface value, may play an important role in modulating the regional scale circulation and the convective weather systems. It is also well known that the vertical gradients of the soil moisture are able to drive the soil moisture and the heat fluxes. For a soil in which the moisture diffusivity is uniform with the depth, and on a site in not arid conditions, it is possible (Cassardo et al. 2006) to suppose that the soil moisture will approach the field capacity at increasing depths. A vertical profile of the initial soil moisture was thus introduced into the WRF-LSPM. The details have already been introduced in the 5.5. In addition, five experiments were conducted in order to examine the role of the initial soil moisture. Also, in the selected domain DM2, located in the Hunan province, the soil was relatively wet at the beginning of the simulation, due to previous rainfalls. For the whole DM2 domain, a vertical profile of soil moisture ranging from 0.16 (hereafter, all soil moistures are expressed in units of saturation ratio) - at the surface - to at the deepest soil layer (located at 3.0 m) - was set up in the first experiment. Another four soil moisture sensitivity experiments were performed, in which the 94

104 initial soil moisture was set, in the whole DM2 domain, constant for all layers and equal to, respectively, 0.1, 0.2, 0.3 and 0.4. The integration time for the five experiments was set to 72 hours, starting from the 00 UTC of August 19 th, 2007, period in which the Hunan province was affected by continuous heavy rainfalls. a b c d e f Fig. 6.10: a): Precipitation observed and b): simulated considering a profile of soil moisture, c): an initial soil moisture equal to 0.1, d) an initial soil moisture equal to 0.2, e): an initial soil moisture equal to 0.3, and f): an initial soil moisture equal to 0.4 in all soil layers. Unit of precipitation: cumulated mm. The results show that the initial profile of soil moisture content, and in any case its value, has a considerably great impact on the intensity of precipitation. The predicted accumulated precipitation in all five experiments show a spatial distribution in 95

105 agreement with the observations over the South-Eastern Hunan province (Fig. 6.10) except the maximum of 100 cm (accumulated precipitation) observed in North central Hunan, whose position in the simulations was predicted slightly rightward in all five experiments, the numerical values remaining close to the observations. Considering these five sensitivity experiments, the first one (in which the initial soil moisture was set with a vertical profile) and the last one (with the initial soil moisture set to 0.2) are those which give the best estimate of the intensity of precipitation for the rainfall maxima, thus these initial soil moisture values can be considered the most realistic. According to the observation of the mesoscale automatic stations, there were 9 stations located in southeast of Hunan province where the precipitation was observed to exceed the threshold of 500 mm. In fact, in the other experiments, the absolute maximum was underestimated by about at least 100 mm. The water content in the upper soil layer affects the evaporation from the surface and the water content in the boundary layer. Due to heavy precipitations occurred before the Sepat typhoon passage, the soil surface water content was high, causing an enhancement of the net radiation (due to the lower surface albedo), which favored a simultaneous increase of the atmospheric water vapor content (due to the larger evapotranspiration, in turn favored both by the high net radiation and by the high soil moisture). Thus, the different initial soil moistures determined the relative magnitudes of latent and sensible heat fluxes into the atmosphere. A relatively wet initial soil moisture condition results in relatively more rainfall, which in general supports the existence of a positive soil moisture rainfall feedback. In this work, the attention has been emphasized on the initial soil moisture conditions, but we need here to remember that also the vegetation type and its density may be important factors able to influence the partitioning of the latent and sensible heat fluxes into the atmosphere. 6.6 Summary A number of short-term numerical experiments on the precipitations associated with the typhoon Sepat was performed to evaluate the performance of the WRF model 96

106 coupled with LSPM. The behaviors of LSPM and other two land surface schemes already coupled with WRF have been documented. A set of sensitivity experiments and control experiment focused on the role of the sensible and latent heat fluxes, and moisture flux fields has been conducted, and the variations on the landfalling typhoon track and rainfall intensity have been investigated. The results show that, despite the underestimation of the rainfall maxima, the good match of timing and localization of the intense rainfall makes WRF-LSPM a very useful tool to simulate such kind of events. Both latent and sensible heat flux provide the energy for sustaining the landfall typhoon, but the latent heat flux plays a most important role on the intensity and track of the typhoon Sepat. The energy derived from the evaporation from the surface layer has been used to sustain the movement of the typhoon Sepat. The lack of the latent heat flux and/or of the moisture flux decreases the intensity of the landfalling typhoon. The latent and sensible heat fluxes are favorable for maintenance of spiral structure of rain belt,the latent has a more significant impact on intensity and distribution of typhoon precipitation. In the comparison of the experiments using the surface schemes NOAH, RUC and LSPM coupled with WRF, the hydrologic variables (soil moisture, precipitation and surface runoff) predicted by WRF-LSPM scheme are similar to (and sometimes especially regarding soil moisture and runoff - slightly most realistic than) those of WRF-NOAH. The WRF-RUC is always lower than that of the other two schemes on soil moisture. A possible explanation could be that the land surface differences largely determine the pattern of latent heat flux uncertainties, while the uncertainties can be amplified by radiation, precipitation, and other differences caused by land-atmosphere feedback. The LSPM and NOAH schemes coupled with WRF give considerable values of soil moisture and temperature in the surface layer, which can be used to provide a realistic picture of the distribution and magnitude of heavy rainfall. Finally, the impact of the soil moisture initialization on the typhoon precipitation has been investigated. Many studies used the simplified representations of vertical exchange physics that incorporate the effects of spatial heterogeneity in topography, soil, and vegetation on soil moisture variation (e.g., Wood et al. 1992; Koster et al. 97

107 2000). The initialization fields are normally altered by increasing or decreasing the soil moisture by constant perturbation in the total soil depth at every grid box over the model domain. However, during this typhoon rainfall event, a high ground water caused by the previous heavy rainfall lead to continuous supply from surface layer to the root zone. In those regions, the role of groundwater in variations of the each layer soil moisture becomes essential because of the uniform moisture diffusivity. The vertical gradients of the initial soil moisture was introduced into WRF-LSPM to present a realistic vertical distribution. The results show that the initial soil moisture content has a considerably great impact on the intensity of the precipitation (and runoff) predicted for such kind of typhoons. A relatively wet initial soil moisture condition results in relatively more abundant rainfall, which in general supports the existence of a positive soil moisture rainfall feedback. Also the initial soil moisture content has a considerably great impact on the intensity of the precipitation predicted for such kind of typhoons. 98

108 Chapter 7 Experiments 2: The 2003 heat wave analysis in Piedmont region, Italy 7.1 Introduction An extreme heat wave affected the Europe in the summer of This event can be considered an extreme climatic anomaly. The June-July-August (JJA) period in Europe might have been the warmest since 1540 (Beniston 2004) and the temperatures in a large area located between France, Germany and northern Italy exceeded the mean by 3-6 C, up to about 5 standard deviations (Cassardo 2007). a b Fig. 7.1: JJA 2003 mean (a) sea level pressure (hpa) and (b) geopotential height (m) at 500 hpa over Europe. Image provided by the NOAA/ESRL Physical Sciences Division, Boulder Colorado from their Web site at The heat wave resulted from a zone of strong high pressure over the western Europe related to a marked ridge of high pressure in the large-scale upper atmospheric wind flow (Fig. 7.1b). The extreme temperatures and lack of precipitation in Europe from May to August 2003 were related to persistent anticyclonic conditions 99

109 throughout the period. During this period there were very slack gradients in mean sea level pressure but there was a weak signature of blocking, with a high over the UK and North Sea, a low over Iberia and a high over the Western Mediterranean (Fig. 7.1a). Precipitation deficits resulting in the positive temperature (Fig. 7.2a) feedbacks alluded to in the preceding introductory section already began in March 2003 in most parts of the Europe, with very low precipitation amounts at the crucial start of the summer from March to May with less a quarter of the normal rainfall (Fig. 7.2b). a b Fig. 7.2: 2003 mean (a) surface temperature anomaly, (b) daily rainfall anomaly (mm/day) from March to May over Europe. Image provided by the NOAA/ESRL Physical Sciences Division, Boulder Colorado from their Web site at Under such circumstances, the soil moisture deficit and humidity stress on vegetation imply unusually strong sensible heat fluxes directed from the surface to the atmosphere, thereby increasing the extremes of temperature beyond the thresholds they would have otherwise attained under normal precipitation conditions. The land surface warmed and dried to such an extent that, during July, when the radiative forcing was weaker, the latent heat fluxes were anomalously negative, due to lack of soil moisture, and the sensible heat fluxes were higher than usual due to the higher surface temperatures (Schär et al. 2004; Fischer et al. 2007). In this section, I am showing the results of the coupling of WRF with three land surface schemes, applied to the case study of the 2003 heat wave analysis in Piedmont region, Italy. My focus will be on the comparisons of model results. The results of two 100

110 land surface schemes (LSPM and NOAH) on precipitation, 2 m temperature, 10 m wind speed will be compared to the data of five observational stations mentioned in the next section. Also the energy and water budget reproduced by the three land schemes (LSPM, NOAH and RUC) will be compared during the JJA of A set of sensitivity simulations with perturbed initial soil moisture conditions (DRY, WET), performed using WRF-LSPM and offline LSPM in this study, will also be commented. 7.2 The Piedmontese station data Fig. 7.3: The position of the five stations selected in Piedmont region (PA: Torino Buon pastore, PB: Alessandria Lobbi, PC: Tricerro, PD: Cuneo Camera Commercio, and PE: Cuneo Cascina Vecchia). In Piedmont region there are about 400 meteorological and hydrological stations. Not all of them are complete. In this study, I have selected five stations (Fig. 7.3) according to the climate status. The first station is located downtown Torino: this is the meteorological station Torino named Buon Pastore ( N, E, hereafter referred as PA), most affected by the urban climate. The second station is located in Alessandria, a city located in the southeastern part of the region: this is the meteorological station named Alessandria Lobbi ( N, E, hereafter be referred to as PB). The third station is located at Tricerro, a town in the Eastern Piedmont: this is the meteorological station named Tricerro ( N, 101

111 E, hereafter be referred to as PC). The fourth and fifth station are located in Cuneo, a city in the Southwest of Piedmont region: one is the meteorological station named Cuneo Camera Commercio ( N, E, hereafter be referred to as PD), and the other one is the meteorological station named Cuneo Cascina Vecchia ( N, E, hereafter be referred to as PE), respectively. The stations of PD and PE have been selected to have a complete database in Cuneo: the PD station is located downtown, while the PE is located in the suburban area. The stations PA, PD and PE are located in the Western part of Piedmont s plain. The other two stations of PB and PC are located in the northeastern flat part of the region; in particular, PC is in the geographic area covered by large rice paddies, irrigated with a fluvial network using the water of the major Piedmont s rivers; PB is instead located in the southeastern piedmont, which is usually quite arid in summer. Torino Buonpastore Tricerro Alessandria Lobbi Cuneo Cascina Vecchia Temperature ( C) Jun 8-Jun 15-Jun 22-Jun 29-Jun 6-Jul 13-Jul 20-Jul Date of JJA Fig. 7.4: Summer (JJA) mean temperatures (in C) recorded at 4 Piedmontese stations Fig. 7.4 shows the time series of the mean JJA air temperatures collected in PA, PB, PC, and PE. In these four stations, the mean values in the JJA period range from 24.2 C (PE) to 26.6 C (PA), while the mean values of PB and PC are 25.2 C. These values may be compared with those of the historical temperature series recorded in Torino, homogenized by Mercalli and Di Napoli (2007). Here, the average temperature for the reference period JJA in Torino is 22.5 ± 0.6 C. Thus, the values of PA-PE are 3 5 C warmer than the historical average temperature. These results show that there was an extreme climatic anomaly. Meehl and Tebaldi (2004) used the climate models to predict an increase in climate variability associated with greenhouse-gas forcing; their result show that the configuration causing extreme 27-Jul 3-Aug 10-Aug 17-Aug 24-Aug 31-Aug 102

112 events like that observed in 2003 will become more frequent in the future. Torino Buonpastore Tricerro Cuneo Cascina Vecchia Alessandria Cuneo Camera Commercio Precipitation (mm) Jun 8-Jun 15-Jun 22-Jun 29-Jun 6-Jul 13-Jul 20-Jul 27-Jul 3-Aug 10-Aug 17-Aug 24-Aug 31-Aug Date of JJA Fig. 7.5: Summer (JJA) daily precipitation (mm) recorded at 5 Piedmont s stations. Fig. 7.5 shows the time series of the daily JJA precipitation collected in PA-PE stations. This figure show that, during JJA, several major episodes of precipitation occurred in the following days: June 3, 4, 5, 18, 28; July 28; August 1, 14, 15, 16, 17. The maximum total precipitation, about mm, was recorded in PA, while the minimum, only 70 mm, in PB. The total precipitation values in PC, PD and PE were mm, mm and mm, respectively. The maximum daily precipitation, 61.8 mm, was observed in PD, on June 7. The highest two maxima of precipitation occurred in PA and PD stations, located downtown. Thus, it seems that these rainfall events were caused by the local thermal convection. In other words, the downtown area acted as a heating center, like a heat island. The increment of temperature observed at the surface in the city lead a stronger development of local thermal convective, comparing to the suburban area, with most rainfall. In addition, during the period JJA, there was not any systematic precipitation events occurred, because, despite a weak mean SLP anomaly over Europe of ±0.5 hpa over central Europe (Fig.7.6a), a strong anomaly of Z500 was present (Fig. 7.6b), with a maximum of more than 60 m over Switzerland, eastern France, northern Italy and Germany (Cassardo 2007). This very stable configuration blocked almost completely the passage of the Atlantic frontal systems for the whole period. 7.3 Setting of the experiments The WRF can be configured as a limited area model, tropical channel model, and 103

113 a b Fig. 7.6: JJA 2003 mean (a) sea level pressure anomaly (hpa), (b) geopotential height anomaly(m) over Europe. Image provided by the NOAA/ESRL Physical Sciences Division, Boulder Colorado from their Web site at global model, with one-way and two-way nesting capability. With Earth system components, WRF can be a useful tool to understand regional system processes, allowing model parameterizations to be evaluated using measurements highly influenced by local conditions (Skamarock et al. 2008). In the chapter 6, the WRF-LSPM coupling was performed to simulate the Typhoon Sepat, and the results show that the WRF-LSPM is able to capture the main features of the on mesoscale weather event. In this simulation, the attention was focused over the Piedmont region during the period JJA of The three land surface schemes received the same atmospheric forcing from the WRF and passed back to WRF the average surface fluxes at each grid point and at every time step Model domain and initial boundary conditions In these simulations, a domain of grids point with a horizontal grid size 15km covering the whole Piedmont region has been used. The central point is located on 45.0N and 8.0E. All the simulations start from the 1 st of June 2003, 00 UTC, and end on the 1 st of September 2003, 00 UTC. Simulations were performed using 24 sigma vertical levels. The initial and lateral boundary conditions were derived from the NCEP Final Analysis (FNL from GFS) database, with a resolution of 1 in latitude 104