Study of the Radiation and Energy Balances Reproduced by WRF Using 10-year ( ): Observations at Cabauw. Wanjun Zhao

Transcription

1 Study of the Radiation and Energy Balances Reproduced by WRF Using 10-year ( ): Observations at Cabauw Wanjun Zhao

2 Study of the Radiation and Energy Balances Reproduced by WRF Using 10-year ( ) Observations at Cabauw MSc thesis Meteorology and Air Quality Wageningen University Wanjun Zhao June, 2013 Supervisor: Jordi Vila Collaboration and providing WRF results and observations: Pedro Jimenez (NCAR, USA) and Fred Bosveld (KNMI) i

3 Abstract: Radiation and surface energy balances are key components of the Earth system and at the diurnal scale control the evolution of the atmospheric boundary layer. To study how the meteorological models reproduced and interconnect these budgets, it is necessary to use complete observational data. However the comparisons between model results and observations are mainly based on short periods like days, weeks and seasons. This investigation compares and discusses in a systematics manner the radiation and surface energy balance in Cabauw area in the Netherlands by using observation data measured at Cabauw and numerical simulations of WRF model for a 10-year period. Besides the high spatial (2 x2 km 2 ) reference numerical experiment for using climatological conditions, two extra experiments specific for 2008 are made to study the response of the radiation and surface energy balance to increased albedo and soil moisture. The comparative analysis between model results and observations indicates the underestimation of shortwave radiation components are due to the mismatch in cloud condition (both cloud cover frequency and transparency of fully covered condition) and the unsuitable albedo. For longwave radiation, the WRF model misrepresents the influence of the upper atmospheric layers. By supporting the study using empirical equations we find the longwave downward radiation from model should be higher. Analysis of upward longwave radiation proves that the L out from model includes only the emitting from surface but not the reflection of Lin whereas the measurements account for both effects. With respect for surface energy balance, the WRF model overestimates sensible heat flux but underestimates the latent heat flux. The results from the experiments show that increased albedo decreases the available energy and results in lower sensible heat flux and latent heat flux. However, increased soil moisture only modifies the partition of turbulent fluxes: more energy is transported through latent heat flux and less for sensible heat flux. Keywords: Radiation budget, surface energy budget, SEB, WRF, clouds, energy closure ii

4 Contents: Abstract:... ii Keywords:... ii 1. Introduction Radiation budget Energy budget Methodology observation data WRF model configurations Radiation balance Shortwave radiation Longwave radiation Downward longwave radiation Upward Longwave radiation Clouds presence sensitivity Surface Energy balance The four components of Surface Energy Balance SEB under clear and cloudy conditions The bulk aerodynamic formulae Conclusions and recommendations Appendix Appendix Appendix References: iii

5 1. Introduction The energy source of the land-atmosphere system is determined by two interconnected budgets: the radiation budget and the surface energy budget (SEB). The radiation budget quantifies the amount of incoming solar energy and the surface energy budget portions the distribution of this energy. Heat and moisture change between land surface and atmosphere is achieved through these two budgets. As radiation budget and SEB are the fundamental processes for boundary layer evolution, the simulation of these two budgets in models are essential for boundary layer modeling. Model performances of these interconnected budgets can be evaluated by using observational data sets (Zhong, In et al. 2007; Steeneveld, Mauritsen et al. 2008; Liu, Liu et al. 2013). However, these comparison observations versus model performance are mainly based on diurnal cycle. Our main goal is to extend the model evaluation with a complete surface and lower atmosphere measurements for a long term period (10-year period). The model chosen in this study is the Weather Research and Forecasting (WRF) model (Skamarock, Klemp et al. 2005) as it is widely used in atmospheric modeling. The study area is Cabauw site in the Netherlands (Beljaars and Bosveld 1997; Gioli, Miglietta et al. 2004). 1.1 Radiation budget Figure 1 The global annual mean Earth's energy budget for the Mar 2000 to May 2004 period (W/m 2 ). The broad arrows indicate the schematic flow of energy in proportion to their importance (Trenberth, Fasullo et al. 2009). Figure 1 introduces the main concepts treated in this research. The radiation budget indicates that net radiation (R n ) is the sum of incoming/outgoing shortwave (S in and S out ) 1

6 and incoming/outgoing longwave (L in and L out ) radiation. As shown in figure 1, the shortwave from the sun cannot completely reach the land surface. It is reflected and absorbed by the clouds and atmosphere. The transmissivity of shortwave is inversely proportional to the cloud cover and cloud thickness. With larger cloud cover or thicker clouds, less solar radiation can reach the surface and vice versa. The representation of clouds is then having considerable influence on radiation budget modeling. In our research, we will evaluate this influence on radiation budget components. After the solar radiation reaches the land surface, part of it will be reflected by the surface as outgoing shortwave. As a result, the shortwave upward radiation is determined by incoming solar radiation together with surface albedo. Our research will consider the impact on radiation budget and evaluate its influence. Surface albedo varies among different vegetation categories, soil characters and seasons (Kung, Bryson et al. 1964; Duchon and Hamm 2006). Based on the Stefan-Boltzmann low, both land surface and atmosphere emit longwave radiation (shown in Figure 1). The emitted longwave radiation is determined by emissivity conditions of the atmosphere/soil and temperature of surface or air. As the emissivity is affected by both temperature and humidity (Brutsaert 1975; Choi, Jacobs et al. 2008), the emitted longwave is then determined by temperature and humidity. From Figure 1 we can find that clouds also affect the longwave components of radiation budget (Kiehl and Trenberth 1997). In our analysis of the model performance, we place special emphasis on how the clouds and surface albedo are influencing the radiation simulation in WRF model, and then analysis how is the representation of WRF model on radiation components in the 10-year period. 1.2 Energy budget The connection and energy transfer from radiative fluxes to turbulent fluxes (thermals and evaporation) is made through the surface energy balance (see Figure1). The net radiation from the radiation budget is absorbed by land surface and used up into three directions: sensible heat flux (H), latent heat flux (LE) and soil heat flux (G). The values of them depend on the atmosphere and surface conditions like temperature, humidity, soil moisture, etc.(christen and Vogt 2004). H and LE transport heat and moisture into atmosphere. When there is sufficient soil moisture availability, the available energy employs to evaporate soil moisture and plant transpiration. As a result, latent heat becomes large while sensible heat becomes smaller. If the land surface is 2

7 relatively dry, evaporation is limited and latent heat becomes smaller, more energy goes into heat transport and sensible heat becomes larger. In the energy budget, net radiation and soil heat flux are collectively called available energy while H and LE are called turbulent fluxes (Wilson, Goldstein et al. 2002; Foken, Wimmer et al. 2006). The available energy should equal to turbulent fluxes to close the SEB. However, with experiment data, the SEB cannot be closed (Mccaughey 1985; Foken and Oncley 1995; Wilson, Goldstein et al. 2002; Foken 2008). The available energy is usually larger than the turbulent fluxes in observations, but in models the energy balance is closed by definition. This difference on energy closure will inevitably lead to bias between observations and model results. Before evaluate the surface energy balance, we investigate only with observations and figure out if the observed energy balance is closed at Cabauw site. We then study how turbulent fluxes (LE and H) are related to variables such as temperature, humidity gradients etc. to determine if the WRF model is able to represent the relations (Zhong, In et al. 2007). To assess the WRF model performance on radiation budget and SEB simulation, comparisons between observations and model results will be done and statistical methods will be used (Willmott 1982). Different from former studies mainly based on diurnal cycles, here we are able to extend the evaluation for a long observational record. As the land-atmosphere system will change from month to month due to seasonality and will also be different for years with different climatic characters, the performance of model on radiation and energy budget during a long period is also worth to analysis. In this study, analysis is done in years and yearly average will used in most comparisons and evaluations. In the following sections, we explain the basic features of the numerical experiment made with WRF model configurations and introduce the 10-year observations in section 2; analysis and discussions of radiation budget is described in section 3, followed by the analysis and discussions of energy budget in section 4; the conclusions and recommendations are in section Methodology Observations and WRF results spanning, 10-year data (from January 1st, 2001 to December 31st, 2010) are analyzed. For observations, the data is available in every 10 minutes, daily, monthly and annual average are calculated from the 10-minutedata. For the high resolution model results, hourly, daily, monthly and annual averages are available. Without indication, the yearly averages for both observations and model results are employed in the analysis. Figure 2 shows locations of domains in the WRF 3

8 numerical simulation and the observation site. The Cabauw site is at the center of the 4 th domain (D4). Figure 2 Spatial configuration of domains used for the numerical simulation. The red dot shows the location of Cabauw site. 2.1 observation data The 10 minutes' observation data were taken at CESAR Observatory website ( The CESAR (Cabauw experimental site for atmospheric research) Observatory is located in the western part of the Netherlands (51.97 o N, 4.93 o E). The topography around the site is characterized by plain and covered with short grass. The nearby region is agricultural. The North Sea is more than 50 km away from the Cabauw site. A continuous boundary layer measuring program runs at the 200-m tower. The measuring program includes temperature, moisture and wind up to 200 m, and also all components of surface energy balance (Beljaars and Bosveld 1997). Observation data that are used in this study includes: a. radiation components: shortwave incoming and outgoing radiation (S in and S out ), longwave incoming and outgoing radiation (L in and L out ); b. energy budget components: net radiation (Qn) which is calculated from radiation budget, latent heat flux (LE), sensible heat flux (H) and soil heat flux (G); 4

9 c. temperature and humidity at 2 m, 10 m and 200 m levels; d. wind speed and u* at 10 m level; e. pressure at 200 m level; f. cloud cover. The cloud cover (value ranges from 0 to 8) is the calculated average of observations from 4 nearby sites. The observation data has 3 categories: invalidated, validated and gap filled. The invalidated datasets are not used in this study. The validated datasets are non-gap filled with interruptions (which shown as in the dataset) and the gap filled datasets are primarily based on the corresponding validated datasets, and are gap filled through interpolation. Mention that for energy budget components, the gap filled data are also modified to avoid problem of surface energy unclosure. Here the observed latent heat and sensible heat fluxes are only used to calculate the Bowen ration, and then apply this ratio to the available energy (Q available =Q n -G) to estimate the new latent heat and sensible heat 1. Without indication, the datasets used are gap filled data. 2.2 WRF model configurations The domain of the WRF numerical experiment for a 2000 km X 2000 km area is centered on the Cabauw site with a horizontal resolution of 54 km as the outmost domain. Three inner domains are 2-way nested progressively and the innermost domain is defined by a horizontal resolution of 2 km. For all domains, the default 31 terrainfollowing hydrostatic pressure levels (Laprise 1992) was used and the top level is configured as 50 hpa. The physical options configurations are shown in table 1 (Jimenez, Gonzalez-Rouco et al. 2010): Table 1 Model configurations in the radiation scheme, cumulus scheme, microphysics and land surface scheme. Categories Specifications Longwave radiation Mlawer et al. (1997) Shortwave radiation Dudhia (1989) Cumulus scheme (outermost 3 domains) Kain and Fritsch (1990, 1993) (modified) PBL scheme YSU (Hong, Noh et al. 2006) Microphysics WRF single-moment six-class scheme Land surface Five layer model (Dudhia 1996) The initial and boundary conditions are obtained from ECMWF (European Centre for Medium-Range Weather Forecasts) re-analysis and operational ECMWF analyses are employed afterward. The WRF simulation consists in a series of short WRF runs of 1 More information can be find in the dataset description files from 5

10 48hours (Jimenez, Gonzalez-Rouco et al. 2010). In each of the short runs, WRF is initialized at the 00 hours of a specific day. The former 24 hours are discarded as a spin up of the model and the later 24 hours are retained as the model results of that day. Besides the 10-year reference run (as described above), two other experiments are done for The first experiment is named run ALB. We employed higher albedo values for both summer and winter. The second experiment is called ALBSM, it is based on experiment ALB and employed higher soil moisture in addition. Experiment ALB has an extended summer (from 15th April to 14th October) albedo of 0.23 and an extended winter (from 15th October to 14th April) albedo of 0.21 while in the reference run, they are 0.17 and 0.2, respectively. In experiment ALBSM, except for the higher albedo the same as ALB, soil moisture is increased by 20%. Other configurations of the two experiments are the same with reference run. WRF the variables from model results used in this study are the same with those from observations (section 2.1, from a to f). Note that the temperatures from WRF model are always represent the potential temperature (θ), the cloud cover index from model result is from 0 to 1, and the 10 m level result is interrupted from neighbouring levels as is not included in model output. 3. Radiation balance The surface radiation balance has four components and can be written as: R n =S in +S out +L in +L out (1) In the above equation, R n is the net surface radiation, S in and S out are downward and upward shortwave radiation respectively, and L in and L out are downward and upward longwave radiation components. Figure 3 shows the annual average of radiation budget components. Comparing the radiation balance of WRF results and observations in long time period (10-years in this research), WRF results have the same trend with observations in all components but the 4-components are always underestimated (about 10Wm -2 in shortwave and 20Wm -2 in longwave radiation). Here we will analyze reasons of the discrepancies in the 4-components between WRF model results and observations. 6

11 Figure 3 The yearly average of radiation components for the 10yrs period. The green dashed lines shows WRF result and red dots shows observation data from CABAUW. Fully dataset is used here. The blue dots show the yearly average of 2008 for the four radiation components after we increase the surface albedo. Our discussion will focus on 4 aspects that we consider are the most important in creating the differences in the radiation balance: presence of clouds, influence of surface albedo, effects of temperature gradient and influence of soil moisture. The analysis will be given component by component and from shortwave to longwave. 3.1 Shortwave radiation The shortwave radiation at surface is determined by the solar irradiance as source, and absorption of atmosphere and reflection of clouds as consumption. Among all the factors that affect shortwave radiation, the presence of clouds is an important component that exerts a strong influence on the radiation budget (Trenberth, Fasullo et al. 2009). Our first assumption of the model s underestimation on shortwave components is the WRF model has a different distribution of clouds, and more specifically has a tendency to have larger cloud cover frequencies with clouds characterized by thick optical properties. 7

12 Figure 4 The frequencies of cloud cover (from 0 to 100%) during the 10-years period. The blue bars show the frequency in WRF and pink bars show the frequency in observation. Numbers on the top or below the bottom of bars are the frequency. The dashed lines separate clear days from cloudy days in our research. Figure 4 shows the frequency of cloud cover during 10 years period. The frequencies of relatively clear days have no obvious difference between model results and observations. However, in the region characterized by frequency of overcast (cc 90%) days in model results is more than 50% higher than observation. As the overcast days accounts for largest partition of the whole period, the over prediction of clouds is a first explanation of the underestimation of the shortwave downward component. The other element relate to overestimation of clouds is cloud thickness. To analyze this factor, we continue our analysis in the regions that play a larger role in the decrease of S in. Figure 5 shows the downward shortwave radiation in largest 3 cloud cover ranges (90-100%, 80-90% and 70-80%) in figure 4.Under conditions of similar cloud cover, thicker clouds will result in lower transmittance and lower surface incoming shortwave radiation. With cloud cover larger than 90% (figure 5.a), model results are lower than observations in all years. For overcast days (cc 90%), WRF results give an overestimation in cloud thickness. However, with cloud cover range 70-90%, no permanent exceed or shortage exists. With cloud cover range from 80 to 90%, model overestimated the cloud thickness in 2004 and 2009, but underestimated in With cloud cover range from 70 to 80%, model overestimated the cloud thickness in 2001, 2005, 2006, 2009 and 2010, but underestimated in 2002 to 2004 and As a conclusion, the WRF model overestimates the cloud thickness. 8

13 a b c Figure 5 Downward shortwave radiation from days with different range of cloud cover during the 10-year period (shown in red and blue color) and the cloudy day average as comparison (shown in black color). From top to bottom: cloud cover range from 90 to 100% (a), 80 to 90% (b) and 70 to 80% (c). Our analysis goes one step further to determine the general performance of S in in clear and cloudy days. To find how large the presence of clouds influence the model results, we separate days with relatively small cloud cover (cc<30%) as clear days and days with relatively large cloud cover (cc>70%) as cloudy days. In clear days, the influence of clouds is tiny while in cloudy days we expect a larger influence. The analysis of S in in clear and cloud conditions is shown in figure 6. For shortwave downward radiation (figure 6.a), WRF model results and observations agree satisfactorily in clear days while in cloudy days, model shows underestimated results. This result indicates that without influence of clouds, WRF performers well in simulation of incoming shortwave and the underestimation in S in mainly comes from cloudy days. The results agree our previous analysis that the WRF model overestimates cloud presence. Relative to S in, figure 6.b indicates that for S out, even without influence of clouds presence, model results cannot match observations. In fact, from figure 6.b, gap between model results and observations in clear days is even larger than that in cloudy days. By noticing the upward radiation is determined by S in together with surface albedo, we come up with our second assumption that in our WRF model run, the albedo is underestimated. 9

14 a b Figure 6 The yearly average of shortwave radiation of observation data (signals) and WRF results (dashed lines). The red color shows data of cloudy days (cc>70%), blue color shows data of clear days (cc<30%) and black color shows data of all the days. The result of new run ALB is shown in triangles. In the reference run, surface albedo over grassland was prescribes 0.20 for winter (15 th October to 14 th April) and 0.17 for summer (15 th April to 14 th October).However, the yearly-average albedo for these two periods from the 10-years observations are 0.21 and 0.23 respectively. Due to limitation, a new 10-years experiment (run ALB) based on higher albedo only done for 2008 which we considered a normal year. Results of run ALB are shown in figure 3 and analysis based on cloudiness for S out is shown in figure 6.b. For S out, model results get close to observations while for S in, L in and L out, no clear difference can be observed. We close this section with statistical evaluation of WRF performance in clear days, cloudy days and all days. In the evaluation, bias is described by the mean bias error (MBE), average difference is described by the mean absolute error (MAE) and the root mean square error (RMSE), and the SDr describes the variance of the distribution of differences (Willmott 1982). Table 2 provides the statistical difference measures for the model performance and the differences in yearly average for Before increase the albedo, MAE, MBE and RMSE of clear days are larger than cloudy days, this indicate the model perform worse in clear days. For 2008, yearly average of WRF is Wm -2 lower than observation in reference run, but only Wm -2 in run ALB. By increase surface albedo, difference between model results and observations reduces. Table 2 Statistical evaluation for the WRF model together with differences of 2008 for S out. Yearly average is used in the evaluation. The bold numbers indicate the best score for a particular statistical measure. Cloudy Days Clear Days All Days MAE

15 MBE RMSE Difference for year of 2008 (reference run) (Wm -2 ) Difference for year of 2008 (run ALB) (Wm -2 ) The statistical evaluation of 2008 is presented in table 3. With increased albedo, model performance improved in all groups (cloudy days, clear days and all days). In run ALB, we find for clear days the smallest difference between model results and observations and the error in all days mainly comes from cloudy days. The model performs better in clear day compares well with our assumption on influence of clouds presence. We observe the SDr does not change much, so the improvement does not change the shape of yearly trend. Table 3 Statistical evaluation for the WRF in ref indicates reference run and A indicates run A. Daily average is used in the evaluation. The bold numbers indicate the best score for a particular statistical measure. Cloudy Days Clear Days All Days ref A ref A ref A MAE MBE RMSE SDr Longwave radiation As presence of clouds influence not only shortwave radiation but the whole radiation budget, longwave radiation components should also show difference between clear days and cloudy days. However, from figure 7, we find that there is no evident improvement in the comparison between observations and model results by separating clear days from cloudy days. Therefore, besides the existence of clouds, other processes are exerting a strong influence on longwave components. Because incoming and outgoing longwave depend on different factors (weather condition of atmosphere and surface respectively), in our analysis, we discuss them separately. 11

16 Figure 7 The yearly average of longwave radiation of observation data (signals) and WRF results (dashed lines). The red color shows data of cloudy days (cc>70%), blue color shows data of clear days (cc<30%) and black color show data of all the days Downward longwave radiation The third assumption of WRF model s underestimation is the longwave radiation comes from upper layers in model results differs from the observation. Here, we will base our analysis on the dependences of longwave radiation on atmospheric and surface temperature, and the thermal emissivity. In the WRF model, longwave radiation is determined by temperature and emissivity: L=εσT 4, (2) Where, ε is the emissivity in the infrared band and is determined by temperature and humidity, σ is the Stefan-Boltzmann constant, T is the temperature of atmosphere or land surface. With different thermal conditions, downward radiation emitted by the upper layers varies. The radiation that reaches the surface becomes part of the surface L in. The different of radiation from upper layers will lead to difference in surface L in (figure 8). To analyze the WRF values of longwave radiation by inferring these components from the temperature and emissivity, we will use two different methods. 12

17 Figure 8 The longwave downward radiation in the lower 200m. The white arrows indicate L emitted by atmosphere and black arrows indicate L reached the surface. The oblique line in the middle shows the temperature lapse rate (γ t ). Left part shows the method considers only 200m height and right part shows the method considers temperature gradient. The first method considers only the thermal condition at 200m height ( 200m method here after, figure 8, left) and the second method considers the temperature and humidity gradient between surface and 200m height ( gradient method here after, figure 8, right). a b Figure 9 The yearly average of potential temperature and specific humidity at 200m height. a: clear days. b: cloudy days. Dashed lines show observations and the blue dashed lines show results of WRF model. a. Incoming longwave determined by the T-q at 200m 13

18 From equation (2), whether the upper longwave radiations are same can be inferred from their thermal conditions. The yearly average temperature and humidity at 200m in clear and cloudy days are shown in figure 9.a and b respectively. At the layer of 200m, WRF results give a lower temperature compare to observations both in clear and cloudy days. But for specific humidity, no obvious trend can be observed. With different temperature, the 200m layer will emit lower longwave radiation towards surface in the model compare to observations. If we add this difference (Dif 200, figure 8) on model results artificially, the difference between model results and observations can be partly covered. We are interested in studying the influence from both temperature and humidity, we therefore use the emissivity calculated through equation proposed by Brutsaert (1975): ε a0 =1.24(e 0 /T 0 ) 0.14 (3) Where, e 0 is the water vapour at 200m height which is calculated from specific humidity and pressure through: e = q P 200 (1 q)ε+q, (4) and P 200 is calculated from: P 200 = P 0 exp [ g R d T 0 Z] (Brutsaert 1975) (5) The Brutsaert s equation considers only clear sky condition, and for cloudy days, Crawford and Duchon (1999) proposed a different equation: L in(cloud) =L in(clear) (1-cc)+cc σt 4, (6) cc here is the cloud cover varies from 0 to 1. We choose Brutsaert (1975) and Crawford and Duchon (1999) here because they are one of the bests to estimate longwave downward radiations (Choi, Jacobs et al. 2008). The difference of downward long wave radiation between L in measurements and WRF model is: Dif 200 =R long_obs -R long_wrf, (7) The model results can be corrected by using this difference: WRF cor =WRF+Dif 200, (8) By using equation (8), we also calculate how much the difference can be covered by correction of upper layer radiation: 14

19 Percentage=(Dif 200 /Dif surface )x100. (9) a b Figure 10 The yearly average surface downward radiation in clear (a) and cloudy (b) days. The blue plus signs show observations, the blue dashed line shows result from WRF model and the red dashed line shows the downward radiation of WRF after correction of the cold bias of the WRF model. Results are shown in figure 10.a and b, here clear days and cloudy days are calculated separately. The corrected model results are larger than results from reference run. Compare to results from reference run, the corrected model results are closer to the observations (table 4). Table 4 Statistic evaluation of long wave downward radiation for WRF model and corrected result by using two different methods. The first 3 columns based on model results and observations, the 4th column uses corrected model results by equation (8) in cloudy days, and the last 2 columns used corrected results by equation (8) and (10) respectively in clear days. Cloudy Days (Calculated) Clear Days (Calculated) Cloud Days Clear Days All Days 200m 200m Gradient (Medium) MAE MBE RMSE SDr This method considers the lower 200m atmosphere as a whole and only top and bottom layers are taken into account. In reality however, as the temperature lapse rate exists, there are many different layer between surface and 200m height. This method is not rigorous enough and another method should be used for more accurate analysis. b. Gradient method Bosveld et al. (2013) calculates the surface long wave radiation including the temperature lapse rate by using the following formula: 15

20 L ref = a + b e 200 σt c + d e 200 σ(t 200 T 4 2 ) + f. (10) Where e 200 is the water vapour pressure at 200m height, T 2 and T 200 are absolute temperatures at 2 and 200m height respectively, σ is the Stefan-Boltzmann constant and a-f are regression coefficients. The optimized parameters are given with deviation range. As the formula is linear with the parameters, the positive and negative deviation will lead to maximum and minimum estimation. The limitation of this method is it can only be applied for clear days, but it can give us an indication of the quality of the former method by comparing these two methods in clear days. As the clear days here we determine are days with daily average cloud cover less than 30% instead of completely cloudless, the reference longwave downward radiation calculated by equation (10) will not match the observation exactly, slight difference will appear between calculation results and observations. Figure 11 shows the range and medium of estimations using observations and WRF results. Corrected result using the 200m method is also shown in this figure. Among the maximum, minimum and medium estimations based on observation temperature and humidity, the last one gives the best correlation to observation radiation. So for model result estimation, we use the medium values. The statistic measures are shown in the last column in table 4. In both methods, calculated model results are better than the reference run. This supports our assumption that WRF does not perform well in counting upper layer long wave down ward radiation. 16

21 Figure 11 The yearly average surface downward long wave radiation in clear days. The red and blue dots show the data of observation and WRF model result respectively. The red filled area indicates rang of reference long wave downward radiation of observation (calculated by gradient method) with red dashed line shows the medium value. The blue filled area indicates range of reference long wave radiation of WRF model (calculated by gradient method) with blue dashed line shows the medium value. The black crosses show the corrected long wave (calculated by 200m method) of WRF model. Compare the 200m method to the gradient method, the former one does not perform as good as the later one, but it is correct in showing the trend. Although not accurate, the analysis of cloudy days using only the 200m method is still receivable Upward Longwave radiation Based on Stefan-Boltzmann law, surface L out is determined by surface temperature and emissivity. By comparing surface condition between model results and observations, their temperature and humidity are close to each other so the upward longwave radiation emitted by surface of observations and model results are close to each other. However, the longwave upward radiation of Cabauw observation is measured at 2m height, which will include not only the radiation from surface but also the reflected longwave downward radiation while in the model results longwave outgoing radiation is only the emitted parts. By adding the reflection part, model results correspond to observations much better (shown in Figure 12). And the emissivity used in reference run is for winter and 0.92 for summer while by 17

22 calculation based on observation temperature and L out, the emissivity is around 1, this also influences the longwave upward radiation simulation. Figure 12 Yearly average long wave upward radiation of observation and WRF model results corrected by adding reflection of longwave downward radiation. The red dots are observations at Cabauw area and blue dashed line shows the corrected model results. 3.3 Clouds presence sensitivity As the presence of clouds is an important component influencing the radiation budget (Trenberth, Fasullo et al. 2009), it is helpful to study the sensitivity of cloud simulation in model. By comparing cloud frequency under different conditions, we try to find effects of surface characters on cloud simulation in WRF model. Here in the analysis we consider influence of increased albedo and increased soil moisture. All together, we have three model experiments: the reference run, the ALB and the ALBSM with increased albedo and soil moisture. Observations are used as standard to evaluate model performance. 18

23 Figure 13 The frequency of cloud cover during year of 2008: reference run (purple bars), observations (pink bars), run ALB with increased albedo (white bars) and run ALBSM with increased albedo and soil moisture (yellow bars). Figure 13 shows the cloud cover frequency in Top half of the figure compares the frequency among observation, reference run and run ALB while bottom half of the figure compares observation, reference run and run ALBSM. For the regime of clear days (cloud cover less than 30%), both cases ALB and ALBSM show that modification of albedo and soil moisture improves the comparison with the observations. For cloudy days however, the improvement is not evident and the ALBSM even compares worst in overcast days. From the figure, with albedo closer to the observations, WRF results can give better result in cloud cover simulation, but the improvement is not very significant. And as soil moisture increase (20% in this case), more overcast days appears in the model and the difference is remarkable. The increase in soil moisture aggravates the overestimation of clouds cover in WRF model. 4. Surface Energy balance 19

24 The energy budget includes four components: the net radiation (R n ) and soil heat flux (G) as available energy and sensible heat flux (H) and latent heat flux (LE) as turbulent fluxes driven by the surface conditions and the atmospheric properties. The surface energy balance (SEB) can be written as following: R n =H+LE+G (12) Notice that in equation (12), we neglected canopy heat storage and additional energy sources/sinks as it is small in the short grass air space (Wilson, Goldstein et al. 2002; Xiao, Zuo et al. 2012). The energy balance closure requires that the available energy (R n +G) is equal to sum of turbulent fluxes (H+LE). However, former studies (Mccaughey 1985; Foken 2008) find that with experimental data, this energy balance cannot be closed as the available energy is always larger than turbulent fluxes. To study if the energy budget observed at Cabauw close, we relate the radiation contribution to the turbulent contribution using a linear equation between available energy and turbulent flux: H+LE=a(R n -G)+b (13) If the surface energy balance can be closed with the observations data, a and b in equation (13) should be 1 and 0, respectively. If not, the energy balance cannot be closed. Here we use the method of least squares (OLS) for finding this linear regression coefficient, then a and b are OLS slope and the intercept respectively. Figure 14 shows the relation between available energy and turbulent fluxes (using monthly average) for the 10-year period. The observations used here is the validated observation data from Cabauw without gap filled (see section 2.1). Numbers in the figure shows the percentage of data that are valid for monthly average calculation. For example, the number 3 means indicates that only 3% of the month's observations (that is 1 day's data) are available for this specific month. The slope and intercept obtained from the linear regression are 0.82 and respectively. So with the observation data from Cabauw the energy closure cannot be closed. 20

25 Figure 14 Relation between available energy and turbulent fluxes for the 10-year period. Blue plus signs are monthly average. The red line represents the linear regression. Numbers after each blue plus are the percentage of data that are valid for monthly average calculation. The linear equation is shown in top left. As the energy balance from WRF model is closed by definition (Stensrud 2007) in the later analysis, we use the gap filled data in which the energy budget is forced to close the surface energy balance by applying Bowen ratio to the available energy (Beljaars and Bosveld 1997). 4.1 The four components of Surface Energy Balance Figure 15 shows the annual average of energy budget components. The net radiation in WRF model results has smaller deviation among the 10-year period compares to the observations. For 2001, 2002, 2005, 2007 and 2008, the WRF model overestimates the net radiation and for 2003 and 2009 the WRF model underestimated the net radiation. For 2004, 2006 and 2010, model results match the observation. For sensible heat and soil heat, the WRF model always show overestimation (around 21

26 10W/m 2 for H and 5W/m 2 for G) while for latent heat flux, the yearly average in WRF results are always smaller than observations. Figure 15 The yearly average of energy budget components for the 10yrs period. The green dashed lines represent WRF results and red dots indicate observations from Cabauw. The gap filled observation data which obtained a closed energy balance is used here. The blue dots are yearly average of 2008 for the four components with increased albedo and the crosses are yearly average of 2008 with increased albedo and soil moisture. Results of the two experimental runs during 2008 are also shown in figure 15. With increased albedo (ALB), the net radiation simulated from WRF becomes lower while the increase in soil heat flux is small. The total available energy at surface (R n -G) decreases. In the experiment with large soil moisture (ALBSM), as shown with cross signs, an increase of 20% of soil moisture has almost no influence on net radiation and slightly increases the soil moisture flux. Compare to the experiment ALB, with increased soil moisture, the available energy has little difference. This is logical as the 22

27 albedo influences the radiation budget by changing upward shortwave radiation while soil moisture does not. For turbulent fluxes, clear decrease and increase can be observed in both experiments. In the experiment ALB, as a result of a reduced (about 5 W/m 2 ) available energy, both sensible heat flux and latent heat flux simulated from model show lower (about 2 to 3 W/m 2 ) yearly average. When we modify the soil moisture (ALBSM), an important character: land surface resistance has been changed. In WRF, the generic expression of the latent heat is represented as: LE = ρl v r a +r s (q sat T s q), (14) Where r a and r s are aerodynamic resistance and surface resistance respectively. With higher soil moisture, r s becomes smaller and the potential of evaporation increases. This lead to more moisture fluxes, so more energy is transported into the atmosphere through vaporization as latent heat flux. As a result of energy balance closure, the sensible heat flux then decreases. Our findings of the two experiments show that change of albedo and soil moisture both influence the energy balance, the former one will affect the available energy and the later one will change the distribution of turbulent fluxes. Both of these changes are non-linear. Former analysis (section Radiation balance) showed that the representation of clouds influence the radiation budget in WRF model. As radiation determines the main part of available energy of energy balance, cloud condition will also influence the energy balance. In the next section, we study the performance of the energy budget under clear and cloud conditions. 4.2 SEB under clear and cloudy conditions Our working hypothesis is that as the net radiation is determined by radiation balance and is the major part (influence of soil heat flux is much smaller) of the available energy, we expect that under clear conditions with increased albedo (run ALB) the net radiation from model would be with a better agreement to observations. Figure 16 shows the analysis of available energy under clear and cloudy conditions. We find that the comparison under clear condition give similar results with that under cloudy condition in the 10-years period datasets. The statistic results for 2008 (see Appendix 2, table 1 and table 2) indicate that for this year, differences between model and observations are always smaller under clear condition in each experiment: the 23

28 RMSE under clear conditions are 12.38, and for reference run, run ALB and run ALBSM respectively. But different from our expectation, results under clear condition in run ALB doesn't show best comparison to observations. If we take all data into consideration, the improvement of run ALB is small compare to reference run. This is because with the increased albedo, WRF model gives more accurate results of short wave radiation so the net radiation becomes closer to the observations. Figure 16 The yearly average of net radiation and soil flux of observations (plus signs) and WRF model results (dashed lines). The red colour shows data of cloudy days (cc>70%), blue colour shows data of clear days (cc<30%) and black colour shows data of all days. The result of run ALB is shown in triangles and run ALBSM moisture is shown in squares. Analysis for turbulent fluxes is shown in figure 17 and Appendix 2 (table 1, 4 and 5). In the reference run, turbulent fluxes show a clear difference under clear and cloudy conditions. Under cloudless conditions, the WRF model shows the largest different compare to the observations. In the experiment ALB (show in triangles), increased albedo has large influence on clear condition, but lead to small changes on cloud condition. Both of sensible heat flux and latent heat flux decreases with higher albedo. In experiment ALBSM (show in squares), soil moisture also has large influence on clear condition. With increased soil moisture, the latent heat increases while sensible heat decreases, but for cloudy condition, latent heat has much larger changes than sensible heat. With increased soil moisture, latent heat increases while sensible heat decreases. 24

29 Figure 17 The yearly average of net radiation and soil flux of observations (plus signs) and WRF model results (dashed lines). The red colour shows data of cloudy days (cc>70%), blue colour shows data of clear days (cc<30%) and black colour shows data of all days. The result of run ALB is shown in triangles and run ALBSM moisture is show in squares. As the surface energy balance is more complicated than radiation balance, besides cloud condition, albedo and soil moisture, more factors such as the temperature and moisture gradient, stability of atmosphere etc. are influencing the quality of model simulation. Due to limitation of time, further study will mainly focus on sensible heat and latent heat flux. 4.3 The bulk aerodynamic formulae The sensible heat and latent heat are proportional to the temperature and humidity gradient difference between land surface and above air layer (see equation 14). Figure 18 shows the temperature and humidity at different levels for from both WRF model results and observations. For potential temperature, value at 2 m level from model results and observations can compare with each other. However, at 10 m level the potential temperature is slightly higher than lower level in observations while in the model results, the 10 m temperature is about 1 K lower than 2 m. The WRF model underestimates the 10 m potential temperature and the temperature gradient is much larger than in observations. For specific humidity, the model also gives an obvious underestimation and larger gradient between these two levels. The difference of temperature and humidity between different levels will influence the turbulent flux and this influence is more obvious on sensible heat flux. As the temperature gradient is larger in WRF model, the sensible heat flux is larger than observations in agreement with our former analysis. 25

30 Figure 18 The yearly average potential temperature (above) and specific humidity (below) from WRF results (shown in blue) and observations (shown in red) for different height. The data from 2 m height is shown with triangles and the data from 10 m height is shown with dashed lines. To know how well the WRF model captures the relationship between turbulent fluxes and measured variables (Zhong, In et al. 2007), we analyse separately the more important components of the representation of SH and LE. We first introduce the expressions that are used to estimate the surface sensible heat and latent heat together with the frictional drag on the surface winds. The respective expressions for sensible heat flux, latent heat flux and momentum flux read (Liu, Liu et al. 2013): H = ρc p C H U (θ s θ), (15) LE = ρl v C q U (q sat T s q), and (16) MF = ρu 2 = ρc m U 2, (17) 26

31 where ρ is the density of air; U is the wind speed at a specific height (normally 10 meter or the first model level); C p is the specific heat of air at constant pressure and L v is the latent heat of vaporization, they are used to transfer kinematic fluxes to dynamic fluxes; u * is the friction velocity; C H, C q and C m are bulk transfer coefficient for heat moisture and momentum, respectively; q sat T s is the saturation specific humidity at the surface temperature. Similar equations are used in the WRF model. In the former study of Zhong et al. (2007), he compared model results and observations by showing the friction velocity as a function of 10 m mean wind speed and heat flux divided by mean wind speed against the temperature difference. Here we employ the same methodology in our analysis. As shown above, the relationship between fluxes and measured variables (T, q and U ) can be determined as: H U = ρc pc H (θ s θ), (18) LE U = ρl vc q (q sat T s q), and (19) u 2 = C m U 2, (20) As C H, C q and C m have different values depending on stable and unstable conditions (Appendix 3), the relation between H/ U and (θ s -θ) or LE/ U and (q sat T s -q) or u * and U will vary under different atmospheric stability conditions. As in summer the observations and model results shows clearer patterns, here we use data from summer (July and August) in 2008, and use 3hours during night-time (0 to 3 UTC) representing stable condition and 3hours during daytime (12 to 15 UTC) representing unstable condition. To further ensure the stable/unstable conditions, we follow the criteria. For stable condition (night-time data), we only use data with H<0 and T 10 -T 2 >0; for unstable condition (daytime data), we only use those with H>0 and T 10 -T 2 <0. Figure 19 shows the above mentioned relations. The slope of plots in the top figures corresponds to the square root of C m, and that in middle and bottom figures should correspond to C H and C q, respectively. For momentum flux (top 2 figures), the WRF model can reproduces the linear relationship in the observations, but the slope which correspond to square root of C m is larger than observations. In both observations and model results, the relation has not obvious difference under stable and unstable conditions. 27

32 In turn, the results for sensible heat flux and latent heat flux show a significant difference between daytime and night-time conditions. In observations, the night-time (stable stratified conditions) shows an almost horizontal linear relation between H/ U and (θ s -θ) or LE/ U and (q sat T s -q), whereas under unstable stratified conditions, the slope of the linear relation changes. Although these patterns are also found in our model results, they are characterized by a larger scatter in both night-time and daytime. Moreover, the temperature and humidity difference between 10 m and 2 m height in model results is smaller than observations, this may also relate to the former analysis (as shown in Figure 18) about temperature and humidity. Figure 19 Observed and simulated frictional velocity u * as a function of 10m mean wind speed (top), sensible heat flux divided by 10m mean wind speed as a function of temperature difference between 10m and 2m levels (middle) and latent heat flux divided by 10m mean wind speed as a function of specific humidity difference between 10m and 2m levels (bottom). The red dots shows data from daytime and blue dots shows data from night-time. 28