Two requirements for evaporation from natural surfaces. The atmospheric boundary layer. Vertical structure of the ABL. Bloc 1. Hydrologie quantitative

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1 3.1 Introduction Figure 3.1 M1 SDE MEC558 Hydrologie continentale et ressources en eau Continental Hydrology and Water Resources Two requirements for evaporation from natural surfaces Bloc 1. Hydrologie quantitative 1. Introduction: water cycles on Earth 2. Water in the atmosphere 3. Evapotranspiration 3.1 Introduction 3.6 Formulations related to the energy budget 1. Energy supply 2. Escape mecanism = turbulence 2 3 Brutsaert, p118 The atmospheric boundary layer Vertical structure of the ABL Fluid mechanics In a fluid in motion along a surface, a boundary layer is the layer of fluid in the immediate vicinity of the surface where the effects of friction are significant. In particular, velocity is zero at the surface. A boundary layer can be either laminar or turbulent (cf Reynolds number) Garratt (1992). The atmospheric boundary layer. In the atmospheric context, it has never been easy to define precisely what the boundary layer is. Nevertheless a useful working definition identifies the boundary layer as the layer of air directly above the Earth s surface in which the effects of the surface (friction, heating and cooling) are felt directly on time scales less than a day, and in which significant fluxes of momentum, heat or matter are carried by turbulent motion on a scale of the order of the depth of the boundary layer or less. Outer layer / couche d Ekman : vent en spirale par équilibre entre gradient de pression, force de Coriolis et friction Couche de surface : direction du vent constante + profils logarithmiques de vitesse Couche rugueuse : où la vitesse tend vers 0 : u(z 0 )=0 Si H 1.5 km ( 850 mb) : 0.1H 150 m 0.01H 0.001H m 0,01H 0,001H 4 5

higher frequency Roughness layer Surface layer the horizontal scales

Interesting consequences from turbulence Surface turbulent fluxes

applies to q and the wind speed components.

transport by mean flow transport by turbulence ABL : scales of

Surface = sink Assuming uniform source/sink at the surface,

2 Figure 3.2 Figure 3.3 Reynolds decomposition Mean over 15min to 1h, fluctuation at much higher frequency Roughness layer Surface layer the horizontal scales of air flow are larger than the vertical ones 6 Brutsaert p38 7 Interesting consequences from turbulence Surface turbulent fluxes Convective transport of water vapor is : Reynolds decomposition applies to q and the wind speed components. After time averaging (in the sense of Reynolds) : Surface = source transport by mean flow transport by turbulence ABL : scales of atmospheric flow and mean velocities are larger along the horizontal Surface = sink Assuming uniform source/sink at the surface, concentrations mostly change along the vertical and canbeassumedconstant in the horizontal direction On account of continuity over a uniform surface, the vertical fluxes must be constant with z 8 9

3 Figure 3.4 Figure 3.5 The land surface is a sink for horizontal momentum (mu) Horizontal momentum in neutral conditions 0 : shear stress at the surface [kg m 1 s 2 ] u * : friction velocity [m s 1 ] u* depends on fluid viscosity surface roughness mean horizontal velocity 10 Dingman p 593 z0 = roughness length = valeur de z où u(z)=0 (par extrapolation) 11 Guyot p83 Figure 3.5 Turbulence closure and dimensionalanalysis Figure 3.6 Horizontal momentum in neutral conditions Stull, An Introduction to Boundary Layer Meteorology When the empirical data are plotted on graphs of one dimensionless group versus another, often data from many disparate meteorological conditions will result in one common curve, yielding a similarity relationship that may be universal. Dimensional analysis has been used extensively and successfully in studies of the atmospheric boundary layer, where turbulence precludes other more precise descriptions of the flow because exact solutions of the equations of motion are impossible to find due to the closure problem. Les différentes courbes correspondent à des vitesses moyennes différentes pour une altitude donnée, i.e. à des u* différentes Eléments de similarité : relations semi log pente = k/u* z0 (lié au site) Guyot p84

4 Figure 3.7 Roughness length z0 Mean q profile in neutral conditions Figure 3.8 Dimensional analysis Eq. de diffusion WARNING : z0v < z0 Analogy with Ohm s law (I=U/R) aerodynamic resistance 14 Brutsaert p45 Brutsaert p45 15 Figure 3.9 Figure 3.10 Generalization Aerodynamic resistance Flux de chaleur sensible : 16 Guyot p91 17 Guyot p139

place, at very high frequency > 5 10 Hz Sonic anemometers Infra red

coefficients» constants : Bulk method Resistance models for different

aerodynamic equation ( Cd, Ce, Ch pour les hauteurs de mesure z1 et z2

and q 0 Surtout utilisé sur les océans et la cryosphère = Tours de flux

relate q 0 to q s (T 0 ) 1. This is trivial for saturated surface!

5 Figure 3.11 Eddy covariance Eddy covariance w and q are measured at the same place, at very high frequency > 5 10 Hz Sonic anemometers Infra red hygrometers Figure 3.12 Mesures atmosphériques à 1 niveau via des «drag coefficients» constants : Bulk method Resistance models for different surface conditions The goal is to estimate E We start from the aerodynamic equation ( Cd, Ce, Ch pour les hauteurs de mesure z1 et z2 (sachant z0, z0v, z0h, ou pas) Mesures : u(z1), q(z2) et T(z2) + T 0 and q 0 Surtout utilisé sur les océans et la cryosphère = Tours de flux We assume we know r a and q(z) the unknown is q 0 The principle is to relate q 0 to q s (T 0 ) 1. This is trivial for saturated surface! In this case, we speak of evaporation at potential rate 2. Evaporation from soils Introduction of a soil resistance, which depends on soil moisture 20 21

conductance as a function of environmental conditions Evaporation of

23 VPD=e s (T a ) e a Guyot p127 15 16 Complex canopy SVAT (Soil

= Ratio of total projected leaf area (one side only) per unit ground

6 Figure 3.13 Transpiration from leaves and stomatal resistance Figure 3.14 Stomatal conductance as a function of environmental conditions Evaporation of free water Transpiration from one leaf Structure of one stomata VPD=e s (T a ) e a Guyot p127 Figure 3.15 Figure 3.16 Complex canopy SVAT (Soil Vegetation Atmosphere Transfers) models LAI = Leaf Area Index = I f = Ratio of total projected leaf area (one side only) per unit ground area Transpiration in parallel from different leaf layers Solar radiation is attenuated by the canopy 24 25

terrestrial radiation Wien displacement law : the wavelength

proportional to its absolute temperature Mars 2000 à Mars

, 2009) 26 27 18 Bilan radiatif en surface Albédo (sans

argileux humide 0,11 Herbe/Gazon/Crops 0,15 0,25 Forêt 0,05

radiation calculated from the ECMWF 40 year reanalysis.

7 Figure 3.17 Bilan d énergie moyen du système Terre Solar and terrestrial radiation Wien displacement law : the wavelength of radiation emitted by a black body is inversely proportional to its absolute temperature Mars 2000 à Mars 2004, valeurs en W/m² (Trenberth et al., 2009) Figure 3.18 Bilan radiatif en surface Albédo (sans unité) Limon silteux sec 0,23 Limon argileux sec 0,18 Limon argileux humide 0,11 Herbe/Gazon/Crops 0,15 0,25 Forêt 0,05 0,20 Eau 0,03 0,1 Neige 0,7 0,95 Annual mean net surface radiation calculated from the ECMWF 40 year reanalysis. Units are W/m 2. From Kallberg et al ERA 40 Atlas, ECMWF. Moraine du glacier Zongo Bolivie, Andes, Alti=5200m (Gascoin et al., 2009) VWC = volumetric water content 28 29

Bilan d énergie d une couche de surface Rôle de l'eau dans le bilan d énergie moyen du système Terre Bilan radiatif de la surface : Température d une couche de surface d épaisseur En régime

(using values from Figure 3.2) 31 3.6 Formulations related to the energy budget Saturated surfaces 3.

8 Bilan d énergie d une couche de surface Rôle de l'eau dans le bilan d énergie moyen du système Terre Bilan radiatif de la surface : Température d une couche de surface d épaisseur En régime stationnaire (équilibre) ou si est assez petit : G peut souvent être négligé devant les autres termes : H LE 30 LE dissipates 50% of absorbed solar radiation, and 80% of net radiation at the surface (using values from Figure 3.2) Formulations related to the energy budget Saturated surfaces 3.6 Formulations related to the energy budget Important définitions Radiative control Aerodynamic control Potential evaporation Evaporation from a large uniform surface that is sufficiently wet so that the air is saturated at the surface (ex: free water, soil or vegetation cover after a rain shower). This quantity does not depend on the soil/vegetation characteristics, apart from their roughness and albedo, thus corresponds to the concept of climatic evaporation demand. Potential ET (Thornthwaite, 1948) Maximum ET from a large area covered completely and uniformly by an actively growing vegetation with a non limiting soil moisture supply The Penman equation has been calibrated for both: free water saturated vegetation covers : Météo France has long used the Penman equation to calculate the reference ET, ET 0 Reference ET = ET 0 Idem, but for a reference grass, with specific properties : height = 0.12 m, albedo = 0.23, r c = 70 s/m (= r cmin as there is no stress) 32 33

9 3.6 Formulations related to the energy budget Reference ET 3.6 Formulations related to the energy budget Figure 3.19 From the unstressed reference grass to generic vegetation covers The Penman Monteith equation can be used for: unstressed reference grass (r 0 = 70 s/m) => ET0 (FAO recommendation) unstressed vegetation stressed vegetation using the adequate set of resistances Formulations related to the energy budget Actual ET Figure Formulations related to the energy budget Figure 3.20 Actual ET with < 1 Stress factor as a function of a soil moisture index Stress factor as a function of soil moisture Unstressed ET The effect of Kc and the environmental stresses on ETc can also be described by appropriate resistance formulations within the Penman Monteith equation. 36 Stressed ET The effect of Kc and the environmental stresses on ETc can also be described by appropriate resistance formulations within the Penman Monteith equation. 37

Evapotranspiration: Theory and Applications

Evapotranspiration: Theory and Applications Lu Zhang ( 张橹 ) CSIRO Land and Water Evaporation: part of our everyday life Evapotranspiration Global Land: P = 800 mm Q = 315 mm E = 485 mm Evapotranspiration