Parameterization of land surface evaporation by means of location dependent potential evaporation and surface temperature range

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1 Exchange Processes at the Land Surface for a Range of Space and Time Scales (Proceedings of the Yokohama Symposium, July 1993). IAHS Publ. no. 212, Parameterization of land surface evaporation by means of location dependent potential evaporation and surface temperature range M. MENENTI Laboratory for Hydrospheric Processes, NASA/GSFC, Greenbelt, Maryland, USA (from September 1990 to February 1992 on leave from DLO Winand Staring Centre for Integrated Land, Soil and Water Research (SC-DLO), PO Box 125, 6700 AC Wageningen, The Netherlands) B. J. CHOUDHURY Laboratory for Hydrospheric Processes, NASA/GSFC, Greenbelt, Maryland 20771, USA Abstract A new parameterization is proposed by defining a locationdependent potential evaporation and surface temperature range to account for spatial variability of actual evaporation due to albedo and aerodynamic roughness. This was done by using a combination type equation which parameterizes actual evaporation in terms of internal and external resistances to heat and vapour flow. This equation was first re-arranged to get the air to surface temperature difference explicitly. Next, the asymptotic forms of this equation were derived by taking the limits for the internal resistance to vapour flow being zero and (o ). Having the maximum and minimum temperature differential for given values of albedo and aerodynamic roughness, a non-dimensional ratio was defined which varies between 0 (no évapotranspiration) and 1 (actual = potential evaporation) as a function of measured air to surface temperature difference. It is proposed to use air potential temperature at the top of the Atmospheric Boundary Layer instead of near surface air temperature. An example of application is presented. INTRODUCTION Evaporation from land surfaces may be observed with two types of physical measurements: (i) direct measurement of either turbulent vapour flux by means of eddy correlation techniques or of water loss of a soil and vegetation sample by means of lysimeters; (ii) indirect measurement as the rest term of either: a) the surface energy balance equation: or R n + G + H + XE = 0 (W m 2 ) (1) where R is net radiation, G soil heat flux, H sensible heat flux and XE latent heat flux, i.e. the amount of energy, X (J kg" 1 ) required in the liquid-to-vapour transition of E (kg nr 2 s" 1 );

2 562 M. Mementi & B. J. Choudhury b) the water balance equation of either a soil column or an atmosphere column (e.g. Menenti, 1993). Equation (1) expresses the balance of vertical heat fluxes at a homogeneous land surface in study of turbulent heat transfer; for non-homogeneous surfaces like partial canopies it implies some kind of definition of effective land surface properties. Regional estimates of evaporation, however, are a necessity for both water balance studies and to understand the land-surface atmosphere interaction. Direct measurement is a difficult proposition when length scales upwards of 10 km are considered, so the use of less accurate methods involving remote measurements is attractive, even if some semiempirical relationships remain necessary. Another manner of using Equation (1) to estimate evaporation is by casting it as a combination-type formula (Penman, 1948; Monteith, 1965). This can be done by conceiving the land surface as a one, two, four or multi-layer system (Van Bavel, 1966; Menenti, 1984; Shuttleworth & Wallace, 1985; Choudhury & Monteith, 1988; Van de Griend & Van Boxel, 1989). To illustrate the conceptual nature of some parameters involved, the two-layer case will be summarized (Fig. 1). At the interface between liquid water and moist air, the latter is vapour-saturated. This implies that even the simplest one-dimensional schematization of evaporation processes should consider separately the liquid-moist air interface and the physical Actual evaporation Potential evaporation r ah Surface mmmcmmmmzzmtm mmtémmzzzmzzzzzzz v//, n Evaporation ] U front I «e k (h m nw?7] Mh m)h m ï Groundwater level Fig.l Schematic representation of the resistances (r) to heat (h) and vapour (v) flow in soil (s) and air (a). The depth of the evaporation front (z^ depends on the soil moisture contribution in the profile, and the hydraulic properties of the soil. Soil hydraulic properties like the water retention characteristic, hj[d), and the hydraulic conductivity curve, K(d), affect the soil water distribution. The depth of the evaporation front, 2^, depends on the vertical distribution of soil water content 6. Actual evaporation is related to values of the transport resistance of vapour, r, v, and heat, r, h, in soil. The deeper the evaporation front, the higher the r sv - and r sh -values. For a zero depth of the evaporation front (z E = 0) evaporation is potential (r sv, r!h = 0).

3 Parameterization of land surface evaporation 563 surface of the evaporating system. Two flow regions result: one between interface and physical surface and a second between the latter and some reference level in the atmospheric surface layer. Using the transfer coefficients indicated in Figure 1, a combination type of equation to compute directly the latent heat flux of actual soil evaporation, XE, can be obtained (Menenti, 1984): XE = - S» r»" (R " + G E) + W.h G B + Pa^O**» ~ e(z) ] ^ YfJav + O + Vah + SsPaCprsh where s a is the slope of the saturated soil vapour pressure curve in air, s s in soil, p a is air density, c p is air specific heat at constant pressure, e* is saturated air vapour pressure, e is actual vapour pressure, r a is resistance to heat and vapour transfer in air, r s is resistance to heat and vapour transfer between the liquid-moist air interface and the physical surface of the evaporating system, y is psychrometric constant and G E is soil heat flux at the evaporation front. Note that in case the evaporation front is located at the soil surface the resistances r sh and r sv become zero, and equation (2) reduces then to: xp S a( R n + Go) + PaS^* ~ ^ ' ^ (3) where XE P is potential evaporation and G 0 is soil heat flux at the soil surface. Stanghellini (1987) proved that a combination equation identical to Equation (2) describes correctly actual plant transpiration. The soil resistances are re-defined by her then as internal resistances to vapour and heat flow from the liquid-to-vapour interface inside the leaves to the physical boundary of the leaves. Equation (3) is a definition of potential evaporation, i.e. a case when the rate of liquid to vapour transition is not affected by liquid water flow beneath the physical boundary of the evaporating body. A few comment, about equations (2) and (3) are mandatory. First of all the resistances are defined implicitly by the transfer equations and as such are not observable. Indirect measurement by inversion of the transfer equations is a possibility for truly homogeneous surfaces with easily identifiable 'physical boundaries'. Similarity theory can be applied to compute resistances; a few more land surface properties, however, become necessary and some measure of atmospheric stratification. Similar comments could be added about soil heat flux. Secondly the justification of the use of equations (2) and (3) is the need to avoid use of temperature at the liquid-vapour interface and at the physical boundary of the evaporating system. In equation (2) we have air temperature and actual vapour pressures. Although this is not an inconvenience when using equations (2) and (3) at field level with actual meteorological observations, it becomes a major challenge when evaporation has to be obtained areawise. The objective of this paper is to present a procedure to estimate E which avoids the use of r ; and uses T 0 instead.

4 564 M. Mementi & B. J. Choudhury A NEW PARAMETERIZATION USING SURFACE TEMPERATURE INSTEAD OF INTERNAL RESISTANCE Another way to obtain LE-estimators is by defining theoretical pixelwise ranges for LE and T 0 and subsequently interpolating by using observed T 0 -values. Equation (2) is first re-written as: LE = - sr (R + G) + p,c (e* - e),,,-. e " - Lî-i: - (W m" 2 ) (4) (s + 7)r c + 7^ where r c is external and r ; internal resistance. Sensible heat flux is written as: H = - ^ (T 0 - T a ) (W m" 2 ) (5) By substitution of Equations (4) and (5) in (1), we have: T 0 - T a = (r. + r) 1 J l ' (e ' -e) (R n + G) - H& Pa C p e : s _ r, _ (K) (6) The range of (T 0 - T a ) corresponding with a hypothetical change in evaporation from zero to potential rate at constant surface reflectance and roughness can now be calculated. The upper limit of (T 0 - TJ can be obtained by taking the limit of Equation (6) for r ; -» 00 (no evaporation) while the limit for r ; -*0 (potential evaporation) gives the lower limit: (T 0 - T a ) u = ^ (R n + G) (K) (7) P^ p (O, 1 1^1 (R n + G) - 1 (e * - e) (T P. c 0 - T a ), = ±2. JL 7 (K) (8) 1 + Equations (6), (7) and (8) imply the following relationship: The ratio in r.h.s. is a more general form of the Crop Water Stress Index (CWSI) of Jackson et al. (1981, 1988). Here we have taken into account the dependence of r e on atmospheric stratification (i.e. on T a - T 0 ). Moreover we have redefined this ratio as a pixelwise parameter since it is calculated at given surface reflectance and roughness observed at (VT a ) _ (Tp-T), 2L = 1 - T.l *JL (9) E p (T 0 -T a ) u CTo-T^ W f e,u r e,l

5 Parameterization of land surface evaporation 565 each location (pixel). Accordingly we will name it Surface Energy Balance Index (SEBI). Relative evaporation E/E p is, therefore, related to SEBI as: E/E p = 1 - SEBI (-) (10) where SEBI is the temperature dependent term on the right hand side of Equation (9). So far we have dealt with a horizontally homogeneous conceptual surface. To deal with heterogeneous land surfaces we have to extend the previous concepts and definitions. Actual evaporation is a simple function of surface temperature only if every other land surface property remains constant. This applies in reality to limited changes in surface conditions. We can, however, define a pixelwise E p and a pixelwise range of (T 0 - T a ) by using Equations (3) and (9) at constant surface reflectance, roughness and T,. To apply Equations (7), (8) and (9) (r e ), and (r e ), have to be determined; another problem is that near-surface air temperature varies with surface temperature and, therefore, is not the same in Equations (7) and (8). Since these problems are the consequence of taking a near-surface reference height, we propose to take the height of the atmospheric boundary layer as a reference to calculate heat fluxes (see also Brutsaert, 1991). Accordingly, T a is here potential air temperature at the top of the ABL. To obtain r e, the flux-profile relationship given by Brutsaert (1982, p. 78), can be applied: ( T o-t a ) z=hi = - 5 [ In - q ] (11) ' a h ku,pcp z 0h where h; is observed ABL height; z 0h is the aerodynamic roughness length for heat transport, taken here as 0.1 z^, the roughness length for momentum; Q is the similarity function for heat transport with h ; as length scale; a,, is a constant taken here to be 1; k is von Karman's constant = 0.41; u. is the friction velocity. This gives the following equation for r e : r. = (In - Q (12) k u, The Cj function is: 1 + x 2 C = 2 In ( l ; x ) (13) with x = (1-16/ij)" 4, tx { = h/l, L is Monin Obukhov's length; the neutral and unstable cases are considered only, i.e. jtt ; < 0. Assuming potential evaporation to occur under neutral conditions is adequate for the calculation of daily values. For e.g. hourly values the effect of atmospheric stability should be taken into account (Allen et al., 1989; Brutsaert, 1982). Effect of atmospheric stability on potential evaporation was studied in detail by Mahrt and Ek (1984). The r c values for the limiting cases mentioned above can be obtained as:

${ instead of (oo) since d(cj)/d^i decreases asymptotically to zero.$

6 566 M. Mementi & B. J. Choudhury (r e ), = r e dui = 0) potential evaporation and (rj u = re(/i; = -150) zero evaporation (14) Here a large negative value has been taken for p. { instead of (oo) since d(cj)/d^i decreases asymptotically to zero. To obtain the r c value applicable to the observed (T a - T 0 ), we need the value of Ci which can be calculated by linear interpolation. RESULTS AND DISCUSSION OF LIMITED CASE STUDY Description of the data The approach presented above gives the opportunity to estimate the surface to air temperature difference that would be observed for a same target (e.g. a pixel) under the same radiation and atmospheric conditions in the two limiting cases of zero and potential evaporation. Data applied here were collected on February during field experiments in the Libyan Desert (Menenti, 1984). We will consider a dry and wet target located at a distance of some 500 m; both targets are hydrological units present in the transition zone between sand dunes and the central part of a large playa in southwestern Libya. Each target is characterized by its hemispherical reflectance, the ratio G/R n and z 0h. Atmospheric conditions are specified by solar irradiance R sw, apparent emissivity and vapour pressure deficit (e*-e). To obtain h ; and T a a radiosounding done at 80 km from the site at local time was applied. Hemispherical reflectance was estimated with Landsat MSS data as described by Menenti et al. (1989). Finally surface temperature was obtained from low altitude airborne thermal imagery collected at local time. Discussion of the data The field data applied here are of relatively poor quality as compared with recent field experiments, so some comments are mandatory to spell out the limits of the present example. (i) The radiosoundings were operational observations done once daily at Sabhah airport; their vertical resolution and, probably, their accuracy is poor. So the determination of ABL height as the point of minimum potential temperature was rather poor. It is self evident that the approach has to be tested with better radiosoundings. (ii) Net radiation was calculated using R, w, apparent atmospheric emissivity, surface emissivity taken to be 0.97, near surface air temperature combined with hemispherical reflectance and surface temperature of the dry and wet target. The use of simultaneous ground measurements is an obvious drawback; net radiation, however, can be estimated with satellite measurements (e.g. Schmetz, 1989; Choudhury, 1991), so the dependence on field measurements could be reduced. (iii) Vapour pressure deficit was also measured in the field; this limitation is, however, less critical than it may appear in first instance. The field observations at the wet target gave (e*-e) = 11.6 hpa. By assuming that air was at saturation in the early

7 Parameterization of land surface evaporation 567 Table 1 Field and remote measurements of surface and atmospheric properties for a wet and dry hydrological unit in a transition zone from sand dunes to the centre of a playa; south-western Libya; February 16, Hydrological unit (Wm" 2 ) (e* - e) (hpa) u«(m s" 1 ) ZOh (m) To (K) Wet Dry Table 2 External resistance for heat transport through the Atmospheric Boundary Layer, r, and surface to air temperature difference (TQ-TJ for the limiting case of a perfectly dry, u, and a perfectly wet, 1, target having the same reflectance and roughness of the hydrological units of this example; "obs" indicates actual measurement. Relative evaporation E/E p calculated with our method is compared with observations (Bowen Ratio Energy Balance method). Hydrological unit (s m" 1 ) (s m" 1 ) (T 0 -Ta) u (K) (To-Ta), (K) (To'TJobs (K) E/E p (-) (E/E p ) obs (-) Wet Dry morning and that vapour pressure was constant throughout the day, surface temperature measurements obtained from the pre-dawn thermal infrared imagery can be used to estimate vapour pressure deficit at This gave 11.3 hpa for the wet target and 10.1 hpa for the dry target, which had a higher predawn surface temperature. The data applied in our example are given in Table 1. The analysis of the radiosounding gave T a = 292 K and h; = 1300 m. By applying Equations (12), (8), (9), (5) and (4) in this sequence we estimated relative evaporation as 0.85 (-) for the wet target and zero for the dry one. Intermediate results of the calculation are given in Table 2. Field measurements done with the Bowen Ratio Energy Balance method gave E/Ep = 0.9 for the wet and 0.2 for the dry target. CONCLUSIONS The estimated relative evaporation compares favourably with field measurements. We do not claim, however, any generality of the results of this example, which had a simple illustrative scope. Temperature at the top of the atmospheric boundary layer is a better boundary condition to estimate heat fluxes at land surfaces than near surface air temperature. We have also shown that actual evaporation is simply related to surface temperature only when all other surface properties and boundary conditions remain constant, as done when comparing actual observations of with the hypothetical values applying to a perfectly wet and perfectly dry "copy" of a given target. Acknowledgements This work was done while the senior author was a National Research

8 568 M. Mementi & B. J. Choudhury Council Senior Research Associate at NASA/GSFC. The authors are grateful to Prof.Dr. R. A. Feddes, Prof.Dr. H.J. Bolle and Dr. J. Kalma for their useful comments and to Mrs. M. van Dijk-Janssen for preparation and revision of the manuscript. REFERENCES Allen, R.G., Jensen, M.E., Wright, J.L. & Burman, R.L. (1989) Operational estimates of reference évapotranspiration. Agron. J. 81, Brutsaert, W. (1982) Evaporation into the Atmosphere. D. Reidel Publ. Co., Dordrecht, The Netherlands. Brutsaert, W. (1991) The formulation of evaporation from land surfaces, in: D.S. Bowles & P.E. O'Connell (eds.). Recent Advances in the Modeling of Hydrologie Systems, Choudhury, B.J. & Monteith, J.L. (1988) A four layer model for the heat budget of homogeneous land surfaces. Quart. J. Roy. Meteorol. Soc. 114, Choudhury, B.J. (1991) Multispectral satellite data in the context of land surface heat balance. Rev. Geophys. 29(2), Jackson, R.D., Idso, S.B., Reginato, R.J. & Pinter, P.J. Jr (1981) Canopy temperature as a crop water stress indicator. Wat. Resour. Res. 17(4), Jackson, R.D., Kustas, W.P. & Choudhury, B.J. (1988) A re-examination of the crop water stress index. Irrig. Sci. 9, Mahrt, L. & Ek, M. (1984) The influence of atmospheric stability on potential evaporation. J. CI. Appl. Meteorol. 23, Menenti, M. (1984) Physical aspects and determination of evaporation in deserts applying remote sensing techniques. Report 10 (special issue). Inst. Land and Water Manag. Res., Wageningen, The Netherlands. Menenti, M. (1993) Understanding land surface évapotranspiration with satellite multispectral measurements. Adv. Space Res. (in press). Menenti, M., Bastiaanssen, W.G.M. & Van Eick, D. (1989) Determination of surface hemispherical reflectance. Remote Sens. ofenv. 28, Penman, H.L. (1948) Natural evaporation from open water, bare soil and grass. Troc. Roy. Soc., Ser. A, 193, Monteith, J.L. (1965) Evaporation and environment. Symp. Soc. Exp. Biol. 19, Schmetz, J. (1989) Towards a surface radiation climatology: retrieval of downward irradiances from satellites. Amos. Res. 23, Shuttleworth, W.J. & Wallace, J.S. (1985) A one dimensional theoretical description of the vegetation-atmosphere interaction. Boundary Layer Meteorol. 10, Stanghellini, C. (1987) Transpiration of greenhouse crops. Inst. Agric. Engrs (IMAG), Wageningen, The Netherlands. Van Bavel, C.H.M. (1966) Potential evaporation. The combination concept and its experimental verification. Wat. Resour. Res. 2(3), Van de Griend, A.A. & Van Boxel, J.H. (1989) A water and surface energy balance model with a multi-layer canopy representation for remote sensing purposes. Wat. Resour. Res. 25(5),

Thermal Crop Water Stress Indices

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