Remote Sensing Based Estimation of Evapotranspiration Rates 2004Boegh

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Remote sensing based estimation of evapotranspiration ratesE. Boegh a; H. Soegaard aa Institute of Geography, University of Copenhagen, 1350 Copenhagen K, Denmark

Online Publication Date: 01 July 2004

To cite this Article Boegh, E. and Soegaard, H.(2004)'Remote sensing based estimation of evapotranspiration rates',InternationalJournal of Remote Sensing,25:13,2535 2551

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Remote sensing based estimation of evapotranspiration rates

E. BOEGH* and H. SOEGAARD

Institute of Geography, University of Copenhagen, Oester Voldgade 10,1350 Copenhagen K, Denmark

(Received 19 June 2002; in final form 18 August 2003 )

Abstract. A remote sensing based method is presented for calculatingevapotranspiration rates (lE) using standard meteorological field data andradiometric surface temperature recorded for bare soil, maize and wheat

canopies in Denmark. The estimation oflE is achieved using three equations tosolve three unknowns; the atmospheric resistance (rae), the surface resistance (rs)and the vapour pressure at the surface (es) where the latter is assessed using anempirical expression. The method is applicable, without modification, to densevegetation and moist soil, but for a dry bare soil, where the effective source ofwater vapour is below the surface, the temperature of the evaporating front (Ts*)can not be represented by the measured surface temperature (Ts). In this case(Ts-Ts*) is assessed as a linear function of the difference between surfacetemperature and air temperature. The calculated lE is comparable to latentheat fluxes recorded by the eddy covariance technique.

1. Introduction

Spatially distributed estimates of evapotranspiration (lE) rates are significant

both for agricultural management planning and climate studies. In agricultural

management planning, expressions based on the atmospheric demand are nor-

mally used to assess lE, and the physiological control of the vegetation is con-

sidered through empirical crop coefficients (i.e. Allen et al. 1998). More precise

solutions are usually confined to research experiments where surface fluxes and/or

leaf stomatal resistance data are recorded.

The PenmanMontieth (PM) equation is a well established physically based

method for estimating evapotranspiration rate (Monteith and Unsworth 1990).Apart from standard meteorological input data, the PM equation requires

information about surface roughness and stability conditions to calculate the

atmospheric resistance to heat transfer (ra); and the surface resistance (rs) needs to

be estimated. Measuring representative values of rs for vegetation canopies is very

time-demanding, while modelling the vegetation surface (stomatal) resistance is

difficult because plant physiological processes are controlled both by the physical

environment and by the selective behaviour of plant species with respect to optimal

functioning (Norman 1993). Empirical models are available for predicting the

International Journal of Remote SensingISSN 0143-1161 print/ISSN 1366-5901 online # 2004 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/01431160310001647975

*Corresponding author; e-mail: [email protected]

INT. J. REMOTE SENSING, 10 JULY, 2004,VOL. 25, NO. 13, 25352551

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stomatal resistance based on climatic and soil moisture input data (i.e. Jarvis 1976,

Lindroth and Halldin 1986), but they are not generally applicable without prior

local determination of the empirical constants. Instead, semi-empirical models

based on functional relationships between photosynthesis and stomatal resistance at

the leaf scale (Ball et al. 1987, Leuning 1995) may be preferred. In this case, the

evapotranspiration/rs-model is coupled to a mechanistic photosynthesis-model (i.e.

Collatz et al. 1991, Sellers et al. 1992, Leuning 1995, Boegh et al. 1999, Thorgeirsson

and Soegaard 1999, Boegh et al. 2002b, among many others). Even though the

process of computing the evapotranspiration rate becomes more complex, the

process of fitting empirical stomata models to a given location and situation is

substituted by functional parameters related to vegetation type.

When the surface is only partly covered by vegetation, the estimation of

evapotranspiration is further complicated because net radiation needs to be

partitioned between soil and vegetation, and a more complex two-layer model

structure (i.e. Shuttleworth and Wallace 1985) is required to allow for the exchange

of energy between soil and vegetation (i.e. within-row advection). From an

operational standpoint, two-layer models are particularly difficult to apply because

of the additional need to estimate the surface resistance of the soil. In practice,

empirical models relating the soil resistance to soil surface moisture do not give

good estimates of hourly and daily evaporation (Daamen and Simmonds 1996), and

alternative methods may be needed for estimating soil evaporation rates (Ham and

Heilman 1991, Yamanaka et al. 1997, van der Keur et al. 2001). Theoretically, the

application of the PM equation (to one or two layers) is not well suited for

calculating evaporation rates from dry bare soils because its derivation is based on

the assumption that the sources of water vapour and heat are represented at the

same temperature, Ts (i.e. Monteith and Unsworth 1990). In reality, the tem-

perature of a dry bare soil surface may be much higher than the temperature of the

evaporating front (Ts*) which is located deeper in the soil.

Nevertheless, if remote sensing data of Ts are available, estimating the bulk

stomatal resistance, the soil surface resistance (for bare soil/sparse vegetation) and

the surface humidity (of dry soils) can be avoided. In such cases, Ts is taken to

represent the aerodynamic temperature at canopy source height (T0) to enable the

calculation of the sensible heat flux (H):

H~rcp T0{Ta

ra W m{2

1

where rcp is the heat capacity (J m23 C21). The evapotranspiration rate can thenbe assessed as the residual in the surface energy balance equation (equation (2))

after estimating or measuring net radiation and soil heat flux (i.e. Seguin et al. 1989,

Humes et al. 1997). However, two significant drawbacks of this method are that Tsmay exceed T0, even for dense canopies (Choudhury et al. 1986, Huband and

Monteith 1986, Kalma and Jupp 1990) and that the atmospheric resistance between

the surface and the air (rae) may be larger than the atmospheric resistance between

canopy source height and the air above the canopy (ra) (i.e. Stewart et al. 1994).

Numerous empirical and theoretical studies have been conducted to determine an

excess resistance to heat transfer between the surface and source height (i.e.

Kustas et al. 1989, Sugita and Brutsaert 1990, Stewart et al. 1994, Troufleau et al.1997, Verhoef et al. 1997, Massman 1999). The classical approach is to use the

quantity kB21 to estimate the excess resistance, rex~kB21/(ku.), where k is the von

Karman constant, u. is the friction velocity (m s21), and kB21 is the natural

logarithm of the ratio of the roughness length for momentum (z0) and roughness

2536 E. Boegh and H. Soegaard

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length for heat (z0h). In remote sensing studies, the kB21 is normally determined

empirically. For dense canopies, it is approximately constant (around 2), but for

sparse canopies, it is usually higher (Kustas et al. 1989, Stewart et al. 1994,

Troufleau et al. 1997, Verhoef et al. 1997), and its dependence on both vegetation

structure, climate and surface conditions has been demonstrated (Troufleau et al.1997). Very complex models are needed to predict this kB21 dependency (Massman

1999), and currently alternative methods are being developed to estimate lE from

Ts where the estimation of the excess resistance to heat transfer is not needed.

Instead, simultaneous measurements of Ts from two different view angles can be

used to calculate lE (Norman et al. 1995, Kustas and Norman 1997) or, assuming

the atmospheric resistance of dry and wet soils to be similar, the surface

temperature of a dry soil column can be included for calculating soil evaporation

rates (Qiu et al. 1998). Methods to assess the atmospheric resistance were suggested

by Bastiaanssen et al. (1998) who used the slope of the Ts-albedo relationship of dry

surfaces to assess the atmospheric resistance from Earth observations, and Boeghet al. (2002a) who introduced an empirical equation for the vapour pressure at the

surface (es) to facilitate mathematical solutions for rae and rs. Because the method

of Boegh et al. (2002a) used the measurement of Ts to assess the surface saturation

vapour pressure, this method needed adjustment to assess the surface humidity (and

lE) for dry bare soils where the effective source area of water vapour is below the

surface.

In the present paper, the method of Boegh et al. (2002a) is further elaborated

and expanded to include an adjustment function accounting for the difference in

temperature between the surface and the evaporating front (Ts-Ts*) of dry soil

surfaces. The method requires inputs of surface temperature, net radiation, soil heatflux, air temperature and vapour pressure. Because the latter two variables are

standard meteorological data and the remaining inputs can be obtained from

remote sensing data, the method could be of particular relevance for monitoring

spatially distributed evapotranspiration using satellite data such as Landsat,

NOAA-AVHRR or EOS-MODIS. In the present paper, the utility of the metho-

dology is demonstrated using thermal infrared field data which were recorded for

bare, sparsely and densely vegetated soils in Denmark. In Boegh et al. (2004), the

method is applied to AVHRR observations and meteorological data which were

predicted by a high resolution weather forecast model.

2. Methodology

The evapotranspiration rate (lE) relates to the surface energy balance as

lE~Rn{H{G W m{2

2

where Rn is net radiation (W m22) and G is the soil heat flux (W m22). In

equation (2), H and lE may be expressed as

H~rcp Ts{Ta

rae W m{2

3

lE~ rcpc

es{ea =rae W m

{2 4

where Ts is the surface temperature (C), c is the psychrometer constant (Pa C21),

ea is the vapour pressure above the canopy (Pa), es is the vapour pressure at the

surface (Pa), and rae is the atmospheric resistance to heat transfer between the

surface and the air above the canopy (s m21), which is given by rae~razrex.

Estimation of evapotranspiration rates 2537

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Assuming the atmospheric resistance to be the same for temperature and water

vapour, an expression for rae is obtained by combining equations (2), (3) and (4)

rae~rcpTs{Ta z es{ea =c

Rn{Gs m{1

5

An equation for the surface resistance (rs) is obtained on the basis of the followingequations; lE~ rcp

c

es{es

rs~ rcp

c

es{ea =rae, where the saturated

vapour pressure at the evaporating front (es*) is evaluated at the temperature

(Ts*). By rearrangement, rs is given by

rs~rae es{es

es{ea s m

{1

6

For dense canopies and moist soils, Ts* equals Ts, but for a dry bare soil, the

evaporating front is located beneath a dry surface layer exhibiting different thermal

properties, and Ts may be much higher than Ts* in this situation. Because an

increase in Ts due to greater solar radiation increases both the soil and the

atmospheric sensible heat flux (Garratt 1992, Cellier et al. 1996), the differencebetween Ts and Ts* may be inferred from the observations of (Ts-Ta). The close

coupling of G and H through the surface temperature allows G to be expressed as a

fraction of H, i.e. G~aH (Berkowicz and Prahm 1982, Novak 1986). Since

G~ks Ts{Ts

zd (ks is thermal conductivity of dry soil and zd is the thickness of

the upper dry soil layer), insertion in equation (3) leads to the following expression

for (Ts-Ts*)

Ts{Ts

~B Ts{Ta

0C 7

where B~arcpzd/(raeks). Equation (7) implies the use of the depth of the evaporating

surface instead of the more traditional use of surface-moisture availability forcalculating soil-limited evaporation rates. A simple energy-balance model applying

zd instead of surface-moisture for calculating lE was also proposed by Yamanaka

et al. (1997). In this study, the coefficient B is evaluated using field data and

literature values of zd and ks of the dry soil layer (4.3).

To solve rae (equation (5)) and rs (equation (6)), an equation for the third

unknown, es, is required. Because es is regulated at the surface by the amount of

feedback which is mediated both by the atmospheric boundary layer and the

surface response functions, its evaluation should take place within a larger scale

environment, such as that represented by the PM equation (Jones 1992; p. 117). By

rewriting the PM equation, the vapour pressure deficit at the surface is given by(Jarvis and McNaughton 1986):

es{es

~V es{es

eqz 1{V ea{ea

8

where V is the decoupling coefficient, V~(D/cz1)/(D/cz1zrs/rae), which quantifies

the degree of atmospheric coupling between the surface and the air; and D is

the slope of the saturation vapour pressure versus temperature relationship

which is evaluated at (TszTa)/2. With an efficient vertical mixing of the air,

rae decreases and Vp0 in which case the atmospheresurface coupling is good.

If the surface is completely coupled to the atmosphere (V~0), the vapour

pressure deficit of the atmosphere (ea*-ea) is imposed at the surface (equation (8)).The surface vapour pressure deficit during decoupled conditions, (es*-es)eq, is

solved by es{es

eq~lEeqrs c

rcp

, where lEeq~D(Rn-G)/(Dzc) is the equilibrium

evapotranspiration rate which is approached during decoupled conditions (Vp1)

(Jarvis and McNaughton 1986).


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When (Ts-Ta) increases above 510C, the linear approximation ofD in the PM

equation is invalid (Paw U and Gao 1988). This temperature difference is typically

reached for bare dry soils in Denmark. When nonlinear solutions are used for the

saturated vapour pressure function instead of the linear approximation, it can be

shown (Paw U and Gao 1988) that the limit of lE during decoupled conditionsapproaches the available energy (Rn-G) which may be very different from the lEeqused to calculate (es*-es)eq in equation (8). The application of equation (8) for

evaluation of es is therefore in error when rs/raep0. In addition, it was already

discussed that differences between Ts and Ts* may be substantial for bare dry soils

which further invalidates the applicability of PM-theory in such situations.

In the present study, measurements rather than predictions are used to assess the

limit of es at any time. If the surface is decoupled from the atmosphere, the

atmospheric vertical transfer of vapour is weak. In this case, water vapour tends to

accumulate at the surface until, eventually, it approaches es*. The limit of es during

decoupled conditions may therefore be calculated from the Ts measurement, or theTs* estimate (for a non-saturated surface). On the contrary, if the surface is well

coupled to the atmosphere (efficient vertical mixing of air), es is expected to

approach ea. In this paper, the feasibility of V as a weighting factor to place esbetween its (measurement-based) limit values, es* and ea, is investigated, i.e.

es~A V esz 1{V ea Pa 9

Substituting equation (9) in equation (6) it can be seen that the empirical factor A

appears to be analytically related to ea/es* by

A~craezcrszDraezDrea

es

craezcrszDraezDrs10

For ea/es*~1, or rs~0, then A~1. For lower values of ea/es*, Av1. In this paper, a

constant value of A (A~0.9) in equation (9) facilitates the calculation of

evapotranspiration rates during a wide range of conditions. For this purpose,

the hypothetical expression for es (equation (9) using A~0.9) is solved together with

equations (5) and (6) using NewtonRaphson iteration (appendix A), thereby

allowing the derived rae and rs to be used for computing lE:

lE~ rcpc

es{ea

raezrs W m

{2

11

Apart from evaluating the usefulness of the simple empirical expression for es by

comparing the ensuing calculations of rae and lE with measurement-based values ofrae (rae~rcp(Ts-Ta)/H) and eddy covariance of lE data, the dependency of es on V

is also evaluated relative to the results given by a more complex canopy scale

vegetationatmosphere transfer (VAT) model. The VAT model applied in this

paper is a slightly simplified version of the model described in Boegh et al. (2002b).

It provides an iterative solution for surface fluxes and surface conditions within a

larger scale environment, and it is validated using the field measurements of lE and

Ts. A summary of the VAT model is given in appendix B.

3. Location and equipmentFor the present study, data collected from two fields cropped with maize

and winter wheat, respectively, are used. The fields are located in an agricultural

area in Denmark (9.423 E, 56.486 N) characterized by sandy loam soils, and the

measurement campaign took place during the spring and summer of 1998.


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Generally, the growth season in 1998 was very humid (figure 1(a)). The winter

wheat was sown in Autumn 1997, and the maize was sown in May 1998. During the

measurement campaign, the leaf area index ranged from 0 to 4.2 for winter wheat,

and from 0 to 4.4 for maize (figure 1(b)).

Leaf area index was measured each week using destructive sampling (Boeghet al. 2002b). A continuous record of the field surface temperature was made in

1998, except for the period 24 July to 6 August for wheat, and in the period 4

August to 9 August for maize. On each field, thermal infrared radiometers (KT17,

Heimann, D; Wiesbaden, Germany) were mounted on masts at 2 m height with

azimuth angles of 60 and pointing 45 towards the surface. An emissivity of 0.99

was applied to convert the thermal radiance to surface temperature. Net radiation

(Q*6, REBS Inc., USA), soil temperature, air temperature and air humidity

(MP300, Rotronic; Bassersdorf, Switzerland) were measured continuously through-

out the study period.

Sensible and latent heat fluxes were measured using the eddy covariancetechnique (Baldocchi et al. 1988). The winter wheat field size is 600 m6800 m, and

the minimum fetch is 300 m. The maize field, which is long and narrow, is located in

an eastwest direction. For this field, data were abandoned in the period between

day 151 and 196 due to an insufficient fetch (Soegaard et al. 2002). The equipment

at each field consisted of a 3-dimensional sonic anemometer (Gill Solent;

Lymington, UK), and an IRGA (Infrared Gas Analyzer; Li-Cor, USA) was

used for measuring water vapour concentrations. The sampling tube (Bev-a-line, Li-

Cor; Lincoln, NE, USA) had an inner diameter of 3.2 mm and it was 10 m in

length. The sensor head was mounted 2.5 m above the top of the canopy. The air

was sucked through the sampling tube by a membrane pump at a flow rate of9lmin21. The Edisol software package was used for data collection and processing

(Moncrieff et al. 1997). The flux data availability is indicated in figure 1(b).

4. Results

4.1. The dependency of es on V for dense vegetation

Because the stomatal cavities of leaves are usually close to saturation, it can be

assumed that Ts~Ts* for dense vegetation canopies. In order to study the

dependency of es on V in such situations, the VAT model (appendix B) is applied to

Figure 1. (a) Mean midday temperature (11.0014.00 h) and precipitation in the experi-mental period. (b) Leaf area index (LAI) of wheat (empty circle) and maize (filledcircle) in the experimental period. The horizontal lines represent the flux dataavailability for wheat (upper line) and maize (lower line).


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evaluate the es-V relationship of a wheat canopy in periods with a dense vegetation

cover (L~4). For inclusion of variability in the environment, the VAT model is

applied both to a dry period (1821 May 1998) and a wet period (2730 May

1998). The chosen dry period is towards the end of the longest dry period in the

study-area that year (the last rain fell on 12 May 1998), whereas the wet periodfollows the occurrence of heavy rainfall (17 mm) on 26 May 1998 (figure 1(a)).

The simulated fluxes and surface conditions by the VAT model are in quite

good agreement with the field measurements of lE and Ts for wheat (figure 2).

Assuming that the model is also capable of predicting es and rs correctly (rae is

calculated from measurements; appendix B), the VAT model can be used to study

the dependency of es on V.

As would be expected, the measurements of ea at reference height are

independent of variations in V (figure 3(a)). The surfaceatmosphere system is well

coupled (Vp0) during early mornings and late afternoons because the leaf stomatal

(surface) resistance is higher during these periods. In such situations, the simulatedes (figure 3(b)) remains in the same range as ea. Towards the less well coupled

conditions prevailing during midday (Vp1), es increases (figure 3(b)), and the same

pattern is recognized in the relationship between es* and V (figure 3(c)). While es is,

in fact, linearly related to es*, it is even better related to the results derived from the

empirical expression for es suggested by equation (9) (figure 4). Using the VAT

model for calculating the factor A (equation (10)), its mean value is found to be 0.87

(SD~0.06) during the 6 days depicted in figures 2 and 3.

4.2. lE calculation based on empirical expression for es

The calculations to estimate lE (equations (5), (6), (9) and (11)) were run on ahalf-hourly basis using the inputs of Rn, Ts, Ta, ea and G during the periods when

flux data are available for validation (figure 1(b)). For this purpose, G is determined

as the residual in the energy balance equation (equation (2)) using the input data of

lE, H and Rn. At first, the calculations of lE are conducted assuming Ts~Ts*

which is valid for dense canopies. In this case, it is seen (figure 5) that the lE

predictions compare well with the measurements when LAI>3 (dense vegetation).

Figure 2. (a) Comparison between the evapotranspiration rates (lE) simulated by avegetationatmosphere transfer (VAT) model (appendix B) and field measurements oflE. (b) Comparison of surface temperature (Ts) simulated by a VAT model and fieldmeasurements of Ts. The figures were produced on the basis of data representingdense vegetation, including both a dry period (18 May to 21 May) and a wetperiod (27 May to 30 May, 1998).


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Figure 3. (a) Measurements of atmospheric vapour pressure (ea) versus the decouplingcoefficient (V) simulated by a vegetation-atmosphere transfer (VAT) model, (b) VATsimulations of the surface vapour pressure (es) versus V, (c) VAT simulations of thesaturated vapour pressure at the surface (es*) versus V. The figures were produced onthe basis of data representing dense vegetation, including both a dry period (18 Mayto 21 May, 1998) and a wet period (27 May to 30 May, 1998).

Figure 4. Comparison between the vapour pressure at the surface (es) estimated using thehypothetical equation (8), es~AVe

sz 1{V ea, and es modelled by a more complex

vegetationatmosphere transfer model. (a) using A~1 in equation(9), (b) usingA~0.9 in equation (9). The figures were produced on the basis of data representingdense vegetation, including both a dry period (18 May to 21 May, 1998) and a wetperiod (27 May to 30 May, 1998).


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On many occasions, the results also perform well for LAIv3, in particular for

wheat. The better performance for the wheat field than for maize relates to

differences in (Ts-Ta).

Generally, the larger values of (Ts-Ta) predominate at low LAI, but these are

much lower for wheat (figure 6(a)) than for maize (figure 6(b)) because the periods

with sparse vegetation at the wheat field were characterized by frequent rain events

(figure 1(a)). In contrast, the exposed soil patches at the maize field cause (Ts-Ta)

to increase dramatically during the dry spells in MayJune as can be seen in

figure 1(b)).Overall, the lE predictions (assuming Ts~Ts*) are in good accordance with field

measurements when (Ts-Ta)v5C (figure 7). However, when (Ts-Ta)w5C, the

calculated lE is overestimated. In this situation, the effective source of water

vapour from the dry soil patches at the maize field is located below an upper dry

layer exhibiting distinct thermal properties. This causes the measurement of Ts to

exceed the hypothetical temperature of the evaporating front which is located

deeper in the soil (Ts*) which, in turn, causes es* and lE to be overestimated.

Figure 5. Comparison between evapotranspiration rates (lE) calculated assuming Ts~Ts*(using equations (5), (6), (8) and (9)) and eddy covariance data of lE. Results areshown separately for bare/sparse canopies where LAIv3 (empty circle) and for densecanopies where LAI>3 (filled circle). (a) Wheat, (b) maize.

Figure 6. Field data of surface temperature (Ts) and air temperature (Ta) are used toillustrate the variations in (Ts-Ta) for (a) wheat and (b) maize during the experimentalperiod.


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4.3. Assessment of Ts* of dry bare soil

The estimation of Ts* during dry conditions can be made using equation (7)

if information on zd is available. Even though the moisture condition in the

upper thin surface layer of soils is generally considered to be very important for

determining rs and soil-water limited rates of lE, only very few registrations of zdhave been reported in the literature. For a sandy loam soil in Japan with a particle

composition (81% sand, 9% silt, 10% clay) very similar to that of the agricultural

topsoils in the present study (80% sand, 10% silt, 10% clay), the maximum depth of

the dry layer was found to be 0.02 m while for a sand dune site (96% sand, 2% silt,

2% clay), the maximum observed zd was 0.08 cm (Yamanaka and Yonetani 1999).

Using zd~0.02 m to represent the soil condition during the very dry period,

1821 May 1998, in this study, measurement-based estimates of G/H (equation (2))

and rae (equation (3)) can be used to calculate B. In this period, the average G/H

was found to be 0.66 (SD~0.29) and the average rae was 53sm21 (SD~1 3 s m21).

Using ks~0.25Wm21

C21 to represent the thermal conductivity of the upper dry

soil layer, B is given by B~(0.66*1227*0.02)/(53*0.25)~1.2. Theoretically, the

factor B should then vary from 0 (in which case Ts~Ts*) for a wet soil to 1.2 for a

dry soil. Because the transition from energy-limited to soil-limited evaporationtends to be abrupt and is accompanied by an increase in surface temperature

(Amano and Salvucci 1999), it is simply assumed that Ts*5C. The sensitivity of the calculated lE to B is evaluated in 4.4.

4.4. lE calculation using empirical estimates of es and Ts*

In the following, the calculation of lE for surfaces characterized by (Ts-

Ta)v5C is based on the assumption that Ts~Ts* while the calculation of lE for

warm surfaces with (Ts-Ta)>5C uses the relationship in equation (7) to assess Ts*.

This causes predictions to be comparable with measurements (figure 8).Figure 9 facilitates a more detailed evaluation of the results at the wheat field

and maize field, respectively. For each field, diurnal predictions of lE and rae are

compared with measurement-based values of lE and rae on three different days

varying in vegetation density and surface temperature (table 1).

Figure 7. Comparison between evapotranspiration rates (lE) calculated assuming Ts~Ts*(using equations (5), (6), (8) and (9)) and eddy covariance data of lE. Results areshown separately for (Ts-Ta)w5C (empty circle) and for (Ts-Ta)5C (filled circle),where (Ts-Ta) is the difference between surface temperature and air temperature.

(a) Wheat, (b) maize.


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Towards the mornings and late evenings, the predictions of rae obtain

large (positive or negative) values when the denominator in equation (5) (Rn-G)

approaches zero. The case is the same for the measurement-based rae when H

approaches zero. During midday, the predictions of rae are in quite good agreement

with the measurement-based rae. For the dense maize field (figure 9( f)), Ts typically

comes very close to Ta during afternoons, and it may even happen that Ts becomes

lower than Ta. Simultaneous observations of negative (Ts-Ta) and positive H

indicate the presence of counter-gradient fluxes in the tall maize canopy which

causes the measurement-based rae to become negative (figure 9( f)). This situationillegitimates both the measurement-based rae and the applied methodology for

calculating lE. On day 222 (figure 9( f)), both (Ts-Ta) and H turn negative during

late afternoon which indicates that sensible heat is being used to increase the

transpiration rates.

The sensitivity of the calculated lE in figure 9 to the various inputs and

parameter settings is illustrated in table 2. Overall, there is a quite broad range of

sensitivities to the individual parameters. For sparse/dense canopies with (Ts-

Ta)v5C, the sensitivity is highest to the observations of Ts, Rn and ea while the

sensitivity to the choice of parameter values for A and B is less. For the dry bare

soil and sparsely vegetated surfaces where (Ts-Ta)>5C, the sensitivity to theempirical surface humidity parameter A is highest, and the sensitivity to the

parameter B is also important. Nevertheless, it seems feasible to use a fixed

parameter value, A~0.9, regardless of vegetation density and dryness condition

(figure 8). Optimally, the setting of parameter B should use information on the dry

surface layer development (4.3) to improve the predicted transition from energy

limited to soil water limited evapotranspiration rates. However, in this study

reasonable results were obtained using a setting of B~1.2 to represent a sandy

loam soil.

5. ConclusionA method is presented to calculate lE using standard meteorological data and

remote sensing based estimates of Ts, Rn and G. The method uses physical

descriptions of the surface energy exchange together with an empirical assessment

of the surface humidity (equation (9)) and, for dry surfaces, the temperature of the

Figure 8. Comparison between predicted evapotranspiration rates (lE) and field measure-ments of lE for (a) wheat and (b) maize. The 1:1 lines are also shown. Thecomparison includes results from all days with available flux data (figure 1(b)).


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evaporating front needs to be evaluated (equation (7)). It is interesting that, whenwe use a more basic and traditional, although more complicated, model, we find

that the hypothetical equation (9) is approximately true. For humid surface

conditions (Ts*


14/18

boundary condition for the atmospheric fluxes and the upper boundary condition

for the soil fluxes (Ts-Ts*) and (Ts-Ta) are closely associated. Theoretically, this

relationship is dependent on the depth of the evaporating surface, but in practice, a

constant coefficient representing the ratio of (Ts-Ts*) and (Ts-Ta) for a dry soil

was found useful for estimating Ts* and calculation of lE for dry surfaces with

(Ts-Ta)>

5

C.Should the expressions for es and Ts* prove to be reasonable approximations

in other studies, they may provide an effective and simple way to calculate

evapotranspiration from standard, easily obtainable meteorological data and

thermal infrared remote sensing data. In Boegh et al. (2004), the application of the

method for calculating lE in Denmark is demonstrated based on inputs of Earth

observations (NOAA AVHRR) and climate predictions which were computed by a

high-resolution weather forecast model.

Appendix A

The NewtonRaphson Method states that if x~c is an approximation to the

solution of the equation f(x)~0, then a better approximation is given by

cnew~c{f c

f0 c A1

Table 1. Leaf area index, LAI, and the difference between surface temperature and airtemperature at 13.00 h (Ts-Ta)13h, on selected days for (a) wheat and (b) maize. Seefigure 9 for results of evapotranspiration rates and atmospheric resistance on thesedays.

(a) Wheat

Day 112 Day 138 Day 189LAI 0.3 3.8 0(Ts-Ta)13h 4.4C 3.6C 4.5C

(b) Maize

Day 138 Day 164 Day 222LAI 0 0.1 4.2(Ts-Ta)13h 15.1 6.4C 2.1C

Table 2. Fractional change of the calculated evapotranspiration rate to independentincreases of 10% in input and parameter settings. Results are shown for wheat andmaize on selected days at midday (13.00 h). See also table 1 and figure 9. (Ts, surfacetemperature; Rn, net radiation; Ta, air temperature; ea, vapour pressure; A, parameterin equation (9); B, parameter in equation (7).

Wheat Maize

Day 112 Day 138 Day 189 Day 138 Day 164 Day 222

Ts 20.57 20.45 0.26 20.26 20.17 0.14Rn 0.09 0.08 20.63 0.09 0.11 0.09T

a0.05 0.07 0.07 0.26 0.01 0.13

ea 20.05 20.06 20.03 0.01 20.31 0.33A 0.08 0.07 0.03 0.39 0.43 0.02B 0 0 0 20.14 20.18 0


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When estimating lE, the function f is given by

f x ~rnewae {rae A2

where rnewae is calculated using equation (5). The derivative of f follows as

f0 x ~drnew

aedre{1 A3

where

drnewaedre~

drnewaedes

des

dreA4

with

drnewaedes~

rcp

c Rn{G A5

and

des

drae~es A

D=cz1

D=cz1zrs=rae 2

rs

r2ae{D=cz1

D=cz1zrs=rae 2

rs

r2aeea A6

Appendix B. Description of VAT model

The VAT-model consists of a coupled photosynthesis/stomatal resistance model

which is connected to the above atmosphere by an atmospheric boundary layer.

The canopy photosynthetic rate is simulated to allow the prediction of stomatal

(surface) resistance which, in turn, is used to evaluate the transpiration rate and the

surface energy balance. The model is applied to a dense canopy only. The model

applied in this paper is a slightly simplified version of the model described in Boeghet al . (2002b). The same model parameters representing wheat (taken from

the literature) are applied, but in this paper, more input data are based on

measurements (rather than predictions) in order to maximize the accuracy of the

simulations. As such, inputs of measured net radiation are used in this version

(rather than global radiation), and the atmospheric resistance between the surface

and the atmosphere above the canopy (rae) is assessed using the measurements ofH,

Ts and Ta:

rae~rcp Ts{Ta

H s m{1

B1

In Boegh et al. (2002b), all leaf level calculations were made separately forshaded and sunlit leaves, but in this version, only the photosynthetic rate is

computed seperately for sunlit and shaded leaves. The radiation absorbed by sunlit

and shaded leaves is evaluated, and an exponential profile of leaf Rubisco capacity

in the canopy is distributed between sunlit and shaded leaves. The canopy

photosynthesis (Ac) is the sum of shaded and sunlit fractions. The (big-leaf)

stomatal conductance (gs~1/rs) is then calculated as (Leuning 1995):

gs~gs0 Lza wsf Ac P

ps{C 1zDs=D0 mol m{2s{1

B2

where P is atmospheric pressure (Pa), ps is the CO2 partial pressure at the surface

(Pa), C is the CO2 compensation point (Pa), Ds is the vapour pressure deficit at thesurface, and gs0, a and D0 are empirical coefficients for wheat. The wsf is a water-

stress factor (set to unity). Because Ds is not known, Ds and gs are solved by

iteration. In Boegh et al. (2002b), the net-isothermal form of the PM equation was

used to compute the transpiration rates, but in this version, it is preferable to keep


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the VAT model completely independent of the linearly approximated definition of

D which is used in the empirical expression for es (to be compared with the VAT-

modelled es). The big-leaf transpiration rate is therefore computed by

lE~ rcpc

es{ea

raezrs W m

{2

B3

and the big-leaf surface temperature (Tl) is calculated as

Tl~Hraercp

zTa

0C B4

where H is the sensible heat flux (H~Rn-lE). The evaluation of the big-leaf

temperature, rather than a separate evaluation of energy balances for shaded and

sunlit leaves (as in Boegh et al. 2002b), allows direct validation of the modelled Tlrelative to the Ts measurements.

Finally, es is calculated by

es~es{lE rs c

rcp

0C B5

The gs, Tl, lE and Ac are solved simultaneously with the computation of es, ps andpi (leaf internal CO2 pressure) through utilizing a NewtonRaphson iterative

solution process for pi, as introduced by Collatz et al. (1991). In order to simulate

a dense winter wheat canopy, the leaf area index is set to 4, and the leaf

photosynthetic capacity at the top of the canopy, Vmax0, is set to 150 mmolm22s21

to represent wheat (Wang and Leuning 1998).

Acknowledgments

The paper was prepared within the projects EO-flux-budget and RS-model

which is financed by the Danish research council, Copenhagen. Information on leaf

area index and precipitation was kindly provided by Anton Thomsen and TomJensen from The Danish Institute of Agricultural Sciences in Foulum, Denmark.

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Remote Sensing Based Estimation of Evapotranspiration Rates 2004Boegh