estimating évapotranspiration from land surfaces in...

Estimation ofArealEvapotranspirationCProceedings of a workshop held at Vancouver, B.C., Canada, August 1987). IAHS Publ. no. 177,1989. 2 4 5

Estimating évapotranspiration from land surfaces in British Columbia

D.L. Spittlehouse Research Branch, B.C. Ministry of Forests Victoria, B.C., V8W3E7 Canada

Abstract The estimation of évapotranspiration from a variety of terrain and vegetation types using minimal weather and site data is a difficult task. A model that estimates évapotranspiration on a daily basis as the lesser of energy and soil limited rates is described. The former rate is estimated using a Priestley-Taylor type of equation requiring only solar radiation and air temperature. The latter rate is a function of the fraction of extractable water in the root zone. Values of the Priestley-Taylor coefficient a, and the coefficient relating the soil limited rate to extractable water are reported for agricultural, forest and urban surfaces in British Columbia. Limitations to using the model are discussed. Some examples are presented illustrating how the model can be used in hydrology and used to relate plant growth to the soil water balance.

Estimation de l'évapotranspiration issue des suriaces terrestres de la Colombie-Britannique

Résumé II n'est guère aisé d'estimer l'évapotranspiration se produisant sur un certain nombre de types de relief et de végétation partir de données minimales sur la météorologie et les lieux. On a décrit un modèle qui évalue quotidiennement l'évapotranspiration comme étant le moindre des taux limités de l'énergie et du sol. On a évalué le premier de ces taux à partir de la radiation solaire et de la température de l'air en se servant de l'équation de Priestley-Taylor. Le deuxième de ces taux est une fonction de la fraction d'eau extractible de la rizhosphère. On a fournit les valeurs du coefficient a de Priestley-Taylor et du coefficient exprimant le rapport entre le taux limité du sol et l'eau extractible pour les surfaces cultivées, forestières et urbaines de la Colombie-Britannique. On a discuté les limites de l'emploi du modèle. On a présenté quelques exemples de l'emploi du modèle en hydrologie ainsi que pour la comparaison du bilan hydrique du sol et de la croissance des plantes.

INTRODUCTION

There is a large range of terrain and surface cover in the province of British Columbia. One aspect of managing this land is the routine determination of évapotranspiration. However, different surfaces differ in their response to the atmospheric evaporative

246 D.L. Spittlehouse

demand for water and the soil's supply of water. Furthermore, information on site characteristics is usually limited, the network of weather stations is sparse, and weather conditions vary greatly in both space and time. Consequently, an évapotranspiration model to be used in water balance calculations in British Columbia must be easily calibrated and be able to operate from synoptic weather data, preferably with a daily time step. These were the criteria for the development of the évapotranspiration model (Spittlehouse & Black, 1981) outlined here.

The model presented has been successfully used to determine évapotranspiration of forested (Spittlehouse, 1985; Giles et al., 1985) and grassland communities (Wallis et al., 1983, 1985) in British Columbia. These authors also related the water balance to the annual growth of the respective crops. Nagpal et al. (1986) used the model to estimate irrigation requirements. Data from other surfaces presented here indicate that the model has a wider application. Similar models have been described by Cordova & Bras (1981), and Fédérer (1982).

THE MODEL

In this approach, the vegetation is treated as a single layer over a single slab of soil. Transpiration from the dry surface (no intercepted rainfall) is limited by the energy available to evaporate water and by the ability of the soil to supply water to the evaporating surface. Following Priestly & Taylor (1972), the energy limited transpiration rate (Emax, mm oM) is taken to be a relatively constant fraction of the equilibrium evaporation rate (Eeq, mm d-1), i.e.

Emax = 01 Eeq ("I)

where

Eeq = (s/[s + -d)(Rn-G) (2)

a is an empirical constant (dimensionless), Rn is the net radiation (mm cM evaporative equivalent), G is the soil heat flux (mm cH) assumed to be a constant fraction of Rn for each surface, s and y are, respectively, the slope of the saturation vapour pressure curve (kPa °C-1) and the psychrometric constant (kPa °C_1) at the daily mean air temperature. Net radiation is calculated from measured or modelled solar radiation, or sunshine hours, and maximum and minimum air temperature. The concept of calculating the energy limited transpiration from a reference, or potential value has been used in agriculture for many years, e.g. Jensen et al. (1971), Doorenbos & Pruitt (1977).

The maximum rate at which the soil can supply water (Es, mm cH)is a function of the water content of the root zone (Cowan, 1965; McNaughton ef ai, 1979). It can be approximated by a linear relationship, i.e.

Es = b 8e (3)

where b is an empirical coefficient (mm oH), and 6e is the fraction of extractable water in the root zone of the vegetation. 8e equals the difference between the actual root zone water content and the root zone water content at zero transpiration, divided by the water storage capacity of the root zone. The water storage capacity is the volume of water that can be stored between field capacity (-0.01 to -0.03 MPa) and the water content at zero transpiration. It is a function of soil texture, stone content and root zone depth. The value of the water content at zero transpiration can be obtained by extrapolation of a plot of transpiration versus water content, or estimated from the water retention characteristic of the soil (Campbell, 1985), i.e. the water content at a soil water potential of -1.5 to

Estimating évapotranspiration from land surfaces 247

-2.5 MPa. Since the root zone is treated as a single layer, rainfall is assumed to be distributed through the whole of the root zone.

The rate of transpiration from a surface with no intercepted rain (Et, mm d-1) is given by

: the lesser of Emax 3nd Es (4)

Equations 1, 3 and 4 are illustrated in Fig. 1. It can be shown that dividing both axes of Fig. 1 by Egq collapses the family of curves on to two lines. Fig. 2 shows these two lines fitted to data obtained for a Douglas-fir stand

3

(mm d-l)

High Em0,

/ Medium E m M

E' / / Low Emai

E t /E eq

0.4

( * ' [ ""'

* 4

/ 4 . . o * V -E r /E , q =*=o.e A / 1 O

* 1 A

1 4 J * A \

* 1 j - E T / e o = b = 10.0 mm d " ' - A Â 1 p

L I c e q (mm d - 1 ) / i * 1 - 2 .

/ I i 2 - 3 - / 1 ! 4 3 - 4 .

/ 1 • 4 - S

./ ! ° >5 . 7 j , t f /b = 0.08

e e / E e q (mmd-O-1

FIG. 1. Schematic of equations (1), (3) and (4). Symbols are explained in the text.

FIG. 2. Daily values of Et/Eeq versus Qe/Egq for days with no rain for a Douglas-fir stand. Symbols are explained in the text. (From Spittlehouse & Black, 1981).

Evaporation of Interception

The approach to evaporating intercepted water follows that of McNaughton & Black (1973), Shuttleworth & Calder (1979) and Gash (1978). Evapotranspiration (E) from wet foliage is made up of evaporating intercepted water and transpiration. Since the presence of intercepted water supresses transpiration, only a certain fraction of intercepted water is a net loss to the water balance of the plants. Following (1), the evaporation rate for intercepted water (Ej, mm cM) is given by

Ej = ocw Eeq (5) where aw is an empirical coefficient (dimensionless) relating evaporation from a 'completely wet' canopy to the equilibrium evaporation rate. If the gross interception loss for the day is I (mm cM), then the fraction of time required to evaporate I is l/Ej. Assuming Et would be the transpiration rate for the day if the foliage were dry, then the


total evaporation for a day with interception (ET, mm d-1) is ET = Et(1- l/Ei) + I. Substituting for Ej from (5) and rearranging gives

ET = Et + gl (6)

where g = (1 - [Et/awEeq]) and Et is calculated using (1) to (4). Consequently, g is at a minimum when Et is energy limited and depends on the ratio of ot/aw. g increases as transpiration becomes increasingly soil limited, reaching a value of 1 when the soil is too dry to allow any transpiration. Fig. 3 shows the lines in Fig. 1 fitted to pasture data with and without rain.

E T / E eq 0-8

04

0

f *

** -tf V T * o

1

O

9 -A S «

1 1 A 1 1

* *T*3jp i ^ A O A A « A * - * „ V t f 0 A A *

A

pb=34mmd"!

J 1

1978 1979 Eeq (mmd"1)

A A | - 2

«> o 2 - 3 v v 3—4

» rainy day

—1 -J- !.. 1 -

0-2 0-4 (mmd-1)"1

0 6

F/G. 3. Daily values of Ej/Eeq versus Qe/Eeq for days with and without rain for a pasture. Symbols are explained in the text. (From Wallis etal., 1983).

VERIFICATION OF THE MODEL

Evapotranspiration rates have been measured using a variety of techniques for a number of surfaces in British Columbia. Energy limited évapotranspiration rates for dry surfaces in British Columbia vary from 3 to 6 mm cM without advection depending on the surface cover, and up to 10 mm d-1 with advection. Values of the Priestley-Taylor coefficient a are summarized in Table 1. The values of a agree well with those from many other parts of the world for similar surfaces.

In general, a ranges from 1.1 to 1.3 for short plants such as grass, and from 0.7 to 1 for forested surfaces (Table 1). Values for b are less readily available. Some of the surfaces described in Table 1 had no soil limited phase. The values of b in Figs. 2 and 3 are 10 and 34, respectively. Surfaces are difficult to compare since b depends on soil type and the 'reference' values used in the calculation of 8e. The value of 0e at which transpiration becomes soil limiting depends upon Eeq (Fig. 1), and can be obtained by determining the value of 9e at which Emax ~ Es. For example, on a sunny day, when Emax


= 4 mm cH, the soil water supply restricts transpiration when the available water content has been depleted by 60 to 70%. Using the soil water retention curves tor the sites shown in Figs. 2 and 3, this represents soil water potentials of -0.2 to -0.3 MPa.

TABLE 1. The Priestley-Taylor coefficient a, or the ratio of the daily energy limited rate (Emax) to the equilibrium evaporation rate (E^ for various surfaces in British Columbia

Surface

Pasture - Peace River

rainy days - Fraser Valley

- Vancouver Isl. - Vane. Airport

Pine Grass - Interior B.C. - Rangeland -100% cover - 60% cover

Alfalfa subject to advection

Bare soil Fraser Valley

Urban Vancouver Vancouver

Douglas-fir stands 11y ,8m"

Fraser Valley 23 y, 10 m

Vancouver Island 70 y, 30 m



Vancouver Island 10 y, clearcut

a

1.27 ± 1.17 ± 1.26 ± 1.15t 1.15 1.09

0.8 1.2 0.9

1.60 ±

1.27 ±

1.31 =1.1

1.05 ±

0.80 ±

0.82 ±

0.70 ±

0.75 ±

0.60 ± Salal + Douglas-fir, Vancouver Island

0.12 0.13 0.1

0.1

0.1

0.08

0.07

0.07t

0.1

0.10

0.05

Days

68 29 15 8

19

17

7

18

19

14

13

44

5

Method*

1 1 1 3 1 1

1 2 2

1

1

1 1

1

1,2

2

2

1

1

Source

Wallis era/. (1983) Goldstein & Black (1978) Yap &Oke (1974) Wallis ef a/. (1985) Oke & McCaughey (1983)

Williams et ai (1978) Blacker al. (1987) Nicholson (1988)

Williams (undated)

Novak & Black (1982)

Oke & McCaughey (1983) Kalandaefa/. (1980)

McNaughton & Black (1973)

Spittlehouse & Black (1981)

Giles etal. (1985)

Blacker al. (1984)

Price (1987)

Price (1987)

'Methods: 1=Energy balance/Bowen ratio, 2=Soil water balance, (Spittlehouse & Black, 1980).

t Daytime value adjusted to 24 hours. ** Age & height

3=Eddy correlation/energy balance


Data for forests from other areas of the world indicate values similar to those noted above for a, and for 8e where transpiration becomes soil limited. For example, Dunin ef al. (1985) present a graph similar to Fig. 1 for eucalypt in Australia. They obtained values between 0.7 and 1.0 for the ratio of actual to potential évapotranspiration (calculated with the Penman-Monteith equation and a fixed canopy resistance of 60 s rrH). Soil water restrictions started to occur at high evaporative demands when the available water storage has been depleted by 60 to 70%. Tajchman et al. (1979) present data for a young pine stand in Germany. Their data indicate a daytime value of a = 0.85 ± 0.05 (n=4) and soil water restriction starting to show at about -0.25 M Pa when E ^ = 5.8 mm cH. Granier (1987) obtained a value of 0.6 for the ratio of actual to potential transpiration (calculated with the Penman equation) for Douglas-fir in France. Transpiration declined linearly with decreasing extractable water content below 70% depletion. Shuttleworth & Calder (1979) obtained a = 0.72 ± 0.07 for spruce in Britain. Monteny ef al. (1985) obtained values of a between 0.75 and 1 for young rubber trees in the Ivory Coast.

Numerous agricultural studies have obtained relationships similar to those shown in Figs. 1 to 3. As with the data for British Columbia, the value of a is greater than that for forests, i.e. a « 1.26 (e.g. Davies & Allen, 1973; Tanner & Jury, 1979; Ritchie, 1973). Tanner & Ritchie (1974) concluded from their survey of crop water experiments that soil water restrictions to transpiration usually begin to occur under high atmospheric demand when 70% of the available water is depleted.

The value of g has been found to be quite variable in the energy limited phase. For example, it was about 0 for a Peace River pasture (Wallis et al., 1983) which implies a « aw (Table 1). McNaughton & Black (1973) obtained 0.17 for a 8 m tall Douglas-fir plantation (aw = 1.27) , while Spittlehouse & Black (1981) and Giles (1985) obtained g = 0.8 (otw = 3.6) for 10 and 30 m tall Douglas-fir forests. Shuttleworth & Calder (1981) reported a value of g = 0.9 (otw » 7.2) for a 24 m tall pine forest. However, the average value can hide a wide range and probably reflects differences in type and intensity of rain storms, and the roughness characteristics of the vegetation.

Evapotranspiration models such as that described here have been criticised for their empiricism (Jarvis et al., 1981). However, the canopy and aerodynamic resistances as well as humidity data required by more detailed models, e.g. the Penman-Monteith equation, are frequently not available, or are difficult to obtain. Figs. 2 and 3 show that the model fits the measured data quite well. The model performed as well as a model based on the Penman-Monteith equation (Spittlehouse & Black, 1982). All models must be calibrated, whether for the values of a and b in (1) and (3), or the stomatal or canopy resistance characteristics required by models that use the Penman Monteith equation (Spittlehouse & Black, 1982: Jarvis et al., 1981).

De Bruin (1983), McNaughton & Spriggs (1985) and McNaughton et al. (1979) have shown that a is strongly dependent on the canopy resistance and the isothermal resistance (ratio of the vapour pressure deficit to the net radiation). Thus, if a is relatively constant it is because these two terms are relatively constant, or vary such that changes in one of them tend to offset changes in the other. McNaughton & Spriggs (in this volume) find good support for the Priestley-Taylor equation. They relate the small variation of a for different conditions to negative feedback withen the boundary layer. The relationship breaks down when the surface resistance increases dramatically as the soil dries since transpiration is not energy limited. In this situation, the soil limiting phase of the model is used to estimate transpiration.


USING THE MODEL

Practical considerations

Usually the model is applied as part of a water balance calculation. This facilitates the calculation of 8e and drainage. An interception model is also incorporated (Spittlehouse & Black, 1981; Spittlehouse, 1985; Giles et ai, 1985). Sophisticated energy balance or eddy correlation data are not necessarily required to obtain the values of a and b. Giles et al. (1985), Black et al. (1987) and Nicholson (1988) show that these parameters can be obtained from weekly measurements of changes in the root zone water content obtained with a neutron probe, and daily solar radiation, air temperature and precipitation data. Considering the terrain and vegetation in British Columbia, and limited funding, this methodology and the model are a practical approach to the routine determination of évapotranspiration.

If field data are not available, a reasonable approximation would be a = 1.26 for agricultural crops, and a = 0.8 for forests. Ritchie (1981) has noted that it is preferable to obtain the estimate of the water storage capacity of the root zone from field measurements. However, an acceptable estimate of b could be obtained from the soil water retention characteristic of the soil at the site (calculate 8e), and the assumption that the soil begins to limit transpiration when 9e = 0.3 and Eeq = 4 mm cM.

The weather data required to run the model (solar radiation, or sunshine hours, air temperature and rainfall) are not always available for the site of interest. Thus there is a need to extrapolate and interpolate over the landscape, i.e. topoclimatic modelling (Nunez, 1980; Taylor & Waite, 1980; Running et ai, 1987). This is not always an easy task, particularly for rainfall.

Soil surface evaporation will become soil restricted much sooner than transpiration, and this must be taken into account when there is an incomplete cover of vegetation. Tanner & Jury (1979) illustrate the use of the model in this situation. The upper limit to transpiration on any day is set by the energy available to evaporate water. Consequently, transpiration will not continue to increase with an increase in leaf area. Leaves deep in the canopy become shaded and cooler, resulting in a transpiration rate lower than that of the upper leaves. Tanner & Jury (1979) suggested that for their potato crop a leaf area index (LAI) of 2.5 was required to shade the surface and produce maximum transpiration rates. Spittlehouse & Black (1981) and Giles et al (1985) obtained similar maximum transpiration rates for forest stands with LAI varying from 6 to 21 m2 leaf per m2 ground. Maintenance of a constant canopy évapotranspiration rate while leaf area is increasing has implications for models that explicitly involve LAI and stomatal resistance.

The model provides point estimates of évapotranspiration. Determination of areal évapotranspiration requires the assumption that the surface being modelled is homogeneous. If different surfaces exist, each must be modelled separately and areal évapotranspiration obtained from the area weighted average for each surface. Advective effects are ignored. However, Shouse ef ai (1980) have shown how (1) can be applied in advective conditions.

Care must be taken when using the model to investigate the effect of changes in the surface cover on the water balance. A knowledge of a and b for the new surface is required. Also, since the model does not contain any interaction with the atmosphere, the user must assume that either there was no change in atmospheric conditions, or that a realistic estimate of possible changes can be made and the weather data adjusted

252 D.L Spittlehouse

accordingly. However, this is true of most évapotranspiration models, there are few models that include the required feedback mechanisms (McNaughton & Jarvis, 1983).

The model was initially used with a daily time step. However, Spittlehouse (unpublished) has shown that weekly and even monthly time steps can provide acceptable estimates of the water balance.

Some examples

The model has been applied in British Columbia to hydrologie and plant water relations problems. The évapotranspiration model was combined with rainfall interception and drainage models to determine the daily water balance of the root zone. Wallis ef al. (1985) and Nagpal et al. (1986) estimated irrigation requirements for the east coast of Vancouver Island. Model simulations were performed for a range of soil depth and textures for a 30 year period. This data was then used to estimate irrigation requirements at various levels of risk for agricultural land in a management unit. An example is shown in Table 2.

TABLE 2. Water use requirements for Irrigation planning determined with the model (summarized from Nagpal et al., 1986)

Volumetric irrigation requirements for mapsheet 92G011 Agricultural capability classes 1-4 (2527 ha)

Risk level (%)

10 20 50

i

Irrigation requirement (105 m3)

Root zone 0.5

1148 1088 974

depth (m) 1.0

1103 1042 921

Wallis et al (1983) used the fact that transpiration is often well correlated with growth to estimate the seasonal course of growth of a pasture in the Peace River region of British Columbia. Their transpiration relationship is shown in Fig. 3.

Spittlehouse (1985) modelled the 1959-1983 April to October water balances for a stand of Douglas-fir trees. Large year-to-year variations were found in water use and these were the result of large intra- and inter-year variations in the rainfall. Yearly basal area increment of the trees was well correlated with the growing season transpiration. The transpiration relationship is shown in Fig. 2.

Giles et al. (1985) compared the growing season water balance of seven forest stands along a moisture gradient. They used the growing season water deficit, equal to the sum of (Emax - Et), as a measure of the water stress on the plants. Seasonal water deficit was well correlated with site index. The year-to-year variations in water deficit for two of the sites are shown in Fig. 4. Site 1 has a 0.5 m deep, stony root zone while site 5 has a 1.1 m deep root zone with less stones and a water table present until the end of May. The greater water storage capacity at site 5 accounts for the lower deficits. About


30% of the years can be considered wet with only minor or no deficits at both sites, while 25% of the years are very dry at site 1. The April to October evaporative demand (i.e. Emax) ranged from 250 to 350 mm. The yearly evaporative demand is estimated to be between 300 and 400 mm. Similar results were obtained by Spittlehouse (1985) for a forest about 150 km further north.

CONCLUSIONS

Routine calculations of areal évapotranspiration using minimal site and weather data are possible. The model described can be calibrated with relatively simple, though labour intensive, field measurements. Furthermore, research in a number of parts of the world suggests that the coefficients in the évapotranspiration equations may be relatively conservative. Although there are some limitations on the use of the model, the examples presented show that the model has many practical applications in hydrology and plant growth studies.

60 -

20

1975 II

FIG. 4. Modelled water deficits for the April to October period, 1951 to 1985 for two forest sites. Site 1 (hatched bar) and site 5 (solid bar) have 0.5 and 1.1 m deep root zones, respectively.

ACKNOWLEDGEMENTS

Information reported in Table 1 comes from the studies of many researchers. Their dedication and perseverance in the collection of the field data, frequently in much less than ideal conditions, is acknowledged. The support and comments of Dr. T.A. Black, University of British Columbia, Vancouver, in the development and testing of this approach to calculating évapotranspiration, and for critical review of this paper, is gratefully acknowledged.


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