Soil Water Balance in the SudanoSdhelian Zone (Proceedings of the Niamey Workshop, February 1991). IAHS Publ. no. 199,1991.

The measurement and modelling of evaporation from semiarid land

J. S. WALLACE

Institute of Hydrology, Wallingford, Oxfordshire OX10 8BB, UK

Abstract Accurate information about the land surface water balance in the Sudano-Sahelian zone is a crucial requirement to understanding variations in crop yield, water resources and climate. Recent developments in micrometeorological and plant physiological equipment provide the means to obtain the evaporation and energy balance data which are required to improve our understanding of the above areas of arid zone hydrology. Significant advances have also been made in our ability to model evaporation from semiarid vegetation. This paper presents a review of some of the most promising developments in this field.

EQTRODUCnON

The Sudano-Sahelian zone is characterized by low and erratic rainfall, the partitioning of which into evaporation, runoff and drainage has profound effects on a wide variety of fields including agriculture, hydrology and, perhaps even on climate itself. Accurate information about the land surface water balance is, therefore, a crucial requirement for understanding variations in crop yield, water resources and climate. The importance of evaporation in agricultural and hydrological studies in the Sudano-Sahelian zone has already been mentioned by Sivakumar & Wallace (1991). They highlight the importance of knowing not only total evaporation, but also how the total is partitioned between its components - transpiration and soil evaporation, since only transpiration is related to yield.

It is becoming increasingly recognized that in the understanding of climate change, information on land surface evaporation is very important. The reduction in evaporation (and the change in surface energy balance) associated with the removal of vegetation in the Sahel has been shown, via general circulation models (GCMs), to produce a reduction in rainfall (e.g. Charney, 1975; Cunnington & Rowntree, 1986). However, the forecasts of these models are very sensitive to the land surface conditions and the presence of vegetation (Xue et al, 1990). There is, therefore, a great need for evaporation (and energy balance) data from typical Sahelian vegetations in order to better understand and hence predict any links between vegetation degradation and climate change. With the current concerns for environmental and climatic change, the management of scarce water resources and the need to sustain crop production in the face of population increase, the need for methods and models for quantifying evaporation from semiarid lands is

131

/. 5. Wallace 132

greater than ever before. Most techniques and models for measuring and calculating evaporation

have evolved in the temperate regions of the world. However direct measurement of evaporation in semiarid zones is generally more difficult than in temperate zones because the vegetation is rarely a homogeneous monoculture giving complete ground cover. The modelling of evaporation from sparse canopies, often of mixed species, is also much more complex. In recent years, however, measurement techniques have been adapted or developed for use in semiarid environments. Progress has also been made in modelling evaporation from sparse semiarid vegetation. This paper presents a brief review of evaporation techniques and models and highlights those which are particularly well suited for measuring or predicting evaporation from semiarid land.

EVAPORATION MEASUREMENT

The measurement of evaporation can be made in the liquid phase, as a rate of loss of water from the surface, or in the gaseous phase, as a rate of gain of water vapour by the atmosphere. Techniques for estimating evaporation can therefore be considered in two principal categories, those using a liquid water balance and those where the flow of water vapour into the air is measured. The main techniques used to measure evaporation have been recently reviewed by Shuttleworth (1990), so this paper concentrates on a brief outline of methods and their applicability for use in semiarid regions.

There are a range of water balance methods used to determine evaporation which differ in their spatial and temporal scales but all of which rely on the basic water balance equation:

E = P - R - Dr - AS (1)

where E is evaporation, P is precipitation, R is runoff, Df is drainage and AS is the change in storage of the soil or other defined system (e.g. a complete catchment). All water balance methods are subject to the problem that the accuracy of the determination of E is dependent on the cumulative errors in the four variables on the right-hand side of equation (1). The most accurate estimates of E are obtained if all these terms are independently measured. Such complete information, however, is rarely available, especially in semiarid areas.

The water balance of complete catchments have been extensively used for some time for the indirect estimation of evaporation over large, often heterogeneous areas (e.g. see Rodda, 1985). In the Sudano-Sahelian zone this is particularly difficult because the precipitation input to a large area is difficult to measure accurately due to the high spatial variability in rainfall. Infiltration and runoff are also very variable in space and it is often difficult to accurately gauge ephemeral streams.

An improvement in accuracy and time resolution can be achieved by using another water balance technique, i.e. lysimeters. Lysimeters are

133 The measurement and modelling of evaporation

essentially artificially constructed "mini-catchments" where a block of soil and its vegetation are isolated from the surrounding soil. Details of the design and construction of lysimeters is given by Aboukhaled et al. (1982). Care must be taken to ensure that the vegetation on (and around) the lysimeter is representative and also that the hydraulic and thermal properties of the soil are kept similar to the surrounding soil. Lysimeters have been used to estimate evaporation from crops in the Sudano-Sahelian zone, e.g. by Kassam & Kowal (1975) and Dancette (1980). Owonubi et al. (1991) list a number of lysimeter studies carried out in northern Nigeria.

Evaporation can also be estimated indirectly by measuring changes in the water content of the soil. Near-surface changes in soil water content are usually measured by gravimetric sampling, but deeper in the soil (i.e. below about 15 cm) a neutron probe is frequently used (Bell, 1969, 1987). The resolution of this technique limits the time scale of the evaporation estimates to periods of over a week. The method has most use during periods when there is little or no rainfall, when the terms P and R in equation (1) are zero. In some circumstances drainage is also insignificant, but even when it is not, the simultaneous measurement of soil water potential profiles with tensiometers (Wellings & Bell, 1982) can provide sufficient information to separate evaporation and drainage. The soil moisture balance method is prob­ably the most widely used technique in water balance studies in the Sudano-Sahelian zone (e.g. Agnew, 1982; Azam-Ali et al, 1984; ICRISAT, 1987; Stroosnijder & Koné, 1982; Vachaud & Vauclin, 1991; Payne et al, 1991).

Plant physiological techniques may be used to measure the transpiration component of evaporation. Most progress in this area has been made since the introduction of porometers. These devices are attached to intact plant leaves and measure the conductance of the epidermis to water vapour. Parkinson (1985) has provided a recent review of the types of porometers available. Most of the work with porometers is directed at studying the behaviour of stomata at the individual leaf level. However, a few studies have shown how porometry can be used to measure transpiration from complete vegetation canopies in both temperate (e.g. Roberts et al, 1980; Waring et al, 1980) and semiarid climates (Azam-Ali, 1983; Wallace et al, 1990). Figure 1 shows an example of the diurnal stomatal response of millet leaves obtained using a diffusion porometer. The conductances vary with leaf age and position in the canopy, but they can be combined with leaf area measurements to calculate total transpiration (see Fig. 2). Although this technique gives very detailed information on the physiological response of the plants, being manual, it is very time consuming and, in practice, cannot be used to measure transpiration continuously for long periods. Computation of transpiration over an entire season therefore requires some detailed modelling of the stomatal behaviour in response to atmospheric and soil conditions (e.g. see Jarvis, 1976).

The use of tracers in measuring transpiration is another technique which has been shown to give very good results (Waring & Roberts, 1979). For example, Waring et al (1980) used a radioactive isotope injected into individual trees as the method to compare with porometry. In the semiarid region of southern India, Calder et al. (1986) have used deuterium oxide as a

/. 5. Wallace 134

o O "to « E o 55

12

10

6 -

400

300

200

100

Leaf

5

6

7

8

9

10

12

Hours (GMT)

15

Fig. 1 Diurnal variation in the stomatal conductance of the leaves in a millet crop before anthesis on 9 July 1986, ICRISAT Sahelian Center, Sadoré, Niger. Leaves are numbered from the bottom to the top of the canopy. (From Wallace et al, 1990)

tracer to measure transpiration in eucalyptus. The isotope was injected into the tree stem and the concentration of deuterium in the transpiration measured by putting plastic bags over samples of the leaves on the canopy. The transpiration over a number of days was then calculated from the shape of the deuterium concentration pulse.

Another form of "tracer" used to measure transpiration is heat: a technique commonly referred to as the heat pulse method. Heat is applied for a short time (a few seconds) at a fixed level on the plant stem and the velocity of the transpiration stream calculated from the time required for the heat to travel a short distance from the point of application. Early work with this method encountered problems with calibration and injury corrections (due to the insertion of the heat pulse probe), but recent developments of this technique appear to have overcome many of these problems (Cohen et al., 1981; Edwards & Warwick, 1984). A further development of the heat pulse technique is the stem heat balance method (Sakuratani, 1981; Baker & van Bavel, 1987). Here the heat is applied using a small electric heating foil wrapped around the plant stem, thereby overcoming the problems encountered above due to insertion of the heat probe. This method also has the advantage of giving a direct measure of the volume flow rate without the need for individual calibration, but is not suitable for large diameter stems (>5-10 cm). All the above tracer techniques are well suited for studying transpiration from

135 The measurement and modelling of evaporation

0.5

0.4

E 0.3 E

0.1 •

LAI=1.3 • LAI=0.26 • LAI=0.23

12 15

Hours (GMT)

Fig. 2 Transpiration rates from millet at the beginning (2 July ••••), middle (18 July ) and end (27 August ) of the 1986 season; ICRISAT Sahelian Center, Sadoré, Niger. The leaf area index, LAI, on each day is also shown. (From Wallace et al., 1990)

semiarid vegetation (e.g. see Valancogne & Granier, 1991) and the first pioneering studies in the Sahel have shown encouraging results (Allen & Grime, personal communication 1990; Brenner et al., 1991). Figure 3 shows some transpiration data from Guiera senegalensis, a common savannah shrub,

500

~ 400 -

3 300

Ï o *• 200

0 -12 24 12 24

Hours (GMT)

12 24

Fig. 3 Diurnal changes in sap flow in Guiera senegalensis measured on 5, 6 and 7 June 1990 using the stem heat balance technique; ICRISAT Sahelian Center, Sadoré, Niger. (From Allen & Grime, personal communication, 1990)

/. S. Wallace 136

obtained by Allen & Grime using the stem heat balance technique at the ICRISAT Sahelian Center, Niger. This technique gives high time resolution data which shows how transpiration responds to the varying radiation load on the canopy.

0.6

0.4

(a)

ate

(mm

DC

ion

2 *

0.2

0 mv.

:j:|:i

*;;

rr^

l 8:

•i-ij v . ;

."•X :•:•:•

;.;.; •è-i

5 9 12 15 1 H ours (G MT )

0.2-

(b)

rm p'n 9 12

Hours (GMT) 15

Fig. 4 Microfysimeter measurements of the diurnal variation in evaporation from the soil (Es ) in a millet crop on two days with (a) wet soil, 19 September 1985 and (b) dry soil, 24 September 1985; ICRISAT Sahelian Center, Sadoré, Niger.

When transpiration is measured separately it is also necessary to measure direct evaporation of water from the soil if the total water use of the vegetation is required. Soil evaporation has been measured directly using small "micro" lysimeters placed between the plants (Boast & Robertson, 1982) and the technique has been applied in semiarid crops by Wallace et al. (1988) and Allen (1990). Great care must be taken to ensure that the soil in these micro lysimeters is in a representative condition, both in terms of maintaining the soil structure and water content. As far as possible undisturbed soil cores should be used and new samples taken every few days, since their water content becomes significantly different from that in the field soil after this time. Figure 4 shows soil evaporation data obtained using micro lysimeters within a millet crop in Niger. On any day the soil evaporation can either dominate the crop water balance (Fig. 4(a)) or become insignificant (Fig. 4(b)), depending on the soil surface wetness. For this

137 The measurement and modelling of evaporation

Crop season rainfall (mm)

Fig. 5 Cumulative seasonal evaporation from the soil in millet crops as a function of seasonal rainfall: (m) data from Bley et al. (1991), (M) Wallace et al. (1988), and (A) Fechter et al. (1991). The dashed lines show Es as a percentage of rainfall.

reason it is imperative that soil evaporation is explicitly recognized when attempting to model sparse crop evaporation (see later). Over an entire rainy season direct evaporation from the soil in millet can be between 35 and 45% of rainfall (Fig. 5); the higher proportions occurring in the lower rainfall (Wallace et al, 1988; Bley et al, 1991; Fechter et al, 1991).

Other methods which have been used to measure soil evaporation include the use of a steady-state porometer adapted for use in soil (Nobel & Geller, 1987), a miniature micrometeorological (Bowen-ratio) system which measures temperature and humidity gradients very close to the soil surface (Ashktorab et al, 1989), soil isotope profile techniques (Taupin et al, 1991) and remote sensing (Chanzy & Bruckler, 1991).

The final set of techniques to be covered in this section are those where the rate of flow of water vapour into the atmosphere is either directly or indirectly measured. A complete description of the theory and assumptions behind these micrometeorological techniques is outside the scope of this paper; however, the reader is referred to Brutsaert (1982) as a detailed account. To use these methods it is necessary to have an area of flat, horizontal land where the vegetation has uniform properties for a distance of some hundred times the height of measurement above the crop.

There are two main types of micrometeorological techniques, the diffusion approach where fluxes of water vapour, heat and momentum are assumed to be proportional to their respective gradients of humidity, temperature and wind speed and the eddy correlation approach where the same fluxes are derived from fluctuations in water vapour content, temperature and wind speed.

/. 5. Wallace 138

The diffusion approach provides two related techniques known as the aerodynamic and Bowen-ratio methods. In the aerodynamic method sensible heat fluxes are calculated from vertical gradients in temperature and wind speed. Evaporation rates can then be calculated if the other terms in the energy balance (net radiation and soil heat flux) are known. However, if humidity gradients are also measured it can be more useful to use the Bowen-ratio method. In this method the ratio of the sensible to latent heat fluxes, or Bowen ratio (0) is calculated from the ratio of the vertical gradients of temperature and humidity. Once 0 has been determined the evaporation rate can again be derived from the surface energy balance.

The aerodynamic method has been used over a number of Sahelian vegetation types by Imbernon et al. (1989) and Sogaard et al. (1989). The technique appears to work over comparatively short dense fallow vegetation, however, there are some problems in its application over tall sparse crops such as millet. These are associated with the heterogeneity of the canopy, the location of the sources of heat and water vapour and the definition of the transfer coefficients.

The eddy correlation technique avoids many of the problems associated with the above diffusion methods. In this method fluctuations in vertical wind

Horizontal Windspeed Sensor

Ultrasonic Vertical Windspeed Sensor

-Thermocouple Thermometer

Infra-red Hygrometer

Fig. 6 The Mark 2 Hydra sensor head comprising the vertical wina speed sensors, the infra-red hygrometer detector (top) and chopped light source (bottom), the thermocouple temperature probe and, vertically above the rear frame support, the fast response cup anemometer. (From Shuttleworth et al, 1988)

139 The measurement and modelling of evaporation

speed and concurrent changes in humidity are measured in the air above the vegetation. Evaporation occurs when the air moving away from the surface has, on average, a higher humidity than the air moving towards it. As much of the flux transfer occurs during very rapid air movements, the method requires wind speed and humidity sensors capable of measuring these rapid fluctuations. Figure 6 shows an eddy correlation system recently developed by Shuttleworth et al. (1988). This system has been successfully tested in the hot semiarid conditions in Niger (Fig. 7) where hourly values of evaporation and sensible heat flux obtained using two completely independent eddy correlation systems agreed to better than ±10%.

(a ) 17 July 1986

18 24

Hours (GMT)

(b) 25 July 1986

18 24

Hours (GMT)

Fig. 7 Fluxes of latent and sensible heat from a millet crop measured with two Mark 2 Hydras on (a) 17 July 1986 and (b) 25 July 1986, ICRISAT Sahelian Center, Sadoré, Niger. The instruments, numbered 202 and 203, were at a height of 4.5 m and ~J m apart. (From Shuttleworth et al, 1988)

EVAPORATION MODELLING

Most models of evaporation are atmospherically driven. That is to say that some atmospheric variables are used to calculate evaporation, generally at some "standard" rate which is a measure of the atmospheric "demand" in the

/. S. Wallace 140

absence of any control or limitation from the surface. The profusion of these standard rates and their associated formulae is confusing. However, Shuttleworth (1990) has recently reviewed the subject and Table 1 is repro­duced with minor modifications from his paper. Potential evaporation refers to Penman's (1948) definition of the quantity of water evaporated from an extensive free water surface and reference crop evaporation follows Doorenbos & Pruitt's (1977) definition as the rate of evaporation from an extensive sward of short green grass adequately supplied with water. Table 1 shows a number of models and formulae which range from simple, highly empirical methods for estimating potential or reference crop evaporation to the very complex physically-based methods used to calculate actual evapora­tion. Care should be taken in the use of some of the more simple methods (e.g. Priestley-Taylor, 1972), which may work well in temperate and humid tropical zones but fail to work in drier, semiarid regions (Gunston & Batchelor, 1983). In general, the physically-based methods are more accurate, but they require a greater data input, so in practice their current use is limited and often restricted to research applications only.

Actual evaporation from crops is commonly estimated using reference crop evaporation and crop factors (Doorenbos & Pruitt, 1977). Reference crop evaporation applies to the condition where the crop is fully supplied with water. This potential rate is then multiplied by an empirical "crop factor" which attempts to account for the different development stages of the crop (Fig. 8). For millet growing in southern Niger, there is a wide discrepancy between the crop factors recommended by Doorenbos & Pruitt and values observed in the field (e.g. Agnew, 1982 - see Fig. 8). Furthermore, Agnew (1991) has reported that observed crop coefficients are much more erratic than the smooth curve shown in Fig. 8. These crop factors are clearly not the universal constants that they are often assumed to be, but are in fact a complex mixture of surface and aerodynamic properties of the crop and also the climate within which they are derived (Shuttleworth, 1990).

Although the Doorenbos & Pruitt method appears to work reasonably well for the calculation of water requirements for irrigated crops, the application of such a simple method becomes more hazardous when the vegetation experiences water stress, when the rate of evaporation can be completely modified by the restricted supply of water from the soil. In practice, evaporation from the vegetation growing in dry soil is often simulated using further empirical factors. The Penman "root constant" approach operates by reducing the evaporation to a fraction of its potential rate if the soil moisture deficit exceeds a threshold value (Penman, 1949; Calder et ai, 1983). An alternative approach is the modification of the crop coefficient (Shuttleworth, 1990). The need for these further levels of empiricism is a clear indication of the limitations of the fundamental approach of beginning with "potential" evaporation and trying to "correct" it to obtain actual evaporation.

Progress in modelling evaporation in sparse vegetation is better where there is an explicit recognition of the role of both the vegetation and the exposed soil in determining the rate of water loss. Successful transpiration modelling has been achieved via the use of a "big leaf model of the canopy

141 T

he measurem

ent and modelling of evaporation

Ï sf a

•s

I

£

I i «

i «

s

lit!

««

It. I a

•ô

! I } a

I a

3 1 i ^

/. S. Wallace 142

-

(i

/

/

/

id

/ / / / / / / / / /

/ i / i / / / i

/ ! - * • 9~

(n i )

\ \ \ \ \ \ \ \ ^ \ \ \ \ \

\ !

"" A Days after sowing

Fig. 8 Changes in crop coefficient for millet during (i) initial stage, (ii) crop development, (Hi) mid-season and (iv) late-season, derived from data given by Doorenbos & Pruitt (1977) ( ) and Agnew (1982) ( ).

(Fig. 9(a)), where the Penman-Monteith (Monteith, 1965) formula applies. To conform with the notation used in Fig. 9(a), this equation can be written as

LA + pc D/(r X£„

+ ' l )

A + y [ l + r*M + K ;>] (2)

where Ec is the canopy transpiration, D is the vapour pressure deficit above the crop, A is the rate of change of saturated vapour pressure with temperature, p is the density of air, c the specific heat of air at constant pressure and y the psychrometric constant and X is the latent heat of vaporization of water. The bulk stomatal resistance of the entire canopy is represented by r£ and the aerodynamic transfer resistance of the crop has two components associated with the leaf boundary layer (rp, and the air between the mean canopy source position and the screen height (rp. However, equation (2) was developed for use in the special case of dense, closed vegetation canopies which absorb most of the available energy and where the soil evaporation is negligible. In semiarid areas vegetation canopies are generally much more sparse than this and rarely give complete ground cover. Under these conditions the evaporation from the soil can be as important as the canopy transpiration (e.g. see Fig. 4(a)). Ritchie (1972) proposed a model which accounted for the contribution of the soil in partial canopies. Immediately after rain, soil evaporation, Es, is determined by the net radiation at the soil surface. Following this Es becomes increasingly limited by the abili-

143 The measurement and modelling of evaporation

(a)

\E,

Screen Height XE

Mean Canopy Source Position

(b) Screen Height

- Mean Canopy të, Source Position

Soil Surface

Fig. 9 The resistance network which represents the vegetation atmosphere sensible heat (H) and latent heat (\E) interactions as (a) a single source in the canopy - the "big leaf" model and (b) with an interactive soil substrate.

ty of water to diffuse through the drying soil surface. In this second phase Ritchie found that the cumulative soil evaporation was related to time t as:

IE, e t f (3)

where a is a soil specific constant. However, in this approach there is no mechanism to allow for interactions between the fluxes from the soil and the canopy. In order to do this the "big leaf concept was extended to sparse canopies by Shuttleworth & Wallace (1985) to include an interactive soil substrate (Fig. 9(b)) which has a surface resistance (r|) associated with surface layer and an aerodynamic resistance (r̂ ) between the soil surface and the canopy. In this model the total evaporation rate (\EC + \EC) is given by:

\E CCPMC + C/M, (3)

where PMQ and PMS are terms each similar to the Penman-Monteith combination equations which would apply to evaporation from a closed canopy and from bare soil, respectively. The coefficients C and C are

7. 5. Wallace 144

functions of the aerodynamic and bulk stomatal resistances associated with the crop and soil.

The Shuttleworth & Wallace (1985) model has been shown to give an improved measure of transpiration from a sparse dryland millet crop in Niger (Wallace et al., 1990) and is beginning to be adopted in other studies of partial canopies (e.g. Lafleur & Rouse, 1990; Smith et al., 1988). The model has also been refined to include more realistic descriptions of heat flow in the soil (Choudhury & Monteith, 1988) and within canopy aerodynamic transfer (Shuttleworth & Gurney, 1990).

Although the Shuttleworth-Wallace model may provide an improved description of sparse canopy transpiration, it has the disadvantage that it requires a knowledge of soil surface resistance (or soil evaporation). The concept of a soil resistance is based on the idea that evaporation occurs from wet soil below a progressively deepening dry layer (Monteith, 1981). Choudhury & Monteith (1988) have shown that this concept leads to the prediction that cumulative soil evaporation will be proportional to the square root of time, in agreement with equation (3) and many other studies of the water loss from drying soils. In inundated crops, such as paddy rice, the substrate surface resistance can be set to zero. For crops growing in drier soil the substrate resistance can be defined as a function of soil surface moisture content and Fig. 10 shows some examples of this reported by Shu Fen Sun (1982), Katerji & Perrier (1985), Wallace et al. (1986) and Camillo & Gurney (1986). The different shape and position of the functions is due to differences in the soil types studied and the different depths of layers used

800

E <£. 600 a> o c

S t/j 'w CD I 400 o CO

•c w S 200

0 0 0.05 0.'1 0!15 0̂ 2

Soil Surface Moisture Content (m3 m'3)

Fig. 10 A comparison of soil surface resistance models reported by Shu Fen Sun (1982) ( ) , Katerji & Perrier (1985) ( ), Camillo & Gurney (1986) ( ; and Wallace et al. (1986) ( ) •

145 The measurement and modelling of evaporation

for surface moisture content. With the ability to detect surface moisture conditions using remote sensing, the soil resistance approach may provide a means of estimating soil evaporation over large areas (e.g. see Chanzy & Bruckler, 1991).

The final class of models illustrated in Table 1 is the simulation type. These models are the most likely to estimate actual evaporation accurately since they simulate as far as possible the physical and physiological processes which actually occur in the soil-plant-atmosphere system. Again these models began their development in the temperate zone (e.g. the SWATR model, Feddes et al., 1978) but have more recently been adapted for use in sparse crops (e.g. ENWATBAL, Lascano et al, 1987). Further details of these models and their application in semiarid zone water balance studies is given by Bley et al. (1991), Fechter et al. (1991) & Lascano (1991).

CONCXUDING REMARKS

Although evaporation is generally more difficult to both measure and model in semiarid regions, much progress has been made recently in both of these fields. Direct measurement of actual evaporation from semiarid land is now possible using micrometeorological techniques and components of evaporation from the plants and soil can also be measured using plant physiological and lysimeter methods. Models which can cope with the more complex nature of sparse vegetation have been developed and are already beginning to be adopted within simulation models specifically designed to estimate the water balance of semiarid land. Further use of the available measurement techniques is now needed in semiarid regions to collect the data required to validate, and update where necessary, the various simulation models. For practical applications and routine operational systems there is a need to develop simpler simulation models which require much less data but retain as far as is possible the accuracy of their more complex relatives. The future promises to be an exciting time for evaporation research in the Sudano-Sahelian zone. Many of the tools and conceptual frameworks are ready, we now need to get on with the hard work of using them.

REFERENCES

Aboukhaled, A., Alfaro, A. & Smith, M. (1982) Lysimeters. FAO Irrigation and Drainage Paper 39. FAO, Rome.

Agnew, C. T. (1982) Water availability and the development of rainfed agriculture in south-west Africa. Trans. Inst. Br. Geogr. N.S. 7, 419-457.

Agnew, C. (1991) Evaluation of a soil water balance model for the analysis of agricultural drought in the Sahel. In: Soil Water Balance in the Soudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 583-592. IAHS Publ. no. 199.

Allen, S. J. (1990) Measurement of evaporation from soil under sparse barley crops in northern Syria. Agric. For. Met. 49, 291-309.

Ashktorab, H„ Pruitt, W. O., Paw U, K. T. & George, W. V. (1989) Energy balance deter­mination close to the soil surface using a micro-Bowen ratio system. Agric. For. Met.

/. 5. Wallace 146

46, 259-274. Azam-Ali, S. N. (1983) Seasonal estimates of transpiration from a millet crop using a

porometer. Agric. Met. 30, 13-24. Azam-Ali, S. K, Gregory, P. J. & Monteith, J. L. (1984) Effects of planting density on water

use and productivity of pearl millet (Pennisetum typhoïdes) grown on stored water. II. Water use, light interception and dry matter production. Expl. Agric. 20, 215-224.

Baker, J. M. & van Bavel, C. H. M. (1987) Measurement of mass flow of water in the stems of herbaceous plants. Plant, Cell and Environ. 10, 777-782.

Bell, J. P. (1969) A new design principle for neutron soil moisture gauges: the 'Wallingford' neutron probe. Soil Sci. 108, 160-164.

Bell, J. P. (1987) Neutron probe practise. Institute of Hydrology Report no. 19, Wallingford, Oxfordshire, UK.

Bley, J., van der Ploeg, R. R., Sivakumar, M. V. K. & Allison, B. E. (1991) A risk-probability map for millet production in southwest Niger. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 571-581. IAHS Publ. no. 199.

Boast, C. W. & Robertson, T. M. (1982) A "Micro-Lysimeter" method for determining evaporation from bare soil: Description and laboratory evaluation. Soil Sci. Soc. Am. J. 46, 689-696.

Brenner, A. J., van den Beldt, R. J. & Jarvis, P. J. (1991) Transpiration from a neem windbreak in the Sahel. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 375-385. IAHS Publ. no. 199.

Brutsaert, W. M. (1982) Evaporation into the Atmosphere. D. Reidel, Dordrecht. Calder, I. R., Harding, R. J. & Rosier, P. T. W. (1983) An objective assessment of

soil-moisture deficit models. /. Hydrol 60, 329-355. Calder, I. R , Narayanswamy, M. N., Srinivasalu, N. V., Darling, W. G. & Lardner, A. J.

(1986) Investigation into the use of deuterium as a tracer for measuring transpiration from eucalypts. / Hydrol. 84, 345-351.

Camillo, P. J. & Gurney, R. J. (1986) A resistance parameter for bare-soil evaporation models. Soil Sci. 141, 95-105.

Chanzy, A. & Bruckler, L. (1991) Estimation de l'évaporation à partir d'informations accessibles par télédétection microonde: approches mechaniste, semi-empirique et empirique. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 149-158. IAHS Publ. no. 199.

Charney, J. G. (1975) Dynamics of deserts and drought in the Sahel. Quart. J. Roy. Met. Soc. 101, 193-202.

Choudhury, B. J. & Monteith, J. L. (1988) A four-layer model for the heat budget of homogeneous land surfaces. Quart. J. Roy. Met. Soc. 114, 373-398.

Cohen, Y., Fuchs, M. & Green, G. C. (1981) Improvement of the heat pulse method for determining sap flow in trees. Plant Cell and Environ. 4, 391-397.

Cunnington, W. M. & Rowntree, P. R. (1986) Simulations of the Saharan atmosphere-dependence on moisture and albedo. Quart. J. Roy. Met. Soc. 112,971-999.

Dancette. C. (1980) Water requirements and adaptations to the rainy season of millet in Senegal. In: Proceedings of the International Workshop on the Agroclimatological Research Needs of the Semi-Arid Tropics (Hyderabad, India, November 1978), 106-120. ICRISAT, Patancheru, India.

Doorenbos, J. & Pruitt, W. O. (1977) Crop Water Requirements FAO Irrigation and Drainage Paper 24, FAO, Rome.

Edwards, W. R. N. & Warwick, N. W. M. (1984) Transpiration from a kiwifruit vine as estimated by the heat pulse technique and the Penman-Monteith equation. N. Z. J. Agric. Res. 27, 537-543.

Fecter, J., Allison, B. E., Sivakumar, M. V. K., van der Ploeg, R. R. & Bley, J. (1991) An evalua­tion of the SWATRER and CERES-Millet models for southwest Niger. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 505-513. IAHS Publ. no. 199.

Feddes, R. A., Kowalik, P. J. & Zaradny, H. (1978) Simulation of Field Water Use and Crop Yield. PUDOC, Wageningen, The Netherlands.

Gunston, H. & Batchelor, C. H. (1983) A comparison of the Priestley-Taylor and Penman methods for estimating reference crop évapotranspiration in tropical countries. Agric. Wat. Manage. 6, 65-77.

ICRISAT (International Crops Research Institute for the Semi-Arid Tropics) (1987) ICRISAT West African Programs Annual Report 1986. ICRISAT Sahelian Center, Niamey, Niger.

Imbernon, J., Lagouarde, J. P., Kerr, Y. & Begue, A. (1989) Suivi agroclimatique des cultures en zone Sahélienne à partir des données de Mas Palomas. Rapport 2 ème

147 The measurement and modelling of evaporation

phase Document provisoire. "Caractérisation par les techniques de la télédétection de la dynamique de la désertification à la périphérie sud du Sahara".

Jarvis, P. G. (1976) The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Phil. Trans. Roy. Soc. Land. B273, 593-610.

Kassam, A. H. & Kowal, J. M. (1975) Water use, energy balance and growth of Gero millet at Samaru, northern Nigeria. Agric. Met. 15, 333-342.

Katerji, N. & Perrier, A. (1985) Determination of canopy resistance to water vapour and its various components: theoretical approach and experimental verification. Agric. For. Met. 34,105-120.

Lafleur, P. M. & Rouse, W. R. (1990) Application of an energy combination model for evaporation from sparse canopies. Agric. For. Met. 49,135-153.

Lascano, R. J., van Bavel, C. H. M., Hatfield, J. L. & Upchurch, D. R. (1987) Energy and water balance of a sparse crop: simulated and measured soil and crop evaporation. Soil Sci. Soc. Am. J. 51, 1113-1121.

Lascano, R. J. (1991) Review of models for predicting soil water balance. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 443-458. IAHS Publ. no. 199.

Monteith, J. L. (1965) Evaporation and environment. In: State and Movement of Water in Living Organisms (19th Symposium of the Society for Experimental Biology), 205-234. Cambridge University Press, UK.

Monteith, J. L. (1981) Evaporation and surface temperature. Quart. J. Roy. Met. Soc. 107, 1-27. Nobel, P. S. & Geller, G. N. (1987) Temperature modelling of wet and dry desert soils.

/. Ecol. 75, 247-258. Owunubi, J. J., Abdulmumin, S., Malgwi, W. B. & Muazu, S. (1991) Review of soil water

balance studies in the Sudano-Sahelian zone of Nigeria. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 329-338. IAHS Publ. no. 199.

Parkinson, K. J. (1985) Porometry. In: Instrumentation for Environmental Physiology (ed. by B. Marshall & F. I. Woodward), 171-191. Cambridge University Press, Cambridge.

Payne, W. A., Lascano, R. J. & Wendt, C. W. (1991) Annual soil water balance of cropped and fallowed millet fields of Niger. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 401-411. IAHS Publ. no. 199.

Penman, H. L. (1948) Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. A193, 120-145.

Penman, H. L. (1949) The dependence of transpiration on weather and soil conditions. /. Soil. Sci. 1, 74-89.

Priestley, C. H. B. & Taylor, R. J. (1972) On the assessment of surfaceheat flux and evapora­tion using large scale porometers. Mon. Weath. Rev. 106, 81-92.

Ritchie, J. T. (1972) Model for predicting evaporation from a row crop with incomplete cover. Wat. Resour. Res. 8,1204-1213.

Roberts, J. M., Pymar, C. F., Wallace, J. S. & Pitman, R. M. (1980) Seasonal changes in leaf area, stomatal and canopy conductances and transpiration from bracken below a forest canopy. J. Appl. Ecol. 17, 490-422.

Rodda, J. C. (1985) Facets of Hydrology II. John Wiley, Chichester. Sakuratani, T. (1981) A heat balance method for measuring water flux in the stem of intact

plants. /. Agric. Met. 37, 9-17. Shu Fen Sun (1982) Moisture and heat transport in a soil layer forced by atmospheric

conditions. MSc Thesis, University of Connecticut. Shuttleworth, W. J. (1990) Evaporation and évapotranspiration. In: Handbook of Hydrology

(ed. by D. R. Maidment). McGraw-Hill, New York. Shuttleworth, W. J. & Gurney, R. J. (1990) The theoretical relationship between foliage

temperature and canopy resistance in sparse crops. Quart. J. Roy. Met. Soc. 116, 497-519. Shuttleworth, W. J., Gash, J. H. C, Lloyd, C. R„ McNeil, D. D„ Moore, C. J. & Wallace, J. S.

(1988) An integrated micrometeorological system for evaporation measurement. Agric. For. Met. 43,295-317.

Shuttleworth, W. J. & Wallace, J. S. (1985) Evaporation from sparse crops - an energy combination theory. Quart J. Roy. Met. Soc. Ill, 839-855.

Sivakumar, M. V. K. & Wallace, J. S. (1991) Soil water balance in the Sudano-Sahelian zone: need, relevance and objectives of the workshop. In: Soil Water Balance in the Soudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (ed. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 3-10. IAHS Publ. no. 199.

Smith, R. C. G. & Barrs, H. D. (1988) Inferring stomatal resistance of sparse crops from infrared measurements of foliage temperature. Agric. For. Met. 42,183-198.

Sogaard, H., Rasmussen, K., Rasmussen, M. S. & Holm, J. (1989) Micro-computer oriented methodologies for deriving agrometeorological parameters and vegetation indicators

/. 5. Wallace 148

from satellite data. Deuxième rapport semestriel. "Caractérisation par les techniques de la télédétection de la dynamique de la désertification à la périphérie sud du Sahara".

Stroosnijder, L. & Koné, D. (1982) Le bilan d'eau du sol. In: La Productivité des Pâturages Sahéliens. Une Etude des Sols, des Végétations et de l'Exploitation de cette Ressource Naturelle (éd. by F. W. T. Penning de Vries & M. A. Djitèye), 133-192. PUDOC, Wageningen, The Netherlands.

Taupin, J. D., Dever, L., Fontes, J. Ch., Guéro, Y., Ousmane, B. & Vachier, P. (1991) Evaluation de Pévaporation à travers les sols par modélisation des profils isotopiques sous climat sahélian: la vallée du Niger. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (éd. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 159-172. IAHS Publ. no. 199.

Valancogne, C. & Granier, A. (1991) Intérêt des méthodes thermiques de mesure du flux de sève pour l'étude du bilan hydrique des savanes. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (éd. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 387-399. IAHS Publ. no. 199.

Vachaud, G., Vauclin, M. & Cissé, L. (1991) Mesure in situ de la consommation en eau de cultures pluviales par humidimétrie neutronique. In: Soil Water Balance in the Sudano-Sahelian Zone (Proc. Niamey Workshop, February 1991) (éd. by M. V. K. Sivakumar, J. S. Wallace, C. Renard & C. Giroux), 275-288. IAHS Publ. no. 199.

Wallace, J. S., Gash, J. H. C, McNeil, D. D. & Sivakumar, M. V. K. (1988) Evaporation from a sparse dryland millet crop in Niger, West Africa. In: Proceedings of the International Conference on Dryland Farming, (ed. by P. W. Unger, T. V. Sneed, W. R. Jordan & R. Jensen), 325-327. Texas Agricultural Experiment Station, Amarillo, Bushland, Texas.

Wallace, J. S., Gash, J. H. C, McNeil, D. D. & Sivakumar, M. V. K. (1985) Measurement and prediction of actual evaporation from sparse dryland crops - scientific report on Phase II of ODA Project 149. ODA Report no. OD149/3.

Wallace, J. S., Roberts, J. M. & Sivakumar, M. V. K. (1990) The estimation of transpiration from sparse dryland millet using stomatal conductance and vegetation area indices. Agric. For. Met. 51, 35-49.

Waring, R. H. & Roberts, J. M. (1979) Estimating water flux through stems of Scots pine with tritiated water and phosphorus-32. J. Exp. Bot.20, 459-471.

Waring, R. H., Whitehead, D. & Jarvis, P. G. (1980) Comparison of an isotropic method and the Penman-Monteith equation for estimating transpiration from Scots pine. Can. J. For. Res. 10, 555-8.

Wellings, S. R. & Bell, J. P. (1982) Physical controls of water movement in the unsaturated zone. Quart. J. Engng Geol. 15, 235-241.

Xue, Y., Liou, K.-N. & Kasahara, A. (1990) Investigation of biogeophysical feedback on the African climate using a two-dimensional model. /. Climate 3, 337-352.