Journal of

Hydrology ELSEVIER

Journal of Hydrology 188-189 (1997) 426-442

Soil evaporation from tiger-bush in south-west Niger J.S. Wallace*, C.J. Holwill Institute of Hydrology, WallingfordOXIO 8BB, UK

Abstract A previous study of evaporation from an area of patterned woodland (tiger-bush) in Niger by Culf et al. (1993) has demonstrated the need to determine the contribution from the bare soil strips which occupy 67% of the surface area. They measured total evaporation from the entire land surface using eddy correlation, but not the individual contributions from the soil and vegetation components. This distinction is necessary to create accurate models of evaporation from the tiger-bush as different processes operate in the two components. The previous study in the same area relied upon untested modelling of the bare soil evaporation as no direct measurements were available. In the present study, carded out during HAPEX-Sahel, hourly fluxes of evaporation from a large patch of bare soil within the tiger-bush were measured using a Bowen ratio system. The data obtained show in detail how soil evaporation varies after rainfall as the surface dried out. Comparison is made on an hourly and daily basis of actual and potential evaporation. A two-phase model based on the Ritchie (1972) approach is calibrated using these data and the model is used to calculate the soil evaporation component of the water balance over a number of seasons with different rainfall. This analysis shows that over the entire tiger-bush area, annual soil evaporation is normally - 2 8 % of annual rainfall, but this percentage increases markedly in dry years. The implications are that in dry years runoff from these bare soil areas will decrease by a greater percentage than rainfall because a greater proportion of rainfall is lost as soil evaporation.

1. Introduction The water balance of arid zones is important for many reasons, including regional water resource assessment, dryland agriculture, and the possible link between the surface energy balance and climate. This latter reason was the main focus of HAPEX-Sahel (Goutorbe et al., 1994), within which this study took place. Between a quarter and one third of the

* Corresponding author. 0022-1694/97/$17.00 © 1997- Elsevier Science B.V. All rights reserved Pll S0022-1694(96)03185-X

J.S. Wallace, CJ. Holwill/Journal of Hydrology 188-189 (1997) 426-442

427

100 x 100 km HAPEX-Sahel study area was occupied by laterite plateaux, on which a type of natural patterned woodland grows (Culf et al., 1993; Wallace et al., 1994). The vegetation on these plateaux often grows in dense strips interspersed with large areas of completely bare soil which forms a distinctive striped pattern which has led to the name "tiger-bush". These areas are thought to have an important influence on the hydrology of this region via their effect on evaporation, runoff and groundwater recharge, yet their water balance is still poorly understood. Total evaporation from tiger-bush is made up of transpiration from the vegetation and evaporation from the soil, each of which has to be measured and modelled separately if they are to be correctly incorporated into climate models of this type of surface (Blyth and Harding, 1995). Culf et al. (1993) presented some measurements of the total evaporation from an area of tiger-bush in Niger and also calculated bare soil evaporation using a model developed for sandy soils in the area. They estimated soil evaporation to be 25% of rainfall, but this needs to be checked using soil evaporation measurements made in the tiger-bush laterite soil, as this is very different from the soils in the surrounding sandy valleys. A commonly used method for measuring evaporation from soils involves the use of micro-lysimeters (e.g. see Daamen et al., 1993). There are, however, difficulties associated with using this technique. The soil in the micro-lysimeters is hydraulically isolated, of limited depth and may wet and dry differently from the surrounding area. The installation of such gauges is also labour intensive and it would be very difficult to obtain the necessary undisturbed soil samples in such an extremely hard, crusted and stony soil as is found in the tiger-bush. In addition, the micro-lysimeter method gives point measurements which need to be extrapolated to a much larger area which may dry out quite variably in space. These disadvantages, together with observations made by Allen (1990) that on days of heavy rain micro-lysimeter data are unreliable, meant that an alternative way of determining the evaporation from the tiger-bush soil was needed. The Bowen ratio energy budget approach has been used to measure soil evaporation by Ashktorab et al. (1989) on a site with a relatively short (36-66 m) fetch. This was achieved by operating the Bowen ratio sensors very close to the soil surface. This method provides a relatively simple and practical way of measuring area-average evaporation from bare soil patches without any disruption to the surrounding soil. This paper presents Bowen ratio measurements of soil evaporation from the tiger-bush at the HAPEX-Sahel Sou~ern Super-Site made during the Intensive Observation Period (lOP) in 1992. The data obtained show in detail how soil evaporation varied after rainfall as the surface dried out. Comparison is made on an hourly and daily basis of actual and potential evaporation. A two-phase model based on the Ritchie (1972) approach is calibrated using these data and the model is used to calculate the soil evaporation component of the water balance over a number of seasons with different rainfall (1983 to 1993).

2. Materials and methods

2.1. Site, vegetation and soil Measurements were made at the Southern Super-Site (Wallace et al., 1994) within an

428

J.S. Wallace,C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442

area of tiger-bush close to the village of Damari, approximately 45 km south o f Niamey, Niger (13 ° 11.89' N, 2 ° 14.37' E). The irregularly shaped area of tiger-bush was about 3 km across, with the vegetation confined to dense bands about 1 0 - 3 0 m wide by 100-300 m long, separated by completely bare crusted soil areas up to 60 m wide. Over the entire tiger-bush site, about 33% of the ground surface area was occupied by the vegetated strips (calculated from aerial photographs). The vegetation is dominated by two species of 2 - 4 - m tall shrubs (Guiera senegalensis L. and Combretum micranthum G. Don) and several tree species (Combretum nigricans Lepr. ex Guill. and Perrott., Acacia ataxacantha DC. and Acacia pennata (L,) Willd.), typically 4 - 8 m tall. The soils on-site mostly consist o f 0.1-0.5 m of gravelly sandy loam or gravelly loam, overlying weathered laterite, with solid laterite starting at 0.2-0.9 m depth. The soil surface is strongly crusted in the bare areas, but well structured and permeable under the bushes. The soils are classified as Xerorthents under the bare areas and as Ustorthents under the bushes (Soil Survey Staff, 1975). Further details of the tiger-bush site are given by Cull et al. (1993) and Wallace et al. (1994).

2.2. Instrumentation Hourly fluxes of evaporation (hEs) and sensible heat (H.0 over bare soil in the tiger-bush were measured using a small modified Bowen ratio system (Campbell Scientific Ltd., Shepshed, UK). This system measured temperature and humidity at two levels (0.05

Fig. 1. A schematicdrawing of the central part of the tiger-bush site showingthe bare soil area (white) and bushes (shaded) around the Bowen ratio equipment (B). Isopleths of the estimated 90% effective fetch calculated using the Schmid and Oke (1990) model under neutral (. . . . . ) and unstable (. . . . . ) conditions are also shown. The positions of the automatic weather station (A) on top of a tower, rain gauge (R) and infra-red thermometers over bare soil (T~ and T2) are also indicated. The tower, R and T2 were within the fenced area shown ( .. ) and the location of the ponding experiment (P) is also shown.

J.S. Wallace, C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442

429

and 0.20 m) above an area of completely bare soil where the fetch in southerly directions was about 50-60 m, Fig. 1. Temperature difference between the two levels was measured using a pair of differential thermocouples. Air samples from the two levels were ducted to a common dew-point hygrometer to measure differences in humidity. The system also had a net radiometer (Model Q*6, Radiation Energy Balance Systems, Seattle, USA) mounted at 25 cm above the soil surface and two flux plates buried at 8 cm depth to measure soil heat fluxes. Each soil heat flux plate had a pair of thermistors buried at 2 and 6 cm depth to allow for the effects of heat storage in the soil above the flux plates to be taken into account. To make these heat storage calculations, the effect of the water content of the surface (0-8 cm) soil on its heat capacity was also taken into account. All the above data were recorded between 28 August and 10 October 1992 as 20-rain averages using a solid state logger (Model 21X - Campbell Scientific Ltd., Shepshed, UK). An estimate of the adequacy of the fetch on this site for a measurement height of 0.2 m was made using the Schmid and Oke (1990) model with the roughness characteristics of a smooth bare soil surface. Any effects of turbulence from the vegetation strips, which are not taken into account in the above model, would tend to shorten the fetch estimates made here. Isopleths of the estimated effective fetch under neutral and unstable conditions are shown in Fig. 1. During the day high soil temperatures produce highly unstable conditions while neutral conditions may occur in the early morning and evening. These calculations indicate that for the prevailing southerly wind directions at least 90% of the measured flux came from the bare soil area immediately around the Bowen ratio equipment. Some evidence to corroborate these fetch estimates came from data obtained several weeks after the last rain. At this time the soil was very dry but the bushes were still green and actively transpiring, yet the Bowen ratio equipment recorded little or no vapour pressure gradient above the soil surface and hence little or no evaporation. Had there been significant contamination of the Bowen ratio fluxes by the bushes this would not have been the case. Rainfall and weather data were recorded - 1 0 0 m from the Bowen ratio equipment using an automatic weather station (Didcot Instrument Company, Abingdon, UK), Fig. 1. Weather data were recorded at 12 m from August 1989 to October 1990 and at 14.5 m from July to October 1992. The rain gauge was operated throughout the IOP in 1992. To model soil evaporation (see later) from 1983 to 1993, rainfall data from the nearby (6 km) ICRISAT Sahelian Center (ISC) were used. To allow aerodynamic transfer resistances to be calculated, soil surface temperature was recorded using infra-red thermometers (Model 4000, Everest Interscience Inc., USA) and air temperature at 0.1 m above the soil surface was recorded using a fine wire thermocouple. Further details of the full range of instruments used at the tiger-bush site are given by Wallace et al. (1994). To obtain further information about the rate of evaporation from the bare soil, a small area was artificially wetted after the last rains of the 1992 season and gravimetric samples of the surface soil taken over the following 7 days as the soil dried. This experiment was carried out at the tiger-bush site in the same bare soil patch where the Bowen ratio equipment was located (see Fig. 1). A 5 m × 5 m area was isolated by surrounding it with a small soil bund. In the afternoon of 6 October 1992, approximately 500 litres of water were poured onto this area, equivalent to a rainfall input of 20 mm. The ponding was completed by 17h00 and the water was left to infiltrate overnight. The following day, five

430

J.S. Wallace,C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442

gravimetric samples from each of the layers 0 - 5 cm and 5 - 1 0 cm were taken at 10h00. This sampling procedure was repeated at 16h00 on the same day and at 14h00 on 7, 8, 9, 11 and 14 October, Samples were weighed before and after drying for at least 24 h in an oven to obtain their volumetric water content.

3. Calculating soil evaporation The most commonly used model to predict direct evaporation of water from bare soil is based on the Ritchie (1972) approach, which considers evaporation to occur in two distinct phases. Initially, evaporation from the soil proceeds at the potential rate Es0 during the 'first phase' immediately following re-wetting of the surface by rain. This lasts for a number of days (tO until the total amount of water evaporated is U, after which the 'second phase' begins where the rate of soil evaporation declines according to the square root of time. This can be expressed mathematically as II

~E~,= ~,E~o=U

(1)

t=0

~, Es2 = c~(V/(V/~-tl )

(2)

where r~Es~ and ~Es2 are the cumulative amounts of soil evaporation in the first and second drying phases respectively, a is assumed constant for any particular soil and is a function of soil diffusivity (Black et al., 1969). First phase evaporation is therefore determined by the potential evaporation rate from bare soil, hEs0, which can be calculated using the Penman-Monteith equation (Monteith, 1965) with a surface resistance of zero, i.e. XE~o= A(Rn s-G~) + p c p D / r a A+7

(3)

where Rns is the net radiation above the bare soil, Gs is the soil heat flux, D is the vapour pressure deficit of the air and ra the aerodynamic resistance to evaporation (see later). A is the rate of change of saturated vapour pressure with temperature, 3' the psychrometric constant, )~ the latent heat of vaporisation of water, p the density of air and Cp the specific heat of air at constant pressure. In his original paper, Ritchie (1972) estimated kEs0 using a formula which neglected any contribution from the aerodynamic term in Eq. (3). This may have been acceptable in the crops dealt with by Ritchie, but we found that for the larger, more open tiger-bush bare soil patches, the aerodynamic term is a significant component of the daily total potential evaporation (i.e. between 15 and 40%). kEs0 can be calculated using Eq. (3) with the values of bare soil net radiation, Rn ~, measured by the Bowen ratio system and vapour pressure deficit, D, and temperature (needed to calculate A) recorded by the automatic weather station at the top of the tower, provided the aerodynamic resistance to bare soil evaporation, ra, is known. Temperature and D were also recorded close to the soil surface, but only during the IOP. Hence calculations of XEs0 outside this period have to be based on values of temperature and D recorded at the top of the tower.

J.S. Wallace, C.J. Holwill/Joarnal of Hydrology 188-189 (1997) 426-442 Reference height

....................

8.0m (2h) . . . . . . . . . . . . . . . . . . . . . . . .

~

~.s~

431

. . . . rl . . . . . . . . . . . . . . . . .

.......................

4.On 2.64 O.ln 0

Fig. 2. A schematic diagram of the aerodynamic resistances to evaporation from the bare soil surface in tigerbush. Conceptually the total aerodynamic resistance to transfer can be split into four components, r~, r~2, ra3, and r a4-

In the absence of the tiger-bush shrubs, the estimation of ra would be relatively simple. However, aerodynamic transfer from the soil in the tiger-bush can be modified by the turbulence caused by the nearby bushes and so the effect of this on r a has to be taken into account. Fig. 2 shows a schematic representation of the transfer resistances associated with evaporation (and heat flux) from the bare soil component of the tiger-bush. Although, in practice, transfer of fluxes from the soil surface to the reference height, zr, is a continuous turbulent process, for the purpose of calculating the total transfer resistance four components can be considered. Firstly, we consider the aerodynamic resistance from the soil surface to a height 0.1 m above it, i.e. ral in Fig. 2. This resistance is identified separately here because it is the largest of all four components and is also one for which we have direct measurements. These measurements were calculated using the flux/gradient relationship rearranged in the following way Ts - Ta ral = pCp

Hs

(4)

Surface temperature, Ts, was taken as the mean of the measurements made using the two infra-red thermometers mounted above the soil surface. Air temperature, Ta, at 0.1 m was measured using a thermocouple and the sensible heat flux, Hs, was calculated from the Bowen ratio measured using the system already described above. Fig. 3 shows the values of ra~ calculated for daylight hours (08h00 to 19hO0) using Eq. (4) plotted as a function of the wind speed at the reference height. Clearly ral is not strongly dependent on the wind speed at the reference height with only a slight tendency to increase at very low wind speeds. These observations are consistent with expectations, since in highly unstable conditions (T~ >> Ta) and with the light winds near the soil surface, transfer becomes

J.S. Wallace, C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442

432

700 600

500

v

.......................................................................

400 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E

• 300

........

200

.....

=

• ...........................................................

i

-'.. ...... II

100

-'.

......

" , , - "

,...,,..;~..

•

...........

• I~ . . . . .

.........

_'. ~

r

.

,

,

. ....

.'.

d

m

: ......................

.. :

" Z'"

"" " ~ ' "

•

*~L ".--i

" " " " "1. . . . . . . . . . . .

wn

0

I 0

,

I

1

2

,

~ 3

,

J 4

,

I 5

,

I 6

7

Wind speed at 14.5m (ms 1) Fig. 3. The a e r o d y n a m i c resistance b e t w e e n the soil surface and 0.1 m ( r . i ) as a function o f w i o d speed at 14.5 m.

dominated by local free convection (Garratt, 1992). The mean value of ral calculated from the data shown in Fig. 3 is 107 s m-'. The second and third components of the total soil evaporation transfer resistance, ra2 and r~3 (see Fig. 2), are taken from the values recommended by McNaughton and Van den Hurk (1995) who examined the problem of aerodynamic transfer in sparse canopies using Lagrangian and diffusion theory. They suggest the following values ra2 = 10/u,

ra3 =

3.6/u,

(5)

where u, is the friction velocity associated with the above canopy wind profile, i.e. uk

(6)

where u is the wind speed at the reference height, zr, and k is yon K~'mgn's constant (0.41). Well above the canopy, the displacement height, d and roughness length, z0, may be approximated as 0.66h and 0.13h, where h is the canopy height. Eq. (6) applies in neutral atmospheric conditions and for the purposes of the current paper no stability corrections are included. Using zr = 14.5 m and h = 4.0 m in Eq. (5) and Eq. (6) gives r,2 = 76.3/u and ra3 = 27.5/u. The fotmh component of the total aerodynamic resistance to soil evaporation is that between 2h and the reference height, zr (Fig. 2). At this distance from the canopy, standard profile theory is also assumed to apply and therefore ra4 is given by

ra4 =

I. Zo J ku,

ln[ ] ku,

(7)

J.S. Wallace, C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442

433

which simplifies to In L~ J ra4 =

(8)

ku.

Eq. (8) can be combined with Eq. (6) to give ran = 14.8/u. The total aerodynamic resistance to evaporation from the soil surface to the reference height can therefore be expressed as ra = 107 + 76.3/u + 27.5/u + 14.8/u = 107 + 119/u

(9)

As expected, most of the resistance to transfer occurs very close to the bare soil surface with progressively less resistance (per unit length) being presented as the flux moves further away from the surface. Eq. (9) gives values of ra which are much lower (e.g. by - 4 0 % when u = 2 m s -m) than those which can be calculated for bare soil without any bushes. The aerodynamic term in Eq. (3), which is dependent on ra, makes a significant contribution to the potential evaporation rate. Around midday the aerodynamic term contribution is smallest, but is still --15% of XE~0. In the early morning and late afternoon, when Rns is small, the aerodynamic term becomes dominant.

4. Results and discussion Fig. 4 shows a comparison of the energy balance of the tiger-bush bare soil on two days with contrasting surface wetness. On the day when the soil had been recently wetted (16 September 1992), there was substantial soil evaporation (hEs) during the morning, 16 S e p t e m b e r 1 9 9 2

7 October 1992 600

600

rl

500

s

Rn s

500

400

400

E

300

E 300

~-

200

u.

200

.5 loo

t~ 100

;;=-- ~

.......

,.~........

-100

-200

I

0

,

,

,

I

4

,

,

,

I

8

,

,

,

i

,

,

12

Hour (GMT)

,

i

16

,

,

,

i

20

B

,

,

-200

~, , , ~ , , 0 4

~ , . , , , ,.,. 8 12 16 Hour (GM-F)

h .... 20

Fig. 4. Energy fluxes over tiger-bush bare soil during two days with wet (16 September 1992) and dry soil (7 October 1992). Evaporation (~.E~), sensible heat flux (H0, net radiation (Rn ~) and soil heat flux (GO are shown.

434

J.S. Wallace, C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442 1

5o

'~ 0.8

40 A

E

e

60.6

3o

~

0.4

2O er '~

0.2

lO

k__J',, t

0

31 Aug

1 Sop

0

2 Sop

Fig. 5. A comparison of hourly rates of measured actual evaporation (hE,) and calculated potential evaporation (hE~o) during three days following thorough wetting of the surface by rain.

however, this declined rapidly during the afternoon, with a consequential increase in the sensible heat flux (H,). Heat fluxes into the soil (G,) became very large (~200 W m -2) around midday, declining very rapidly thereafter and becoming quite large and negative overnight. These large negative overnight values of G~ coincided with similar sized negative values of net radiation (Rn,). The energy balance of the bare soil was very different when the soil surface was dry. For example, on 7 October, when there had been no rain for 24 days, there was very little soil evaporation and the sensible heat flux had increased to - 3 0 0 W m -2 at midday. Soil heat fluxes were still a large component of the energy balance, but were smaller than those measured when the soil was wet. Net radiation was also lower over dry bare soil, presumably because of its higher albedo and surface temperature compared with wet soil (e.g. see Allen et al., 1994). Fig. 5 shows a comparison of hourly rates of measured actual evaporation (hE,) and calculated potential evaporation (hEs0) shortly after the surface was wetted by 36 mm of rain on 30 August 1992. On the following day, actual evaporation followed potential evaporation very closely throughout the day. Over the entire day, actual evaporation was 3.7 mm compared to a potential evaporation of 3.8 ram. On the second day after rain, XE~ rates were close to the potential rate in the morning, but began to depart significantly from kE~0 in the afternoon. By the third day after rain, actual soil evaporation was well below the potential rate for most of the day. These results indicate that on the first day after rain actual evaporation fully meets atmospheric demand, and begins to decline below this rate from the second day onwards. When using a daily time step model, the choice of t t has to be an integral number of days, so the best approximation is to assume 'first phase' evaporation on the day immediately following rain, after which evaporation proceeds at less than the potential rate and is in 'second phase' drying. The variation in daily total soil evaporation (E0 and potential evaporation (E,0) over the period from 30 August to 10 October 1992 is shown in Fig. 6. Some Es data are missing immediately after rain because splashing of the raindrops on the surface caused some ingress of water into the vapour pressure sampling intake tubes of the Bowen ratio equipment. This water took several hours to evaporate after the rain had stopped. However, once this had cleared reliable data were recorded. Fig. 6 shows that actual evaporation increased

J.S. Wallace, C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442

435

7 E tO

>

5

3

>, 2

0 40 E

rr

10

25

30

5

10

August

15

20

25

September

30

5

10

15

October

Fig. 6. Variation in the daily total soil evaporation (E~) and potential evaporation (E~) during the period from 30 August to 10 October 1992. The rainfall over this period is also shown for comparison.

after the surface was re-wetted by rain, e.g. on 31 August and 13 September, reaching rates of between 3 and 4 m m d -I which were close to the potential evaporation rate, E~0. After this time, evaporation declined rapidly to ~0.5 m m d -~ when it had not rained for a week or more. The rapid drying of the soil observed here has also been reported for sandy soil under millet in this environment (Wallace et al., 1992). Fig. 7 shows the cumulative evaporation, measured using the Bowen ratio technique, plotted against the square root of time since the start of second phase drying. This drying phase is taken from E~ measurements made after the last large rainfall event (26 mm) of the 1992 wet season on 12 September. Second-phase drying was taken to start on 14 September, but because of the small rainstorms on 15 September (2.5 mm at ~00h00 and 1.5 m m at 1 lh00) this day is omitted from the EE~ on the assumption that the rainfall "g

12

E_.IO 8 > .-¢ o

6

2

O0

--Y"

1

2

3

4

Fig. 7. A plot of the cumulative evaporation in second-phase drying as a function of the square root of time. The line fitted through zero has the slope 2.11 (0.01, standard error) with r 2 = 0.999,

436

J.S. Wallace, C.J. Holwill/Journal of Hydrology 188-189 (1997) 426-442

and soil evaporation were the same on this day. The data in Fig. 7 fall very closely around a straight line through the origin, with a slope of 2.11 (0.01, standard error) mm day -t. This is the value of the constant ~ in Eq. (2). Very similar values of this constant were found for the sandy soil in nearby millet fields, i.e. o~= 2.15 mm day -~ (Wallace et al., 1986) and o~= 2.1 mm day -l (Bley, 1990). Despite the differences in soil structure on the tiger-bush plateaux and in the sandy valleys, these soils appear to evaporate water at very similar rates during second phase drying. The E~ data from the Bowen ratio equipment allow us to construct a simple soil evaporation model based on the Ritchie (1972) approach (i.e. Eq. (1) and Eq. (2)). To allow the model to be used with rainfall data only, the mean rate of potential soil evaporation,/~.~0, was calculated using hourly automatic weather station data in Eq. (3) for both rain days and the first day after rain for the 14 month period from 22 July 1989 to 1 October 1990. This gave a value of E~0 on rain days as 3.2 (1.1, standard deviation) mm. In our model, half of this value is used for rain days, since it can rain at any time during the day and over a very long time period the 'average' time at which it rains is 12h00. The value of E~0 on the first day after rain for the same period as above was 4.0 (0.4, standard deviation) ram. This value is higher than the equivalent rate for sandy soil (i.e. - 3 mm day -I) reported by Bley (1990). In the present study, first-phase drying was taken to occur up until the end of the first day after rain, so tt in Eq. (1) and Eq. (2) is 1 day and the total amount of water evaporated in phase 1 (U) is 3.2/2 + 4 = 5.6 ram. A similar value of U was found in another sandy soil by Black et al. (1969). To use the above soil evaporation model with rainfall data only, it is necessary to run a simple surface (available) water content (W~) budget to ensure that the model does not continue to evaporate when W~ is zero. This was done by assuming that all rainfall infiltrated the soil surface up until its water content exceeded a maximum value, W l l lsa x • From our observations in the soil ponding experiment we found that the top 10 cm of soil lost 12.5 mm of water in the 7 days following saturation of the soil. The residual available 12 "

t

F~h

~-

10

8

a

~

6

E 0

~

• ptlll~

i

i

/

J

II

2 i i

0-

i i

I

I

I

I

2

4

6

8

10

Time (days)

Fig. 8. A comparison of cumulative measured evaporation (0) and cumulative modelled evaporation ( an artificially wetted area of tiger-bush bare soil.

) from

J.S. Wallace, C.J. H o l w i l l / J o u r n a l o f H y d r o l o g y 1 8 8 - 1 8 9

(1997) 426-442

437

water in this layer was estimated as ~ 2 mm, giving a value for W~ ax of 15 m m (to the nearest mm). The soil evaporation model was found to be fairly insensitive to the value of wl/lax .~ once it is greater than - 1 0 mm. The above soil evaporation model was compared with the observations made in the artificially wetted area after the last rains. To reconcile the daily time step of the model with the timing of soil water content measurements, the start time for the comparison was chosen as 14h00 on 7-10-92 and 'days' were taken to run from 14h00 to 14h00 the next day. The 'day' from 6-10-92 to 7-10-92 includes the ponding exercise which went on until 17h00; so this day was designated the 'rainday'. The 'day' following this is therefore the first day of comparison of the model with observations, shown in Fig. 8. Modelled soil evaporation is only slightly less (--0.4 mm) than the observations, implying that errors in the model or data are small and the assumption that there was no drainage from the soil during the period compared is reasonable. Clearly, agreement between the model and data is very dependent on the value of Es0 during phase 1 drying. The measured value of Es0 during phase 1 may have been affected by advection of energy from the dry soil surrounding the wet 5 x 5m plot. This could have increased evaporation from the plot by about 25% (Brutsaert, 1982), but only on the first day after wetting. Phase 2 evaporation should not be affected by advection since it is controlled by the soil hydraulic properties and not evaporative demand. The good agreement between the model and data gives us some confidence in applying the model with the parameters derived here to other years where rainfall data are available. Fig. 9(a) shows the total annual rainfall (P) and modelled annual evaporation (E0 from the tiger-bush bare soil over the period from 1983 to 1993. Total annual Es is much less variable than annual rainfall. In the 11 years examined here, whereas rainfall ranged from a maximum of 699 mm to a minimum of 260 mm, soil evaporation only varied from 284 mm to 207 mm. In years where rainfall was close to average for the area, i.e. P - 5 0 0 mm, Es was ~ 4 2 % of rainfall. The proportion of rainfall lost as soil evaporation increased E 800 600 40O

0 ,0 0.8 [-

~

.

.

.

.

.

Es11Es

"I

P

0,4

o.o°2

- 83

84

85

86

87

8B

E~ 89

90

91

92

93

Year

Fig. 9. (a) Total annual rainfall (P, solid bar) and soil evaporation (Es, shaded bar) from tiger-bush in south-west Niger over the eleven year period from 1983 to 1993. (b) The ratio of E , I P ( - - ) and the fraction of total evaporation lost in phase 1 ( E s I I E , - - - -) and phase 2 (Es21E,, •....... ).

438

J.S. Wallace, C.J. Holwill/Joumal of Hydrology 188-189 (1997) 426-442

markedly in drier years, e.g. in 1984 where 79% of the low rainfall (260 mm) was evaporated from the bare soil patches. Similar high bare soil evaporation losses have been reported by Mauchamp et al. (1994), i.e. 52% of rainfall, and Cornet et al. (1992), i.e. 60% of rainfall, for tiger-bush like vegetation in the Chihuahan desert in Mexico. The tendency for EJP to increase in dry years is discussed in more detail below. Fig. 9(b) shows the proportions of total soil evaporation lost in phase 1 (E~m)and phase 2 (E~2). Most of the water which evaporates is lost in phase 1, with only 20-30% being lost in second-phase drying. The proportion of total annual Es lost in Phase 1 drying also tends to increase slightly in wet years. This means that it is important to specify accurately the first phase part of the soil evaporation model. In practice, most of our E~ measurements are in second-phase drying, as are soil evaporation data reported by other authors working in this field (e.g. Allen, 1990; Wallace et al., 1986, 1992; Bley et al., 1991; Daamen et al., 1993). Clearly, measurement techniques need to be developed to measure soil evaporation rates during first-phase drying. The micro-meteorological technique used here could be improved in this respect by taking precautions to prevent the ingress of water into the air intakes, e.g. by physically protecting them from splashing from the soil surface and stopping or reversing the air intake pumps during rain. Previous studies of soil evaporation have expressed the loss rates over the total ground area rather than just that occupied by the bare soil (e.g. Culf et al., 1993). To allow comparison with these studies, the average value of soil evaporation for the entire tigerbush area (E0 was estimated using the modelled values of E~ shown in Fig. 9 multiplied by the fraction of the total area occupied by bare soil (0.67). This assumes that Es is insignificant under the vegetation strips, which may be reasonable where the vegetation is dense, but not if it is sparse (Mauchamp et al., 1994). The relationship between the tiger-bush area-average annual soil evaporation (/~) and annual rainfall is shown in Fig. 10. When rainfall is close to its long-term mean ( - 5 0 0 mm), about 28% of it evaporates directly from the soil. Culf et al. (1993) used the first-phase drying rate 300

c 0

,

,

,

200 0

I.

~

~

~

•

•

I

_

-,II~

•

o

100

o