Evaluation of the temporal variability of the evaporative fraction in a tropical watershed

Transcription

1 International Journal of Applied Earth Observation and Geoinformation 5 (24) 29 4 Evaluation of the temporal variability of the evaporative fraction in a tropical watershed H.O. Farah a,, W.G.M. Bastiaanssen b, R.A. Feddes c a Department of Civil and Structural Engineering, Moi University, P.O. Box 39, Eldoret, Kenya b Garstsraat 23, 42 AB Maurik, The Netherlands c Sub-Department of Water Resources, Department of Environmental Sciences, Wageningen Agricultural University, Nieuwe Kanaal, 67 PA Wageningen, The Netherlands Received 4 September 23; accepted 26 January 24 Abstract Evaporation exhibits diurnal variation in response to the changes in the available energy at the land surface. This requires continuous measurements of evaporation to determine daily total evaporation. This is not feasible without sophisticated field equipment, which at the end, only provides field scale evaporation rates. Remote sensing methods are a good alternative but these give snapshot measurements. If the partitioning of available energy into the different surface fluxes can be assumed to be diurnally constant, then instantaneous remotely sensed measurements could be used to derive daily total evaporation. In situ evaporation measurements were obtained for about a year at a grassland and woodland site in the Lake Naivasha basin, Kenya. These measurements were used to test the validity of the diurnal constancy of the partitioning of the available energy, expressed as evaporative fraction, and the extrapolation of evaporation from instantaneous to daily totals. A good relationship between midday and average day evaporative fraction was obtained at the two sites. Estimated daily evaporation from midday evaporative fraction was within % of measured evaporation for both sites. The deviation reduced if evaporation is further integrated in time. The seasonal progression of evaporative fraction is gradual at both sites although grassland evaporative fraction responds faster to changes in rainfall and moisture availability. The results provide a basis for the determination of regional evaporation across a season in tropical watersheds if evaporative fraction is determined instantaneously at intermittent intervals of 5 days. 24 Elsevier B.V. All rights reserved. Keywords: Evaporation; Evaporative fraction; Remote sensing; Lake Naivasha basin. Introduction Evaporation is required on a daily as well as longer time scales for applications in hydrology, agriculture, forestry and environmental studies in general. However in practice, continuous daily evaporation measurements are rarely available. Daily reference or po- Corresponding author. address: highlandeld@africaonline.co.ke (H.O. Farah). tential evaporation can be estimated from mean daily values of available meteorological variables such as temperature, solar radiation, humidity and wind speed (Allen et al., 998). More recently, one or more instantaneous measurements of evaporation have been used to estimate daily total evaporation (Brutsaert and Suigita, 992). There has been a growing interest in this approach because of its attractiveness for remote sensing applications. Remote sensing offers a means of estimating actual evaporation at a large /$ see front matter 24 Elsevier B.V. All rights reserved. doi:.6/j.jag.24..3

2 3 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) 29 4 spatial scale, which is not possible with the traditional point methods. Many techniques have been proposed to solve the surface energy balance from remotely sensed surface temperature, surface reflectance and vegetation indices (Moran and Jackson, 99; Kustas and Norman, 996; Bastiaanssen et al., 999). Remote sensing data are however instantaneous measurements and a method is required to temporally integrate instantaneous estimates of evaporation. Latent heat flux (L) and other components of the energy balance display considerable diurnal variation over land surfaces. However several ratios of the fluxes have been shown to be relatively constant during daylight hours (Jackson et al., 983; Shuttleworth et al., 989; Bastiaanssen et al., 996). The classical energy partitioning indicator is the Bowen ratio ( ), which is a ratio of the sensible heat flux (H) and L. The pitfall of applying β for time integration is that it shows distinct diurnal variation features. More recently the evaporative fraction (Λ) has been found to have little variations during daytime, although it is directly related to β (Crago and Brutsaert, 996). Evaporative fraction is defined as: L Λ = R n G = L L + H = () + β where, R n is the net radiation and G the soil heat flux. Shuttleworth et al. (989), were the first to notice the constancy of Λ during daylight hours. They analyzed 4 clear sky days data from the first ISLSCP field experiment (FIFE) over relatively homogeneous grasslands and found that midday Λ is nearly equal to the average daylight Λ. Nichols and Cuenca (993), used 72 days data from Hydrologic Atmospheric Pilot Experiment-Modelisation du Bilan Hydrique (HAPEX-MOBILHY) experiment and showed that the midday Λ was highly correlated with average daytime Λ but that the midday and daytime Λ are not statistically equal. Crago (996a), evaluated 77 days data from FIFE. He used the data irrespective of weather conditions of a particular day and concluded that midday Λ is significantly different from the average daytime value, the reason being the concave-up shape of the diurnal progression of Λ. The central question is whether an instantaneous value of Λ can be used to estimate daily actual evaporation (E) as: E d = Λ ins (R n G) d (2) where, the subscripts d and ins indicate total daytime and instantaneous values respectively. This way of expressing E is a simple approach to integrate E on a daily basis and across a season, if at least the temporal variations of Λ are known. However, Eq. (2) may not be valid under non-clear sky conditions because the diurnal constancy of Λ may not be satisfied under cloudy conditions (Zhang and Lemeur, 995). For areas with persistent cloud cover, such as in the humid tropics, it is important to test the validity of Eq. (2). In order to assess the performance of the Λ approach, long term data series of measurements are required so that a wide range of different conditions are encountered. Most of the previously published studies have used data from relatively short time periods as reported above. In this study, field data collected over a period of about year in Lake Naivasha basin in Kenya is used to investigate the applicability of the Λ method to estimate E at daily scale and for a season. Continuous daily E measurements at two sites were compared with daily E estimated by using Eq. (2). The objective of this paper is to demonstrate the capability of instantaneous measurements of Λ to estimate the average day Λ and E throughout a season in tropical watersheds with data scarcity problems. Although only field data was used in this study, the results are expected to establish a sound basis for the estimation of E from instantaneous remote sensing data and routine daily weather data. The theoretical background of Λ and reasons for its stable diurnal behavior are discussed in Section 2. The field measurements carried out are detailed in Section 3. In Section 4, the diurnal stability of Λ is discussed. The results of the comparison between instantaneous and average day Λ are presented in Section 5, while the results of estimating time integrated E is presented in Section 6. Finally the seasonal variations of Λ are described in Section Theoretical background 2.. Reasons for the diurnal stability of Λ The diurnal behavior of Λ can be understood from its relationship with atmospheric conditions and surface characteristics. The Penman Monteith equation

3 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) of L combines these conditions and is expressed as: L = (R n G) + ρc p [e (z) e(z)]/r a (3) + γ( + r s /r a ) where, is the slope of the saturation vapor pressure curve, e*(z) and e(z) are the saturation vapor pressure and actual vapor pressure at height z, C p the specific heat of air at constant pressure, ρ the air density, γ the psychrometric constant, r s the surface resistance to water vapor transport and r a is the aerodynamic resistance to vapor transport. Λ can be obtained by dividing both sides of Eq. (3) by R n G giving the following expression: [ Λ= + ρc p(e ] (z) e(z))/r a +γ( + r s /r a ) R n G (4) Eq. (4) shows that Λ is a function of vapor pressure deficit (VPD = e (z) e(z)), r a and r s, besides available energy R n G. The transfer equations for heat and water vapor between the surface of the earth and the atmosphere can also be used to express Λ without the explicit involvement of R n G: H = ρc p(t T a ) r a (5) LE = ρc p(e (T ) e(t a ) (6) γ(r s + r a ) where, T and T a are the surface temperature and air temperature, respectively. By Further expressing Λ as L/(L + H) (see Eq. ()), an alternative expression for Λ becomes: Λ = L L + H = ( + [r s ((e T ) e(t a ))]/ γ(r a + r s )(T T a ) (7) For ideal conditions with no cloud obstructions and no heat or moisture advection, R n G, r s, and VPD follow a regular diurnal cycle. Rowntree (99), showed that Λ is more sensitive to R n G when R n G is small. Fig. a shows Λ as a function of R n G.Itcan be seen that up to a value of 2 Wm 2, Λ decreases rapidly with increasing R n G. Λ then remains almost constant with further increase in R n G. Available Evaporative fraction(-) (a),8,6,4, Rn-G( W m -2 ) Evaporative fraction(-) (b),8,6,4, r s (m s - ) Evaporative fraction(-) (c),8,6,4, To-Ta( o C) Evaporative fraction(-) (d),8,6,4, VPD(hP) Fig.. Evaporative fraction as a function of available energy, R n G, surface resistance, r s, from Eq. (4) and surface and air temperature difference, T T a and vapour pressure deficit, VPD, from Eq. (7), with the following conditions prevailing on 28th October 998 at a grassland site: (a) r s = 3 s m, r a = 7 s m, VPD = 5 mb; (b) R n G = 3 wm 2, r a = 7 s m, VPD = 5 mb; (c) r s = 3 s m, r a = 7 s m, VPD = 5 mb (d) r s = 3 s m, r a = 7 s, T T a = 2 C.

4 32 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) 29 4 energy greater than 2 Wm 2, usually occurs between 9. and 6. h. This means that variations in Λ is largest in the mornings and the evenings when R n G is small (<2 Wm 2 ). Rowntree (99) also demonstrated that variations of Λ due to r s are larger for small values of r s (wet conditions) than for larger r s values (dry conditions). Fig. b illustrates Λ as a function of r s. Λ decreases rapidly when r s increases from 2 s m to approximately 5 s m, but decreases at much smaller rate afterwards. Because R n G often exceeds 2 Wm 2 during midday conditions, Λ can be expected to behave temporally stable especially for moderately wet and to dry surface conditions with r s larger than 5 ms. Eq. (7) introduces (T T a ) as an important variable in the determination of Λ. The diurnal trend of T T a follows closely that of solar radiation reaching the earth surface (K ), T and T a. Crago (996b), illustrated the dependence of Λ on T T a for different surface conditions. He used the formulation of Eq. (7) for Λ to show that Λ is most sensitive to T T a when T T a is small (<2 C). Fig. c shows the variation of Λ with T T a. Λ remains fairly stable for T T a larger than 3 C. Such values of T T a occur in the middle of the day under clear sky conditions. Fig. d presents the relationship between Λ and VPD using Eq. (7). Λ increases with increasing VPD, however Λ increases at lower rate for VPD values larger than mb. Values of VPD larger than mb usually prevail during day light hours Computation of Λ and E In this study Λ is derived from β measurements. β is determined from the difference in vapor pressure and temperature between the two observational levels: β = H L = γ dt de = γ Ta Ta2 e e2 (8) where, the subscripts and 2 indicate the lower and upper levels, respectively. Λ under field conditions is then computed as follows: Λ = (9) + β Daytime E is calculated as E = t2 t Λ(R n G)dt () where the time difference t 2 t, represents the time from 8. to 7. h in the present study. Daytime E can in a simplified manner be estimated from midday Λ (Λ mid ) and morning Λ (Λ mor ) as follows: t2 E = Λ mid (R n G)dt () t For Λ mid and Λ mor measurements conducted between 2. and 3. h and 9. and. h, respectively have been used. The daily net radiation is given by: R n = ( α)k +Ln (2) where, α is the surface reflectance and Ln is the net longwave radiation. K was obtained from direct measurements of solar radiation and Ln was evaluated from T a and Relative Humidity (RH) by using empirical functions (Holtslag and Van Ulden, 983). G is estimated as% of R n during daytime hours (de Bruin and Holtslag, 982) and ignored on a daily basis. 3. Field experiment and study area The study area comprises the Lake Naivasha basin located in central Kenya (Fig. 2). Two sites, namely Ndabibi and Eburu, with different canopy cover and at different altitudes were selected for in situ measurements. The topography of the Ndabibi site varies from slightly undulating to flat terrain and is at an altitude of 9 m. The vegetation consists mainly of annual grasses. The Eburu site is at an altitude of 22 m and being a hilly terrain, is covered by woodland and forest. Maximum T a is approximately 32 C in the months of January and February and the minimum day T a of approximately 6 C occur in July and August. RH (midday) varies from 7% in the July August months to approximately % in the January February months. The average annual rainfall at the grassland site is approximately 7 and 95 mm in the woodland site. There is one main rainy season between March and June, with peaks occurring in April and May. The driest months are January, February and December. Two Bowen ratio towers were erected at the experimental sites. T a and RH were measured at two levels (.3 and 2 m) with temperature and humidity sensors having an accuracy of ±.2 C and % relative humidity. K was measured with a pyranometer with a sensitivity of.5%. Rainfall was measured with a tipping

5 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) km woodland Lake Naivasha Basin Kenya grassland Study area 2 km Nairobi Fig. 2. Location of study area showing the grassland and woodland sites where micrometeorological measurements were carried out. Table Measured meteorological variables which were used to determine evaporative fraction and evaporation Measured variable Height above surface (m) Measurement interval Period grassland Period woodland Air temperature, T a.5, 2 2 min 4th May 98 4th April th September 98 4th April 999 Air relative humidity, RH.5, 2 2 min 4th May 98 4th April th September 98 4th April 999 Shortwave incoming 4 2 min 4th May 98 4th April th September 98 4th April 999 radiation, K Shortwave reflected 2 h (once 4th May 98 4th April th September 98 4th April 999 radiation, K a month) Rainfall.3 2 min 27th September 98 4th April th September 98 4th April 999 bucket rain gauge. These measurements were collected by a data logger and recorded as twenty minute averages. The surface reflectance, α was measured day in each month at h intervals at both sites. Table shows the details of the measurements. Malfunctioning instruments caused a period of 36 days in February and March 999 with missing data for the grassland site. 4. Diurnal stability of Λ The standard deviation of measured Λ (SD ) between 8. and 7. h was calculated and used as an indicator of the diurnal stability of Λ. The mean SD for the grassland site is.7 at an average Λ of.4 yielding a coefficient of variation of.8. SD varies considerably during the study period. The months of March June, have the largest diurnal variations with mean standard deviation of.82 with minimum.2 and maximum.7 values occurring on single days. The remaining period had a mean standard deviation of.6 with a minimum of. and maximum of.5. For the woodland site, the mean SD is.45 at an average Λ of.33, hence a coefficient of variation of.4 arises. The months of March and April had the highest SD of.6. At both sites the periods of largest SD coincide with rainy season. During the rainy days R n G, T a T a2 and VPD are small. It was shown on theoretical basis that Λ is most sensitive to variations in R n G, T a T a2 and VPD when these variables are small values. These affect the diurnal cycle of the surface energy fluxes and the stability of Λ. In comparison, the SD of the woodland site is much lower than that of the grassland site. This indicates that the diurnal stability is site dependent. An analysis of the relationship between SD and T a, RH and the degree of cloudiness was undertaken to see if routinely collected weather data could be used to understand the diurnal stability of Λ. The degree of cloudiness is more accurately expressed as a shortwave

6 34 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) 29 4 Table 2 Relationship between the daytime standard deviation of evaporative fraction and meteorological variables used to explain the diurnal stability of the evaporative fraction Meteorological variables day, r 2 day, r 2 Grassland n = 34 Woodland n = 24 Grassland Woodland Shortwave transmittance, τ Relative humidity, RH Air temperature, T a transmittance (τ): τ = K (3) K TOA where K TOA is the solar radiation incident on the top of the atmosphere which can be calculated on the basis of standard astronomical equations (e.g. Iqbal, 983). Table 2 shows the coefficient of determination (r 2 )of the relationships. The relationships were modeled by polynomial curves having an order 2. The daily SD has a very weak relationship with T a,rhandτ. The relationship between -day average SD and -day average T a,rhandτ was also weak (Table 2). To examine the effect of cloudiness on the stability of Λ, the days were stratified according to the daily average τ values and put into three groups. The groups were defined as cloudy (τ <.5), partly cloudy (.5 > τ<.65) and clear (τ >.65). Table 3 shows that the average SD for the three groups is almost the same indicating that cloudiness is not related to stability of Λ. Hence, the stability of the diurnal cycle of Λ can not be adequately explained by micrometeorological state variables only. There is no consensus in the literature on the effects of clouds on the diurnal cycle of Λ. While Hall et al. (992) conclude that variations in R n due to cloudiness should not affect Λ significantly. Suigita and Brutsaert (99), attribute daytime changes in Λ to changes in cloudiness. They attribute increase in Λ to decrease in R n as clouds pass over. Crago (996b), observes that cloud fields tend to change R n G and surface temperature erratically and thereby cause changes in Λ. However, he concludes that the effect on Λ may not be observed in practice as it may masked by coincident changes in RH and wind speeds. This implies that diurnal variability of Λ is a complex phenomenon and other factors influencing the variations of Λ in Eqs. (3) and (7) need to be considered more carefully. The other variables that control Λ, are r s and r a (see Eq. (4)), of which r s is the dominant surface variable, which regulates Λ. r s depends on micrometeorological variables, soil moisture and plant physiology (Jarvis, 976; Stewart, 988). Surface resistance has a diurnal trend. Modeling of surface resistance is therefore required in order to understand better the diurnal dynamics of Λ, but considered outside the scope of the present paper where a large divergence of time scales is discussed. 5. Relationship between midday and morning Λ and daytime Λ The relationships between Λ mid and average daytime Λ are presented in Fig. 3a and b. All days were Table 3 Average daytime standard deviation of evaporative fraction grouped according to shortwave transmittance, τ, in order to understand the relationship between cloudiness and diurnal stability of evaporative fraction Number of days τ Mean standard deviation of evaporative fraction, Λ Grassland Woodland Grassland Woodland 4 4 < and >

7 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) Daytime evaporative fraction (a) Daytime evaporative fraction(-) (b),8,6,4,2,6,5,4,3,2, R 2 =.74,2,4,6,8 Evaporative fraction(2-3hrs) R 2 =.75,,2,3,4,5,6 Evaporative fraction(2-3hrs) Fig. 3. Relationship between midday and daytime evaporative fraction at (a) grassland site for the period May 998 April 999 and (b) woodland site for the period October 998 April 999. The relationships between average Λ mor between 9. and. h and average daytime Λ was determined to study the potential of using satellite remote sensing based data acquired during the morning hours. The r 2 for the 9.. h period is lower with.64 and.65 for the grassland and woodland sites, respectively as compared to the midday conditions. Poorer RMSE of.2 and.6 were also obtained at the grassland and woodland site, respectively. The implication of the results for remote sensing studies is that midday satellite passes (e.g. NOAA AVHRR) will give better average daily Λ than the morning satellite passes (e.g. Landsat). 6. Seasonal variations of actual evaporation Daytime E estimated from Λ mid and Λ mor simulate the results of E obtainable from the satellite data with morning (e.g. Landsat) or afternoon (e.g. NOAA AVHRR) over passes at the equator. Fig. 4 shows the comparison of measured E and estimated E from Λ mid used irrespective of weather conditions. There is a strong relationship between Λ mid and daily Λ. The r 2 for the regression lines through the origin are.74 and.75 while the root mean square error (RMSE) are.95 and.7 for the grassland and woodland site respectively. The : line (Fig. 3a) shows that Λ mid larger than.65 are higher than corresponding daytime values while Λ mid values smaller than.3 are less than the daytime values, which reveals a slight concave type of relationship. Λ values larger than.65 occur in the rainy months of May, June and April. During these wet periods, when there is no moisture deficit, evaporation is highest at midday when solar radiation is highest. Λ is therefore expected to be higher at midday as compared to the rest of the day. In contrast Λ values less than.3 mostly occur in the dry months of January, February and December. Evaporation is significantly reduced for the whole day, however available energy (R n G) is highest at midday. Λ values will therefore tend to be lower at midday as compared to the rest of the day and under estimate the daytime Λ. Fig. 4. Comparison of measured evaporation, E and estimated E by midday evaporative fraction at (a) grassland site for the period May 998 April 999 and (b) woodland site for the period October 998 April 999.

8 36 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) 29 4 Table 4 Root mean square error of E on daily, day and monthly time scales at the two sites for the whole study period RMSE ET (mm) Grassland Woodland Daily.7.4 day day.5.4 for the two sites. The r 2 and RMSE are also presented in Fig. 4 and Table 4 respectively. The values of measured and estimated E compare very well at both sites. The RMSE for daily values are.7 and.4 mm at the grassland and woodland sites, respectively. These results are for the whole study period, however on individual monthly basis the largest RMSE for daily values obtained are.2 and.8 mm for the month of April for the grassland and woodland sites respectively. With respect to r 2, the lowest values are.77 for the month of January at the grassland site and.66 for the month of February at the woodland site. The months of January and February are the driest months in the year and therefore E is very small during this period. Although the comparison between measured and estimated E may appear poorer for the drier months, the RMSE are comparable to the other months. Table 4 shows the RMSE of estimated E on daily, day and monthly scales. It can be seen that the RMSE reduces with longer time scales. This indicates that accumulated E is more accurate than daily E if estimated from instantaneous evaporation. It can also be seen that the relationship between measured and estimated E is better than the relationship between average day Λ and Λ mid. This is because more weight is given to the midday period in the calculation of daytime E, when R n G is large and Λ is more stable. The daytime E estimated by Λ mor gave poorer results than for Λ mid. The RMSE values are.37 and.29 mm at the woodland and grassland sites, respectively. These values are about two times larger than those obtained when Λ mid was used. The r 2 obtained are.33 and.65 for the grassland and woodland sites respectively. This implies that in remote sensing studies, data from satellites with afternoon overpass will give better estimate of E compared to those with morning overpass. 7. Seasonal variations of Λ The pattern of the seasonal variation of Λ is presented in Fig. 5. Each of the points represents the average value of Λ between 8. and 7. h. The seasonal variation of Λ is a reflection of the climate of the area, in particular of rainfall and soil moisture. Superimposed on this trend are fluctuations of Λ from day to day caused by variations in the micrometeorological conditions elucidated in the previous sections. It can be seen that for the grassland site, Λ drops quickly from.7 at the end of May to.3 in approximately 6 days. The reduction in Λ may be attributed to the reduction of soil moisture availability in the root zone due to sharply reduced rainfall rates. Λ Evaporative Fraction(-) Apr Jun Jul Sep- 98 -Nov-98 2-Dec- 98 Date 9-Feb-99 3-Mar May- 99 woodland grassland Fig. 5. Seasonal progression of evaporative fraction at the grassland site for the period May 998 April 999 and woodland site for the period October 998 April 999.

9 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) fluctuates around.3 for about days between the end of July and beginning of November. This is followed by a sharp decline in Λ, reaching virtually zero within 45 days. This indicates that Λ responds to soil moisture condition when a certain critical level of moisture and soil water potential is reached and plant stress is triggered. Periods when Λ is zero imply that all of the available energy is partitioned into sensible heat flux. There is an increase of Λ in the month of January from to.4 in response to a rainfall event (see Fig. 5). However Λ declines to zero in a few days. Λ, finally increases from zero at the end of January to.8 by April in the response to the rain period starting at the end of March. Although no Λ data is available in the month of February and the beginning of March, rainfall data was available. During this period there was only.5 mm of rainfall recorded. It is therefore expected that Λ remains in the range between and. between February and March. For the woodland site, Λ remains fairly constant at about.4 from the end of September for about 8 days. Λ then begins to decline steadily to reach zero in about 7 days. The Λ declination takes a longer period as compared to the grassland site. This, may be related to the differences at the two sites. These differences are caused by differences in rooting depth of the vegetation at the two sites besides that the forest receives more rainfall annually. For the grassland site vegetation, can only get moisture from the top soil surface and as soon as the soil surface dries vegetation stress emerges. Furthermore, the grasses at this site begin to senescence, just before the dry season. Evaporation from soils is the dominant component of evaporation at this time. Evaporation therefore stops a day or two after a rainfall event. The woodland site has vegetation with deeper roots, which can extract moisture from deeper soil layers. The vegetation continues to transpire even after the surface soils have dried up two months after the last rainfall event. The value of Λ, finally increases in response to rainfall and soil moisture replenishment in early March. However, Λ increases to a maximum of.5 by the end of April as compared to.8 in the grassland site. This could be ascribed to the lower VPD prevailing in the woodland site which causes lower degrees of partitioning of R n G into L and hence limits evaporation. The seasonal progression of Λ is gradual at both sites. The implication of this for the monitoring of Λ is that it would be sufficient to measure Λ say every 5 days to capture the seasonal evolution of Λ. Interpolation between the measurements can be done to estimate Λ on days when there are no Λ measurements. This means that for remote sensing programs processing of daily images is not necessary to estimate the seasonal variations of Λ for large watersheds, albeit daily acquisition might be required to select the qualitative best cloud free image for a given period. 7.. Estimation of Λ by standard meteorological data Soil moisture dynamics and thus indirectly the rainfall events, control the long term seasonal variations of Λ. The seasonal trends of micro-meteorological variables such as T a, RH and τ follow the annual rainfall regime. These variables obtained from standard weather stations could be used to estimate the seasonal variations of Λ, rather than the daily processing of satellite images. A regression analysis between Λ and T a, RH and τ was performed on the basis of and -day average values. Multiple linear regression between Λ and all the three micrometeorological variables was performed as well. The relationships between Λ and the variables at the grassland site at the seasonal scale are presented in Fig. 6, while the coefficient of determination, r 2, of the relationships at the two sites are shown in Table 5. The maximum value of Λ coincides with T a of 25 C (see Fig. 6). The optimum RH for both sites is 5%. These agree with the optimum meteorological condition for evaporation for vegetated surfaces found by Stewart (988). RH best explains the av- Table 5 Relationship between evaporative fraction and meteorological variables at the two sites for the whole study period Meteorological variables day average, r 2 day average, r 2 Grassland Woodland Grassland Woodland τ RH T a RH T a τ RH T a

10 38 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) 29 4 Evaporative fraction(-) Evaporative fraction (a) Evaporative fraction(-) (b) (c),8,6,4,2,8,6,4,2,8,6,4,2 y = -.x 2 +.2x -.26 r 2 = Relative Humidity(%) y = -.38x x r 2 = Temperature( o C) y = x r 2 =.25,2,4,6,8 Transmission(-) Fig. 6. Relationship between evaporation fraction and air temperature, relative humidity and atmospheric transmission at the grassland site for the period May 998 April 999. erage day Λ with an r 2 of.69. As expected, there is an improvement in the relationships if -day average values are considered due to smoothing effects (see Table 5). In the multiple linear regression an r 2 of.67 for daily averages and.87 for the -day average values for the grassland site was obtained. It is worthwhile to note that standard meteorological data can explain 87% of the variations of Λ in the -day average values. This has important implications for hydrological applications requiring -day average. During periods when satellite data is not available, readily available standard meteorological data could be used to estimate Λ empirically, once the site specific relationships are established. 8. Conclusions The objective of this study was to investigate the use of the diurnal constant behavior of Λ to estimate daytime average Λ and daytime total of E throughout a complete season. The results presented show that the diurnal stability of Λ varies significantly during

11 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) the study period. The daily standard deviation of Λ varies from as low as. to as high as.6 for individual days indicating that Λ is not stable under all vegetation, soil and atmospheric conditions. The results also show that on the daily time scale, the variations of Λ cannot be explained well by meteorological variables and cloudiness alone. The variations could be due to other causes such as the diurnal variation of surface resistance and energy and moisture advection. The evaporative fraction is more unstable during the cloudy and rainy period (April June) as compared to the other months due to low R n G, VPD and T a T a2 values. The evaporative fraction is more temporally stable at the woodland site than at the grassland site. The data presented showed that there is a strong relationship between Λ mid and daytime Λ with the average r 2 of the regression lines through the origin at the two study sites being.74 and.75. The changes of Λ over an annual period are gradual. It can be concluded that for remote sensing programs, an acquisition of images say every 5 days may be able to capture the seasonal evolution of Λ for large watersheds. Furthermore the interpolation of Λ, between remote sensing days, can be accomplished by routinely collected weather data. The estimated daytime E from Λ mid compare very well with measured daytime E (RMSE =.7 mm, r 2 =.88 for the grassland). For the whole study period the average daily difference between the estimated E and the observed E was within %. The differences reduced even further if day and monthly integrated E values are considered. Poor E results were obtained from Λ mor (RMSE =.37 mm, r 2 =.33 for the grassland). This indicates that the use of data from satellites with morning overpasses will give less accurate daily E values in the environmental conditions of Kenya. NOAA AVHRR satellite images with afternoon over pass are preferred although a loss of spatial scale accuracy should be accepted. The important conclusion from this study is that the hypothesis of quasi-constant Λ to estimate seasonal variations of evaporation is valid for tropical watersheds under general weather conditions. This provides a basis for the use of remote sensing methods in applied regional hydrology in tropical watersheds with data scarcity problems. References Allen, R.G., Preira, L.S., Raes, D., Smith, M., 998. Crop evapotranspiration: guidelines for computing crop waterrequirements. FAO irrigation and Drainage Paper 56. Bastiaanssen, W.G.M., Pelgrum, H., Menenti, M., Feddes, R.A., 996. Estimation of surface resistance and priestley and Taylor -parameter at different scales. In: Stewart, J.B., Engman, E.T., Feddes, R.A., Kerr, Y., (Eds.), Scaling Up in Hydrology Using Remote Sensing. Inst. of hydrology, 93. Bastiaanssen, W.G.M., Sakthivadivel, R., van Dellen, A., 999. American Geophysical Union, Monograph. de Bruin, H.A.R., Holtslag, A.A., 982. A simple parameterization of the surface fluxes of sensible and latent heat during daytime compared to Penman Monteith concept. J. Appl. Met. 2, Brutsaert, W., Suigita, M., 992. Application of self preservation in the diurnal evolution of the surface energy budget to determine daily evaporation. J. Geophys. Res. 97 (D7), Crago, R.D., 996a. Comparison of the evaporative fraction and Priestly Taylor for the parameterizating daytime evaporation. Water Resour. Res. 32 (5), Crago, R.D., 996b. Conservation and variability of the evaporative fraction during the daytime. J. Hydrol. 8, Crago, R., Brutsaert, W., 996. Daytime evaporation and the self-preservation of the evaporative fraction and the Bowen ratio. J. Hydrol. 78, Hall, F.G., Huemmrich, K.F., Goetz, S.J., Sellers, P.J., Nickeson, J.E., 992. Satellite remote sensing of the surface energy balance: success, failures and unresolved issues in FIFE. J. Geophys. Res. 97 (D7), Holtslag, A.A.M., Van Ulden, A.P., 983. A simple scheme for daytime estimates of the surface fluxes from routine weather data. J. Appl. Met. 27, Iqbal, M., 983. An Introduction to Solar Radiation. Academic Press, Toronto. Jackson, R.D., Hatfield, J.L., Reginato, R.J., Idiso, S.B., Pinter Jr., P.J., 983. Estimation of daily evapotranspiration from one time day measurements. Agric. Water Manage. 7, Jarvis, P.G., 976. The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Phil. Trans. R. Soc. London B273, Kustas, W.P., Norman, J.M., 996. Use of remote sensing for evapotranspiration monitoring over land surfaces. Hydrol. Sci. J. 4 (4), Moran, S.M., Jackson, R.D., 99. Assessing the spatial distribution of evaporation using remotely sensed inputs. J. Environ. Qual. 2, Nichols, W.E., Cuenca, R.H., 993. Evaluation of the evaporative fraction for the parameterization of the surface energy balance. Water Resour. Res. 29 (), Rowntree, P.R., 99. Atmospheric parametrization schemes for evaporation over land: basic concepts and climate modeling aspects. In: Schumugge, T.J., Andre, J.C., (Eds.), Landsurface Evapoartion. Springer, New York, pp

12 4 H.O. Farah et al. / International Journal of Applied Earth Observation and Geoinformation 5 (24) 29 4 Shuttleworth, W.J., Gurney, R.J., Hsu, A.Y., Ormsby, J.P., 989. FIFE: the variation in energy partition at surface flux sites. IAHS Publ. 86, Suigita, M., Brutsaert, W., 99. Daily evaporation over a region from lower boundary layer profiles measured with radiosondes. Water Resour. Res. 27 (5), Stewart, J.B., 988. Modeling surface conductance of pine forest. Agric. Forest Met. 43, Zhang, L., Lemeur, R., 995. Evaluation of daily evapotranspiration estimates from instanteneous measurements. Agric. Forest Met. 74,