A simple satellite-based algorithm for estimating actual evaporation based on Makkink’s equation is applied to a seasonal cycle in 2002 at three test sites in Ghana, West Africa: at a location in the humid tropical southern region and two in the drier northern region. The required input for the algorithm is incoming solar radiation, air temperature at standard level, and the green-vegetation fraction. These data are obtained from Meteorological Satellite (Meteosat) and Moderate-Resolution Imaging Spectroradiometer (MODIS) images. The observation period includes the rapid wet-to-dry transition after the wet season. Incoming solar radiation and air temperature are validated against local measurements at the three sites. It is found that the incoming solar radiation obtained from Meteosat corresponds well with the measurements. For air temperature from Meteosat data, the diurnal cycle is realistically reproduced but is in need of a bias correction. The algorithm output is compared with the evapotranspiration data obtained from hourly large-aperture scintillometer observations and simultaneous “in situ” measurements of net radiation and soil heat flux. It is found that the actual evapotranspiration can be monitored using the modified Makkink method, with daily mean errors of between 5% and 35% of measured evapotranspiration and a seasonal error smaller than 5%. Furthermore, it appears that the algorithm realistically describes the daily cycle of evapotranspiration.
A quantitative knowledge of the loss of water by actual evapotranspiration (latent heat flux) is crucial in hydrological studies and water resource management, because it serves as a link between the land surface and the atmosphere. In particular, in semiarid tropical regions, knowledge of the loss of water by evapotranspiration is important, because of the large magnitude and variability of its occurrence. During recent decades, the predictive capability of meteorological and hydrological models has improved to tackle that need. However, there is still a lack of input and validation data for these models in semiarid regions such as the Volta River basin in West Africa. The regional climate is characterized by a strong north–south gradient of mean annual rainfall and the occurrence of pronounced wet and dry seasons within one annual cycle. This causes a strong seasonal variation in the natural vegetation cover and a large variability in actual evapotranspiration.
Because of the lack of data, there is a necessity to employ remote sensing information for further validation and improvement of evapotranspiration models. During the last decade, a growing number of satellite algorithms have been developed to estimate actual areal-averaged evapotranspiration [the Surface Energy Balance over Land (SEBAL), see Bastiaanssen et al. (1998a, b; the Surface Energy Balance System (SEBS), see Jia et al. (2003); and the method proposed by Ma et al. (2004)]. Because these algorithms are based on the radiometric temperature, they are limited to cloud-free situations, a condition that makes it difficult to obtain evapotranspiration on a daily or weekly basis under the conditions in West Africa. In addition, a radiometer on board a polar-orbiting satellite receives an instantaneous estimate of the radiometric temperature at a limited number of times per day or week (depending on the spatial resolution), which may or may not be representative of the full diurnal cycle of the flux. These limitations show that there is a need for a robust algorithm that works under partly cloudy conditions and allows one to analyze temporal trends in the flux.
In the interest of clarity, some basic quantities need to be defined in this context. Potential evaporation (PE) is the amount of water evaporated per unit area per unit time from an idealized extensive free water surface under existing atmospheric conditions (Shuttleworth 1993). The optimal evapotranspiration (OE) corresponds to the ability of plants to transpire under ideal conditions (full vegetation cover, well watered) with a nonzero resistance to water vapor flux. Optimal evapotranspiration is always lower then PE. Last, one can estimate the actual evapotranspiration (AE), which is dependent on actual vegetation cover and soil moisture status. The actual evapotranspiration should equal optimal evapotranspiration under ideal conditions.
One way to derive optimal evapotranspiration that is not based on the radiometric temperature and is not necessarily a remote sensing technique is to use the crop factor method (Doorenbos and Pruitt 1977; Allen et al. 1998). For this approach, the optimal evapotranspiration is determined in the following way:
where kc is a crop factor and Eref is the reference crop evaporation. The crop factor is an empirical quantity that is dependent on the type of vegetation and on the phenology of the vegetation. Allen et al. (1998) discuss the values of kc for a large range of crops as well as corrections for incomplete cover, mixed crops, and phenology. For the estimation of Eref the Penman–Monteith equation (e.g., Allen et al. 1998, 2000) is utilized. It requires the input of net radiation, air temperature, humidity, and wind speed. Most of these input variables are difficult to derive from remote sensing data. The estimation of net radiation in particular can cause large errors, because it cannot be obtained directly from remotely sensed measurements and the surface conditions for the studied region change noticeably during the year.
An alternative and simpler way of deriving reference evapotranspiration is the approach developed by Makkink (1957), who found that the equation of Penman (1956) could be simplified. De Bruin (1987) showed that the Makkink formula can also be “derived” from the empirical formula of Priestley and Taylor (1972) and modified it accordingly. With this modified Makkink formula, the reference evapotranspiration can be defined as follows:
where Lυ is the latent heat of vaporization (J kg−1), Rs is the incoming solar radiation (W m−2), s is the slope of water vapor pressure at constant temperature (Pa K−1), and γ is the psychrometric constant (Pa K−1).
To calculate the optimal evapotranspiration, the reference evapotranspiration has to be multiplied by the crop factor [Eq. (1)]. In this study, kc is set to 1. At this stage of algorithm development, this value is justified by the fact that large parts of the test sites were covered with grass and a smaller fraction consisted of mixed tree species. For this natural vegetation, the uncertainty in the crop factor was largely due to the wide variations in plant density, leaf area, and water availability (cf. Allen 2000). Given the presence of trees, however, the crop factor might turn out to be larger than 1. Last, the actual evapotranspiration is estimated as follows:
Here, VF is the actual green-vegetation fraction. The introduction of VF could be interpreted as a modification of the crop factor to take into account incomplete cover [see Allen et al. (1998) for more elaborate corrections for incomplete cover]. Because the method is fairly simple, it can be regarded as a first-order approach to estimate actual evapotranspiration. Justification for applying this modified Makkink approach is that in the semiarid regions vegetation adjusts its cover to the available water: if there is less water to evaporate, this situation will be reflected in the vegetation cover. This justification is reasonable, because recent research has revealed that the semiarid areas are dominated by vegetative pathways (via stomatal conductance and vegetation cover), whereas the midlatitudes show a more soil wetness–related feedback (Niyogi et al. 2002). This method only reacts to changes in the vegetation cover. In the case of the vegetation suffering water stress and closing its stomata, it will not be reflected in the estimated actual evaporation. Furthermore, this method is not appropriate where bare-soil evaporation is the dominant process.
Choudhury and De Bruin (1995) examined various methods of using remotely sensed information to obtain optimal evapotranspiration and found the modified Makkink formula to be a suitable approach, but they stated that critical evaluation of the components was needed.
In the current study, this approach was utilized and incoming solar radiation was obtained from Meteorological Satellite (Meteosat) data. To calculate the slope of water vapor pressure s at temperature T, the temperature obtained from Meteosat data was utilized. Small errors in temperature were not expected to affect the results considerably, because temperature was only used to calculate s. For the estimation of the green-vegetation fraction, the enhanced vegetation index (EVI) obtained from Moderate-Resolution Imaging Spectroradiometer (MODIS) data was utilized.
When using remote sensing estimates for latent heat flux (or sensible heat flux), one critical issue is the validation. No clear method exists for this purpose. Often methods suitable for homogenous surfaces (point observations) are used, which are not applicable for the heterogeneous surfaces in West Africa. The use of a large-aperture scintillometer (LAS), proposed by, for example, De Bruin et al. (1995) for sparse vegetation in Spain, was expected to help to validate the remote sensing estimates. The advantage of the LAS technique is that areally averaged sensible heat flux can be obtained (up to scales of 5 km), which means that information is provided on satellite pixel scale. Therefore, scintillometry was used in this study as a basis for validating evapotranspiration. Scintillometry has been applied for remote sensing validation before in other regions (Hemakumara et al. 2003; Jia et al. 2003).
The main objective of this study was to investigate whether long-term monitoring of daily values for actual evapotranspiration under partly cloudy conditions in the Tropics is feasible. Therefore, first, a validation of the necessary input parameters, incoming solar radiation and temperature, derived from Meteosat data was performed. Second, the evaluation of actual evapotranspiration estimates based on the derived products was performed.
The focus here is on discussing the accuracy and time variability of incoming solar radiation, air temperature, green-vegetation cover, and the estimated evapotranspiration. The algorithms to obtain solar radiation and temperature from Meteosat data and green-vegetation fraction from MODIS are described in section 2. Section 3 describes the experimental setup and observations, including a more detailed site description. Section 4 provides a description of the validation of the incoming solar radiation and temperature derived from Meteosat data against measurements. This is followed by an outline of the comparison between the actual evapotranspiration derived from the satellite data and the measurements. Section 5 provides a summary and conclusions.
2. Satellite data
Satellite data are widely applied for the determination of atmospheric and surface properties. Depending on the satellite system, the spatial and temporal resolution can range from tens of meters to several kilometers and from half-hourly to half-daily images.
Data from geostationary satellites can be utilized, for example, to estimate incoming solar radiation or land surface temperature. With their so-called visible (VIS) and infrared (IR) sensors, information on the reflected shortwave and emitted longwave radiance of the earth–atmosphere system is gathered. For this study, data from the geostationary Meteosat operated by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) were utilized. This satellite revolves around the earth sun-synchronously at an altitude of 36 000 km at 0° latitude and 0° longitude. Meteosat scans the earth every 30 min from south to north with three radiometers—one at the VIS wavelengths (0.45–1.0 μm), one at the IR wavelengths (10.5–12.5 μm), and one at the wavelength of the water vapor absorption band (WV; 5.7–7.1 μm). Data from the WV channel are not used in this study. One full-disk image consists of 2500 × 2500 pixels on the IR channel and 5000 × 5000 pixels on the VIS channel; therefore, the spatial resolution is 5 × 5 km2 and 2.5 × 2.5 km2 respectively, at nadir.
a. Determination of incoming solar radiation from Meteosat
Many approaches exist to derive the incoming solar radiation at ground level using geostationary satellite data. Newer methods are described, for example, in Stuhlmann et al. (1989), Hammer et al. (2003), Ineichen and Perez (1999), and Rigollier et al. (2001). All of these methods relate the reflected sunlight measured by the Meteosat VIS channel covering the range of 0.45–1.0 μm to the incoming solar radiation at the surface of the earth. The method used in this study has been described in Perez et al. (2002), who derive it as an evolution of the model of Cano et al. (1986). This method was developed for the determination of incoming solar radiation using data from the Geostationary Operational Environmental Satellite (GOES). For this study, data from the VIS channel of Meteosat-7 were adapted and included in the calculation scheme. The measured reflectance was usually low for earth surfaces and high for clouds. The information on the clouds is expressed in the cloud index (CI):
where ρ is the actual satellite count and ρmin corresponds to the minimum count for a given location, which is derived by an analysis of cloud-free satellite scenes; ρmax gives the maximum reflexivity for overcast skies. The cloud index varies between 0 for cloud-free conditions and 1 for overcast conditions. For the determination of the incoming solar radiation, also known as global horizontal irradiance (GHI), for cloudy conditions CI was used according to Perez et al. (2002):
The global horizontal irradiance for clear-sky conditions was calculated according to Ineichen and Perez (2002) using
where I0 is the eccentricity-corrected extraterrestrial irradiance, h is the solar elevation, am is the altitude-corrected air mass, TL is the Linke turbidity, a1 = 5.09 × 10−5 × altitude + 0.868, a2 = 3.92 × 10−5 × altitude + 0.0387, fh1 = exp(−altitude/8000), and fh2 = exp(−altitude/1250), with the altitude above mean sea level expressed in meters. The Linke turbidity represents the number of clean and dry atmospheres that would be needed to produce the observed extinction. To take the cloud-free atmosphere into account, the Linke turbidity database provided by the Solar Radiation Database (SODA) server was used (Wald et al. 2002). For Ghana, TL varies between values of 4 and 6.
b. Determination of near-surface temperature from Meteosat
The IR sensor measures the outgoing longwave irradiance of the earth–atmosphere system for a specific wavelength. The measured value can be used to assess a kind of land surface temperature (e.g., Schädlich et al. (2001); Sun and Pinker (2003)). The approach used in this work was developed by Mannstein et al. (1999). The (near) surface temperature is a by-product of the cloud-detection scheme. Clouds show up in the IR channel of Meteosat as cold pixels. For detection, a reference temperature is needed that represents the cloud-free surface temperature (warmer than clouds). Because measurements of surface temperature were not available at sufficient temporal and spatial resolution, especially in the rural areas of West Africa, the reference temperature was derived from the Meteosat data themselves, as follows. We first calibrated the Meteosat count to obtain the equivalent blackbody temperature. We then sorted the available images as a three-dimensional array for each day with the X and Y spatial coordinates and the t temporal coordinates (every half-hour, from 1 to 48). The reference temperature Tref of the land surface is described by the following parametric function for every pixel:
with x = 2πt/24 and t = decimal hours of the satellite scan (UTC). Parameter a0 gives the daily mean temperature, a1 gives the temperature amplitude, a2 influences the width and steepness of the daily temperature wave, and a3 gives the phase shift, which is dominated by the local solar time. These four parameters were fitted daily for each land pixel, using all cloud-free half-hourly values for each day for each pixel (maximum of 48 values per day and per pixel). The derived Tref was used in this work as an estimate of the 2-m air temperature.
c. Green-vegetation fraction from MODIS
Since the launch of the first Advanced Very High Resolution Radiometer (AVHRR), information on the vegetation at the earth’s surface has been obtained from the normalized difference vegetation index (NDVI). Although related to vegetation properties such as leaf-area index (LAI) and VF, NDVI is not a direct measure of those properties. With increasing LAI values, NDVI tends to saturate, where the threshold LAI for which this occurs depends on the vegetation type and vegetation cover (see Carlson and Ripley 1997). Furthermore, the relationship between VF and NDVI depends critically on the relative brightness of the soil and the vegetation, as well as on the NDVI of soil and vegetation separately (Hanan et al. 1991).
The enhanced vegetation index was developed to take into account the influence of both the atmosphere and the soil on the vegetation index (Liu and Huete 1995). The EVI appears to suffer less from saturation at high values of LAI and is more directly related to vegetation characteristics (Huete et al. 2002). If the maximum value of EVI (EVImax) is assumed to be the EVI of vegetation, and the minimum value (EVImin) is assumed to be the background value, the vegetation fraction can be determined as
This linear dependence is based on the quadratic dependence of VF on a scaled NDVI (e.g., Carlson and Ripley 1997), in combination with an approximate quadratic relationship of EVI and NDVI as is apparent from the images we have used.
Based on Fig. 17 in Huete et al. (2002), the extreme values of EVI, EVImax and EVImin, are estimated to be 0.65 and 0.08, respectively. The sensitivity of the expression for VF is as follows, given the above values for EVImax and EVImin. The relative error in VF is −1.1 times the relative error in EVImax. The sensitivity to errors in EVImin depends on EVI: for VF = 0.1 the relative error in VF is −1.3 times the relative error in EVImin, whereas for VF = 0.5 it is −0.14 times the relative error in EVImin. Last, the error in VF is 2.4 times the relative error in EVI at VF = 0.1 and is 1.3 times the relative error in EVI at VF = 0.5. It can be concluded that the relative errors in VF resulting from the input parameters for Eq. (8) are of the same order as the errors in the input parameters themselves but are larger for small VF. Provided that cloud contamination of the EVI is properly detected, the impact of errors in EVI will be small relative to the error resulting from the uncertainty in EVImax and EVImin. The latter errors are estimated to be on the order of 10% and 50%, respectively. Another source of uncertainty is the effect that, after rain, the wet surface absorbs near-infrared radiation rather than reflects it, giving an underestimation of EVI.
EVI data were routinely produced from the data of the MODIS on board the Terra and Aqua satellites. In this study, we used 16-day composites of EVI, gridded at a spatial resolution of 1000 m. Level-3 data (version 4) from the Aqua satellite were used. For the combination with the Meteosat data, a composite was made of the four pixels surrounding each of the field sites. The quality flag of the MODIS data was used to determine possible cloud contamination, and data with cloud contamination were discarded. The compositing algorithm used for this MODIS product ensures that the highest EVI value of the 16-day period is retained (excluding possible conditions of wet surfaces).
3. Experimental setup and observations
a. Site description and experimental setup
All analyzed measurements are part of long-term observations of the water and energy balance in the Volta Basin within the Globaler Wandel des Wasserkreislaufes (Global Change in the Hydrological Cycle; GLOWA) Volta project. GLOWA Volta is a multidisciplinary effort to study the physical and socioeconomic determinants of the hydrological cycle (Van de Giesen et al. 2001). The climate system in the Volta basin is mainly controlled by the meridional movement of the intertropical convergence zone, the African easterly jet, and pressure disturbances that traverse from east to west across Africa (Burpee 1972). They all act under the influence of the Hadley and Walker cell circulation. These mechanisms lead to a pronounced wet and dry season during the year, the length of which depends on the actual latitude. During the time of the year when the wet period ends and the dry period starts (time of transition), the contrast between dry and moist air is probably more pronounced in time and space than at any other period (Hólm et al. 2002).
The data used in this study were based on measurements from automatic weather stations (AWS) and LAS measurements in Navrongo (10°55′N, 1°2′W), Tamale (9°29′N, 0°55′W), and Ejura (7°20′N, 1°16′W). The exact locations are given in Fig. 1. The distance between the stations is about 100–200 km. The three sites show major differences concerning the vegetation, soils, land use, slopes, and climate and were chosen to account for the large variability during the season in the region. The test site in Navrongo is located in northern Ghana. The area is characterized by a mixture of grass, some scattered trees (mainly baobabs), and agricultural crops during the wet season. During the dry season, it is mainly characterized by bare soil. The landscape is nearly flat. The LAS transmitter and receiver were installed at a distance of 1040 m from each other, with a weighted effective height of 12.8 m.
The research site in Tamale is mainly characterized by grassland with scattered trees that have a maximum height of 5–8 m. The landscape is slightly hilly. The LAS transmitter and receiver were installed on two hills at a distance of about 2420 m from each other. The weighted effective height of the LAS was estimated at 19.5 m. The AWS was installed next to the receiver of the LAS.
The site in Ejura is the tropical site. The landscape is hilly. Here the transmitter and the weather station were located in a cashew orchard. The receiver was located at the edge of a forest. The LAS path had a length of 2030 m. The weighted effective height of the LAS was estimated at 30.1 m. The terrain was heterogeneous. The area between the transmitter and the receiver could roughly be divided into two parts. On the transmitter side, the vegetation consisted of cashew trees with a maximum height of 4 m, with maize and grass between them. On the receiver side, there were bushes, trees, and small swamps but almost no agriculture.
All sites were equipped with an AWS, which measured temperature, humidity, and incoming solar radiation at a height of 2 m, in accordance with World Meteorological Organization (WMO) standard meteorological weather stations. Wind speed, wind direction, and net radiation were measured at 8-m height. In addition, surface observation for soil heat flux, precipitation, and runoff were recorded. Data availability exceeded more then 90% for most of the measurements for all three sites during 2002. The types and brands of the instruments used are described in Table 1. All quantities were originally averaged for 10-min intervals.
To measure incoming solar radiation, Kipp and Zonen CM3 pyranometers were used. The CM3 pyranometer measured the solar irradiance from the whole hemisphere (180° field of view). According to WMO standard, it is a second-class instrument. The spectral range spanned 305–2800 nm. The response time was about 18 s. The directional error was less than ±25 W m−2 at 1000 W m−2. The expected accuracy for daily sums was about ±10%. All instruments were regularly checked to ensure that the sensor was not tilted. During the study period, the sensors were cleaned on a 1–2-week basis, depending on the actual site.
To measure air temperature, the Vaisala, Inc., 50Y temperature and relative humidity probe was used. It used a 1000-Ω platinum-resistance thermometer to measure temperature. The instrument was calibrated for a temperature range from −10° to +60°C. The accuracy was ±0.35°C at −10°C and ±0.6°C at +60°C. All measurements were recorded in UTC, and there was no daylight saving time.
b. Flux measurements with scintillometry
The LAS consists of a transmitter emitting electromagnetic radiation toward a receiver. The distance between both can be up to 5 km for a beam diameter of 0.15 m. In this study the distance varied between 1040 and 2420 m for the different sites. It is installed at a certain height above the surface. The emitted radiation is scattered by the turbulent medium in the path. The variance of intensity of received radiation is proportional to the structure parameter of the refractive index of air C2n. At the wavelength used (940 nm), the refractive index mainly depends on temperature, and so C2n is mostly determined by temperature fluctuations C2T:
with AT = T(∂n/∂T) and Aq = q(∂n/∂q), which are both dependent on optical wavelength, pressure, temperature, and humidity content. Here, T is the mean air temperature, q is the mean specific humidity, cp is the specific heat of air at constant pressure, and β is the Bowen ratio. The last factor on the right-hand side of Eq. (9) reflects an estimate of the influence of humidity on the refractive index (Wesely 1976; Moene 2003). Here β is estimated as follows:
where HLAS is the sensible heat flux obtained from the scintillometer, Rn is net radiation, and G is the soil heat flux. Sensible heat flux is calculated from C2T by using the following expression: HLAS = ρcpu*Θ*, with u* being the friction velocity and Θ* being the temperature scale from Monin–Obukhov similarity theory. In this study, a standard Businger–Dyer flux-profile relation was utilized to estimate u* from wind speed and roughness length, and HLAS was calculated iteratively. Stability functions proposed by Wyngaard (1973) were used for daytime values. For night values we followed the formulation of De Bruin et al. (1993). Several tests were made for the use of different stability functions for day and night situations. In general, the results were steady and differed at most by 10%, but, especially during the night, the formulation of de Bruin gave the most reliable results. For a more detailed description of the LAS theory and its applications see, for example, De Bruin et al. (1995) and Meijninger et al. (2002).
The LAS at each site was installed on top of two opposite hills using towers with a minimum height of 5 m. The setup with small differences in installation height of transmitter and receiver and changes in terrain height along the path implied that the beam above the terrain varied along the path. Therefore, the effective height was calculated using the method of Hartogensis et al. (2003), using the fact that the LAS signal is weighted toward the middle of the path. All measured quantities were originally averaged for 10-min intervals.
Latent heat flux was calculated as a residual from the energy balance, which showed good correspondence with eddy covariance data obtained during an intensive observation period (IOP) during the drying up in 2002. One has to remember that this approach forces the measured energy balance to close. The error in measured energy balance closure was smaller than 10% for the IOP in 2002 in Tamale and for large parts of the season in Ejura (Schüttemeyer et al. 2006).
4. Results and discussion
This section describes the validation of the key variables for estimating AE and the estimated evapotranspiration, with a focus on discussing accuracy and time variability. The validation was performed for the period from 26 August 2002 to 31 December 2002. The period covered the transition time from the wet season to the dry season in the studied region. Forty years of rainfall for different stations in the Volta basin were analyzed for the onset and termination of the rainy period using the method of Kasei (1988). It was found that both the start and the end of the rainy season for 2002 were within the range of one standard deviation when compared with the climatological values. This demonstrated that the analyzed period should not be exceptional in terms of varying vegetation cover and evapotranspiration. Satellite-based AE was validated against measured AE derived from ground observations. Furthermore, the remote sensing algorithm was also tested using measured incoming solar radiation and temperature (henceforth ground-based AE) and was compared with measured AE.
a. Validation of satellite-derived incoming solar radiation
The first test of the calculated incoming solar radiation was to calculate the correlation coefficient, the mean bias error (MBE), and the RMSE. The term MBE refers to the difference between the modeled value and the measured value. Positive (negative) MBE occurs when the modeled value is higher (lower) than the measured value.
The overall results based on hourly observations showed a reliable estimation of incoming solar radiation by the satellite retrieval when compared with the local measurements for all three sites (Fig. 2). The correlation coefficient was high for Navrongo (0.97) and Tamale (0.96) and lower for Ejura (0.94). Linear regression gave a slope close to 1 and an intercept that was smaller than 1 W m−2 for all three sites. The RMSE was high for all three sites, as confirmed by the amount of scatter seen in Fig. 2. One explanation for the amount of scatter was that a point measurement was compared with an areal average from the satellite. The Meteosat algorithm cannot resolve every single detail in the point measurements. In addition, Fig. 3 shows that the diurnal cycle of incoming solar radiation was realistically reproduced, but not every detail could be resolved by Meteosat data. The only solution to this problem would be to use a network of radiometers to obtain areally averaged incoming solar radiation. On days of rainfall, the daily differences get larger. This could be related to the changing albedo after rain events, which changes the CI through a change in the reflectance in Eq. (4), and also because the sensors were not cleaned immediately after rain events. For Ejura, the RMSE was higher in comparison with the other two sites (Fig. 2), which could be explained by the fact that the rainy period stopped later in Ejura and more clouds were detected during the studied period.
The seasonal dynamics based on the daily daytime differences between satellite-based and measured incoming solar radiation (Fig. 4) showed comparable results for the three sites. The Meteosat algorithm worked well throughout the season, with values fluctuating around zero. Only on days of rainfall did the daily differences get larger. The period after 30 September 2002 showed higher daily differences and also higher values for the RMSE in comparison with the rest of the season, with a time shift between the three sites. The errors were explained by large-scale features that traversed from east to west across Africa. This was confirmed by the daily cloud cover derived from Meteosat data and the local precipitation measurements. For the period when the rain stopped, the RMSE decreased for all three sites.
b. Validation of satellite-derived reference temperature
The overall results for temperature estimation showed a comparable MBE for the three sites (Table 2). The comparable MBE implies that the reference temperature can be used as a proxy for air temperature with a constant adjustment over a considerable region. Correlation coefficients were lower in comparison with incoming solar radiation. The differences for the correlation coefficients and RMSE between Navrongo and Tamale are small. For Ejura the RMSE was higher and correlation was lower in comparison with the other sites. The more heterogeneous terrain might explain the lower correlation and higher RMSE for Ejura. The AWS was located in a cashew orchard, between the trees, which might influence the measurements. Furthermore, the landscape was hilly, which poses the question of how representative the point measurements were.
Figure 5 shows the diurnal cycles for temperature for a 10-day period at the three different sites. They were adjusted using the mean of the MBE of all three sites. The diurnal cycle was realistically reproduced by Meteosat data. On some days the differences get larger. This should not affect the results for the estimation of AE too much, because temperature was only used to calculate the slope of water vapor pressure s at temperature T. For a couple of days, the reference temperature dropped too early in the afternoon, which might be related to the fact that Eq. (7) gives a limited degree of freedom in the shape of the diurnal cycle.
The seasonal dynamics based on the daily differences in satellite-based and measured temperature showed a trend to smaller differences toward the end of the season. This result is explained by a decrease in the amount of water vapor in the air toward the dry season.
c. Validation of actual evapotranspiration
The comparison of incoming solar radiation and temperature started on 26 August 2002, but, because of measurement problems of the LAS, the comparison of latent heat flux was limited in Navrongo and is therefore excluded from the statistical analysis. For Tamale it started on 14 October 2002 and continued until the end of the year, and for Ejura it started on 27 September 2002 and also continued until the end of the year. During these time periods, the mean daily evapotranspiration for both sites decreased from 100 to 25 W m−2, with slightly lower values for Tamale test site. Because precipitation already introduced an error in the estimation of incoming solar radiation, those days were excluded from further analysis. Furthermore, the evapotranspiration of intercepted rainfall and bare-soil evaporation are definitely expected to give erroneous results for evapotranspiration under rainy conditions. One possibility of quantifying evaporation from interception would be to use NDVI or LAI from satellite observations. Because there were no rain events in Tamale and only a limited number in Ejura, this was not taken into account. Bare-soil evaporation was also not taken into account. Wallace and Holwill (1997) and Wallace et al. (1992) analyzed bare-soil evaporation within the Hydrological Atmospheric Pilot Experiment in the Sahel (HAPEX-Sahel) and found that rapid drying of the soil led to values of a maximal 0.5 mm day−1 after 1 week. In addition, Gash et al. (1997) found that bare-soil evaporation decreased to less than 20% of total evaporation within 2 days after a rain event. Because for Tamale the rainy period stopped before the analyzed period started, the amount of bare-soil evaporation should be small. For Ejura, there were only some small showers detected at the beginning, and on the days immediately following the rainfall the errors in evapotranspiration are expected to be larger. During the night, the satellite-based AE could not be used to calculate evapotranspiration. This fact introduced an error in daily sums of evapotranspiration, which is expected to be small because the measured values were close to zero.
To evaluate if the vegetation fraction is, in this case, an important factor in the estimation of actual evaporation, we first evaluated the spatial and temporal variation of the vegetation fraction as estimated from the MODIS data. Figure 6 shows the temporal development of VF for the three sites. It is apparent that the change in VF through the season was very large for all sites (from around 0.7 to 0.25). Furthermore, the southernmost site (Ejura) had a significantly higher VF for most of the season, until mid-January. Both the temporal and spatial variation of VF will affect the variation of AE.
The overall results for satellite- and ground-based AE estimation at the two test sites in Tamale and Ejura are given in Table 3. The correlation coefficient was lower in comparison with incoming solar radiation but higher than for air temperature. The MBE for both sites was small. The RMSE was acceptable for both sites given a maximum flux of about 400 W m−2. The results also include a linear regression forced through the origin (zero intercept). Figure 7 show the scatterplots for satellite-based AE at Tamale and Ejura, including only daytime values for rain-free situations. For Tamale, it is clear that AE was lower in comparison with Ejura and there was more scatter for higher values. For both sites it can be seen that, especially for high evapotranspiration, the satellite-based AE was underestimated. This calls for a refinement of the method and inclusion of other effects on the crop factor (cf. Allen et al. 1998). The daily errors are shown in Fig. 8. For more than 70% of all days, the MBE is smaller than 20% at both test sites. When these results are compared with other studies, it is found that this simple approach estimates actual evapotranspiration fairly reliably on a daily basis. For example, Hemakumara et al. (2003) found SEBAL errors to range between 4% and 32% on a 10-day basis. Bastiaanssen et al. (2005) found monthly differences for a test site in Idaho of about ±16% in 1985 and ±20% in 1989. Kite and Droogers (2000) compared different methods to estimate evapotranspiration and found error ranges similar to those in the current study. From the daily error it was concluded that, for Ejura, the biggest deviations appeared just after the rain had stopped. This could be related to the neglected bare-soil evaporation. During the dry part of the season it was found that for both sites larger errors emerged on days with daily mean wind speed of more than 3 m s−1.
To explore the limits of the satellite-based AE, AE is also calculated using locally observed incoming solar radiation and measured air temperature. All scatter between AE estimated with local variables and the LAS-derived AE was due to errors in the method used. All additional scatter when using remote sensing incoming solar radiation and temperature was due to differences between remotely sensed and locally measured values.
The ground-based AE shows less scatter (Fig. 9), and from a direct comparison of satellite-based AE and ground-based AE (Fig. 10) it was concluded that the satellite-based estimates introduced some extra scatter, which might be related to errors in estimated incoming solar radiation and/or temperature. The comparison of satellite AE and ground-based AE for daily error estimates gave comparable results for the days with errors smaller than 20%. The class with errors lower than 10% showed slightly higher percentages for the ground-based AE.
However, it should be kept in mind that when two different methods for measuring evapotranspiration or, more general, surface fluxes are compared, there will always be a certain amount of scatter. This scatter may be due to statistical errors, deficiencies in the measurement method, or a failure of the measured energy balance to close. Schüttemeyer et al. (2006) compared LAS-derived fluxes with eddy covariance data from an intensive observation period at the Tamale and Ejura test sites and found scatter similar to that observed in the current study for daytime evapotranspiration between the direct method (eddy covariance) and LAS-derived evapotranspiration.
Figure 11 shows the mean diurnal cycle for measured and satellite-based evapotranspiration for two 10-day periods at the two sites. These periods were at the end of the wet season and the beginning of the dry period. The algorithm reproduced the diurnal cycle for both periods well. The diurnal cycle for Ejura at the beginning of the dry period shows higher values in comparison with Tamale. This is explained by the fact that VF decreased more slowly than in Tamale (cf. Fig. 6).
5. Summary and conclusions
The accuracy and variability in time of satellite-based estimates of incoming solar radiation, air temperature, and actual evapotranspiration according to Choudhury and De Bruin (1995) was presented. The evaluation was carried out using ground observations from three different sites in Ghana during the time of transition from the wet period to the dry period. The ground-based evapotranspiration was calculated from the residual of the energy balance by using area-averaged sensible heat flux from a large-aperture scintillometer.
It was shown that the satellite retrieval for incoming solar radiation was in good agreement with the local measurements. Only small differences could not be resolved, which is not unexpected because only point measurements were used for comparison. In addition, it was shown that the reference temperature used in the Meteosat retrieval correlated with local measurements but needed to be bias corrected when used for evapotranspiration calculation. The bias correction for temperature differed by at most 1 K among the three test sites.
The tested method is intended as a first-order approach to estimate evapotranspiration for an entire season on a daily basis without needing to exclude partly cloudy situations. In contrast, methods that use a remotely sensed surface temperature to estimate surface fluxes have problems under partly cloudy conditions because the scattered clouds can easily contaminate the estimated surface temperature if the cloud-detection scheme misses the clouds.
It was shown that certain limits exist when such a first-order approach is applied. The first limit is related to the use of Makkink’s equation, which makes use of global radiation rather than net radiation for estimating optimal evapotranspiration. Furthermore, eventual effects of wind speed and humidity in the atmosphere were neglected. A second limit is related to the fact that the errors became larger if there was a considerable amount of evaporation from interception and/or bare-soil evaporation. Including bare-soil evaporation and evaporation from interception would be crucial to extend the application of the method to a full seasonal cycle. The most important limit is the assumption that the crop factor is equal to 1 for the fractional area that is covered with active vegetation. This introduced a bias error for all days.
Despite the mentioned limits, the approach for estimating AE, which was formerly developed for evapotranspiration estimation under ideal conditions for grass, worked with acceptable errors for diurnal and seasonal time scales under the conditions in the Volta basin of West Africa.
The results suggest that the simple satellite-based method is also suitable to verify meteorological models in regions under consideration where ground-truth weather data are scarce. A small network of scintillometers might be added to validate the satellite-based algorithm at a limited number of sites.
For the future, a combined approach of the shown method with skin-temperature estimation from Meteosat as shown by Sun and Pinker (2003) might help to improve quality for evapotranspiration estimation.
With the new satellite Meteosat-8, also known as Meteosat Second Generation, more-accurate information on the incoming solar radiation can be achieved because of increased spatial (1 km × 1 km and 3 km × 3 km), temporal (15 min), and spectral (12 bands) resolution. Meteosat-8 officially replaced the actual Meteosat-7 on 14 June 2006.
Special thanks are given to Richard Perez at the University at Albany (part of the State University of New York) for providing the algorithm for the irradiance model. Also, thanks are given to Hermann Mannstein at the DLR-Institute of Atmospheric Physics, Oberpfaffenhofen, Germany, for providing information on the Meteosat cloud-detection scheme. All Meteosat data are under copyright of EUMETSAT, Darmstadt, Germany. Many thanks for access to the dataset go to the crew of the Meteosat Archive and Retrieval Facility (MARF), Darmstadt, and to the Deutsches Fernerkundungs-Datenzentrum (DLR-DFD). Last, we thank the three anonymous referees for their constructive and motivating comments.
Corresponding author address: Dirk Schüttemeyer, Ludwig-Maximilians-University Munich, Luisenstraße 37, 80333 Munich, Germany. Email: email@example.com