Estimation of evapotranspiration through an improved daily global solar 1 radiation in SEBAL model : a case study of the middle Heihe River Basin

Abstract. The agricultural activities, hydrologic cycle, and ecological environment are seriously influenced by evapotranspiration (ET), especially in arid and semi-arid areas. A new method for estimating daily global solar radiation (GSR) over rugged terrains in the middle Heihe River Basin is developed on the basis of Iqbal model C. And with the land surface parameters retrieved from multisource remote sensing data, a daily surface ET on June 21–24, 2009, is simulated by using surface energy balance algorithm for land (SEBAL) model. The results show: 1. An improved daily GSR with a resolution of 100 m × 100 m is implemented. The mean absolute bias error (MABE) is 9 W/m2, and the mean absolute relative bias error (MARBE) is 2.5 %. The MABE of the daily GSR using the SEBAL model is 122.2 W/m2, and the MARBE is 33.9 %. 2. The spatial distribution of the daily GSR is more reasonable using the improved model than the original model. The GSR is larger on a sunny slope (an open place) than on a shady slope (a rugged place). 3. Bringing the new model into SEBAL significantly improves the accuracy of the ET. The MABE of ET decreases from 2.1 mm (original scheme) to 0.6 mm (improved scheme), and the MARBE declines from 44 % to 13 % accordingly. Moreover, the spatiotemporal resolution of the ET simulation is effectively improved by the combined moderate-resolution imaging spectroradiometer and thematic mapper surface parameters. 4. All highest ET value appeared in all types of water bodies, followed by farmland, forest, wetland, and residential areas, the lowest values appeared over bare rock land. The water consumption in these areas is dominated by agriculture. The new results provide better theoretical basis and scientific guidance for ecosystem protection and sustainable utilization of water resources.


1998a and 1998b) is currently a crucial method for estimating water and heat fluxes. the website of Digital Heihe (http://heihe.westgis.ac.cn). The land cover map is 110 created by a computer-assisted visual interpretation at the scale of 1:100,000 on the 111 basis of the TM image (Fig. 2).  117 where 24 a R is the daily GSR, sc G is the solar constant, that is, 1367W/m 2 , r d is the 118 earth-sun distance factor (dimensionless), 1  and 2  represent the solar hour angles 119 (radians) at 5 min after sunrise and at 5 min before sunset, respectively, and  is the 120 solar zenith angle. cos  is calculated by Chen et al., method(2013).

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In Eq. (1), only sun-earth spatial relations on a specific date, slope, and aspect 122 relations are considered. The effects of wet-clean air conditions and the terrain 123 shading are disregarded. The improved daily GSR model includes the above 124 mentioned factors, which can be categorized into two main models.

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(1) Determination of GSR over a horizontal surface 126 The effects of air molecules, O 3 , CO 2 , oxygen, and other mixed gas and water 127 vapor on short-wave solar radiation are considered in this part by using Iqbal Model C.

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A detailed description is presented in Shi et al., method (2018). 129 We obtain the daily global radiation under wet-clean air conditions using where -0  and 0  represent the solar hour angles at sunrise and sunset, T is the 132 length of a day, and t I is global irradiance.

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(2) Determination of GSR over rugged terrains 134 The effects of aerosol, land surface factors (slope, aspect, terrain shading, and 135 surface cover), and cloud are considered in this part.

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The daily GSR received on land surface consists of three parts (Fu, 1983). To determine b Q  , we assume that where d Q is the diffuse solar radiation in the horizontal surface, andV is the terrain 154 openness (terrain openness + terrain shading = 1). The method for determining V is 155 described by Qiu (2003).  Finally, the reflected radiation from the sloped surface can be computed by the 160 following expressions: The SEBAL procedure consists of a series of algorithms. In this study, this 166 procedure is implemented using the ModelMaker module of ERDAS software. The 167 algorithms solve the complete energy balance equation

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Theoretically, the GSR is larger on a sunny slope (an open place) than on a shady 226 slope (a rugged place), thereby indicating that the daily GSR is large where the 227 sunshine duration is long.

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The spatial distribution of the daily GSR calculated using the SEBAL model 229 presents discontinuous and improper stripes (Fig. 3a). However, the calculation of the 230 improved model is more reasonable, because the effects of the spatial position 231 relations, percentage of sunshine, slope, aspect, terrain shading, and atmospheric 232 influence are comprehensively reflected.

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An obvious difference between the SEBAL and the improved models is observed 234 in the southern area and the Longshou Mountain (Fig. 3b). The daily GSR in the 235 SEBAL model has reached the maximum value in the two areas. However, the daily 236 GSR in the improved model is near the minimal value. This result can be attributed to 237 the terrain shading that included a diffuse and reflected solar radiation in the new model. In addition, the percentage of sunshine is higher in the northwest, thus 239 implying that sunshine duration is long, and the corresponding daily GSR is high ( Fig.   240 3b). However, these distribution features are unclear in the daily GSR in the SEBAL 241 model.

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The daily GSR of 0°, 45°, 90°, and 360° in the slope direction of the study area 243 are statistically analyzed, and then the mean value is calculated (Fig. 4). In terms of 244 local surface distribution pattern, the daily GSR must reach the maximum value near 245 the south slope at 180°. However, the simulated results using the SEBAL model show 246 that the daily GSR is only the minimum value (Fig. 4a), and the error is corrected by 247 the improved model (Fig. 4b).
248 Therefore, the improved daily GSR model improves the calculation accuracy and 249 makes the spatial distribution more reasonable than the original model.  Table 4. The mean measured ET for 4 259 days was 4.8 mm. The MABE of the improved scheme-simulated ET is 0.6 mm, and addition, the ET is low in the area around the oasis. The differences in ET over the 283 various land types mainly depends on the NDVI. A large NDVI value indicates a high 284 ET.

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In Fig. 5 and 6, the simulation ET based on the improved scheme declines more 286 than the original scheme. In the improved scheme, the desert ET is mainly distributed 287 in the vicinity of 0 mm, and the oasis ET is in the vicinity of 4.8 mm. In the original 288 scheme, the desert ET is mainly distributed in the vicinity of 0 mm, and the oasis ET 289 is in the vicinity of 6.5 mm.

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The TM strategy has the highest resolution (Figs. 5a and 6a), whereas the 291 MODIS strategy has the lowest ( Fig. 5b and 6b); many features retrieved by the TM   The simulated ET declines more based on the improved scheme than based on 329 the original scheme. The mean measured ET of the oasis station in 4 days is 4.8 mm.

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The original scheme ET is 6.9 mm, and the improved scheme ET is 4.2 mm using the 331 TM/MODIS hybrid strategy. The MABE of ET decreases from 2.1 mm (original 332 scheme) to 0.6 mm (improved scheme), and the MARBE declines from 44% to 13% 333 accordingly. And in all schemes desert ET is mainly distributed in the vicinity of 0 334 mm.

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All simulated ETs show that the highest ET value is found in farmland, except 336 for water bodies considering the presence of irrigation water, followed by farmland, 337 forest, wetland, and residential areas, the lowest values appeared over bare rock land.