The accurate estimation of actual evapotranspiration can help improve the utilization of water resources and ease the ecological stress. Based on the generalized complementary principle proposed by Brutsaert in 2015, we used meteorological and hydrological data to estimate the actual evapotranspiration at a resolution of 1 km × 1 km between the years of 1961 and 2000 and also verified the model’s stability. In this study, we used the water balance equation to calibrate the parameters, coupled with the spatial simulation results of the meteorological elements in the actual evapotranspiration model. The estimation results of actual evapotranspiration show that the generalized complementary principle model had high estimation precision in this basin, with an average absolute error of 16.64 mm and an average relative error of 2.25%. With respect to spatial distribution, the average actual evapotranspiration over the years in the basin tended to have high and low distribution in the northern and southern parts of the basin, respectively. The actual evapotranspiration in the basin showed a decreasing trend over the period, with a rate of 24.1 mm/10 years. Correlation coefficient analysis showed that the percentage decreases in percentage sunshine and the decreases in the daily range of temperature were the main reasons for the decrease in actual evapotranspiration.
Evapotranspiration from the land surface plays a key role in maintaining the balance of land surface water-lakes-reservoirs and the energy balance of the earth’s surface [
Actual evapotranspiration is defined as a combined process of both evaporation from soil and plant surfaces and transpiration through plant canopies [
Water resources per unit area and per capita in China are below the world average, and freshwater resources per capita in China are only a quarter of the world’s per capita freshwater resources. The distribution of water resources in China is extremely uneven, and the evapotranspiration process is an important process of the water cycle. The accurate estimation of evapotranspiration has a very important value for water resources assessment and vegetation drought monitoring. In China, scarcely any research has been done based on the principle of generalized complementary correlation. In this study, we selected the basin above Wangjiaba in the upper Huaihe River as the study area and calculated the annual evapotranspiration over 40 years according to the generalized complementary principle of Brutsaert [
The Huaihe River Basin is in eastern China between the Yangtze River and the Yellow River. The Huaihe River is divided into three parts: the upper, middle, and lower reaches. The upper reach is Honghekou and above and is 360 km long between longitudes 113°27′ and 115°62′E and latitudes 31°47′ and 33°53′N. The watershed control area is approximately 31,000 km2. The Huaihe River Basin is in the transitional climate zone between North China and South China and is characterized by a warm temperate and semihumid monsoon climate. Additionally, the winter and spring are characterized by droughts with rare rainfall, and the summer and autumn are usually hot with frequent rain. The rainfall in the basin is sufficient, and the annual average rainfall is approximately 920 mm. The spatial distribution of rainfall roughly decreases from the south to the north, with the mountainous areas receiving more rain than the plains areas. The annual average temperature is generally 11–16°C, and the monthly average temperature of July is the highest, usually approximately 25°C. The monthly average temperature of January is the lowest, usually approximately 0 °C [
Distribution of the water system, meteorological stations, and hydrological stations in the upper reach of the Huaihe River Basin and its surrounding areas.
The meteorological data between 1956 and 2000, which were obtained from the National Meteorological Information Center, include the daily average temperature, daily minimum temperature, daily maximum temperature, daily range of temperature, percentage sunshine, daily average wind speed, and daily precipitation data. The level-2 water resources data were obtained from the Water Resources, Hydropower Planning and Design Institute of the Ministry of Water Resources. The level-2 river network data and the digital elevation model (DEM) data source were derived from the National Geomatics Center of China. We estimated the distributed results of the monthly albedo from 1961 to 2000 using the data from NOAA/AVHRR satellite channels 1 and 2 from 1961 to 2000 and the estimation formula for the surface albedo.
In this study, the actual evapotranspiration is calculated based on the generalized complementary principle proposed by Brutsaert. He introduced nondimensional
The polynomial implementation can be written by expressing the relationship of
To develop a significant equation, Brutsaert [
Under very moist conditions, (i) shows that
The actual evapotranspiration can be expressed by (
Since the formula [
Flow chart of the spatial distribution result of actual evapotranspiration based on the generalized complementary principle.
Calculation of total radiation under the complex terrain
The method of calculating the total solar radiation received by the surface under the complex terrain is as follows: Estimation of the surface albedo by remote sensing
The surface albedo can be calculated by climatological calculation or satellite remote sensing inversion. The surface albedo of this study is calculated by the method given by Valiente [
The surface albedo inversion is calculated using monthly measurements over the 1961–2000 period [ Calculation of NSLR under the complex terrain
The NSLR under the complex terrain is calculated as follows [
Simulation parameters of net surface longwave radiation.
P | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
|
0.447 | 0.473 | 0.522 | 0.577 | 0.642 | 0.691 | 0.705 | 0.661 | 0.554 | 0.497 | 0.45 | 0.438 |
|
−0.042 | −0.04 | 0.049 | −0.065 | −0.073 | −0.085 | −0.088 | −0.083 | −0.068 | −0.058 | −0.047 | −0.044 |
|
0.201 | 0.16 | 0.16 | 0.171 | 0.101 | 0.152 | 0.123 | 0.128 | 0.211 | 0.184 | 0.173 | 0.199 |
The units need to be unified when calculating
The first evaluation of water resources in China occurred from 1956 to 1979, and a large number of reservoirs were built after 1980. These greatly affected the water balance and are not conducive to estimating the actual evapotranspiration in the river basin. Therefore, the data from 1956 to 1976 were chosen for estimation. The
Estimation error of actual evapotranspiration in the upper reach of the Huaihe River Basin.
Validation period | Water balance (mm) | Estimated result (mm) | Absolute error (mm) | Relative error (%) |
---|---|---|---|---|
1967–1977 | 746.16 | 716.16 | 30 | 4.02 |
1968–1978 | 713.62 | 715.9 | 2.28 | 0.32 |
1969–1979 | 733.71 | 716.08 | 17.63 | 2.4 |
Regression plot of water balance and generalized complementary simulation using the
Based on the simulation method in this study, we obtained the spatial distribution of annual average actual evapotranspiration in the upper reach of the Huaihe River Basin from 1961 to 2000 (Figure
Spatial distribution of annual actual evapotranspiration in the upper reach of the Huaihe River Basin for the period 1961–2000.
Variation of annual actual evapotranspiration in the upper reach of the Huaihe River Basin during 1961–2000.
Pearson correlations between actual evapotranspiration and the percentage sunshine, maximum temperature, minimum temperature, average temperature, daily temperature, 2-meter average wind speed, relative humidity, daily range of temperature, actual vapor pressure, and other variables are shown in Table
Correlation coefficients between meteorological factors and actual evapotranspiration.
Percentage sunshine | Relative humidity | Maximum temperature | Minimum temperature | Average temperature | Daily range of temperature | Actual vapor pressure | 2-meter average wind speed | |
---|---|---|---|---|---|---|---|---|
Actual evapotranspiration | 0.771 |
−0.292 | 0.337 |
−0.185 | 0.1 | 0.557∗∗ | −0.019 | 0.328 |
Variation trend graphs of maximum temperature, daily range of temperature, 2-meter average wind speed, and percentage sunshine with actual evapotranspiration.
In this study, we estimated actual evapotranspiration based on the generalized complementary principle. The model components (drying power, soil heat flux, net radiation, constant of wet and dry tables, etc.) and surface albedo all affect the accuracy of the actual evapotranspiration. Using the Priestley–Taylor formula as a possible evapotranspiration formula, the parameter
Since the formula is based on the assumption that there is no advection, the inhomogeneity of the underlying surface of the basin will lead to the occurrence of advection. There can be no full advection in the actual environment; thus, the
The sensitivity coefficient is a dimensionless index
Sensitivity level.
Sensitivity coefficient | Sensitivity levels |
---|---|
|
Small to negligible |
|
Medium |
|
High |
|
Very high |
Sensitivity of actual evapotranspiration to other variables.
Variables | Sensitivity coefficient |
Sensitivity levels |
---|---|---|
Slope of the saturation vapor pressure curve | 0.365 | High |
Psychrometric constant | −0.352 | High |
Net radiation | 0.999 | High |
Soil heat flux | −0.001 | Small to negligible |
Drying power | 0.000 | Small to negligible |
Many researchers [
The theoretical model of the generalized complementary correlation principle was used to calculate the actual evapotranspiration using the spatial simulation results of meteorological elements in the upper reach of the Huaihe River. Estimation was successful, and the spatial distribution of the average actual evapotranspiration was well characterized by the distributed simulation. The estimated average annual evapotranspiration absolute error was 16.64 mm, and the average relative error was 2.25%. Pearson’s correlation coefficient analysis showed that the reduction in the percentage sunshine and the decreases in the daily range of temperature and 2-meter average wind speed were the main reasons for the decrease in actual evapotranspiration. Therefore, for vegetation and drought monitoring and ecological modeling, estimating evapotranspiration and evaluating water resources in the basin are very important.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this article.
This work was supported by the National Natural Science Foundation of China Project (41330529). The meteorological data between 1956 and 2000 could be obtained from the China Meteorological Data Service Center (CMDSC) at