Evapotranspiration (ET) is a significant component in the water cycle, and the estimation of it is imperative in water resource management. Regional ET can be derived by using remote sensing technology which combines remote sensing inputs with ground-based measurements. However, instantaneous ET values estimated through remote sensing directly need to be converted into daily totals. In this study, we attempted to retrieve daily ET from remotely sensed instantaneous ET. The study found that the Gaussian fitting curve closely followed the ET measurements during the daytime and hence put forward the Gaussian fitting method to convert the remotely sensed instantaneous ET into daily ETs. The method was applied to the middle reaches of Heihe River in China. Daily ETs on four days were derived and evaluated with ET measurements from the eddy covariance (EC) system. The correlation between daily ET estimates and measurements showed high accuracy, with a coefficient of determination (
Evapotranspiration (ET), which is crucial to the hydrological cycle, is defined as the synthesis process of evaporation and transpiration. It is the link of energy and water exchanges among the biosphere, atmosphere, and hydrosphere [
Satellite remote sensing makes it possible for acquiring regional ET over various spatial scales, ranging from individual pixels to an entire raster image that may cover a whole river basin [
Several instantaneous ET extrapolation methods are proposed and developed to derive daily ET, such as the sine function method [
The aforementioned instantaneous ET extrapolation methods request numerous variables, and some of the variables may be difficult to attain through remote sensing. For example, the EF method needs an instantaneous EF value and daytime total available energy, the sine function method requests several variables related to geographic location, and the ETrF method demands variables linked with specific crops. To simplify the computation process of daily ET, the study put forward a method of deriving daily ET, which was based on the ET diurnal course and similar to the sine function method. In this paper, we assume that, for clear sky days, the diurnal course of solar radiation and ET can be adequately expressed by the Gaussian fitting curve and then develop the Gaussian fitting approach for calculating daily ET from instantaneous ET. Section
In the study, we adopted the energy balance theory to compute the instantaneous ET. Without considering the energy transported by horizontal advection and consumed by photosynthesis, the energy exchanged between the land surface and the atmosphere can be described by the energy balance equation:
The latent heat flux, LE, can be acquired as the following equation by integrating equations (
Jackson et al. put forward the assumption that the diurnal course of ET was similar to that of solar irradiance and could be approximated by a sine function [
According to our observations, we found that not only the diurnal course of net radiation but also the diurnal course of ET during the daytime can be approximated by the Gaussian fitting curve [
Diurnal course of solar radiation (a) and latent heat flux (b) at middle reaches of Heihe River for a clear sky day: August 14, 2012. Symbols represent experimental data. The lines were calculated from the Gaussian fitting function.
The Gaussian fitting function can be expressed as follows:
To explain the meanings of the variables in equation (
A Gaussian fitting curve of equation (
From formula derivation above, we know that the unique advantage of the Gaussian fitting method is that the expression of Gaussian fitting equation has already contained the daily ET. In equation (
As for
To find out the relationship between
Details on EC stations used for validity verification.
Name | EC1 | EC4 | EC10 | EC17 |
---|---|---|---|---|
The underlying surface | Vegetable | Village | Maize | Orchard |
Days to test the validity | 9 days | 12 days | 12 days | 12 days |
The relationship between
Belonging to the middle basin of the second longest inland river of China, Heihe River, the study area is located in Zhangye Oasis, Gansu, China, with the latitude of 38.83°N∼38.93°N and the longitude of 100.32°E∼100.42°E, as shown in Figure
Location of the study area with land use types and 17 stations.
For retrieving the daily ET, remote sensing data, such as ASTER images and HJ-1 A/B images, together with ground-based measurements including meteorological variables and surface fluxes are utilized.
ASTER is a sensor that acquires numerous images in different bands including multispectral visible, near-infrared, and thermal infrared. It is intended to monitor climate, land surface energy balance, and hydrological processes [
Ground-based observations were provided by Heihe Watershed Allied Telemetry Experimental Research (HiWATER), which was an ecohydrological and watershed-scale experiment. From an interdisciplinary perspective, the HiWATER experiment was designed to address studies including uncertainty, scaling, heterogeneity, and closing of the water cycle in the watershed scale [
There are 17 elementary sampling plots (as shown in Figure
Original EC measurements were collected at a sampling frequency of 10 Hz. The processing work on EC data includes spike detection, lag correction of H2O/CO2 relative to the vertical wind component, sonic virtual temperature correction, coordinating rotation using the planar fit method, corrections for density fluctuation (WPL correction), and frequency response correction. The postprocessing software named “EdiRe” was utilized to make the above corrections (University of Edinburgh;
The automatic meteorological stations can monitor meteorological variables, such as solar radiation, wind speed, wind direction, air pressure, air temperature, and air humidity, with the sample intervals of 10 minutes and 1 minute. The EC stations can acquire surface fluxes including latent heat flux and sensible heat flux with a sample interval of 30 minutes [
To test the validity of the Gaussian fitting method, we utilized the Gauss fitting curve to simulate the diurnal variation of instantaneous ET observed at EC stations with different underlying surfaces. Table
To make the validity verification more persuasive, we used the whole EC data in June, except that on cloudy, rainy, and data missing days, from four sites (EC1, EC4, EC10, and EC17) to make the Gaussian fitting analysis. Figure
Gaussian fitting results on ET measurements at EC1 on cloud-free days in June 2012.
Gaussian fitting results on ET measurements at EC4 on cloud-free days in June 2012.
Date | Fitting equation |
|
RMSE (W/m2) |
---|---|---|---|
June 7 | ETfit = 3.81 + 216.4 ∗ exp(−0.044 ∗ ( |
0.90 | 7 |
June 8 | ETfit = −2.9 + 162.5 ∗ exp(−0.034 ∗ ( |
0.85 | 8 |
June 9 | ETfit = −4.48 + 158.7 ∗ exp(−0.038 ∗ ( |
0.87 | 6.5 |
June 11 | ETfit = 5.9 + 156.6 ∗ exp(−0.043 ∗ ( |
0.92 | 4.5 |
June 15 | ETfit = 0.1 + 148.8 ∗ exp(−0.041 ∗ ( |
0.91 | 4.6 |
June 16 | ETfit = 0.7 + 153.4 ∗ exp(−0.037 ∗ ( |
0.89 | 5.69 |
June 19 | ETfit = −2.9 + 165 ∗ exp(−0.038 ∗ ( |
0.87 | 7 |
June 20 | ETfit = 10.56 + 136.2 ∗ exp(−0.037 ∗ ( |
0.97 | 5.8 |
June 21 | ETfit = 4.85 + 144.8 ∗ exp(−0.041 ∗ ( |
0.87 | 5.7 |
June 24 | ETfit = 1.88 + 193 ∗ exp(−0.045 ∗ ( |
0.84 | 7.9 |
June 29 | ETfit = 4.5 + 255.2 ∗ exp(−0.036 ∗ ( |
0.94 | 7.3 |
June 30 | ETfit = 6.6 + 204.4 ∗ exp(−0.037 ∗ ( |
0.86 | 8.7 |
Gaussian fitting results on ET measurements at EC10 on cloud-free days in June 2012.
Date | Fitting equation |
|
RMSE (W/m2) |
---|---|---|---|
June 7 | ETfit = −5.9 + 435.5 ∗ exp(−0.047 ∗ ( |
0.95 | 9.4 |
June 8 | ETfit = −8.6 + 353.3 ∗ exp(−0.040 ∗ ( |
0.95 | 8.7 |
June 9 | ETfit = −1.87 + 269.7 ∗ exp(−0.045 ∗ ( |
0.95 | 8.3 |
June 11 | ETfit = 1.10 + 409.9 ∗ exp(−0.047 ∗ ( |
0.95 | 8.7 |
June 15 | ETfit = −7.1 + 432.6 ∗ exp(−0.048 ∗ ( |
0.96 | 7.7 |
June 16 | ETfit = −4.52 + 441.3 ∗ exp(−0.044 ∗ ( |
0.97 | 8 |
June 19 | ETfit = −1.88 + 519.8 ∗ exp(−0.042 ∗ ( |
0.96 | 11 |
June 20 | ETfit = −2.48 + 698.6 ∗ exp(−0.055 ∗ ( |
0.97 | 9.8 |
June 21 | ETfit = 14.1 + 676.2 ∗ exp(−0.057 ∗ ( |
0.93 | 16 |
June 24 | ETfit = −2.85 + 731.4 ∗ exp(−0.058 ∗ ( |
0.94 | 15.5 |
June 29 | ETfit = 5.6 + 627.5 ∗ exp(−0.053 ∗ ( |
0.96 | 11 |
June 30 | ETfit = 9.8 + 593 ∗ exp(−0.054 ∗ ( |
0.91 | 16.5 |
Gaussian fitting results on ET measurements at EC17 on cloud-free days in June 2012.
Date | Fitting equation |
|
RMSE (W/m2) |
---|---|---|---|
June 7 | ETfit = 6.7 + 437.6 ∗ exp(−0.049 ∗ ( |
0.92 | 12 |
June 8 | ETfit = −4.89 + 423.2 ∗ exp(−0.045 ∗ ( |
0.92 | 12 |
June 9 | ETfit = 4 + 454.5 ∗ exp(−0.057 ∗ ( |
0.94 | 9.6 |
June 11 | ETfit = 2.2 + 439.5 ∗ exp(−0.045 ∗ ( |
0.93 | 11.5 |
June 15 | ETfit = 0.68 + 342.2 ∗ exp(−0.045 ∗ ( |
0.94 | 8.7 |
June 16 | ETfit = 4.8 + 367.2 ∗ exp(−0.044 ∗ ( |
0.93 | 10 |
June 19 | ETfit = −14 + 414.7 ∗ exp(0.042 ∗ ( |
0.93 | 12 |
June 20 | ETfit = −12 + 418.2 ∗ exp(−0.047 ∗ ( |
0.92 | 12 |
June 21 | ETfit = 1.96 + 473 ∗ exp(−0.066 ∗ ( |
0.92 | 12 |
June 24 | ETfit = −11 + 443.8 ∗ exp(−0.049 ∗ ( |
0.95 | 9 |
June 29 | ETfit = −1.1 + 489.1 ∗ exp(−0.043 ∗ ( |
0.88 | 17.5 |
June 30 | ETfit = −4.1 + 517.7 ∗ exp(−0.047 ∗ ( |
0.93 | 13 |
Four clear sky days, June 24, July 10, and August 11 and 27, 2012, were utilized to calculate the daily ET by the Gaussian fitting method. As mentioned in Section
Daily ET calculated by the Gaussian fitting method on June 24 (a), July 10 (b), and August 11 (c) and 27 (d), 2012.
Daily ET estimates derived by the Gaussian fitting method for the four days are tested against ET measurements (68 points) at ground-based EC stations (Figure
Comparison between daily observed ET by EC stations and that estimated by the Gaussian fitting method.
The study made error analyses from two aspects, one is the percent error and the other is the relationship between errors and land use.
According to the error analysis and the numerical analysis theory, the percent error is more scientific and more robust than the absolute error for assessing the accuracy of estimates [
Figure
The frequency distribution of percent errors on daily ET estimates obtained by the Gaussian fitting method.
As for the relationship between errors and land uses, we utilized estimations from land covers of vegetable, village, maize, and orchard and their corresponding ground-based observations that were at the site of EC1, EC4, EC10, and EC17 on June 24, July 10, and August 11 and 27, 2012, to calculate and analyze the estimation errors. To avoid abnormal variation, the study used the average values of observations and estimations for four days to analyze, and the results are shown in Table
Estimation errors at the site of EC1 EC4, EC10, and EC17.
Site | Observation (mm) | Estimation (mm) | Estimation error (mm) |
---|---|---|---|
EC1 | 5.3 | 4.7 | −0.6 |
EC4 | 2.2 | 3.1 | 0.9 |
EC10 | 5.8 | 5.4 | −0.4 |
EC17 | 4.9 | 5.2 | 0.3 |
Previous studies suggested that the spatial distribution of ET was strongly related to land cover types and that studies on ET estimates at a regional scale always required the incorporation of heterogeneous surface status [
The statistical work was done to make the analyses quantitatively. In the study area, there were four main land use types including maize, vegetable, orchard, and village. For each land use type, average daily ET on the four days was computed (Table
Daily ET estimates derived by the Gaussian fitting method of the four different land use types on June 24, July 10, and August 11 and 27, 2012.
Land use type | June 24 | July 10 | August 11 | August 27 |
---|---|---|---|---|
Maize (mm) | 6.6 | 6.1 | 4.2 | 4.6 |
Vegetable (mm) | 5.3 | 4.7 | 3.5 | 3.6 |
Orchard (mm) | 6.8 | 5.9 | 4.3 | 5.1 |
Village (mm) | 4.0 | 3.6 | 2.2 | 2.4 |
The spatial distribution of daily ET was strongly connected with the land cover. In June, July, and August, maize and fruit trees were in the vigorous growth season and with frequent irrigation. As a result, the vegetation cover was dense and the daily ET was high. Compared with maize and orchard, vegetables including pepper, leek, and cauliflower had a sparse vegetation cover during this time, and therefore, their daily ET values were lower than those of maize and orchard. Since villages were covered with buildings and the underlying surfaces were largely bare and solidified, the daily ET values over villages were the lowest.
Generally, high daily ET always agrees with a dense vegetation cover and low daily ET is usually in accordance with a sparse vegetation cover, which indicates that the daily ET results obtained by the Gaussian fitting method are consistent with the objective knowledge and can well perform the daily ET differences brought about by land use status.
Similar to the sine function method, the Gaussian fitting method is also based on the diurnal variation of ET; hence, this section gives the comparisons between the Gaussian fitting method and the sine function method. According to Xu et al. [
Comparison between daily ET observed by EC stations and that estimated by the sine function method (a) and the ETrF method (b).
The Gaussian fitting method applies the Gaussian fitting curve to simulate the diurnal course of ET. Hence, the principle of the method is clear to be understood, and the method is convenient to be utilized. The most obvious advantage of the Gaussian fitting method is that the Gaussian fitting equation has already contained the variable
The Gaussian fitting method also has some uncertainties. The crucial step in the applications of the Gaussian fitting method is determining the variables
Remote sensing is a promising tool to retrieve instantaneous ET on a regional scale. However, the daily ET or a longer timescale ET is more significant to monitor and manage the water resource. Hence, it is essential to convert instantaneous ET into daily ET. The study proposes the Gaussian fitting method to derive daily ET from remotely sensed instantaneous ET. Model validation and application were conducted to test the validity and evaluate the accuracy of the Gaussian fitting method. Model validation showed that the Gaussian fitting curve could well describe the diurnal course of ET measurements at EC stations, with high coefficients of determination and low root mean square errors. As a result, the Gaussian fitting method could be taken as an appropriate approach to simulate daily ET. A case study was performed in the middle reaches of Heihe River, China, to derive daily ET from remotely sensed instantaneous ET. The comparison between daily ET estimates derived by the Gaussian fitting method and measurements obtained from EC stations showed an
The data used in the manuscript include two types, the remote sensing data and the ground-based data. For remote sensing data, the readers can apply for and obtain ASTER images and HJ-1 A/B images through the official websites of USGS (
An earlier and simpler version of a fraction of this paper has been presented as a conference paper in “Geoscience and Remote Sensing Symposium (IGARSS), 2017 IEEE International.”
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences (grant number XDA20010302), the National Natural Science Foundation of China (grant numbers 41571356, 41671368, 41671354, and 41671373), the National Basic Research Program of China (grant number 2013CB733406), the Henan Province University Scientific and Technological Innovation Team (18IRTSTHN009), and the Key Project of National Natural Science Foundation of China (41301363).