Advances in Meteorology

Volume 2019, Article ID 6253832, 13 pages

https://doi.org/10.1155/2019/6253832

## Based on the Gaussian Fitting Method to Derive Daily Evapotranspiration from Remotely Sensed Instantaneous Evapotranspiration

^{1}School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450046, China^{2}Henan Key Laboratory of Water Environment Simulation and Treatment, Zhengzhou 450046, China^{3}Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China^{4}Department of Civil, Environmental and Geomatics Engineering, Florida Atlantic University, Florida, FL 33431, USA^{5}Shenzhen Environmental Monitoring Center, Shenzhen 518049, China

Correspondence should be addressed to Hongbo Su; gro.eeei@obgnoh and Jing Tian; nc.ca.rrnsgi@b40.jnait

Received 21 April 2018; Accepted 3 December 2018; Published 14 January 2019

Academic Editor: James Cleverly

Copyright © 2019 Suhua Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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 (*R*^{2}) of 0.82, a mean average error (MAE) of 0.41 mm, and a root mean square error (RMSE) of 0.46 mm. To make more scientific assessments, percent errors were calculated on the estimation accuracy, which ranged from 0% to 18%, with more than 80% of locations having the percent errors within 10%. Analyses on the relationship between daily ET estimates and land use status were also made to assess the Gaussian fitting method, and the results showed that the spatial distribution of daily ET estimates well demonstrated ET differences caused by land use types and was intimately linked with the vegetation pattern. The comparison between the Gaussian fitting method and the sine function method and the ETrF method indicated that results derived through the Gaussian fitting method had higher precision than that obtained by the sine function method and the ETrF method.

#### 1. Introduction

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 [1–5]. In most cases, ET is the largest loss of precipitation, and it is a significant outgoing water flux from the earth’s surface. In semiarid areas, the amount of ET almost equals that of precipitation [6]. Hence, accurate estimation of ET is beneficial to improve applications in many fields, such as drought mitigation strategies, irrigation system performance, optimization of irrigation water use, hydrological modeling, and accurate initialization of climate prediction models, and is also very useful for understanding the global climate change, the local to global energy and water cycles, ecosystem processes, and land-atmosphere interaction [7–12]. Ground-based observations including Bowen ratio tower, eddy covariance [13], lysimeter, and large aperture scintillometer can provide ET measurements with some advantages. However, regional ET acquired through these methods is time-consuming and labour-intensive because it requires numerous installations and considerable spatial interpolations [8].

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 [14]. In the last two decades, the recent advances of remote sensing technology together with the requirement for quantifying regional ET have brought about numerous researches in obtaining large-scale ET [8, 10, 15, 16]. Remote sensing can retrieve an instantaneous ET on a regional scale at the time of satellite overpass. However, daily ET estimates are required for water resources monitoring and ecological management purposes [14, 17]. Consequently, it is of significance to convert instantaneous ET into daily ET [18, 19].

Several instantaneous ET extrapolation methods are proposed and developed to derive daily ET, such as the sine function method [20], the evaporative fraction (EF) method [21], and the reference ET fraction (ETrF) method [22]. Jackson et al. [20] proposed a technique based on the ratio of daily solar radiation to instantaneous solar radiation. Given it was similar to that of solar irradiance throughout the daylight period, they assumed the generic trend for the ET diurnal course could be approximated by a sine function which is named the sine function method. Zhang and Lemeur [23] did researches on the sine function method, and they concluded that the sine function method was preferable to estimate daily ET using remote sensing data. The disadvantage of this method is that it is limited by its empirical nature in applications [14]. The EF, defined as the latent heat flux divided by the latent heat flux plus sensible heat flux (available energy (AE)), is nearly constant during the daytime period [24, 25]. Hence, the method can utilize instantaneous EF and continuous measurements of the available energy flux to determine daily ET. Studies [23] showed that the assumption of a constant EF was valid under cloud-free conditions. Sugita and Brutsaert [26] also yielded accurate estimates of daily ET by the EF method. However, some studies found that EF changes with the available energy, surface resistance, and other environmental variables, which caused uncertainties in applying the EF method [23]. Tasumi et al. [27] investigated a method labeled “reference ET fraction,” which was defined as the ratio of actual ET to reference ET (ETr) for an alfalfa crop. This method assumes that the instantaneous ETrF is similar to the daily average ETrF. Many studies have been conducted to utilize the ETrF method to derive daily ET, and the results show that the ETrF remains constant during the daytime [28]. The ETrF method, however, seems to perform well under homogeneous surface conditions [29].

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 2 includes two subsections: Section 2.1 presents a description on the theory of retrieving instantaneous ET by remote sensing and Section 2.2 introduces the Gaussian fitting method for deriving daily ET. Section 3 describes the datasets and the study area used to assess the Gaussian fitting method. Section 4 shows the results. Section 5 provides discussions on the advantages and limitations of the Gaussian fitting method, and Section 6 summarizes a conclusion of the work.

#### 2. Methodology

##### 2.1. Obtaining the Instantaneous ET

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:where , , , and are the net radiation, sensible heat flux, latent heat flux, and soil heat flux, respectively. Units of the four items are W/m^{2}. In equation (1), net radiation, , sensible heat flux, , and soil heat flux, , can be determined by the following equations, respectively:where (W/m^{2}) is the downward shortwave radiation, is the surface albedo, (W/m^{2}) is the downward longwave radiation, is the Stefan–Boltzmann constant and the value of it is 5.67 × 10^{−8} W·m^{−2}·K^{−4}, is the surface emissivity, (K) is the aerodynamic temperature and is usually substituted with land surface temperature (LST) in applications [30, 31], is the air density, (1004 J/(kg·K)) is the specific heat at constant pressure of air, and (s/m) is the air aerodynamic resistance and can be calculated by the classical formulae that take into account the stability correction functions for temperature and wind. Readers can refer to the calculation process of by Abdelghani et al. [32]. (K) is the surface air temperature, and is the fractional vegetation cover which was calculated using NDVI images, with of the bare soil and of dense vegetation. The formula is as follows [33]:where NDVI is the ratio of the differences in reflectivity between the near-infrared (NIR) band and the red (R) band to their sum:where and are the reflectivities for near-infrared and red bands, respectively.

The latent heat flux, LE, can be acquired as the following equation by integrating equations (1)–(4):where variables including , , , and can be calculated through remote sensing images, is attained by referring to Abdelghani et al. [32], and variables including , , and are acquired from the meteorological stations.

##### 2.2. Obtaining the Daily ET

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 [20, 23]. The attempt provided in our study is also an approximation similar to the sine function method, which is named the Gaussian fitting method.

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 [34]. Hence, we applied the Gaussian fitting curve to fit the diurnal course of ET on several clear sky days. A comparison between ET measurements at EC stations and ET estimates by the Gaussian fitting curve is shown in Figure 1. The points represent the values of net radiation measurements observed every 10 minutes (Figure 1(a)) and ET measurements observed every 30 minutes (Figure 1(b)) throughout the day, respectively. The lines represent the best fits of Gaussian fitting curves to the experimental data. It is obvious that the Gaussian fitting curves closely follow the experimental data during the daytime (from sunrise to sunset).