1. Introduction
Net radiation (
Rn) is the balance between the downward and upward shortwave and longwave radiation and is a key component of the Earth’s surface energy balance. It is the main source of energy for the physical and chemical processes that occur in the surface-atmosphere interface, the heat and water budgets, photosynthesis [
1] and evapotranspiration [
2], which are used as input for global and regional climate change and eco-hydrological models. Net radiation especially affects the energy balance closure and the accuracy of evapotranspiration estimation algorithms [
3,
4]; therefore, the accurate estimation of net radiation is important for researchers in the fields of meteorology, hydrology, global change and agriculture [
5,
6,
7].
Net radiation can be reliably obtained using net radiometers or shortwave and longwave radiometers, and it is routinely recorded at meteorological and radiation stations. Although such instruments are accurate for measuring net radiation at a station (representative for a certain area), their use for large regional net radiation assessments is time consuming and expensive because numerous ground installations are required, especially when large spatial coverage and a high sampling frequency are desired. Net radiation is not measured directly in most national basic meteorological stations due to restrictions imposed by economic and technical conditions, unless the station is required for radiation studies. In addition, few national radiation stations exist, resulting in insufficient net radiation data in some areas.
Various methods have been recommended for obtaining net radiation on a regional scale. Currently, the most commonly used methods for calculating net radiation are applied to the calculation of net shortwave and net longwave radiation. Net shortwave radiation is obtained by using the surface albedo and global solar radiation. The surface albedo can be calculated from remote sensing data using different band reflectances [
8]. Global solar radiation can be obtained by several empirical models involving various climatic variables, including extra-terrestrial solar radiation, sunshine duration, mean temperature, maximum temperature, minimum temperature, water saturation deficit, soil temperature, the number of rainy days, altitude, latitude, total precipitation, the Sun-Earth distance, and the Julian day [
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37]. The most widely used method is the Angstrom-Prescott model, which has been applied in many countries [
24,
38,
39,
40,
41,
42,
43] in various forms, such as quadratic, third degree, logarithmic and exponential forms. The Angstrom-Prescott model and its revised variants most commonly use sunshine duration for estimating global solar radiation. According to the comparative study by Can and Oman [
44] and Kadir [
35], global solar radiation models based on sunshine duration could give more accurate results than those based on other meteorological variables without sunshine duration. Although sunshine duration can be obtained from ground measurements, their application to regional and global solar radiation calculations suffers from the limited availability of ground data. Robaa [
45] developed an empirical method based on the amount of clouds to estimate sunshine duration, in which empirical equations were proposed based on relative sunshine duration and readily available cloud amount data from Moderate Resolution Imaging Spectroradiometer (MODIS). This method does not consider the changes in the cloud amount between sunrise and sunset, and it can calculate only monthly sunshine duration, not daily sunshine duration. Wu et al. [
46] proposed a new method to derive sunshine duration from geostationary meteorological satellite hourly cloud classification data based on a new index—the cloud classification coverage-type sunshine factor—and this method can accurately estimate daily sunshine duration without ground measurements.
In addition to sunshine duration, the empirical Angstrom
as and
bs coefficients are needed to calculate global solar radiation using the original and revised variants of the Angstrom-Prescott model. Common values of these coefficients range between 0 and 1 (0.25 and 0.5 have been recommended when no ground measurements are available for calibration). The former expresses the fraction of extra-terrestrial radiation reaching the ground on an overcast day (
n = 0) and depends on the atmospheric conditions (humidity and aerosols) and the solar angle [
9,
35,
47]. Ground measurements are commonly used to fit the values of
as and
bs, and several researchers [
36,
48,
49,
50,
51] have estimated these coefficients on an annual scale in different regions. However, using a fixed coefficient on an annual scale is not appropriate for our purposes because of the regional environmental characteristics, and thus, the monthly empirical Angstrom coefficient should be fitted. Zhao et al. [
37] suggested a new approach based on Air Pollution Index (API) data from ground measurements to adjust the Angstrom coefficients. Because of the limited number of ground stations and the short site observation time, this method has high precision but is not generalizable. Therefore, ground-measured radiation and meteorological data can be fully utilized to fit the monthly empirical Angstrom coefficients
as and
bs, which is a better method to estimate global solar radiation based on sunshine duration data.
Meteorological variables are commonly used to estimate net longwave radiation: water vapour pressure, air temperature, and downward shortwave radiation or sunshine duration, as in the Food and Agricultural Organization of the United Nations (FAO)-56 Penman equation [
17,
27,
52]. The daily net longwave radiation equation coefficients based on the FAO-56 Penman equation have been applied to various situations in many countries and regions. However, it must be calibrated with local ground measurements [
47,
53,
54,
55], and the downward shortwave radiation and sunshine duration required in the calibration process can be calculated based on geostationary meteorological satellite hourly cloud classification data.
The objective of this study was to investigate an improved method to derive daily net radiation based on remote sensing products coupled with field measurement data. We focused on calculating global solar radiation based on sunshine duration from Feng-Yun (FY)-2D geostationary meteorological satellite data using the method described by Wu et al. [
46], monthly
as and
bs Angstrom coefficients based data from radiation stations, and the calibration of daily net longwave radiation based on ground measurements. The estimated daily net radiation values from this proposed algorithm were validated with independent ground observation data, and the spatial distribution was compared with the results of net radiation based on the sunshine duration using meteorological station data interpolation.
4. Discussion
Daily net radiation plays an essential role in determining the thermal conditions of the Earth’s surface. It is an important variable in modelling studies of land-surface processes and global climate change. The goal of this study was to accurately and easily estimate daily net radiation based on remote sensing products coupled with field measured data. This new method has the potential to estimate daily variations of surface net radiation and evapotranspiration over large regions.
Equation (4) indicates that a positive relationship exists between sunshine duration and global solar radiation. Additionally, the accuracy of the sunshine duration calculation directly affects the accuracy of the net radiation obtained by combining Equations (2), (27) and (28). The method based on the hourly FY-2D cloud type used to estimate sunshine duration is different from the interpolation method used for the ground measurement data, and it can better express the spatial variation of sunshine duration on a regional scale without ground measurements. For the downstream Heihe River Basin in particular, because of the lack of ground observation stations indicated in
Figure 1, sunshine duration based on the hourly FY-2D cloud type can significantly improve the estimation of net radiation on a spatial scale, as shown in
Figure 4.
The Angstrom coefficients
as and
bs affect the solar radiation and net radiation based on Equations (2) and (4). Because of complex changes in the atmospheric conditions (humidity and aerosols) and the solar angle, an annual coefficient does not appropriately reflect the complex atmospheric conditions, and because of the limitations of the ground measurement data, it is impossible to obtain the daily Angstrom coefficients
as and
bs. Therefore, in this study, the monthly Angstrom coefficients were calculated instead, as shown in
Table 4, and better reflect the changes in the regional atmospheric conditions used to estimate the daily global solar radiation. In addition, the estimate of global solar radiation based on the spatial interpolation of the monthly Angstrom coefficients
as and
bs from the ground sites was also better than that for the solar radiation based on a fixed coefficient on an annual scale, regardless of the spatial interpolation method applied.
Currently, various researchers are using different net longwave radiation estimation methods, all of which must be re-calibrated when applied to a new study site. In this paper, a set of parameters for the Heihe River Basin was calibrated for calculating net longwave radiation combined with LAI data and field measurement data. The parameter values were slightly different from those of Allen et al. [
47] and Huang et al. [
50] and could improve the net longwave radiation results.
Regarding the sunshine duration in mountain areas determined based on the Wu’s method using hourly FY-2D cloud-type data [
46], because of the effects of topography and the heterogeneity of the mountain surface, the accuracy of the sunshine duration in the mountain area was less than that in the plain area. While more human activity occurs in the lowlands than in the mountains, the modification of atmospheric environment conditions affected by human activities in the lowlands was more frequently, so the monthly Angstrom coefficients
as and
bs may also change in other years in the plain area even if the higher accuracy of the monthly Angstrom coefficients
as and
bs have been obtained based on the historical data. Therefore, based on the Angstrom coefficients and sunshine duration, no obvious difference in the estimation accuracy of the net radiation between the mountain and plain areas was noted from
Figure 3 and
Table 6.
Figure 4 compares the results of the proposed method and that based on meteorological data interpolation for the Heihe River Basin. An obvious difference between the two methods for estimating the spatial distribution of net radiation was noted. Wu et al. [
46] has described the spatial distribution of the sunshine duration based on the hourly FY-2D cloud-type data, in which the spatial distribution was better than by a method based on interpolation among meteorological stations data. While the proposed method does not depend on the number of surface weather stations, the monthly Angstrom coefficients of
as and
bs were used instead of fixed coefficients, and a set of parameters was calibrated to calculate net longwave radiation combined with LAI data and field measurement data over the Heihe River Basin. Therefore, as shown in
Figure 4 and
Table 6, the method proposed in this paper can better reflect the difference in the spatial distribution of daily net radiation, especially in the upstream and downstream regions.
The proposed method allows daily net radiation to be derived from remote sensing products. For cloud-type data from FY-2D, the pixel value represents the average sunshine duration for an area of 5 km × 5 km. In addition, the cloud-type data do not account for smaller clouds, which also affect the sunshine duration estimation and daily net radiation. Ground measurements of sunshine duration and net radiation represent a much smaller area, which does not correspond to the area covered by a pixel. Consequently, some outliers would be expected in
Table 6 and
Figure 3, in which the estimated values are compared with the measured values. However, the terrain near most ground measurement stations is relatively flat with fairly homogeneous surface coverage. Thus, the ground measurement values can be assumed to represent the average value for the surrounding region and be appropriately matched with remotely sensed pixel values.
Whether fitting the monthly angstrom coefficients as and bs, calibrating net longwave radiation parameters, or optimizing the FY-2D cloud-type factors, the proposed method requires a large quantity of ground data. Therefore, calculating the net radiation on a regional scale in the absence of ground data is difficult. Fortunately, data from reanalysis products (National Centers for Environmental Prediction [NCEP], Modern Era Retrospective Analysis for Research and Applications [MERRA] and Global Land Data Assimilation System [GLDAS]) can provide hourly, 3-h, 6-h or daily radiation and meteorological data. Thus, data from reanalysis products can be used in the proposed method to replace ground data for the fitting and calibration steps to estimate net radiation on a regional scale, even if the data from those reanalysis products are of low resolution.
The accuracy of net radiation estimates, net longwave radiation calibration and the Angstrom coefficients is negatively affected by the limited number of ground stations that measure radiation and other variables. More ground data or data from reanalysis products will be needed for model fitting and calibration to apply the proposed method in other regions.