June, 214 Journal of Resources and Ecology Vol.5 o.2 J. Resour. Ecol. 214 5 (2) 132-138 DOI:1.5814/j.issn.1674-764x.214.2.5 www.jorae.cn Article Solar Radiation Climatology Calculation in China WAG Chenliang 1, 2, YUE Tianxiang 1 * and FA Zemeng 1 1 State Key Laboratory of Resources and Environment Information System, Institute of Geographic Sciences and atural Resources Research, CAS, Beijing 111, China; 2 University of Chinese Academy of Sciences, Beijing 149, China Abstract:The Angstrom-Prescott formula is commonly used in climatological calculation methods of solar radiation simulation. Fitting the coefficients is carried out using linear regression and in recent years it has been found that these coefficients have obvious spatial variability. A common solution is to divide the study area into several subregions and fit the coefficients one by one. Here, we use ground observation data for sunshine hours and solar radiation from 1961 to 21. Adopting extraterrestrial radiation as the initial value, Angstrom-Prescott coefficients are obtained by Geographically Weighted Regression at a national scale. The surfaces of solar radiation are obtained on the basis of the surfaces of sunshine hours interpolated by high accuracy surface modeling and astronomical radiation; results from spatially nonstationary and error comparison tests show that Angstrom-Prescott coefficients have significant spatial nonstationarity. Compared to existing research methods, the method presented here achieves a better simulation effect. Key words:total solar radiation; extraterrestrial radiation; Geographically Weighted Regression; spatial nonstationarity; Angstrom-Prescott formula; HASM; climatology. 1 Introduction Solar radiation is the main source of photothermal energy on earth and is the basic force driving atmospheric motion, the water cycle and human activity. The spatial distribution of solar radiation is the basis of resource and ecological studies, including climate change science (Ao et al. 212; Huang et al. 213), hydrology (Xu et al. 28), crop yield (Zhu 1964; He et al. 212) and food security (Yue et al. 28). The observation sites for solar radiation are sparse and restricted by objective conditions and the acquisition of spatially continuous surface radiation is carried out in general by simulation. Currently, simulation methods for the spatial distribution of solar radiation include trend surface or interpolation (Zhu et al. 25; Lu et al. 21a), Angstrom- Prescott formula (Liu et al. 29b) and remote sensing retrieval (Sahin 213). Among these, the Angstrom-Prescott formula for climatological calculation is relatively mature and a common computation method for solar radiation (Angstrom 1924; Glover et al. 1958; Rietveld 1978). The basic principles are as follows: Q = Q ( a + bs ) (1) where, Q represent total solar radiation; Q is initial value for computation and its value can be the one of radiation including clear-sky solar total radiation, extraterrestrial radiation and total radiation of ideal atmosphere; S is sunshine percentage of the same period (%) and its value is equal to the ratio of observed sunshine hours and maximum sunshine hours; a and b constitute climatology coefficients in the Angstrom-Prescott formula. The Food and Agriculture Organization (FAO) recommended values of a and b are.25 and.5 at a global scale and values need to be corrected according to local climatic data. As a result, parameter determination and localization have become major problems for related research. According to Iranian meteorological data for 198 27 the coefficient values are calibrated by linear regression (Sabziparvar et al. 213), which increased accuracy of the FAO recommended value by 72.7 %. Many studies have revealed that the fitting effect of coefficients a and b are influenced by time scale, which can be improved at a finer scale (Li et al. 212). Liu et al. (29a) found Received: 213-12-9 Accepted: 214-3-31 Foundation: ational Key Technologies R & D Program of China (213BAC3B5); ational High-tech R & D Program of China (213AA1223). * Corresponding author: YUE Tianxiang. Email: yue@lreis.ac.cn.
WAG Chenliang, et al.: Solar Radiation Climatology Calculation in China 133 that partial coefficients are difficult to fit under linear relationship. In addition to localization calibration and time scale, climatology simulation precision can be influenced by computational relationships. For example, the formula using the difference between cloudless sky maximum sunshine hours and observed sunshine hours corrected maximum sunshine hours is more suitable for intermountain areas (Zand-Parsa et al. 211); nonlinear relationships can improve simulation when linear fitting is invalid (Pelkowski 29). The understanding of these climatology coefficients is being strengthened amongst the Chinese research community. Zuo et al. (1963) firstly adopted clear-sky solar total radiation as the initial value and developed the global climatology coefficients at the national level according to observations from 26 sites from 1957 196 in China. Weng (1964) found spatial variability of climatology coefficients and divided the national area into four districts. In his study, extraterrestrial radiation is selected as the initial value, every coefficient for the subregions is constructed according to 5 radiation stations across China from 1958 to 196, and rationality of choosing astronomical radiation as the initial value is also proven. According to 75 radiation sites from1957 to 1977, Zhu (1982) established three computation models based on astronomical radiation, clear-sky solar total radiation and total radiation of the ideal atmosphere respectively. This research analyzed spatio-temporal variation characteristics and physical meaning of coefficients, and discovered that the best initial value is extraterrestrial radiation. He et al. (21) also constructed three different regression formulas according to observations from 1961 to 2, and verified initial values based on extraterrestrial radiation. Ju et al. (25) simulated coefficients using astronomical radiation as the initial value, and analyzed spatial and temporal variation. In summary, simulation based on astronomical radiation is more accurate than other initial values. Climatology coefficients have variability at spatial and temporal scales and accuracy is influenced by partition granularity of the spatio-temporal scale. The differences between spatial and temporal scale is deficiency of objective partition granularity at the spatial level. Previous research has lacked a yardstick for spatial variability and a standard for separating subregions. Due to variability, the merged results have boundary effects at the edges of different zones (Costa 29). Here, we explore spatially nonstationary Angstrom- Prescott coefficients at the national level. Taking extraterrestrial radiation as the initial value, a solar radiation climatology model based on Geographically Weighted Regression (GWR) is established according to 752 sunshine hours of observations over a long-term sequence from 1961 to 21. Surfaces of total solar radiation are generated with surfaces of extraterrestrial radiation and sunshine hours climatology coefficients. 2 Data and methods 2.1 Data sources and processing Radiation and sunshine hour monthly data were obtained from the ational Meteorological Information Center in China. Observations were extracted during from1961 to 21 because of difference in temporal series. In order to improve simulation of total solar radiation climatology computation (Tang et al. 211), missing data were filled by Multivariate Imputation by Chained Equations (MICE) (van Buuren et al. 211). The 1 DEM data for the study area were obtained from the GTOPO3 dataset provided by the United States Geological Survey. Assuming that the complete data Y is a partially observed random sample from the pvariate multivariate distribution P(Y θ), and the multivariate distribution of Y is entirely specified by θ, a vector of unidentified parameters. In order to get the multivariate distribution of θ, the MICE algorithm achieves the posterior distribution of θ by sampling iteratively from conditional distributions of the form P(Y 1 Y -1,θ 1 ) P(Y p Y -p,θ p ). The parameters θ 1,,θ p are specific to the respective conditional densities and are not necessarily the product of a factorization of the true joint distribution P(Y θ). Starting from a straightforward draw from observed marginal distributions, the tth iteration of chained equations is a Gibbs sampler that successively draws: θ 1 ~ P(θ 1 Y 1 obs,y 2 (t 1),, Y p (t 1) ) Y 1 ~ P(Y 1 Y 1 obs,y 2 (t 1),, Y p (t 1), θ 1 ) θ 1 ~ P(θ P Y obs P, Y (t) () t 1,, Y ) p 1 Y P ~ P(Y P Y P obs,y 1 (t),,y p (t),θ P ) (2) (t) where, Y j =(Y obs j,y j ) is the jth imputed variable at iteration *(t-1) t. Observe that previous imputations Y j only enter Y j through its relation with other variables, and not directly. 2.2 Research method 2.2.1 Angstrom-Prescott formula R t = (a+ b n )R a (3) where, represents monthly maximum sunshine hours (h); n is monthly mean sunshine hours (h); R t stands for monthly total solar radiation ( ); and R a represents monthly extraterrestrial radiation for initial value ( ). Angstrom-Prescott coefficients expressed by a and b. Annual total solar radiation is calculated by the sum of all monthly solar radiations. 2.2.2 Theoretical calculation of extraterrestrial radiation and maximum sunshine hours Extraterrestrial radiation and maximum sunshine hours are computed according to theoretical equations for daily period
134 Journal of Resources and Ecology Vol.5 o.2, 214 (Zuo et al. 1991; Allen et al. 1998): = (4) R ad = G sc d r [ω s sinφsinδ+cosφcosδsin(ω s )] (5) φ = latitude (6) d r = 1+.33cos( d) (7) δ = 9sin( d 1.39) (8) ω s =arccos[-tanφtanδ] (9) where, φ is latitude(radians); δ represents declination of the sun (radians); G sc is solar constant being equal to.82 MJ m -2 min -1 ; d r is the inverse relative distance Earth-Sun; ω s is sunset hour angle; d is the order number of solar calendar; and R ad represents extraterrestrial radiation ( d -1 ). ly maximum sunshine hours and extraterrestrial radiation are computed with corresponding daily values. 2.2.3 Simulation of sunshine hours surfaces Besides continuous surfaces of extraterrestrial radiation and maximum sunshine hours, construction for spatial surface of total solar radiation requires the surface of sunshine hours. HASM is adopted for establishing sunshine hour surfaces in this study and can be expressed as: H = T + E (1) where, T represents entire trend of spatial distribution of sunshine hours and describes the relationship between surface and relevant explanatory variables, which constitutes deterministic law of spatial distribution of sunshine hours; E is high accuracy local information generated by HASM (Lu et al. 21b; Yue et al. 211), which represents stochastic microcosmic details of spatial distribution; and H expresses sunshine hours surfaces, which can be generated by the stacking of T and E. Significant linear relationships are exist between sunshine hours and independent variables including DEM, location of sites and climate elements in the same period for the monthly scale. Meteorological data are summarized by month linked with DEM and geographic location during data handling. Precipitation, mean temperature and mean relative humidity were selected as climate explanatory variables. DEM and coordinates of 1 1 grid were adopted as geographic independent variables. Multivariate linear stepwise regression was carried out by AIC criteria (Weisberg 25), generating T in equation; HASM is performed to solve E. H is the sum of T and E. Due to limited space, we have omitted some details and analysis which will be summarized in another article. 2.2.4 Determination of Angstrom-Prescott coefficients Determination for Angstrom-Prescott coefficients are critical for solar radiation climatological calculation methods Equation can be transformed as: R` = a + bn` (11) where, R` and n` are the ratio of R t and R a ; and n and respectively in equation. According to equation, a and b can be estimated using linear regression. However, the national region is broad and geographic environment is complicated, the global coefficients estimated by linear regression (OLS) have difficulties when describing the spatial variation relationship between radiation and climate elements. Using Geographically Weighted Regression (Brunsdon et al. 1998), spatially continuous climatology coefficients were computed under a Gaussian kernel function and crossvalidation to choose optimal bandwidth. 3 Results and analysis 3.1 Analysis of coefficient fit Coefficients are estimated by OLS and GWR at 122 radiation sites in China (Table 1). Influenced by stochastic factors including sunbeam incident angle and observation error, sum of a and b is not equal to 1 but exhibits a certain statistical relationship (Zhu 1982). The coefficients comprehensively reflect weakening effect of radiation influenced by atmosphere. There are also complementary relationship between a and b for every month in gross. Moran s index for OLS and GWR residuals are carried out to test autocorrelation (Leung et al. 2b); F1, F2, F3 (Leung et al. 2a) and F4 tests (Fotheringham et al. 22) are also performed in comparative trials. F1, F2 and F4 test comparison of goodness-of-fit; F3 tests every parameter s spatial variation. According to Table 2, correlations between predictions and explanatory variables are higher than.87, but Moran s indexes indicate OLS residuals show significant autocorrelation (P <.1). The test for GWR residuals can not reject the null hypothesis which indicates GWR fuse spatial variability in the process of fitting. F1, F2 and F4 testing shows that GWR is significantly better than OLS in every month except January. The F3 test shows that some spatial nonstationarity of coefficients are not significant (1, 2,6,7,8 and 9). This variation is most probably caused by measurement error. In other months, the significance level of coefficient b s spatial nonstationarity in May reaches.5; all other values are.1. As Fig. 1 indicates, RSS of OLS and GWR have similar trends. RSS reaches its maximum in January, declines in May, and increases gradually. In winter (Dec. to Feb.), OLS residuals are much higher than for other seasons because of relatively high spatial variability (Table 2; Fig. 4), and the goodness of fit is much lower. GWR is still better than OLS in July and August, although variability is decreased (Figs. 2 and 3).
WAG Chenliang, et al.: Solar Radiation Climatology Calculation in China 135 Table 1 Parameters for OLS and GWR fitting. OLS GWR Coefficient a Coefficient b Coefficient a Coefficient b Range Mean Range Mean 1.14.757.178.235.87.538 1.26.77 2.11.667.38.351.132.368.792.623 3.112.737.112.986.145 7 1.147.678 4.119.682.44 8.149.237.941.623 5.138.681.23.294.167 19 -.858.621 6.152.624.98.311.18.398.73.57 7.182.586.116.384.216.33.792.518 8.178.584.62 6.227.12.871 86 9.151.65.85.357.171.315.754.578 1.135.661.132-47.149.23 1.25.634 11.18.698.214.82.145.377 1.132.625 12.113.74.34 1.42.166 1.327.863.637 Mean.133.668.87.227.161 86.77.614 Table 2 Correlation between parameters and P-values of relevant tests on OLS and GWR every month. COR Moran_OLS Moran_GWR F1 F2 F3_a CV_a (%) F3_b CV_b (%) F4 1.938..934.13.11.798 88.28.748 16.8.7 2.968..861.14.2.821 31.98.767 11.45. 3.97..784.1.4.2 84.89.1 28.45. 4.966..99.2..4 41.62.3 16.63. 5.966..174.5..171 27.84.42 14.. 6.954..111.15..36 22.57.296 12.1.1 7.895..268.3..635 23.41.593 17.28. 8.873..841.1.1.542 28.54.19 25.57. 9.94..79.24.1.58 32.7.276 16.17.1 1.96. 7.7.1.6 58.6.1 22.48. 11.956..732... 75.52. 28.25. 12.938..574... 87.96. 36.44. ote: COR represents correlation between radiation and sunshine hours monthly; Moran_OLS and Moran_GWR are Moran test s P-value of OLS and GWR residuals..3 RSS-OLS RSS-GWR 1. RSS.2 R 2.8.1.6 R2-OLS R2-GWR 1 2 3 4 5 6 7 8 9 1 11 12 1 2 3 4 5 6 7 8 9 1 11 12 Fig. 1 Residual sum of squares of Angstrom-Prescott coefficients estimated by OLS and GWR. Fig. 2 Goodness of fit for Angstrom-Prescott coefficients estimated using OLS and GWR.
136 Journal of Resources and Ecology Vol.5 o.2, 214 1. 1..8 cv-a cv-b Adj R 2.8 R 2.6.6 1 OLS-adjR2 GWR-adjR2 2 3 4 5 6 7 8 9 1 Fig. 3 Adjusted goodness of fit for Angstrom-Prescott coefficients estimated using OLS and GWR. 11 12.2 1 2 3 4 5 6 7 8 9 1 11 12 Fig. 4 Coefficient of variation of Angstrom-Prescott a and b. Table 3 Relative error (%) of OLS and GWR. OLS regression GWR regression Range Median Standard deviation Mean Range Median Standard deviation Mean 1 2 43.96 6.91 6.75 8.42.3 4.25 4.54 6.55 6.3 2.4 22.94 5.13 4.73 6.13.4 17.38 2.99 3.93 4.25 3.6 19.11 4.6 4.2 5.22. 15.42 2.11 2.98 2.97 4.1 16.42 3.43 3.62 4.58.4 13.95 2.48 2.67 3.17 5.5 16.6 3.67 3.37 4.14.5 13.36 2.48 2.49 2.96 6.4 15.8 4.16 3.78 4.81.6 14.74 2.45 3.8 3.47 7.9 18.46 4.16 4.8 5.17.1 1.73 2.36 2.89 3.22 8.2 17.11 4.94 4.27 5.67.3 16.34 2.8 2.94 3.29 9.1 24.65 4.48 4.38 5.4.1 23.34 2.68 3.7 3.93 1.6 25.35 5.34 4.47 5.94. 22.89 2.86 4.4 3.86 11.18 21.41 4.74 4.66 5.72.1 15.64 2.45 3.27 3.51 12.31 37.67 5.9 5.83 7.21.2 19.44 2.94 4.6 4.8 Mean.95 15.95 4.85 3.13 5.7.11 14.7 3. 2.64 3.81 Comparison of the time trend between a and b (Fig. 4) shows that variability of a is much higher that b in the high variability period; RSS (Fig. 1) and relative error (Table 3) are also increasing, goodness of fit decreases. GWR improves OLS consistently. 3.2 Comparisons with previous research The results of this study are relatively better than existing research because of long-term sequence fitting, preprocessing of missing data and very accurate sunshine hours data (Table 4). 3.3 Spatial distribution of Angstrom-Prescott coefficients and radiation According to coefficients estimated by OLS and GWR, predictions are generated every month (Harris et al. 21), whereby we divided the sum of daily astronomical radiation in Equation to obtain solar radiation. Taking January, April, July and October to represent seasons (Ju et al. 25), coefficient surfaces and prediction are established (Fig. 5). The ranges of monthly solar radiation are 117.9 541.2 (Jan.), 292.4 738.3 (Apr.), 41. (Jul.) and 26.37 69.83 (Oct.). Solar radiation was 485 to 541.2 in southwest Xizang and Yunnan in January; 292.4 to 346.8 in most regions of Guangxi, Guangdong and Guizhou in April; 541 to in Xinjiang, Xizang, Qinghai and Inner Mongolia in July; and 26.37 to 264.39 in east parts of Sichuan, Chongqing and eastern regions of Inner Mongolia. 4 Conclusions and discussion According to 752 observations for sunshine hours and 122 observations for radiation from 1961 and 21 and using extraterrestrial radiation as the initial value, a national total solar radiation climatic model was established based on GWR. This approach yielded better results than previous methods. Given that GWR can fit spatio-continuous variable regression coefficients in the study area, the model proposed here removes the subjectivity of global or subregional
WAG Chenliang, et al.: Solar Radiation Climatology Calculation in China 137 Table 4 Comparisons of relative error with existing research. Study Initial value Sites data Coefficients Relative error (%) Range Mean Zuo et al. (1963) Clear-sky solar total radiation 26 sites in 1957 196 a =.248, b =.752 2.94 25.83 8.86 Weng (1964) He et al. (21) Extraterrestrial radiation 5 sites in 1958 196 a =.13, b =.625 (South China) 4.79 19.48 9.92 a =.25, b =75 (Central China) 4.82 16.34 9.96 a =.15, b =.78 (orth China) 5.5 12.39 8.53 a =.344, b =.39 (orthwest China) 3.78 23.56 17 Extraterrestrial radiation 54 sites in 1961 2 a =.126, b =.648 3.33 18.75 8.39 Clear-sky solar total radiation a =.26, b =.89 3.3 22.31 8.47 Total radiation of ideal atmosphere a =.138, b =.731 2.87 18. 8.54 This study Extraterrestrial radiation 122 sites in 1961 21 a =.133, b =.668 (OLS mean).95 15.95 5.7 a =.161, b =.614 (GWR mean).11 14.7 3.81 January April July October Fig. 5 Spatial distribution of total monthly solar radiation. division computation. Simulation by GWR is much better than OLS because of spatial nonstationarity fusion in the GWR fitting. Data quality control is critical for studies of solar radiation. When simulating total solar radiation climatology computation, filling missing data and the extension of time series is momentous. High accuracy data for sunshine hours and appropriate regression methods can also eliminate simulation error. References Allen R G, L Pereira, D Raes, et al. 1998. FAO irrigation and drainage paper o. 56. Rome: Food and Agriculture Organization of the United ations, 26-4. Angstrom A. 1924. Solar and terrestrial radiation. Report to the international commission for solar research on actinometric investigations of solar and atmospheric radiation. Quarterly Journal of the Royal Meteorological Society, 5(21): 121-126. Ao, H, M J Dekkers, G Xiao, et al. 212. Different orbital rhythms in the Asian summer monsoon records from orth and South China during the Pleistocene. Global and Planetary Change, 8-81(): 51-6. Brunsdon C, S Fotheringham, M Charlton. 1998. Geographically weighted regression Modelling spatial non-stationarity. Journal of the Royal Statistical Society Series D-the Statistician, 47(3): 431-443. Costa J F. 29. Interpolating datasets with trends: A modified median polish approach. Computers & Geosciences, 35(11): 2222-223. Fotheringham S, C Brunsdon, M Charlton. 22. Geographically weighted regression: The analysis of spatially varying relationships. Wiley. Glover J, J S G McCulloch. 1958. The empirical relation between solar radiation and hours of sunshine. Quarterly Journal of the Royal Meteorological Society, 84(36): 172-175.
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(in Chinese) Zuo D K, Zhou Y H, Xiang Y Q, et al. 1991. On surface radiations. Beijing: Science Press. (in Chinese) 中国太阳总辐射的气候学计算法研究 王晨亮 1,2, 岳天祥 1 1, 范泽孟 1 中国科学院地理科学与资源研究所资源与环境信息系统国家重点实验室, 北京 111 ; 2 中国科学院大学, 北京 149 摘要 :Angstrom-Prescott 公式的气候学计算法是应用较广的太阳辐射模拟方法, 其系数一般通过线性回归确定 近年来, 许多研究显示该系数存在明显的空间变异性, 常见的解决方法是将研究区划分子区域逐个拟合 本研究采用 1961-21 时段日照时数与太阳辐射站点资料, 以天文辐射为起始值, 基于地理加权回归得到全国尺度连续变化的 Angstrom-Prescott 系数 通过高精度曲面建模方法 (HASM) 构建的日照时数资料和天文辐射曲面, 得到国家尺度太阳辐射曲面 空间非平稳和误差比较检验等结果表明, 系数存在显著的空间非平稳性 ; 与已有研究相比, 本研究的模拟方法效果较好 关键词 : 太阳总辐射 ; 天文辐射 ; 地理加权回归 ; 空间非平稳性 ;Angstrom-Prescott 公式 ;HASM