Sunshine percentage is one of the important factors that influences the computation of sunshine hour and solar radiation. The computational results of sunshine percentage will undoubtedly affect the relevant researches. In order to solve the error problem that had long troubled the interpolation method, Yue developed a novel surface modeling method, High Accuracy Surface Modeling (HASM), based on the fundamental theorem of surfaces which makes sure that a surface is uniquely defined by the first and the second fundamental coefficients of it. Numerical tests have shown that HASM is much more accurate than the classical methods such as kriging, Inverse Distance Weighted (IDW) method, and spline. Surface modeling of Digital Elevation Model (DEM), ecosystem change and soil properties also indicate that HASM has increased interpolation accuracy. Despite its popularity, however, a common phenomenon is found that the result of HASM is not optimal since the theoretical basis of it is not complete. To improve HASM's simulation skills in interpolating sunshine percentage in China, this research gives a modification of HASM, namely HASM.MOD, which introduces the mixed partial derivative term, considers the local details of the surface and is theoretically perfect. The introduction of the mixed partial derivative term in HASM.MOD reflects the local warping of the surface, namely its deviation from tangent plane at the point under consideration. We then use Gauss synthetic surface to validate the performance of HASM.MOD and HASM. HASM.MOD is then used to simulate the monthly mean sunshine percentage by using observed data from 752 stations for the considered period (1950-2010). We also compare the performance of HASM.MOD with those of HASM and other interpolators: kriging and inverse distance method (IDW). Numerical tests and real world studies show that the simulation accuracy of HASM. MOD is higher than that of other methods in this study. As the basic geographical data, the sunshine percentage produced by HASM.MOD can provide support for other applications.
[1] 张智, 林莉, 孙银川, 等. 银川市日照时数气候变化特征分析. 干旱区研究, 2006, 23(2): 344-348. [Zhang Zhi, Lin Li, Sun Yinchuan, et al. Analysis on climate change characteristics of sunshine duration in Yinchuan city. Arid Zone Research, 2006, 23(2): 344-348.]
[2] 丁一汇, 任国玉, 赵宗慈, 等. 中国气候变化的检测及预估. 沙漠与绿洲气象, 2007, 1(1): 1-10. [Ding Yihui, Ren Guoyu, Zhao Zongci, et al. Detection, attribution and projection of climate change over China. Desert and Oasis Meteorology, 2007, 1(1): 1-10.]
[3] 黄晚华, 帅细强, 汪扩军. 考虑地形条件下山区日照和辐射的GIS 模型研究. 中国农业气象, 2006, 27(2): 89-93.[Huang Wanhua, Shuai Xiqiang, Wang Kuojun. A study on GIS-based model of sunlight and radiation in view of terrain in mountain areas. Chinese Journal of Agrometeorology, 2006, 27(2): 89-93.]
[4] 王怀清, 殷剑敏, 占明锦, 等. 考虑地形遮蔽的日照时数精细化推算模型. 中国农业气象, 2011, 32(2): 273-278. [Wang Huaiqin, Yin Jianfei, Zhan Mingjin, et al. Refine project model of sunshine resources in China considering terrain masking. Chinese Journal of Agrometeorology, 2011, 32(2): 273-278.]
[5] 潘永地. 地形起伏下日照时间计算模型的修正. 资源科学, 2012, 32(8): 1493-1498. [Pan Yongdi. Corrections for sunshine duration models under rugged terrain conditions. Resources Science, 2012, 32(8): 1493-1498.]
[6] Angstrom A. Solar and atmospheric radiation. Quarterly Journal of the Royal Meteorological Society, 1924, (20): 6121-6126.
[7] 郝成元, 许传阳, 吴绍洪. 基于DEM模型和气候学计算的滇南山区太阳总辐射空间化. 资源科学, 2009, 31(6): 1031-1039. [Hao Chengyuan, Xu Chuangyang, Wu Shaohong. Total solar radiation spatialization in mountainous region based on DEM and climatological calculation. Resources Science, 2009, 31(6): 1031-1039.]
[8] 和清华, 谢云. 我国太阳总辐射气候学计算方法研究. 自然资源学报, 2010, 25(2): 308-319. [He Qinhua, Xie Yun. Research on the climatological calculation method of solar radiation in China. Journal of Natural Resources, 2010, 25(2): 308-319.]
[9] 辛渝, 赵逸舟, 毛炜峄, 等. 新疆太阳总辐射资料的均一性检验与气候学估算式的再探讨. 高原气象, 2011, 30(4): 878-889. [Xin Yu, Zhao Yizhou, Mao Weiyi, et al. Homogeneity test of the total solar radiation data series and further research on climatological calculation over Xinjiang. Plateau Meteorology, 2011, 30(4): 878-889.]
[10] Smith B, Prentice I C, Sykes M T. Representation of vegetation dynamics in the modeling of terrestrial ecosystems: comparing two contrasting approaches within European climate space. Global Ecology and Biogeography, 2001, 10 (6): 621-637.
[11] Sitch S, Smith B, Prentice I C, et al. Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biology, 2003, 9: 161-185.
[12] 袁淑杰, 缪启龙, 邱新法, 等. 贵州高原起伏地形下日照时间的时空分布. 应用气象学报, 2008, 19(2): 233-237.[Yuan Shujie, Miao Qilong, Qiu Xinfa, et al. The spatial and temporal distribution of insolation duration over rugged terrains in the Guizhou plateau. Journal of Applied Meteorological Science, 2008, 19(2): 233-237.]
[13] Yue T X. Surface Modeling: High Accuracy and High Speed Methods. New York: CRC Press, 2011.
[14] 岳天祥, 杜正平. 高精度曲面建模与经典模型的误差比较分析. 自然科学进展, 2006, 16(8): 986-991. [Yue Tianxiang, Du Zhengping. High accuracy surface modeling and comparative analysis of its errors. Progress in Natural Science, 2006, 16(8): 986-991.]
[15] 史文娇, 杜正平, 宋印军, 等. 基于多重网格求解的土壤属性高精度曲面建模. 地理研究, 2011, 30(5): 861-870. [Shi Wenjiao, Du Zhengping, Song Yinjun, et al. High accuracy surface modeling of soil properties based on multi-grid. Geographical Research, 2011, 30(5): 861-870.]
[16] Yue T X, Du Z P, Song D J, et al. A new method of high accuracy surface modeling and its application to DEM construction. Geomorphology, 2007, 91: 161-172.
[17] Yue T X, Fan Z M, Chen C F, et al. Surface modeling of global terrestrial ecosystems under three climate change scenarios. Ecological Modeling, 2011, 222: 2342-2361.
[18] 杜正平, 范泽孟, 岳天祥. 基于HASM的省级尺度气候与植被生态系统模拟分析. 地理研究, 2013, 32(9): 1591-1601.[Du Zhengping, Fan Zemeng, Yue Tianxiang. Simulation of climate vegetation system based on HASM method on a provincial scale. Geographical Research, 2013, 32(9): 1591-1601.]
[19] Golub G H, Van Loan C F. Matrix Computations. Beijing: Posts & Telecom Press, 2009.
[20] Somasundaram D. Differential Geometry. Harrow: Alpha Science International Ltd., 2005.
