哈尔滨工业大学学报  2021, Vol. 53 Issue (1): 193-200  DOI: 10.11918/201911110 0

### 引用本文

YU Ying, JIA Xiaoyu, CHEN Xiao. Selection method of statistical duration in solar radiation model based on climate abrupt change year[J]. Journal of Harbin Institute of Technology, 2021, 53(1): 193-200. DOI: 10.11918/201911110.

### 基金项目

“十三五”国家科技支撑课题(2018YFC0704504)

### 文章历史

Selection method of statistical duration in solar radiation model based on climate abrupt change year
YU Ying, JIA Xiaoyu, CHEN Xiao
School of Mechanical and Electrical Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China
Abstract: Establishing a solar radiation model which employs pertinent meteorological parameters for the estimation of solar radiation is essential for enhancing solar radiation data. The statistical duration used by the radiation model influences the model's coefficients and further affects its estimation errors. To select a proper statistics duration and minimize the radiation model estimation error, this paper proposes a kind of method that chooses an appropriate statistical duration based on the climate abrupt change year. By analyzing the meteorological and radiation data records of more than 25 years from 90 observatories and meteorological stations in China, three meteorological elements that are closely related to solar radiation, namely, sunshine duration, temperature and humidity, are used for abrupt change inspection. The coefficient of variation method is used to determine the climate abrupt change year. Daily global radiation model and daily diffuse radiation model are established respectively by choosing the statistics duration of observation data for over 25 years and the statistics duration after climate abrupt change year. The estimation errors of different models using different statistics duration are compared. According to the error results, the Root Mean Square Error percentage can be reduced by above 2% if data record years after the climate abrupt change year, which serves as the time node, are used as the modeling statistics duration. It demonstrates that the method of choosing radiation modeling duration using climate abrupt change year can reduce the modeling estimation error effectively. The method provides a reference to select the statistical duration in radiation models.
Keywords: solar radiation model    statistical duration    meteorological element    climate abrupt change year    error analysis

1 数据获取及质量控制

2 气候突变年的确定

2.1 气象要素突变检验 2.1.1 温度

 图 1 温度M-K突变检验 Fig. 1 Abrupt change in temperature using Mann-Kendall test
2.1.2 相对湿度

 图 2 相对湿度M-K突变检验 Fig. 2 Abrupt change in humidity using Mann-Kendall test
2.1.3 日照时数

 图 3 日照时数累积距平突变检验 Fig. 3 Abrupt change in sunshine hours using cumulative anomaly curve
2.2 气候突变年确定

 ${w_j} = \frac{{{C_v}_{_i}}}{{\sum\limits_{i = 1}^n {{C_v}_{_i}} }}i = 1, 2, \cdots , n.$ (1)

 图 4 90个台站气候突变年 Fig. 4 Climate abrupt change years of 90 stations
3 统计时长对模型估算误差的影响 3.1 模型选择和建立

 ${K_t} = a + b\left( {\frac{S}{{{S_0}}}} \right),$ (2)
 $\begin{array}{l} {K_d} = a + b{K_t} + cK_t^2 + d{K_t}^3 + {\rm{ }}\\ \;\;\;\;\;\;\;\;e\left( {\frac{S}{{{S_0}}}} \right) + f{\left( {\frac{S}{{{S_0}}}} \right)^2} + g{\left( {\frac{S}{{{S_0}}}} \right)^3}. \end{array}$ (3)

3.2 模型评价指标

 ${{\rm{RMSE}}\% = \frac{{\sqrt {\frac{1}{n}\sum\limits_{i = 1}^n {{{\left( {{I_{{\rm{ob}}}} - I} \right)}^2}} } }}{{\bar I}}, }$ (4)
 ${{R^2} = 1 - \frac{{\sum\limits_{i = 1}^n {{{\left( {{I_{{\rm{ob}}}} - I} \right)}^2}} }}{{\sum\limits_{i = 1}^n {{{\left( {I - \bar I} \right)}^2}} }}.}$ (5)

 ${{E_{{\rm{RMSE\% }}}} = {Ⅱ_{{\rm{RMSE\% }}}} - {Ⅰ_{{\rm{RMSE\% }}}}, }$ (6)

3.3 估算误差分析

 图 5 日总辐射模型R2和误差分布 Fig. 5 Distribution of R2 and error of daily global radiation model

 图 6 散射辐射模型R2和误差分布 Fig. 6 Distribution of R2 and error of diffuse radiation model

4 结论

1) 借助气候突变年的判别方法，对我国90个台站进行气候突变年检验，发现75%的台站气候突变年均集中在1990年~2005年之间，说明近30年间我国大多数地区气候都发生了变化.当台站之间地理距离相近，且经济发展水平、人口等因素相差不大时，气候突变年也相近.

2) 以突变年为时间节点，选取突变年后数据时段作为统计时长分别建立日总辐射模型和散射辐射模型，将模型估算误差与观测数据超过25年统计时长的模型估算误差比较，结果显示借助气候突变年选取建模统计时长的方法可以有效减少估算误差，提高模型拟合程度.该方法可为太阳辐射模型统计时长的选取提供依据.