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基于Shepard和OI方法对雨量计逐时资料的分析
Gauge Hourly Observations by Shepard Interpolation Method and Optimum Interpolation Method
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摘要: 引入地形影响效应的日降水量气候分析场，分别运用Shepard和最优插值（OI）两种插值方法对广东和广西2007年5月20日—8月30日汛期小时雨量计降水量进行插值，得到0.125°×0.125°分辨率的规范化网格资料。结果表明：无论是直接插值还是用降水比率（地形影响效应的日降水量气候分析场）插值，两种方法均能很好地体现广东和广西雨量计站点观测降水的季内变化和日变化特征。虽然用直接插值方法比用降水比率插值方法得到的降水空间分布更为平滑，但估值精度没有用降水比率插值方法高。通过交叉检验进一步表明，总体上OI方法优于Shepard方法，而考虑地形影响效应的降水比率OI方法为最优，能有效提高相关性，并减少均方根误差和系统误差。Abstract: The precipitation is one of the most important meteorological factors that impact on human activities. The high resolution precipitation products are useful on weather and climate monitoring, calibration of numerical model and hydrologic prediction. Due to the asymmetry and discontinuity of precipitation in spatial and temporal distribution, the excessive and absent asymmetric rainfall resulted in the meteorological disasters such as flood and drought. In order to avoid and reduce these disasters, it is important to know the amount and distribution of precipitation exactly. Using the rainfall recorder observation is the most direct, effective and common method to obtain precipitation information. But the rainfall recorder data only represent several isolated stations information, not the continuous grid data. In order to obtain the standard grid data, it is necessary to process the original rainfall data with math methods. A lot of interpolation methods have been proposed, such as Cressman, Barnes, Gandin, Shepard, Hulme. Bussieres and Hogg as well as Chen have compared and verified the interpolation methods in application of the daily and monthly rainfall analysis. It has been concluded that Gandin optimal interpolation possesses much more exactly, effectively and stably. But for smaller time scales, what math interpolation can be used to obtain a better results and how to set the correlative parameters needs further researches. Using the Parameter elevation Regressions on Slope Model (PRISM), an objective analysis of gauge hourly regional observation precipitation in Guangdong and Guangxi from 20 May to 30 August 2007 with the spatial resolution of 0.125°×0.125° by Shepard interpolation method are implemented, the results are compared with optimum interpolation method too. The comparison analysis shows that both the results can represent the inter seasonal and diurnal variation of gauge regional mean precipitation well between direct interpolation and PRISM interpolation. Although the spatial distribution of precipitation gained by the direct interpolation is smoother than that by PRISM interpolation, but the estimated precision of direct interpolation is lower than that of PRISM interpolation. The cross validation indicates that the accuracy of precipitation products by the optimum interpolation is better than that by Shepard interpolation. The PRISM optimum interpolation is an optimal method that can improve correlation and reduce root mean square error as well as system error.
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图 1 2007年5月20日-8月30日21°~26°N, 106°~117°E区域雨量计观测值时间平均空间分布（单位：mm）（a）OI方法插值格点平均，（b）比率OI方法插值格点平均，（c）Shepard方法插值格点平均，（d）比率Shepard方法插值格点平均
Fig. 1 Distribution of temporal mean gauge observations in the region of 21°-26°N, 106°-117°E from 20 May 2007 to 30 Aug 2007 by interpolation at grids (unit:mm)(a) OI, (b) OIratio, (c) Shepard, (d) Shepard ratio
图 2 2007年5月20日-8月30日21°~26°N, 106°~117°E区域平均的逐日降水量变化曲线（a）OI与比率OI插值方法，（b）Shepard与比率Shepard插值方法
Fig. 2 Variationof regional 24-hour mean precipitation in the region of 21°-26°N, 106°-117°E from 20 May 2007 to 30 August 2007(a) OI and OI ratio, (b) Shepard and Shepard ratio
图 3 2007年5月20日-8月30日21°~26°N, 106°~117°E区域平均的降水日变化（a）OI和比率OI插值方法，（b）Shepard和比率Shepard插值方法
Fig. 3 Diurnal variation of regional mean precipitation in the region of 21°-26°N, 106°-117°E from 20 May 2007 to 30 August 2007(a) OI and OI ratio, (b) Shepard and Shepard ratio
表 1 OI、比率OI和Shepard、比率Shepard方法得到的均方根误差百分比（单位：%)
Table 1 Contrast of root-mean-square error percentage between the gauge and grid interpolation by OI, OI ratio, Shepard and Shepard ratio (unit:%)
表 2 逐时变化降水量概率密度分布（单位：%)
Table 2 Hourly probability density distribution (unit : %)
表 3 降水量月变化OI和Shepard方法的交叉检验
Table 3 Cross-validation of monthly rain variation by OI as compared with Shepard
表 4 降水量逐日变化OI和Shepard方法的交叉检验
Table 4 Cross-validation of daily rain variation by OI as compared with Shepard
表 5 降水量日变化OI和Shepard方法的交叉检验
Table 5 Cross-validation of diurnal rain variation by OI as compared with Shepard
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