日降水量空间插值方法研究

采用反距离权重法和普通克里格方法对26°~34°N, 103°~115°E范围内2004年逐日降水量进行空间插值试验分析, 分辨率为1 km×1 km。采用交叉检验方法和准确率方法对两种方法插值的总体效果及不同等级的降水插值效果进行综合对比。结果表明:两种方法插值效果近似, 插值结果与实测值相关系数分别为0.83和0.82。但对日雨量较大的情况, 两种方法插值效果均有所降低, 相关系数为0.66和0.67。两种方法的实测值与插值结果的相关系数在不同季节非常接近, 并且均以春季最大, 其次为冬、秋季, 夏季相关系数最小; 通过采用平均误差、平均绝对误差和均方根3个指标衡量及不同等级雨量的插值准确率统计比较, 普通克里格方法插值效果略好于反距离权重法。     

不同空间插值方法对重庆地区降水的适用性分析

利用中国气象局全国综合气象信息共享平台（CIMISS）提供的1981~2018年重庆地区35个国家气象站逐日降水资料,采用最小曲率插值法、径向基函数插值法、克里金插值法、局部多项式插值法、反距离加权插值法以及改进的Shepard插值法,对平均累计降水、降水极值以及夏季极端降水空间插值模拟结果进行交叉检验。结果表明:空间插值方法在渝西和渝中大部分地区以及长江沿线地区适用性较好,在渝东北、渝东南地区北部以及渝西地区南部的山区适用性较差。对于平均累计降水,各插值方法的均方根误差随着降水量的增加而增大,其中最小曲率插值法整体表现最为稳定,最小曲率插值法在渝东南、渝中以及渝西地区最为适用,径向基函数插值法在渝东北地区最为适用。对于降水极值,量级模拟最好的插值方法为径向基函数插值法,位置模拟最好的方法为最小曲率插值法。对于夏季极端降水,最小曲率插值法插值结果与实况最为接近。      

Spatial interpolation of monthly and annual rainfall in northeast of Iran

Precipitation maps are the key input to many hydrological models. In this paper different univariate (inverse distance weighing and ordinary kriging) and multivariate (linear regression, ordinary cokriging, simple kriging with varying local mean and kriging with an external drift) interpolation methods are used to map monthly and annual rainfall from sparse data measurements. The study area is Golestan Province, located in northeast of Iran. A digital elevation model is used as complementary information for multivariate approaches. The prediction performance of each method is evaluated through cross-validation and visual examination of the precipitation maps produced. Results indicate that geostatistical algorithms clearly outperform inverse distance weighting and linear regression. Among multivariate techniques, ordinary cokriging or kriging with an external drift yields the smallest error of prediction for months April to October (autumn and winter) for which the correlation between rainfall and elevation is greater than 0.54. For all other months and annual rainfall, ordinary kriging provides the most accurate estimates.     

The influence of interpolation and station network density on the distributions and trends of climate variables in gridded daily data

We study the influence of station network density on the distributions and trends in indices of area-average daily precipitation and temperature in the E-OBS high resolution gridded dataset of daily climate over Europe, which was produced with the primary purpose of Regional Climate Model evaluation. Area averages can only be determined with reasonable accuracy from a sufficiently large number of stations within a grid-box. However, the station network on which E-OBS is based comprises only 2,316 stations, spread unevenly across approximately 18,000 0.22° grid-boxes. Consequently, grid-box data in E-OBS are derived through interpolation of stations up to 500 km distant, with the distance of stations that contribute significantly to any grid-box value increasing in areas with lower station density. Since more dispersed stations have less shared variance, the resultant interpolated values are likely to be over-smoothed, and extreme daily values even more so. We perform an experiment over five E-OBS grid boxes for precipitation and temperature that have a sufficiently dense local station network to enable a reasonable estimate of the area-average. We then create a series of randomly selected station sub-networks ranging in size from four to all stations within the E-OBS interpolation search radii. For each sub-network realisation, we estimate the grid-box average applying the same interpolation methodology as used for E-OBS, and then evaluate the effect of network density on the distribution of daily values, as well as trends in extremes indices. The results show that when fewer stations have been used for the interpolation, both precipitation and temperature are over-smoothed, leading to a strong tendency for interpolated daily values to be reduced relative to the “true” area-average. The smoothing is greatest for higher percentiles, and therefore has a disproportionate effect on extremes and any derived extremes indices. For many regions of the E-OBS dataset, the station density is sufficiently low to expect this smoothing effect to be significant and this should be borne in mind by any users of the E-OBS dataset.     

基于台站降水资料对不同空间内插方法的比较

如何把离散的气象台站资料通过合适的空间内插方法转变成规则的网格数据,对于气候变化分析和模拟研究具有重要的意义.作者利用中国区域160个常用台站10年降水观测资料为例,分别采用克里格(Kriging)插值、反距离加权、Delaunay三角剖分线性插值、双谐样条(Biharmonic Spline)插值和Cressman客观分析等几种常见的空间内插方法,较为系统地分析和比较了这几种内插方法插值结果之间的异同,对其优缺点和适用范围进行了适当讨论,并采用不同的网格分辨率和影响半径对Cressman客观分析方法做了进一步分析比较.结果表明:在台站分布密集的区域不同空间内插方法之间差异较小,在台站分布稀疏的区域则差异较大;与更加密集的台站观测资料的比较显示,自动调节影响半径的Cressman客观分析方法与双谐样条插值方法误差相对较小.     

北京地区夏季多模式降水预报的降尺度集成应用

以2008—2010年5—9月日本、德国、T639数值预报模式降水产品为基础,采取反距离插值的统计降尺度分析方法,将数值预报模式降水格点数据插值到北京西北、东北、西南、东南区域的延庆、密云、房山、观象台4个典型代表站点上;再结合统计分析,将夏季产生降水的天气系统分为西来槽、东北低涡、蒙古低涡、其他系统4种类型,采用预报准确率定级方法对各家模式配以不等权权重系数,从而建立北京地区夏季多模式集成降水预报模型,并用独立的样本对预报模型进行了业务试运行检验,检验结果表明:所建模型对降水预报的改进效果较好,优于单个数值模式降水预报。该模型的建立和应用方法为其他区域本地释用数值模式降水预报产品提供了一定的客观参考。     

Usage of multivariate geostatistics in interpolation processes for meteorological precipitation maps

Long-term meteorological data are very important both for the evaluation of meteorological events and for the analysis of their effects on the environment. Prediction maps which are constructed by different interpolation techniques often provide explanatory information. Conventional techniques, such as surface spline fitting, global and local polynomial models, and inverse distance weighting may not be adequate. Multivariate geostatistical methods can be more significant, especially when studying secondary variables, because secondary variables might directly affect the precision of prediction. In this study, the mean annual and mean monthly precipitations from 1984 to 2014 for 268 meteorological stations in Turkey have been used to construct country-wide maps. Besides linear regression, the inverse square distance and ordinary co-Kriging (OCK) have been used and compared to each other. Also elevation, slope, and aspect data for each station have been taken into account as secondary variables, whose use has reduced errors by up to a factor of three. OCK gave the smallest errors (1.002 cm) when aspect was included.     

Delaunay三角剖分法在降水量插值中的应用

Delaunay三角剖分方法在空间分析中具有重要地位,文中简要介绍了Delaunay三角网特性和常用的3类算法,并对随机增长法实现过程进行了详细阐述.根据三角分片线性插值原理,求得插值系数,实现对任意点的三角分片线性插值.利用2008年中国2200个观测站的08时24 h降水量资料,对全中国范围及划分的8个区域内相应的0.28125°×0.28125°降水量格点场,使用交叉检验方法,对比分析了三角分片线性插值和反距离权重法的估值准确率.结果表明:在各区域,三角分片线性插值法的均方根误差偏小;在站点较密集的区域,均方根误差、平均绝对误差比较中,三角分片线性插值都有一定的优势;在平均误差对比中,三角分片线性插值优势明显,在全中国范围交叉检验中,三角分片线性插值法对应的年平均误差是0.005 mm,而反距离权重法为-0.107 mm,对其可能的原因进行了分析,证明了Delaunay三角剖分法的合理性.同时,从图形上展示了降水量的Delaunay三角网的三维结构图和三角分片线性插值后的格点场,在直观上,Delaunay三角剖分后得到降水分布和实况保持一致,并有较好的视觉效果;通过三角分片线性插值得到的格点场降水量分布图,克服了反距离权重法的固有缺陷,使获得的降水量格点场趋于合理,提高了插值精度.最后,探讨了Delaunay三角网在气象领域的应用前景.     

Mapping near-surface air temperature,pressure, relative humidity and wind speed over Mainland China with high spatiotemporal resolution

As part of a joint effort to construct an atmospheric forcing dataset for mainland China with high spatiotemporal reso- lution, a new approach is proposed to construct gridded near-surface temperature, relative humidity, wind speed and surface pressure with a resolution of 1 km× 1 km. The approach comprises two steps： （1） fit a partial thin-plate smoothing spline with orography and reanalysis data as explanatory variables to ground-based observations for estimating a trend surface; （2） apply a simple kriging procedure to the residual for trend surface correction. The proposed approach is applied to observations collected at approximately 700 stations over mainland China. The generated forcing fields are compared with the corresponding components of the National Centers for Environmental Predic- tion （NCEP） Climate Forecast System Reanalysis dataset and the Princeton meteorological forcing dataset. The comparison shows that, both within the station network and within the resolutions of the two gridded datasets, the interpolation errors of the proposed approach are markedly smaller than the two gridded datasets.     

空间回归检验方法在气象资料质量检验中的应用

该文详细介绍了空间回归检验方法, 并使用2003年我国671站的逐日平均气温、最高气温、最低气温、平均水汽压、平均风速、平均0 cm地温、降水量资料, 检验该方法在气象资料质量检验中的适用性。按区号将全国划分为10个区, 利用该方法分别对各区7个要素进行了检验试验。结果表明:空间回归检验方法能够有效检验出可疑数据, 适用于对单一要素的检验; 对降水、风速等空间变化比较大的要素, 该方法有比较好的检验效果; 应用该方法计算时, 在不同地区、不同要素之间存在差异; 当固定出错比率时, 各区应该选择不同的f值。与一般空间检验方法相同, 该方法也与地理环境、周边台站分布有关, 并受台站密度的影响。     

东北地区逐日气象要素的空间插值方法应用研究

针对作物生长动力模型区域应用时对高精度格点逐日气象要素输入值的需要，以东北地区为例，选用克立格法 (Kriging)、以经纬度分布方向为权重的距离权重反比法（IDW）及带高度梯度订正的距离权重反比法（GIDW）3种插值方法进行有限气象站点4~10月逐日气象要素空间插值方法研究，并进行插值的统计量分析和估值的交叉验证。结果表明，对温度而言，GIDW方法估值精度较高，插值结果的平滑程度适中，插值结果分布趋势也较为接近实际站点的分布。对降水而言，IDW估值精度高于Kriging, 而且插值结果的平滑程度较小，更适合于日降水量的空间插值。GIDW、IDW估值精度较高的原因是研究中考虑到日最高温度、最低温度和降水量的经向、纬向梯度、海拔高度梯度存在明显的季节性变化，采用了根据气象要素经纬度方向确定权重，以及根据气象要素高度梯度年内变化进行高度订正的结果。     

Consistency analysis of pluviometric information in Galicia (NW Spain)

An important issue in pluviometric data analysis from rain gauges is the verification of their consistency. In general, this attribute is assessed using double-mass curves. This technique compares cumulative monthly rainfall from a gauge with that averaged from meteorological stations located nearby. The aim of this study was to analyze the quality of monthly rainfall data registered in Galicia (NW Spain) in a five year period (2002–2006). Initially, 159 meteorological stations were evaluated; however, 59 gauges were withdrawn because 10% of their data were missing. Double-mass analysis was performed following two procedures: a) data from each gauge were compared to those obtained in the nearby main station and b) data from each site were compared to the average from five nearby gauges, including data from neighboring regions. The second procedure proved to be more reliable. Rainfall data did not show any outlier for the study period. Determination coefficients were greater than 0.95 in all cases. A graphical analysis showed some deviations from the trend lines in certain stations. First, rainfall maps were obtained by inverse distances weighting. Furthermore, a comprehensive geostatistical analysis, centered in the characterization of the structure of rainfall spatial variability, was performed. Differences between two kriging methods, ordinary and kriging with an external drift, were confirmed, considering the later as a more appropriate technique for rainfall interpolation in the region.     

Mapping the mean monthly precipitation of a small island using kriging with external drifts

This study focuses on the spatial distribution of mean annual and monthly precipitation in a small island (1128 km²) named Martinique, located in the Lesser Antilles. Only 35 meteorological stations are available on the territory, which has a complex topography. With a digital elevation model (DEM), 17 covariates that are likely to explain precipitation were built. Several interpolation methods, such as regression-kriging (????????, ????????, and ????????) and external drift kriging (??????) were tested using a cross-validation procedure. For the regression methods, predictors were chosen by established techniques whereas a new approach is proposed to select external drifts in a kriging which is based on a stepwise model selection by the Akaike Information Criterion (AIC). The prediction accuracy was assessed at validation sites with three different skill scores. Results show that using methods with no predictors such as inverse distance weighting (??????) or universal kriging (????) is inappropriate in such a territory. ?????? appears to outperform regression methods for any criteria, and selecting predictors by our approach improves the prediction of mean annual precipitation compared to kriging with only elevation as drift. Finally, the predicting performance was also studied by varying the size of the training set leading to less conclusive results for ?????? and its performance. Nevertheless, the proposed method seems to be a good way to improve the mapping of climatic variables in a small island.     

都江堰特大暴雨过程中GIS的多种面雨量计算方法对比

本文采用GIS栅格插值的常用方法,反距离权重法(IDW),样条函数法(Spline),克里金法(Kriging),协同克里金法(Co-Kriging),泰森多边形法(Thissen)对2013年7月8～11日都江堰特大暴雨过程进行面雨量计算的对比分析,并用FLood Area模型对此次过程中白沙河流域的暴雨洪涝过程进行模拟,结果显示:5种面雨量计算方法的结果受雨量站密集程度和降水空间分布特征的制约,特别是样条函数法和泰森多边形法,对雨量站分布影响较为敏感;小时面雨量计算中站点分布对样条函数法影响更大;协同克里金法计算面雨量可使FLood Area模拟结果更优,更接近于真实值;在复杂地形条件下面雨量计算中,考虑地形的相关影响可有效提高降水插值精度,使Flood Area模型的模拟结果误差更小。      

重庆山地区域气象要素空间插值方法对比

利用重庆地区1999年和2018年气象数据, 分别采用薄盘光滑样条、协同克里金、普通克里金、反距离加权4种方法, 从年和月两种尺度对气温、降水、太阳总辐射三个要素进行空间插值; 采取交叉验证方法, 用MAE、MRE、RMSE评估插值精度, 确定各要素最优插值方法。结果表明: 气温和太阳总辐射最优插值方法为薄盘光滑样条, 降水为反距离加权; 插值精度上气温、太阳总辐射高值月份优于低值月份, 降水则相反, 但三个要素均表现出年尺度优于月尺度。MRE检验表明, 插值精度为气温>太阳总辐射>降水, 1999年年尺度插值精度分别为1.86%、4.60%、6.87%, 月尺度插值精度分别为2.79%、5.82%、17.42%;2018年太阳总辐射年、月尺度插值精度分别为3.03%、4.88%, 区域站加密后气温、降水年尺度插值精度分别为2.03%、11.20%, 月尺度对应插值精度分别为3.20%、23.14%。     

近38年中国气温和降水的1 km网格数据集

对中国38年的气温和降水进行了空间插值分析,选取最优模型去生成1km网格数据集,为中国大陆的植被分布、气候变化和环境生态等研究提供支持。基于国家气象中心839个气象站的逐日气温和降水数据,用经度、纬度和海拔作为ANUSPLIN软件插值的3个变量,对降水进行开平方预处理,采用3次样条的薄盘光滑样条法,得到了1980—2017年中国大陆月平均气温和月累计降水1km网格插值数据集。数据集的广义交叉验证均方根(RTGCV)和均方根误差(RMSE)具有年周期性和明显的季节变化特征;各站点的平均误差(MBE)的频率分布近似正态分布,绝对误差(MAE)的空间分布也符合中国大陆气候的变化特征。数据集在精准度和时间序列上较新,且提供公共下载服务,可为全国陆地生态系统的研究提供信息支持。     

Postprocessing of simulated precipitation for impact research in West Africa. Part II: A weather generator for daily data

Data from global and regional climate models refer to grid cells and, hence, are basically different from station data. This particularly holds for variables with enhanced spatio-temporal variability like precipitation. On the other hand, many applications like for instance hydrological models require atmospheric data with the statistical characteristics of station data. Here, we present a dynamical-statistical tool to construct virtual station data based on regional climate model output for tropical West Africa. This weather generator (WEGE) incorporates daily gridded rainfall from the model, an orographic term and a stochastic term, accounting for the chaotic spatial distribution of local rain events within a model grid box. In addition, the simulated probability density function of daily precipitation is adjusted to available station data in Benin. It is also assured that the generated data are still consistent with other model parameters like cloudiness and atmospheric circulation. The resulting virtual station data are in excellent agreement with various observed characteristics which are not explicitly addressed by the WEGE algorithm. This holds for the mean daily rainfall intensity and variability, the relative number of rainless days and the scaling of precipitation in time. The data set has already been used successfully for various climate impact studies in Benin.     

基于气象要素内插的GPS水汽反演方法研究与精度分析

准确获取测站气压和温度对GPS水汽反演至关重要。由于我国地域辽阔、经济和社会发展的差异较大,我国GPS气象站网有部分站点未布设气象传感器,无法准确获取测站的气压和温度,其对测站上方水汽造成了较大影响。本文提出一种增加高度订正的反距离加权法,并利用全国113个GNSS气象站(包括25个实验站点,88个插值站点)的连续3个月的气象数据对该方法进行验证。结果表明,内插得到的气压和温度的均方差为1.53 hPa和1.18 K,平均偏差为0.94 hPa和0.82 K。精度随着内插站点与实验站点之间高差的增大,偏差随之增大。最后将内插得到的气压和温度应用于GPS水汽解算,并与GPT-2模型的精度对比。内插气象数据得到的PWV(Precipitale Water Vapor)的均方差和平均偏差为0.59 mm和0.38 mm,精度明显优于GPT-2模型。     

Comparison of spatial interpolation methods for gridded bias removal in surface temperature forecasts

All numerical weather prediction (NWP) models inherently have substantial biases, especially in the forecast of near-surface weather variables. Statistical methods can be used to remove the systematic error based on historical bias data at observation stations. However, many end users of weather forecasts need bias corrected forecasts at locations that scarcely have any historical bias data. To circumvent this limitation, the bias of surface temperature forecasts on a regular grid covering Iran is removed, by using the information available at observation stations in the vicinity of any given grid point. To this end, the running mean error method is first used to correct the forecasts at observation stations, then four interpolation methods including inverse distance squared weighting with constant lapse rate (IDSW-CLR), Kriging with constant lapse rate (Kriging-CLR), gradient inverse distance squared with linear lapse rate (GIDS-LR), and gradient inverse distance squared with lapse rate determined by classification and regression tree (GIDS-CART), are employed to interpolate the bias corrected forecasts at neighboring observation stations to any given location. The results show that all four interpolation methods used do reduce the model error significantly, but Kriging-CLR has better performance than the other methods. For Kriging-CLR, root mean square error (RMSE) and mean absolute error (MAE) were decreased by 26% and 29%, respectively, as compared to the raw forecasts. It is found also, that after applying any of the proposed methods, unlike the raw forecasts, the bias corrected forecasts do not show spatial or temporal dependency.     

面雨量空间扩展估算法

以温州地区1991～2001年90个观测站的月平均降雨为例,在GIS支持下,对样条函数法、克立格内插法及距离平方反比法这3种插值方法进行了对比研究;并在90个观测站中筛选出最少量的、能达到稳定结果的站点数;还考虑了插值的空间分辨率对结果的影响。对上述3点进行大量的计算、统计分析的结果表明:①在选择距离平方反比法及样条函数法对月平均降雨量插值效果均较好;②利用这两种插值方法对不同站点密度选取不同空间分辨率插值后得出,选取50站误差趋于稳定,利用距离平方反比法插值结果误差较小,而空间分辨率对结果几乎没有影响。利用距离平方反比法,选择50个站得到了温州地区1km×1km面雨量空间扩展结果,为水文预报工作提供一种较精确的面雨量估算和输入方法。