Spatial Interpolation of Annual Precipitation in South Africa-Comparison and Evaluation of Methods

Abstract

Data from 545 rainfall gauges were used to interpolate the spatial distribution of annual rainfall in South Africa. Several spatial interpolation methods (inverse distance weighting (IWD), ordinary kriging, universal kriging, cokriging) were tested by variation analyses and cross-validation to determine the most suitable one. The best results were achieved by ordinary kriging, whereby the setting of the parameters was determined through sensitivity analyses. The median of the errors turned out to be 61 mm (11%). The interpolation errors were generally small for the interior of the country and high for coastal and mountainous regions.     

Comparison of Interpolation Methods for the Prediction of Reference Evapotranspiration—An Application in Greece

The objective of this paper is to evaluate four interpolation methods, concerning their suitability for spatial prediction of long-term mean daily reference evapotranspiration (calculated by Penman–Monteith equation) for each month in Greece. The methods studied were ordinary kriging (OK) and inverse distance squared (IDS) and their modifications in which elevation data was incorporated into the interpolation process. The modified methods were named residual kriging (RK), and gradient-plus-inverse distance squared (GIDS). Apart from interpolation methods, two different approaches were studied in order to define what the proper sequence of steps is in the case of the interpolation of reference evapotranspiration. More particularly the ‘calculate first, interpolate later’ (CI) procedure was compared to the reverse procedure, namely ‘interpolate first, calculate later’ (IC). The assessment criteria of the methods accuracy were: mean error (ME), mean absolute error (MAE) and root mean squared error (RMSE). The results revealed that the incorporation of elevation significantly improved the performance of interpolation methods. On the contrary, procedures CI and IC were very similar since they had no effect on the performance of the four interpolation methods studied.     

多维线性插值方法的构建及应用

根据全国2010年607个气象站点的日降水量资料以及各站点平面分布与高程信息,构建了多维线性空间插值方法。在不同插值控制站点数目(n=4,8,12)情景下,分析了多维线性空间插值方法与反距离权重插值、样条插值和克里格插值法(球面模型和高斯模型)在我国年降水量空间插值中的应用情况。对比发现,不同的控制站点情境下,各种插值方法的插值结果差异显著,但随着控制站点数目的增加,各插值结果的差异性减小;多维线性插值方法在多种情景下都表现出较好的插值精度。     

ESTIMATION OF WATER TABLE ELEVATION BY UNIVERSAL COKRIGING

When water resource or quality problems assoelated with phreatic water in geological settings are studied,information about water table elevations is often crucial. In those eases where the water table is a subdued replica of the ground surface, universal cokriging can be used to estimate water table elevations at un sampled locations on the basis of water table and ground surface elevation measurements obrained at well locations. In this paper, universal cokriging,with ground surface elevation considered as a co variate, was used to estimate water table elevations. Universal cokriging equations were derived, an iterative method for obtaining experimental variograms was established, and a ease study of an initial groundwater flow simulation in the Xiuwu County,Henan Province, China, was presented. In the ease study,the initial groundwater flow regime was represented both by universal cokriging with the ground surface elevation serving as a covariate and by universal kriging without the inclusion of ground surface elevation as a covariate. A comparison of the results from these two approaches shows that groundwater levels of phreatic water at locations without measurements in regions with unconsolidated porous media can be estimated more accurately by universal cokriging.     

基于地统计学的柬埔寨年降水量数据空间插值

为了更好地分析区域水资源量、水文平衡及灌溉需水量,需要对降水的时空分布进行定量分析。由于气象站点布设的局限性,针对资料短缺地区的空间插值就显得尤为重要。以柬埔寨的20个气象站降水数据为插值实验样本,研究基于Arc GIS的空间插值和分析功能,探讨普通克里金、简单克里金、析取克里金及经验贝叶斯克里金法等4种地统计学插值法的优劣及其适用性。通过插值误差分析来检验插值精度,并模拟年降水量的空间分布图来进行比较分析,结果表明经验贝叶斯克里金插值法最优。研究结果可为资料短缺地区降水量空间插值提供参考。     

A New Method for Estimation the Regional Precipitation

In this article we propose a new method - the Most Probable Precipitation Method (MPPM) - for estimating the precipitation at regional scale. Comparisons with the Thiessen polygons methods (TPM), inverse distance weighting interpolation (IDW) and ordinary kriging (OK) on annual, monthly, seasonal and annual maximum monthly precipitation are provided. In all cases MPPM performs better than IDW and OK, and in most of them, better than TPM.     

基于广义可加模型的降水空间估算模型

采用太湖流域浙西区33个站点1989—2013年的降水观测资料,基于广义可加模型建立了该区域年降水空间估算模型,得到了该区域分辨率为1 000 m×1 000 m的降水栅格数据。借助多种统计指标,分析了不同预测因子对降水空间估算结果的影响,特别比较了是否将高程作为预测因子情况下的年降水量估算差异。结果表明:加入高程因子作为广义可加模型的预测变量后,无论是模型的优良性还是降水空间估算精度均有所提高,能够更合理地描述浙西区降水空间分布受地形影响的特征。此外,从模型偏态效应图来看,浙西区降水量随着纬度的增加明显减小,随着高程的增加显著增大,而随经度的变化则不明显。     

Geospatial Rainfall Modelling at Eastern Nepalese Highland from Ground Environmental Data

The study presents a geospatial knowledge transfer framework by accommodating precipitation maps for the Eastern Nepalese Highland (ENH) across an area of about 100,000 km². For this remote area, precipitation–elevation relationships are not homogeneously distributed, but present a chaotic gradient of correlations at altitude ranges. This is mainly due to impervious orography, extreme climate, and data scarcity (most of the rain gauges in Himalaya are located at valley bottoms). Applying geostatistical models (e.g. multivariate geospatial approaches) is difficult in these zones. This makes the ENH an interesting test area where we obtained monthly precipitation spatial patterns for a 30-year period (1961–1990). The aim was to both capture orographic meso-α spatial regimen (~30 km) and local pattern variability (~10 km). Data from 58 FAO raingauges were used plus data from an atmospheric weather station (AWS Pyramid) operating at 5,050 m a.s.l., used to compensate the gap of precipitation pattern presents in the area surrounding the Mount Everest. In these complex orographically remote areas of the Himalayas, monsoon precipitation systems exhibit important topographical interactions and spatial correlations, depending on the scale at which the primary variable (e.g., precipitation) and co-variables (e.g., elevation) are recorded and analysed. Precipitations were assessed for months—May, July and September—representative of the monsoon season. For the rainiest month (July), cokriging indicated a range of precipitation values from ~100 mm over the Tibetan Plateau to ~500 mm in the southern part of Nepal, up to ~900 mm towards the pre-Himalayan range. For July, cokriging precipitation map also showed correspondence with the map of vegetation pattern, and therein lies the clue to using multivariate geostatistical models as flexible approaches for estimating precipitation spatial patterns in remote areas.     

广州市降水量空间插值方法研究

采用广州市境内及周边的55个雨量站点的2015年年累计降水量数据,选取9种空间插值方法对广州市年降水量进行了空间插值,将插值估算结果与检验点作对比分析,并对广州市2015年降水量的时空分布特征进行分析。综合分析得出:广州市降水量的空间插值方法误差顺序为KSNNRBFLPIKrigingSplineIDWGPIDK;KS雨量等值面光滑,没有出现"牛眼"和边界突变,计算方便快捷,估算结果准确,在广州市雨量空间插值中获得很好的效果。分布特征表现为:广州市降水量空间分布由北向南呈现明显递减的分布规律,高值区在流溪河流域,在2 500 mm以上,低值区在南沙区,在1 500 mm以下。其他区域基本在2 000~2 300 mm。     

Integrating Ground-based Observations and Radar Data Into Gridding Sub-daily Precipitation

A new and general approach is proposed for interpolating 6-h precipitation series over large spatial areas. The outputs are useful for distributed hydrological modelling and studies of flooding. We apply our approach to large-scale data, measured between 2014 and 2016 at 159 weather stations network of Meteo Romania, using weather radar information and local topography as ancillary data. Novelty of our approach is in systematic development of a statistical model underlying the interpolation. Seven methods have been tested for the interpolation of the 6-h precipitation measurements: four regression methods (linear regression via ordinary least squares (OLS), with and without logarithmic transformation, and two models of generalized additive model (GAM) class, with logarithmic and identity links), and three regression-kriging models (one uses semivariogram fitted separately every 6-h, based on the residuals of the GAM with identity links models, and other two with pooled semivariograms, based on the OLS and GAM with identity links models). The prediction accuracy of the spatial interpolation methods was evaluated on a part of the dataset not used in the model-fitting stage. Due to the good results in interpolating sub-daily precipitation, normal general additive model with identity link followed with kriging of residuals with kriging parameters estimated from pooled semivariograms was applied to construct the final 6-h precipitation maps (PRK-NGAM). The final results of this work are the 6-h precipitation gridded datasets available in high spatial resolution (1000 m?×?1000 m), together with their estimated accuracy.

     

1971-2018年汉江流域陕西段降水时空特征分析

基于1971-2018年汉江流域陕西段 27个气象站点的逐日降水数据,选择了年降水量、降水强度、最大日降水量、年降水日数、中雨日数和大雨日数6个降水指数分析其降水时空特征,分析方法包括线性估计法、小波分析法、滑动均值法、IDW 空间插值法及Mann-Kendall检验法。结果表明：在研究时段内,汉江流域陕西段降水强度有缓慢增加趋势,其余5个降水指数均呈缓慢减小趋势,且6个降水指数的变化趋势均不显著;研究区域仅年降水日数无突变点,且在1995年后呈现显著减小趋势,其余降水指数均有突变点;年降水量有7 a的副周期和27 a左右的主周期,主周期有3个循环交替,且丰、枯交替突变点在1983和2000年。汛期降水量与年降水量周期基本一致,而非汛期有4和16 a两个副周期和1个28 a的主周期;年降水量空间分布呈现由北到南逐渐增大的趋势,除了年降水日数的高值中心在宁强县外,其余5个降水指数的高值中心均在镇巴县,而低值中心除了降水强度在太白县外其余的均在商县。在研究时段内各年代际降水指数的比较中,1971-2018年的年降水量、降水强度和年降水日数均仅次于最大值,预计未来极端降水事件可能更加频繁,严重的情况下会影响水生态、水环境、水安全等的健康发展。     

基于地理因子的福建省年降水空间估算模型研究

为研究福建省多年平均降水量的空间分布格局,为工农业生产、自然灾害预测、生态环境建设提供科学依据,利用福建省及周边区域35个气象站点1951—2011年降水资料,分析年均降水量与海拔、纬度、距海岸距离、坡向的相关性;同时,结合多元回归方程和克里金插值构建降水空间估算模型,反映出年均降水量空间分布的总体趋势,突出局部地区降水的差异,估算福建省1951—2011年年均降水量空间分布。结果表明:已知气象站点年均降水量估算的平均相对误差为3.4%,绝对误差为56 mm,验证站点的平均相对误差为3.6%;福建省年均降水量从东南沿海向西北山区呈现波动式上升的特点。     

Spatial Analysis of Seasonal and Annual Temperature and Precipitation Normals in Southern Ontario,Canada

This study presents some univariate and multivariate low-pass filtering methodologies (ordinary kriging, ordinary cokriging, modified residual kriging, inverse distance weighting) to spatially model seasonal temperature and precipitation normals in an environment where climate patterns are variably modified by regional water bodies and physiography. Cross-validation and maps of modeled climate patterns are used as a criteria to assess particular climate realizations. The results of the exercise show how an agro-climatologist might use these methods to assess spatial representations of the modeled phenomena, the relevance of covariates, and the shortcomings and strengths of different techniques to characterize lake-physiography-climate interactions on a seasonal basis. The methods are also useful for evaluating station networks for capturing important Great Lakes climate patterns.     

Co-Kriging Estimation of Nitrate-Nitrogen Loads in an Agricultural River

Daily nitrate-nitrogen (NO₃-N) loads in the Raccoon River, Iowa, were estimated using Ordinary kriging (OK), Cokriging (CK), and a standard rating curve method (LOADEST) based on a dataset of 3451 measurements of NO₃-N concentration collected over 19 years. The CK estimation utilizes the temporal correlation of NO₃-N load with daily discharge and honors the measured points to improve estimation relative to regression based models. Loads were estimated using the observed concentrations and three subsets of the measured data that correspond to three frequencies (weekly, biweekly, and monthly). Results indicated that daily NO₃-N loads were best estimated by CK using measured loads with daily discharge. Daily load estimates produced by OK using weekly data matched well with measured values, but discrepancies emerged when samples were collected less frequently, e.g., biweekly and monthly. For the entire 19-year dataset, compared to measured loads, the estimated total NO₃-N load decreased using OK when samples were collected monthly, but increased using CK. Load estimation using the seven-parameter LOADEST model did not perform well for the Raccoon River because the correlation of NO₃-N concentration to river discharge was poor. For the site studied, weekly and biweekly sampling may be sufficient to estimate daily NO₃-N loads with CK when daily discharge data is available.     

基于空间插值方法的重庆降水信息展布

不同空间插值方法在不同地区的插值精度不同。为确定重庆市降雨量的空间分布,采用重庆市12个气象站1960-2014年降水数据,运用系数为2、3、4的反距离权重法、普通克里金法、考虑高程的协同克里金法及考虑温度的协同克里金法,按多年平均、最大3个月及最小3个月不同降水量指标进行分析,并以均方根误差和纳什效率系数进行验证。结果表明,对于三种指标,不同插值方法的优劣从好到差均为考虑高程的协同克里金法、考虑温度的协同克里金法、普通克里金法、系数分别为4、3、2的反距离权重法。对于反距离权重法,系数越大则误差越小。三种降水量指标以多年平均降水量为输入数据的插值结果更加准确。考虑温度的协同克里金法在降水量较小或降水与温度相关性较强时有良好的插值精度。在重庆地表变化幅度较大的地区,考虑高程的协同克里金法更能体现高程变化对降水量的影响。     

1970-2013年大西安地区降水时空变化特征分析

大西安地区降水资源空间差异较大,为深入了解大西安不同区域降水时空分布特征,利用大西安地区14个气象站1970-2013年的逐月降水观测资料,采用滑动平均法、Mann-Kendall检验法、小波分析法以及克里金插值法,对大西安5个区域降水量的时空变化特征进行了分析.结果表明:大西安地区年均降水量为576.65 mm,整体呈下降趋势,下降率为-10.04 mm/(10 a),东部较西部下降显著,北部较南部下降显著;年内降水量分配不均,降水主要集中在7-9月份,占全年降水总量的50.84％,春、秋季降水量呈下降趋势,夏季降水量呈上升趋势;研究区年降水量变化的第1主周期为28 a;全区多年降水量呈现出少—多—少—多的波动趋势,突变年份为1980年和1991年;年代际降水量呈现出增加—减少—增加的趋势;年降水量空间分布不均,呈现自东南向西北逐渐减少的趋势.上述研究成果可为大西安地区降水资源的合理利用提供参考.     

Comparison of IDW and Physically Based IDEW Method in Hydrological Modelling for a Large Mountainous Watershed,Northwest China

Topography and spatial patterns of landscape significantly affect spatial distribution of precipitation and, in turn, hydrological modelling, especially in high elevation, mountainous watersheds of arid regions. This study incorporates a physically based inverse distance and elevation weighted (PBIDEW) method into a distributed conceptual hydrological model, distributed large basin runoff model, and compared with an inverse distance weighted (IDW) method to assess the performances of both methods in precipitation estimation for hydrological modelling at watershed scale. The PBIDEW method considers the impacts of topography using month‐dependent parameters in its interpolation of meteorological variables while the IDW method does not. Both the IDW and the PBIDEW methods are evaluated and compared in hydrological modelling at different spatial resolutions in the upper reach of the Heihe River Watershed, Northwest China. Results show that the IDW method underestimated the areal precipitation, and the PBIDEW method produced more realistic precipitation estimations in the study area. Both methods have some limitations, the performance of the IDW method was mainly influenced by the availability of observation data, while that of the PBIDEW method was mainly influenced by the representation of topographical information. Considering more detailed information for precipitation estimates, the PBIDEW method performed better at finer spatial resolution. Overall, the PBIDEW method, using month‐dependent physical interpolation parameters, seems more suitable for precipitation estimation in hydrological simulations in data‐scarce, high elevation and topographically complex mountainous watersheds in arid area. Copyright © 2017 John Wiley & Sons, Ltd.     

红河流域TRMM卫星降水数据精度评价

利用红河流域及周边地区45个气象站点1998-2015年实测降水数据,在不同时空尺度上对TRMM3B43V7卫星降水数据进行精度评价,并分析高程、坡度和坡向对降水数据精度的影响。结果表明:在年尺度上,TRMM降水数据与站点实测降水数据拟合优度R~2为0.75,整体上TRMM降水数据比站点实测降水数据偏高7.73%,月尺度上,TRMM降水数据与站点实测降水数据拟合优度R~2为0.84,两者之间相关性显著,季尺度上,春季降水拟合优度(R~2=0.77)高于其余3个季节,冬季降水拟合优度最差(R~2=0.64);流域尺度上,降水重心移动轨迹表明TRMM降水数据基本能反映降水的空间分布及演变过程,站点尺度上,各站点的相关系数均大于0.84,相对偏差较大的站点主要分布在河谷和盆地地区;TRMM降水数据在海拔大于1 000 m、坡度小于2°以及东南方向上的精度较高;主成分分析方法表明坡度和坡向对TRMM降水数据精度的影响大于高程。     

新安江流域降雨量空间插值方法和参数筛选

选取新安江流域48个雨量站点2000-2010年的降雨量数据以及地理地形资料,利用反距离权重(IDW)、径向基函数(RBF)、普通克里金(OK)和残差克里金(RK)方法进行插值,根据交叉验证结果筛选最佳的方法和参数.结果表明:年尺度上,考虑高程、纬度等地形因子影响的RK方法插值精度最高,然后是IDW,OK和RBF;邻近站点的搜索策略对IDW插值精度影响较大;考虑各向异性的OK法插值精度较高,模型之间的差别不大.月尺度上,IDW法对降雨量丰富的月份插值精度较高;RBF对降雨较少且分布均匀的月份插值效果好;数据越符合正态分布,OK法的插值精度越高;RK方法则适用于降雨与地理因素相关性好的月份.     

1960—2013年贵州省强降水天数时空变化特征

为深入了解贵州省强降水天数变化规律,基于贵州省1960—2013年19个气象站逐日降水资料,利用气候变化趋势分析法和Kriging插值法分析了贵州省54 a来强降水天数时空变化特征。结果表明:1960—2013年贵州省强降水天数整体呈下降趋势;空间变化趋势呈现中西部大幅减少,东部、南部和北部小幅减少或小幅增加的特点;各坡度带上强降水天数接近,随着高程增加,强降水天数呈减少趋势;北盘江、都柳江、红水河和南盘江强降水天数高于赤水河、牛栏江横江、乌江和沅江;都柳江和南盘江强降水天数呈增加趋势,其他流域呈减少趋势;汛期与非汛期强降水天数分布及变化趋势在高程带、坡度带及各流域上存在差异。研究结果可为贵州省气象灾害防治提供参考。