Estimation of mean annual precipitation as affected by elevation using multivariate geostatistics

This paper presents the results of the interpolation of annual precipitation over a regular grid performed in Aragón (Spain). The main objective was the quantification of the improvement in estimation uncertainty by including elevation in the interpolation and by using base 10 logarithms of both annual precipitation and elevation versus the original values.Long-term annual precipitation (APRE) was available at 182 weather stations. Elevation above sea level (ELEV) was available at those stations and at 1913 additional points over a regular 5 km grid. The spatial variability of APRE, ELEV and their base 10 logarithms (LAPRE and LELEV, respectively), and the spatial correlation between APRE and ELEV, APRE and LELEV, LAPRE and ELEV, and LAPRE and LELEV were described by gaussian direct- and cross-semivariogram models with nugget effects.Geostatistical interpolation methods, ordinary kriging and cokriging, were used to estimate APRE and LAPRE at the 1913 additional elevation points. Estimates of LAPRE were transformed back to APRE values. Cokriging estimates were in general higher than kriging ones, mainly at points of high elevation. The average percent difference among cokriging and kriging estimates was 9–12%. Cokriging estimates obtained with the different sample data sets were in general terms similar. However, at points of high elevation, cokriging with ELEV as the auxiliary variable seemed to overestimate annual precipitation.Estimation error standard deviations (EESD) also were computed in each interpolation point. For all points, the EESD obtained using LAPRE values were lower than those obtained using APRE values, being the average percent differences of –38 to –42%. Likewise, for all interpolation points, cokriging EESD were lower than kriging ones. Using LAPRE and LELEV values, the average percent difference among cokriging and kriging EESD was –11.0%, with minimum and maximum percent differences of –6.7 and –35.8%, respectively.     

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.     

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.

     

Geostatistical analysis of spatial variability of rainfall and optimal design of a rain gauge network

Kriging is a geostatistical estimation technique for regionalized variables that exhibit an autocorrelation structure. Such a structure can be described by a semivariogram of the observed data. The punctual-kriging estimate at any point is a weighted average of the data, where the weights are determined by using the semivariogram and an assumed drift, or lack of drift, in the data. The kriging algorithm, based on unbiased and minimum-variance estimates, involves a linear system of equations to calculate the weights. Kriging is applied in an attempt to describe the spatial variability of rainfall data over a geographical region in northern Greece. Monthly rainfall data of January and June 1987 have been taken from 20 measurement stations throughout the above area. The rainfall data are used to compute semivariograms for each month. The resulting semivariograms are anisotropic and fitted by linear and spherical models. Kriging estimates of rainfall and standard deviation were made at 90 locations covering the study area in a rectangular grid and the results used to plot contour maps of rainfall and contour maps of kriging standard deviation. Verification of the kriging estimates of rainfall are made by removing known data points and kriging an estimate at the same location. This verification is known as the jacknifing technique. Kriging errors, a by-product of the calculations, can then be used to give confidence intervals of the resulting estimates. The acceptable results of the verification procedure demonstrated that geostatistics can be used to describe the spatial variability of rainfall. Finally, it is shown how the property of kriging variance depends on the structure and the geometric configuration of the data points and the point to be estimated can also be used for the optimal design of the rain gauge network in an area.     

基于克里格方法估算流域降雨量的模式

目前常用的流域雨量插值方法中，大多数都没有考虑雨量的空间分布特征，无法检验插值结果，因此经常会出现一定的误差。地质统计学中的克里格方法是一种使插补误差达到最小并且对误差进行精确估计的插值方法。为此，尝试采用克里格方法对流域雨量进行估值，并分别将年平均、月平均、时段雨量的插值结果与距离反比法以及最临近法的插值结果进行了对比性检验。依据分析，得出了克里格方法内插估值的优势和不足。     

Geostatistical mapping of precipitation: implications for rain gauge network design.

This study examined four univariate kriging techniques; simple kriging (SK), ordinary kriging (OK), multi-Gaussian kriging (MGC), and log-normal kriging (LNK); and two multivariate kriging algorithms; kriging with external drift (KED) using elevation and slope in two different models for the estimation of daily rainfall in a 250 m x 250 m grid over a 750 km2 area in the Canadian Boreal forest. Multivariate kriging did not enhance daily rainfall predictions. SK, OK, and LNK produced statistically comparative results with OK being slightly better. MGC was the worst univariate estimator, mainly due to the high percentage of data spikes. Sequential Gaussian simulation (SGS) was then implemented to produce 100 equiprobable maps of rainfall. A multi-objective approach; that is based on overlaying the map of the kriging variance, the DEM, and land use/land cover maps in a GIS framework to identify the areas of commonly favourable features; was proposed to identify potential future sampling locations.     

空间插值方法在锦州湾海水富营养化评价中的应用

采用空间插值和营养指数方程相结合的方法,对锦州湾海域海水富营养化状态进行评价.选择反距离权重(IDW)、径向基函数(RBF)和普通克里金(OK)三种插值方法及相应的关键参数,对2009年8月份锦州湾附近表层海水的高锰酸盐指数(COD)、无机氮(DIN)和无机磷(DIP)指标进行空间插值,通过交叉验证筛选出精度最高的插值方法.结果表明:(1)从插值精度上看,除了RBF法的薄盘样条(TPS)函数精度较低外,其余方法精度差别不显著;(2)从等值线图对空间变化趋势的表现效果上来看,OK法效果较好.最后利用OK法所得的插值结果评价锦州湾海水的富营养化状态,得出营养指数E≥1的海域面积占调查海域的2.4％,与传统的评价方法相比,所绘出的富营养化空间分布图可直观、准确地反映该海域的富营养化状况,为海水水质评价工作提供了新思路.     

西南地区降水量插值方法比较——以丽江市为例

我国西南地区由于地形复杂,海拔落差大,且雨量站分布不均,资料代表性差,针对这一区域的降雨预报效果不尽如人意,每年因局地强降水造成的损失巨大。旨在探讨适合山区等海拔落差较大地区的降水插值方法的一般思路,提高该地区降水估测精度。丽江市最大海拔落差达4 516 m,是西南地区典型的山地型城市。以丽江市40个雨量站40 a的月降雨数据为基础,选择6个站为检验站,运用反距离权重法、普通克里金法、样条函数法、趋势面法进行了最优插值方法的探讨。插值误差分析的结果表明:反距离权重法在该研究区域效果较好,幂指数增加到8以上时,相对误差基本稳定在7.8%;克里金法对降雨量的插值效果也较好,生成的插值图平滑;样条函数法插值效果最差。研究成果可为我国西南地区及其他山地地区降雨预报提供参考。     

Regionalized Design Rainfall Estimation: an Appraisal of Inundation Mapping for Flood Management Under Data-Scarce Situations

Availability of regionalized design rainfall is crucial for flood modeling, particularly over the regions with sparse raingauge networks. This study proposes a new comprehensive framework for generating regionalized design rainfall time series for data-poor catchments involving non-linear and non-parametric optimization approaches. A large set of parametric and non-parametric families of distribution were considered for multivariate rainfall frequency analysis using at-site station data, while a unique design temporal pattern over the region was derived by quantifying the flood causing potential of design hyetographs. The regionalized design rainfall time series was used as one of the inputs to a two-dimensional (2D) flood model. The accuracy and performance of the derived regionalized design rainfall for flood inundation modeling were evaluated by comparing with those derived from different spatial interpolation methods. There was a high consensus of the former with those of widely used kriging and spline interpolation methods. A severely flood-prone and data-poor (no raingauge available within study area) large coastal catchment lying along the coast of the Bay of Bengal, India, was chosen for a demonstration of the proposed framework. The study showed that the framework can be used for extreme events arising due to floods, even under changing climatic scenarios. It further invokes the necessity for incorporating the proposed framework into various commercially and freely available flood models along with other existing interpolation techniques to support improved flood management.     

Regression Kriging Analysis for Longitudinal Dispersion Coefficient

Prediction of longitudinal dispersion coefficient (LDC) is still a novel topic for both environmental and water sciences due to its practical importance. In this study, the appraisal of LDC is considered as a spatial modelling problem and the analyses are carried out by regression kriging. Since LDC prediction includes some geometrical (spatial) parameters, the analyses have been performed such that it takes spatial variability of data into account. The modelling procedure consists of two stages. In the first stage, spatial variables are analyzed via multi-linear regression technique and deterministic relationships are identified. In the second stage, based on the spatial auto-correlations of the residuals, the regression-based kriging procedure is applied. The capacity and accuracy level of the method has been compared with former models. As a consequence, the applications revealed that analyzing hydraulic and geometrical parameters with spatially correlated errors is a convenient approach for evaluating LDC in a hydrological system.     

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。     

雨量站网分布对雨量插值算法及径流响应的影响

为比较雨量站网密度及分布对不同空间插值算法的影响,选取6种雨量站密度的不同分布,采用4种空间插值算法对研究区2006—2014年的日降雨进行插值,并将面均雨量作为新安江模型的输入,分析和比较其降雨径流响应。结果表明:①雨量站网空间分布越均匀,降雨插值误差越小,其径流模拟的精度也越高;②在雨量站网均匀布置的情况下,各空间插值算法的插值结果差异较小;雨量站网布置不均匀时,站点数目越少各空间插值算法插值结果差异越大;③计算点雨量时,考虑空间变量的克里金法能更准确地计算日降雨的结果;计算面雨量时,不同插值算法间差异较小,建议选用计算简便的插值算法,比如泰森多边形、反距离权重法。     

粒子群算法优化BP在降雨空间插值中的应用

为更好地表达降雨量的空间分布,将粒子群算法(PSO)优化后的反向传输(BP)神经网络分别运用于三峡区间流域日、月和年降雨量的空间插值中,并与单纯BP神经网络和克里金的插值效果作对比。研究结果表明:在日和年的时间尺度上,PSO-BP插值性能较BP有明显改善,且优于克里金的插值效果;在月时间尺度上,PSO-BP插值效果与BP接近且优于克里金。因此,PSO-BP能较好地揭示降雨量在空间的分布规律,也具备在不同时间尺度上对降雨量进行空间插值的能力,是一种较优的降雨空间插值方法。     

基于数据同化的降雨数值空间分布模拟研究

降雨数值模拟是延长水文预报预见期的重要方法,但由于降雨数值模拟中驱动数据所提供的初始场和边界场条件和大气的实际状态并不是完全吻合,导致模拟结果存在误差。减小降雨数值模拟的误差是提高水文预报精度的关键问题,特别是在大气数值模式和分布式水文模型耦合模拟过程中,高精度的降雨信息是准确模拟的关键。本文基于WRF模式和三维变分数据同化方法,选取雷达反射率和GTS(Global Telecommunication System)数据作为同化资料,开展基于数据同化的降雨数值空间分布模拟研究,从降雨的空间展布和指标评价两方面对同化前后的模拟结果进行对比。结果表明:同化后的模拟数据在CSI指标和RMSE指标上都优于同化前的模拟数据,说明同化后模拟数据的误差小于同化前的误差;将同化前后的数据展布在网格图中,发现同化后的数据可以更加准确地刻画降雨的空间分布规律,说明通过数据同化方法提高了模拟降雨和实际降雨空间分布的一致性,改善了WRF模式模拟降雨空间分布的能力。     

Groundwater Vulnerability Modeling to Assess Seawater Intrusion: a Methodological Comparison with Geospatial Interpolation

Seawater intrusion has become a growing threat in coastal urban cities due to overexploitation of groundwater. This study examines the accuracy of the commonly used geospatial quality assessment models (GQA) and groundwater vulnerability assessment models (GVA) in determining the extent of seawater intrusion in urban coastal aquifers. For that purpose, interpolation methods (kriging, IDW and co-kriging) and vulnerability assessment models (DRASTIC, EPIK) were compared using groundwater salinity criteria (TDS, Cl^?) collected at three pilot areas along the eastern Mediterranean (Beirut, Tripoli, Jal el Dib). The results showed that while the GIS-based interpolation methods and the vulnerability assessment models captured elements of the groundwater quality deterioration, both had a limited ability to accurately delineate saltwater intrusion. This emphasizes that while interpolation methods and conventional vulnerability models may give general information about groundwater quality, they fail to capture the status of the aquifer at a finer spatial resolution.

     

区域尺度地下水埋深与矿化度对土地盐碱化转变概率研究

为探明受地下水埋深与矿化度影响的极度干旱荒漠区土地盐碱化转变概率,选定甘肃省景泰川电力提灌灌区(简称"景电灌区")为研究区,分别利用ArcGIS空间插值中的反距离权重法、样条函数法、趋势面法及普通克里金法对2017年的地下水埋深和矿化度监测数据进行插值,结合误差矩阵选取最优插值方法,并对研究区1994、2008和2017年三期监测数据进行插值分析,再通过重分类消除量纲进行叠加,将土地盐碱化难易程度划分为5级,分析了研究区土地盐碱化转变概率。结果表明,地下水埋深和矿化度平均值在1994年至2017年间呈不断上升趋势,灌区土地盐碱化转变概率西南低东北高,地下水埋深较深区域不易形成盐碱地,地下水埋深较浅区域,矿化度越大越易形成盐碱地,研究可为干旱荒漠区区域地下水利用提供理论依据。     

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。     

非平稳区域化变量克立格插值方法的比较

为了减少非平稳区域化变量的插值计算的工作量,以中国中东部地区59站1960~2000年的年平均降水量为数据源,采用普通克立格法与泛克立格法两种方法对降雨量进行空间插值,对其插值结果进行比较。结果表明,两者的插值结果非常相似,且前者的插值精度略优于后者。认为在无需详细了解变量的空间变异性情况,而只进行空间插值研究时,用普通克立格法代替泛克立格法进行非平稳区域化变量的空间插值具有计算简单、无需确定漂移等优点,同时可以取得较好的插值效果。     

Statistical tools for thermal regime characterization at segment river scale: Case study of the Ste‐Marguerite River

Suitable thermal fish habitats are constrained by both maximum and minimum temperature tolerances. A multivariate and geostatistical approach was developed to estimate stream thermal characteristics at the river segment scale. Data from 22 temperature‐monitoring stations during summer 2007 were used to estimate monthly maximum temperature as well as thermal characteristics such as the number of events, the cumulative degree–days and the associated duration over specific temperature thresholds of 19 and 21°C. The probability of exceeding these temperature thresholds has also been interpolated. The methodology relies on the construction of a multivariate space using physiographic and hydrological characteristics of gauging stations as inputs in a canonical correlation analysis (CCA). A geostatistical interpolation technique, ordinary kriging, was subsequently used to perform interpolation in the physiographical space constructed using CCA. Results from this study were obtained for thermal characteristics estimated into two different interpolation spaces: (1) a 7 metrics space, and (2) an 8 metrics space. Cross‐validation technique has been performed and satisfactory results were obtained. Kriging thermal characteristics (magnitude and duration) into the 7 metric space for a 19°C threshold exceedance leads to best results with Relative Root Mean Square Error (RRMSE) ranging between 9.66 and 15.08%. The study shows that kriging in a multivariate space is a promising tool for water resources managers, especially in cases where risk mapping for lethal or sub‐lethal temperature thresholds may be required for a specific fish species. Copyright © 2010 John Wiley & Sons, Ltd.     

Spatial Distribution of Rainfall in Indian Himalayas – A Case Study of Uttarakhand Region

Continuous rainfall data in grid format are required to run models for hydrological and agricultural research as well as water resources planning and management. The present work attempts to prepare a normal annual rainfall map in Himalayan region of India lying in Uttarakhand state at 1 km spatial resolution which currently is not available. In the region, India Meteorological Department maintains observatories/raingauge stations and data from 44 stations were used in this study. A comparative analysis of interpolation techniques like Inverse Distance Weighted, Polynomial, Splines, Ordinary Kriging and Universal Kriging shows that Universal Kriging with hole-effect model and natural logarithmic transformation with constant trend having Root Mean Square Error (RMSE) of 328.7 is the best choice. This is followed by Ordinary Kriging (RMSE 329.1), Splines (RMSE 392.4), Inverse Distance Weighted (RMSE 409.8) and Polynomial Interpolation (RMSE 418.5). Cross validation of the results shows the largest over prediction at Tehri rainfall station (62.5%) and largest under prediction at Nainital station (−36.5%). Physiographic zone wise, the least errors occur in the plains and the largest in the Great Himalayas. The spatial average rainfalls are 1,472 mm for Terai/Bhabar, 1,782 mm for the Shivalik ranges, 1,591 mm for the Lesser Himalayas and 1,635 mm for the Great Himalayan region. The mean areal rainfall in the region is 1,608 mm.