Effects of Raingauge Distribution on Estimation Accuracy of Areal Rainfall

Rainfall analysis is important to managing water resources. Mean rainfall is usually used to calculate the spatial rainfall status of a region and is the input into various rainfall-runoff models. However, this method relies on an adequate raingauge network. This study identifies the effects of raingauge distribution based on estimation results of areal rainfall using the Thiessen polygon and block Kriging methods. Twelve rainfall events with complete data from 14 raingauges were selected to complete the goal of this study. The block Kriging method in this study uses a dimensionless semivariogram to obtain hourly semivariograms based on a standardized rainfall depth. The power semivariogram model was used to describe the temporal-spatial variation of rainfall. The analytical process in this study uses raingauge weight and rainfall volume as evaluation criteria. All raingauges were in turn removed from the original raingauge network. The effects of removing each raingauge were compared with computations using all raingauges. Comparison results indicate that (1) the block Kriging method can accurately describe rainfall processes in terms of the spatiotemporal structure of a semivariogram. (2) the block Kriging method is better than the Thiessen polygon method at obtaining exact mean rainfall, and (3) the effects of different raingauge distributions on a mean hyetograph warrant further investigation.     

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.     

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.

     

Nested Augmentation of Rainfall Monitoring Network: Proposing a Hybrid Implementation of Block Kriging and Entropy Theory

One of the most influential environmental variables is rainfall which has significant effect on water resources management, agricultural development, hydrology, and climate change studies. Due to high spatiotemporal variability of rainfall, its monitoring network design can be considered as a useful tool to improve the efficiency of recorded rain gauge stations within the study area. In this study, a new methodology of augmentation of rain gauge network is developed using coupled Block Kriging (BK) and entropy theory methods. In the proposed method, a nested approach of a two-stage positioning of rain gauge stations has been demonstrated. In the first stage, large-scale or fast positioning was done in which the optimal number of candidate blocks was identified. Then, local scale or fine-tuned positioning was done in the second stage. In this stage, to develop the network, accurate locations of rain gauge stations in each block are determined. Besides the main point of this paper, the effect of two kriging estimators, BK and Ordinary Kriging (OK), on the developed network has been investigated and compared. The study area is the Namak Lake watershed with various climates and altitudes. To assess the performance of the optimal rainfall network, three diagnostics were utilized; spatial distribution of annual precipitation, Estimation Error Variance (EEV) maps and histograms. Based on the results, 30 (more than 30% percent of the current stations) rain gauge stations have been proposed scattered over the watershed. Evaluation of the results has shown that the augmented rain gauge network proposed by the BK method outperformed dramatically that of the OK method. EEV maps and also statistical analysis of EEV values confirms the EEV value reduction of almost 25% in augmented network, as well.

     

Remote Sensing and GIS Innovation with Hydrologic Modelling for Hydroelectric Power Plant (HPP) in Poorly Gauged Basins

Within the last two decades, modelling of rainfall–runoff has become an important topic in water resources assessment due to increasing water demand and energy, particularly in the determination of hydropower potential. In addition to remote sensing (RS) and geographical information systems (GIS), with the development on satellite technologies, it becomes possible to asses rapid and economic solutions to determine a practical rainfall–runoff relation, particularly poorly gauged or ungauged basins. In this paper, Solakli Watershed which is located in Eastern Black Sea Region of Turkey is selected as the study area. To determine the hydroelectric water potential in a poorly gauged basin, basin boundary and area, minimum maximum and mean elevation, slope information of the basin have been derived from the digital elevation model (DEM) using remote sensing (RS) and geographical information systems (GIS) techniques. IRS P5 stereo satellite data with 2.5-m spatial resolution has been used for deriving the DEM. This DEM is used to produce the flow direction and flow accumulation maps of the basin. Afterward, synthetic drainage network is obtained with the analysis of these maps. Using topographical data such as area, mean basin elevation and limited point observations of rainfall data; a regression model was derived for the whole watershed. This regression model was validated on a sub-basin with satisfactory results using mean areal rainfall which was calculated isohyetal map produced by kriging method. Suggested hydropower station points are also determined.     

DESIGN OF GROUNDWATER LEVEL MONITORING NETWORK WITH ORDINARY KRIGING

The primary network of groundwater level observation wells aims at realizing a regional groundwater management policy. It may give a regional picture of groundwater level with emphasis on the natural situation. Observation data from the primary network can be used to estimate the actual state of groundwater system. Since the cost of the installation and maintenance of a groundwater monitoring network is extremely high, the assessment of effectiveness of the network becomes very necessary. Groundwater level monitoring networks are the examples of discontinuous sampling on variables presenting spatial continuity and highly skewed frequency distributions. Anywhere in the aquifer, ordinary kriging provides estimates of the variable sampled and a standard error of the estimate. In this article, the average Kriging standard deviation was used as a criterion for the determination of network density,and the GIS-based approach was analysized. A case study of groundwater level network simulation in the Chaiwopu Basin, Xinjiang Uygur Autonomous Region, China, was presented. In the case study, the initial phreatic water observation wells were 18, a comparison of the three variogram parameters of the three defferent variogram models shows that the Gaussian model is the best. Finally, a network with 55 wells was constructed.     

协方差矩阵上-下三角分解法在区域土壤水盐条件模拟的应用

本文运用协方差矩阵的上-下三角分解法对黄河河套平原上土壤水盐的空间变异性进行了条件模拟，利用55个大网格的规则采样点模拟了小尺度待估点的土壤水盐含量，模拟结果的空间分布趋势、半变异函数以及其统计特征值与普通kriging的相应估计值进行了比较。结果表明，kriging估计结果大大缩小了实测值的变异系数具有明显的平滑效应，为条件模拟的变异系数则接近于实测值，能够很好的保持土壤水盐含量的空间结构；多个条件模拟能给出土壤特性的一个波动范围及极端值。这一效果对改造中低产田、提高灌溉效率和水土资源的监测和管理决策都十分重要。由于协方差矩阵的上-下分解法避免了常用的条件模拟实现法中转向带法和傅立叶转换法的一些缺陷，其理论简单，约束条件少，可将模拟和条件化同时进行。本文的研究说明该方法应用于水土科学是可行的。     

Hydroacoustic Estimation of Zooplankton Biomass at Two Shoal Complexes in the Apostle Islands Region of Lake Superior

Hydroacoustics can be used to assess zooplankton populations, however, backscatter must be scaled to be biologically meaningful. In this study, we used a general model to correlate site-specific hydroacoustic backscatter with zooplankton dry weight biomass estimated from net tows. The relationship between zooplankton dry weight and backscatter was significant (p < 0.001) and explained 76% of the variability in the dry weight data. We applied this regression to hydroacoustic data collected monthly in 2003 and 2004 at two shoals in the Apostle Island Region of Lake Superior. After applying the regression model to convert hydroacoustic backscatter to zooplankton dry weight biomass, we used geostatistics to analyze the mean and variance, and ordinary kriging to create spatial zooplankton distribution maps. The mean zooplankton dry weight biomass estimates from plankton net tows and hydroacoustics were not significantly different (p = 0.19) but the hydroacoustic data had a significantly lower coefficient of variation (p < 0.001). The maps of zooplankton distribution illustrated spatial trends in zooplankton dry weight biomass that were not discernable from the overall means.     

应用析取克里格方法估计区域地下水埋深分布

本文比较了几种常用的估计土壤空间变异的计算方法，介绍了析取克里格的理论和计算方法，给出计算区域地下水埋深分布的实例，并对普通克里格和析取克里格的计算方差作了比较。     

海拔高程对泄洪雾化影响的敏感分析

针对海拔高程对于泄洪雾化降雨分布的影响,提出了一种改进的随机溅水数学模型。运用小湾水电站泄洪洞雾化实测降雨资料进行模型验证,两者结果吻合良好。敏感分析表明,随着海拔高程的增加,泄洪洞下游雾化降雨范围有增大的趋势,当海拔高程从50 m增加到3000 m时,泄洪雾化雨区在两岸的爬升高度增加50 m,纵向范围增大100 m;同时,降雨强度等值线分布发生坦化,在降雨强度大于400 mm/h的等值线区域,分布范围缩小,而在400 mm/h以下区域,雨区分布范围明显增大。上述研究为今后全面考虑海拔高程与气象条件对于泄洪雾化过程的影响建立了基础。     

Rainfall Extremes: a Novel Modeling Approach for Regionalization

The rainfall events of extreme magnitude over the past few decades have caused destructive damages to lives and properties, especially in the subcontinent (e.g. Pakistan, India, Bangladesh etc). Rainfall hazard maps for these areas can be of great practical and theoretical interests. In our work, we used extreme value analysis and spatial interpolation techniques to provide such maps through a combination of the Tropical Rainfall Measuring Mission Precipitation (TRMM) 3B42 product and raingauge data. This mixed approach takes advantage of both the long time series available at a limited number of stations, and the large spatial coverage of the satellite data which, instead, has a poor temporal extent. The methodology is implemented by (1) creating a unique growth curve for the homogeneous region by utilizing in-situ rainfall data and (2) mapping the parameters of intensity-duration functions for the entire length of the study area by using TRMM 3B42 product. The regional results obtained by using mixed approach and TRMM 3B42 are compared with the estimates obtained by using in-situ data. The comparison showed that the overall output of mixed approach is more consistent with what transpired by in-situ data for a pre-defined return period.     

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。     

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。     

Regionalization of the Modified Bartlett–Lewis rectangular pulse stochastic rainfall model across the Korean Peninsula

The six parameters of the Modified Bartlett–Lewis Rectangular Pulse (MBLRP) model were regionalized across the Korean Peninsula for all 12 calendar months. The parameters of the MBLRP model were estimated at each of the 59 rain gauges and they were spatially interpolated using the Ordinary Kriging method in order to produce maps. The parameter search space used in the parameter estimation process was repetitively narrowed through cross-validation in order to remove the impact of the multi-modality of the MBLRP model. The synthetic rainfall time series generated based on the parameter maps successfully reproduced the various statistical properties of the observed rainfall, such as mean, variance, lag-1 autocorrelation, and probability of zero rainfall at a wide range of time accumulation levels (e.g. hourly through daily). The maps representing the general rainfall characteristics, such as the average rainfall depth per rain storm, the average rain storm duration, the average number of rain cells per rain storm, and the average rain cell duration were also produced based on the estimated parameters. Lastly, some helpful tips in regionalizing the parameters of the Poisson cluster rainfall models are discussed.     

Predicting Shallow Water Table Depth at Regional Scale: Optimizing Monitoring Network in Space and Time

Shallow water table levels can be predicted using several approaches, either based on climatic records, on field evidences based on soil morphology, or on the outputs of physically based models. In this study, data from a monitoring network in a relevant agricultural area of Northern Italy (ca. 12,000 Km²) were used to develop a data driven model for predicting water table depth in space and time from meteorological data and long-term water table characteristics and to optimize sampling density in space and time. Evolutionary Polynomial Regressions (EPR) were used to calibrate a predictive tool based on climatic data and on the records from 48 selected sites (N?=?5,611). The model was validated against the water table depths observed in 15 independent sites (N?=?1,739), resulting in a mean absolute error of 30.8 cm (R ²?=?0.61). The model was applied to the whole study area, using the geostatistical estimates of the average water table depth as input, to provide spatio-temporal maps of the water table depth. The impact of the degradation of data input in the temporal and spatial domain was then assessed following two approaches. In the first case, three different EPR models were calibrated based on 25 %, 50 % and 75 % of the available data, and the error indexes compared. In the second case, an increasing number of monitoring sites were removed from the initial data set, and the associated increased kriging standard deviation was assessed. Reducing the average sampling frequency from 1.5 per month to 1 every 40 days did not impact significantly on the prediction capability of the proposed model. Reducing the sampling frequency to 1 every 4 months resulted in a loss of accuracy <3 %, while removing more than half locations from the network, resulted in a global loss of information <15 %.     

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。     

泰森多边形法在小流域面雨量计算中的应用

为探究泰森多边形法在小流域面雨量计算中的适用性,以地处江淮丘陵区适宜进行产汇流机制等水文基础理论研究的典型闭合小流域花山流域为例,结合流域现状站点分布和地形特点,选取流域多年面雨量、典型场次与典型日面雨量三种不同降雨量级实例,分别采用算术平均法、泰森多边形法和等值线法计算面雨量进行对比。年面雨量和场次面雨量计算中泰森多边法对比等值线法计算值相对误差小于 1.00%,日面雨量计算值相对误差小于 2.00%;算术平均法在典型场次面雨量样本中有 40.0%的计算值相对误差大于 1.00%,最大相对误差为 -2.47%,在典型日面雨量样本中有36.8%的计算值相对误差大于 2.00%,最大相对误差为 9.38%。结果表明：不同降雨量级使用泰森多边形法计算面雨量比算术平均法更接近于等值线法计算值;算术平均法在降雨量较小时受局部降雨影响计算误差较大,在年面雨量计算时可以和泰森多边形法互换使用。     

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.     

Effects of Urbanization Factors on Model Parameters

This study mainly explores effects of urbanization factors on hydrograph parameters. Urbanization impacts of the developing watershed are evaluated based on rainfall–runoff simulations. A total of 51 rainfall–runoff events occurred from 1966 to 2002. Forty of these were calibrated, and effects of urbanization factors on runoff hydrographs resulting from a simple hydrological model were assessed. The block Kriging method was used to estimate the mean rainfall of the Wu-Tu watershed, and its hourly excesses were calculated by using the non-linear programming method. The remaining 11 cases were used to test the established relationships. The calibration and verification results confirm that the integral methods used in this study effectively illustrate the hydrological and geomorphic conditions in complex urbanization processes. Parameter n responds more sensitively than parameter k to increasing impervious areas and population densities. Additionally, parameter n responds more strongly to imperviousness than to population. Therefore, an impervious area is an important reference for analyzing hydrological changes of urbanization in the Wu-Tu watershed.