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1.
Abstract

Rainfall is the most important input parameter for water resource planning and hydrological studies because flood risk assessment, rainfall harvesting and runoff estimation depend on the rainfall distribution within a region. Due to practical and economic factors, it is not possible to site rainfall stations everywhere, so representative rainfall stations are sited at specific locations. Rainfall distribution is then estimated from such stations. In this study, rainfall distribution in the southwestern region of Saudi Arabia was estimated using kriging, co-kriging and inverse distance weighted (IDW) methods. Historical records of rainfall from 47 stations for the period 1965–2010 and the altitude of these stations were used. The study shows that co-kriging is a better interpolator than the kriging and IDW methods, with a better correlation between actual and estimated monthly average rainfall for the region.  相似文献   

2.
Top‐kriging is a method for estimating stream flow‐related variables on a river network. Top‐kriging treats these variables as emerging from a two‐dimensional spatially continuous process in the landscape. The top‐kriging weights are estimated by regularising the point variogram over the catchment area (kriging support), which accounts for the nested nature of the catchments. We test the top‐kriging method for a comprehensive Austrian data set of low stream flows. We compare it with the regional regression approach where linear regression models between low stream flow and catchment characteristics are fitted independently for sub‐regions of the study area that are deemed to be homogeneous in terms of flow processes. Leave‐one‐out cross‐validation results indicate that top‐kriging outperforms the regional regression on average over the entire study domain. The coefficients of determination (cross‐validation) of specific low stream flows are 0.75 and 0.68 for the top‐kriging and regional regression methods, respectively. For locations without upstream data points, the performances of the two methods are similar. For locations with upstream data points, top‐kriging performs much better than regional regression as it exploits the low flow information of the neighbouring locations. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

3.
Abstract

This paper compares the performance of three geostatistical algorithms, which integrate elevation as an auxiliary variable: kriging with external drift (KED); kriging combined with regression, called regression kriging (RK) or kriging after detrending; and co-kriging (CK). These three methods differ by the way by in which the secondary information is introduced into the prediction procedure. They are applied to improve the prediction of the monthly average rainfall observations measured at 106 climatic stations in Tunisia over an area of 164 150 km2 using the elevation as the auxiliary variable. The experimental sample semivariograms, residual semivariograms and cross-variograms are constructed and fitted to estimate the rainfall levels and the estimation variance at the nodes of a square grid of 20 km?×?20 km resolution and to develop corresponding contour maps. Contour diagrams for KED and RK were similar and exhibited a pattern corresponding more closely to local topographic features when (a) the network is sparse and (b) the rainfall–elevation correlation is poor, while CK showed a smooth zonal pattern. Smaller prediction variances are obtained for the RK algorithm. The cross-validation showed that the RMSE obtained for CK gave better results than for KED or RK.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Feki, H., Slimani, M., and Cudennec, C., 2012. Incorporating elevation in rainfall interpolation in Tunisia using geostatistical methods. Hydrological Sciences Journal, 57 (7), 1294–1314.  相似文献   

4.
Rainfall data in continuous space provide an essential input for most hydrological and water resources planning studies. Spatial distribution of rainfall is usually estimated using ground‐based point rainfall data from sparsely positioned rain‐gauge stations in a rain‐gauge network. Kriging has become a widely used interpolation method to estimate the spatial distribution of climate variables including rainfall. The objective of this study is to evaluate three geostatistical (ordinary kriging [OK], ordinary cokriging [OCK], kriging with an external drift [KED]), and two deterministic (inverse distance weighting, radial basis function) interpolation methods for enhanced spatial interpolation of monthly rainfall in the Middle Yarra River catchment and the Ovens River catchment in Victoria, Australia. Historical rainfall records from existing rain‐gauge stations of the catchments during 1980–2012 period are used for the analysis. A digital elevation model of each catchment is used as the supplementary information in addition to rainfall for the OCK and kriging with an external drift methods. The prediction performance of the adopted interpolation methods is assessed through cross‐validation. Results indicate that the geostatistical methods outperform the deterministic methods for spatial interpolation of rainfall. Results also indicate that among the geostatistical methods, the OCK method is found to be the best interpolator for estimating spatial rainfall distribution in both the catchments with the lowest prediction error between the observed and estimated monthly rainfall. Thus, this study demonstrates that the use of elevation as an auxiliary variable in addition to rainfall data in the geostatistical framework can significantly enhance the estimation of rainfall over a catchment.  相似文献   

5.
Multigaussian kriging technique has many applications in mining, soil science, environmental science and other fields. Particularly, in the local reserve estimation of a mineral deposit, multigaussian kriging is employed to derive panel-wise tonnages by predicting conditional probability of block grades. Additionally, integration of a suitable change of support model is also required to estimate the functions of the variables with larger support than that of the samples. However, under the assumption of strict stationarity, the grade distributions and important recovery functions are estimated by multigaussian kriging using samples within a supposedly spatial homogeneous domain. Conventionally, the underlying random function model is required to be stationary in order to carry out the inference on ore grade distribution and relevant statistics. In reality, conventional stationary model often fails to represent complicated geological structure. Traditionally, the simple stationary model neither considers the obvious changes in local means and variances, nor is it able to replicate spatial continuity of the deposit and hence produces unreliable outcomes. This study deals with the theoretical design of a non-stationary multigaussian kriging model allowing change of support and its application in the mineral reserve estimation scenario. Local multivariate distributions are assumed here to be strictly stationary in the neighborhood of the panels. The local cumulative distribution function and related statistics with respect to the panels are estimated using a distance kernel approach. A rigorous investigation through simulation experiments is performed to analyze the relevance of the developed model followed by a case study on a copper deposit.  相似文献   

6.
Snow availability in Alpine catchments plays an important role in water resources management. In this paper, we propose a method for an optimal estimation of snow depth (areal extension and thickness) in Alpine systems from point data and satellite observations by using significant explanatory variables deduced from a digital terrain model. It is intended to be a parsimonious approach that may complement physical‐based methodologies. Different techniques (multiple regression, multicriteria analysis, and kriging) are integrated to address the following issues: We identify the explanatory variables that could be helpful on the basis of a critical review of the scientific literature. We study the relationship between ground observations and explanatory variables using a systematic procedure for a complete multiple regression analysis. Multiple regression models are calibrated combining all suggested model structures and explanatory variables. We also propose an evaluation of the models (using indices to analyze the goodness of fit) and select the best approaches (models and variables) on the basis of multicriteria analysis. Estimation of the snow depth is performed with the selected regression models. The residual estimation is improved by applying kriging in cases with spatial correlation. The final estimate is obtained by combining regression and kriging results, and constraining the snow domain in accordance with satellite data. The method is illustrated using the case study of the Sierra Nevada mountain range (Southern Spain). A cross‐validation experiment has confirmed the efficiency of the proposed procedure. Finally, although it is not the scope of this work, the snow depth is used to asses a first estimation of snow water equivalent resources.  相似文献   

7.
In this article, an approach using residual kriging (RK) in physiographical space is proposed for regional flood frequency analysis. The physiographical space is constructed using physiographical/climatic characteristics of gauging basins by means of canonical correlation analysis (CCA). This approach is a modified version of the original method, based on ordinary kriging (OK). It is intended to handle effectively any possible spatial trends within the hydrological variables over the physiographical space. In this approach, the trend is first quantified and removed from the hydrological variable by a quadratic spatial regression. OK is therefore applied to the regression residual values. The final estimated value of a specific quantile at an ungauged station is the sum of the spatial regression estimate and the kriged residual. To evaluate the performance of the proposed method, a cross‐validation procedure is applied. Results of the proposed method indicate that RK in CCA physiographical space leads to more efficient estimates of regional flood quantiles when compared to the original approach and to a straightforward regression‐based estimator. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

8.
Abstract

The present research study investigates the application of nonlinear normalizing data transformations in conjunction with ordinary kriging (OK) for the accurate prediction of groundwater level spatial variability in a sparsely-gauged basin. We investigate three established normalizing methods, Gaussian anamorphosis, trans-Gaussian kriging and the Box-Cox method to improve the estimation accuracy. The first two are applied for the first time to groundwater level data. All three methods improve the mean absolute prediction error compared to the application of OK to the non-transformed data. In addition, a modified Box-Cox transformation is proposed and applied to normalize the hydraulic heads. The modified Box-Cox transformation in conjunction with OK is found to be the optimal spatial model based on leave-one-out cross-validation. The recently established Spartan semivariogram family provides the optimal model fit to the transformed data. Finally, we present maps of the groundwater level and the kriging variance based on the optimal spatial model.

Editor D. Koutsoyiannis; Associate editor A. Montanari

Citation Varouchakis, E.A., Hristopoulos, D.T., and Karatzas, G.P., 2012. Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application. Hydrological Sciences Journal, 57 (7), 1404–1419.  相似文献   

9.
In Seo and Smith (this issue), a set of estimators was built in a Bayesian framework to estimate rainfall depth at an ungaged location using raingage measurements and radar rainfall data. The estimators are equivalent to lognormal co-kriging (simple co-kriging in the Gaussian domain) with uncertain mean and variance of gage rainfall. In this paper, the estimators are evaluated via cross-validation using hourly radar rainfall data and simulated hourly raingage data. Generation of raingage data is based on sample statistics of actual raingage measurements and radar rainfall data. The estimators are compared with lognormal co-kriging and nonparametric estimators. The Bayesian estimators are shown to provide some improvement over lognormal co-kriging under the criteria of mean error, root mean square error, and standardized mean square error. It is shown that, if the prior could be assessed more accurately, the margin of improvement in predicting estimation variance could be larger. In updating the uncertain mean and variance of gage rainfall, inclusion of radar rainfall data is seen to provide little improvement over using raingage data only.  相似文献   

10.
ABSTRACT

Evapotranspiration (ET) is an important ecohydrological process especially in arid and semi-arid regions. In this study, a new radiation module based on MODIS data has been coupled with the Surface Energy Balance Algorithms for Land (SEBAL) to better estimate ET. The accuracies of the coupled model for estimating available energy and sensible heat (H) were improved significantly compared with the outputs from the original SEBAL which was based on empirical equations. The coupled SEBAL modelled instantaneous λET agreed much better with observations in the arid land of Central Asia than the original SEBAL, with a bias of ?2.86 W m-2, root mean square error (RMSE) of 9.75 W m-2, and normalized RMSE (NRMSE) of 0.13. The accuracy was blurred when scaling ET to a daily or monthly scale, mainly due to the uncertainties associated with temporal upscaling methods that were applied. Sensitivity analysis, which was conducted using numerical variance-based techniques, indicated that the estimated ET is sensitive to the available energy, suggesting the importance of obtaining accurate estimates of net radiation when applying the coupled SEBAL to estimate ET. This study provides a simple and reliable way to utilize MODIS products and contains sensitivity analysis for helping to correctly interpret the outputs, which are both important for large-scale ET estimation.  相似文献   

11.
The level of Lake Tana, Ethiopia, fluctuates annually and seasonally following the patterns of changes in precipitation. In this study, a mass balance approach is used to estimate the hydrological balance of the lake. Water influx from four major rivers, subsurface inflow from the floodplains, precipitation, outflow from the lake constituting river discharge and evapotranspiration from the lake are analysed on monthly and annual bases. Spatial interpolation of precipitation using rain gauge data was conducted using kriging. Outflow from the lake was identified as the evaporation from the lake's surface as well as discharge at the outlet where the Blue Nile commences. Groundwater inflow is estimated using MODular three‐dimensional finite‐difference ground‐water FLOW model software that showed an aligned flow pattern to the river channels. The groundwater outflow is considered negligible based on the secondary sources that confirmed the absence of lake water geochemical mixing outside of the basin. Evaporation is estimated using Penman's, Meyer's and Thornwaite's methods to compare the mass balance and energy balance approaches. Meteorological data, satellite images and temperature perturbation simulations from Global Historical Climate Network of National Oceanographic and Atmospheric Administration are employed for estimation of evaporation input parameters. The difference of the inflow and outflow was taken as storage in depth and compared with the measured water level fluctuations. The study has shown that the monthly and annually calculated lake level replicates the observed values with root mean square error value of 0·17 and 0·15 m, respectively. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

12.
A methodology is developed for estimating temporally variable virus inactivation rate coefficients from experimental virus inactivation data. The methodology consists of a technique for slope estimation of normalized virus inactivation data in conjunction with a resampling parameter estimation procedure. The slope estimation technique is based on a relatively flexible geostatistical method known as universal kriging. Drift coefficients are obtained by nonlinear fitting of bootstrap samples and the corresponding confidence intervals are obtained by bootstrap percentiles. The proposed methodology yields more accurate time dependent virus inactivation rate coefficients than those estimated by fitting virus inactivation data to a first-order inactivation model. The methodology is successfully applied to a set of poliovirus batch inactivation data. Furthermore, the importance of accurate inactivation rate coefficient determination on virus transport in water saturated porous media is demonstrated with model simulations.  相似文献   

13.
Estimating and mapping spatial uncertainty of environmental variables is crucial for environmental evaluation and decision making. For a continuous spatial variable, estimation of spatial uncertainty may be conducted in the form of estimating the probability of (not) exceeding a threshold value. In this paper, we introduced a Markov chain geostatistical approach for estimating threshold-exceeding probabilities. The differences of this approach compared to the conventional indicator approach lie with its nonlinear estimators—Markov chain random field models and its incorporation of interclass dependencies through transiograms. We estimated threshold-exceeding probability maps of clay layer thickness through simulation (i.e., using a number of realizations simulated by Markov chain sequential simulation) and interpolation (i.e., direct conditional probability estimation using only the indicator values of sample data), respectively. To evaluate the approach, we also estimated those probability maps using sequential indicator simulation and indicator kriging interpolation. Our results show that (i) the Markov chain approach provides an effective alternative for spatial uncertainty assessment of environmental spatial variables and the probability maps from this approach are more reasonable than those from conventional indicator geostatistics, and (ii) the probability maps estimated through sequential simulation are more realistic than those through interpolation because the latter display some uneven transitions caused by spatial structures of the sample data.  相似文献   

14.
Compositional Bayesian indicator estimation   总被引：1，自引：1，他引：0  
Indicator kriging is widely used for mapping spatial binary variables and for estimating the global and local spatial distributions of variables in geosciences. For continuous random variables, indicator kriging gives an estimate of the cumulative distribution function, for a given threshold, which is then the estimate of a probability. Like any other kriging procedure, indicator kriging provides an estimation variance that, although not often used in applications, should be taken into account as it assesses the uncertainty of the estimate. An alternative approach to indicator estimation is proposed in this paper. In this alternative approach the complete probability density function of the indicator estimate is evaluated. The procedure is described in a Bayesian framework, using a multivariate Gaussian likelihood and an a priori distribution which are both combined according to Bayes theorem in order to obtain a posterior distribution for the indicator estimate. From this posterior distribution, point estimates, interval estimates and uncertainty measures can be obtained. Among the point estimates, the median of the posterior distribution is the maximum entropy estimate because there is a fifty-fifty chance of the unknown value of the estimate being larger or smaller than the median; that is, there is maximum uncertainty in the choice between two alternatives. Thus in some sense, the latter is an indicator estimator, alternative to the kriging estimator, that includes its own uncertainty. On the other hand, the mode of the posterior distribution estimator, assuming a uniform prior, is coincidental with the simple kriging estimator. Additionally, because the indicator estimate can be considered as a two-part composition which domain of definition is the simplex, the method is extended to compositional Bayesian indicator estimation. Bayesian indicator estimation and compositional Bayesian indicator estimation are illustrated with an environmental case study in which the probability of the content of a geochemical element in soil being over a particular threshold is of interest. The computer codes and its user guides are public domain and freely available.  相似文献   

15.
Various regional flood frequency analysis procedures are used in hydrology to estimate hydrological variables at ungauged or partially gauged sites. Relatively few studies have been conducted to evaluate the accuracy of these procedures and estimate the error induced in regional flood frequency estimation models. The objective of this paper is to assess the overall error induced in the residual kriging (RK) regional flood frequency estimation model. The two main error sources in specific flood quantile estimation using RK are the error induced in the quantiles local estimation procedure and the error resulting from the regional quantile estimation process. Therefore, for an overall error assessment, the corresponding errors associated with these two steps must be quantified. Results show that the main source of error in RK is the error induced into the regional quantile estimation method. Results also indicate that the accuracy of the regional estimates increases with decreasing return periods. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

16.
In a spatial property modeling context, the variables of interest to be modeled often display complex nonlinear features. Techniques to incorporate these nonlinear features, such as multiple point statistics or cummulants, are often complex with input parameters that are difficult to infer. The methodology proposed in this paper uses a classical vector-based definition of locally varying anisotropy to characterize nonlinear features and incorporate locally varying anisotropy into numerical property models. The required input is an exhaustive field of anisotropy orientation and magnitude. The methodology consists of (1) using the shortest path distance between locations to define the covariance between points in space (2) multidimensional scaling of the domain to ensure positive definite kriging equations and (3) estimation or simulation with kriging or sequential Gaussian simulation. The only additional parameter required when kriging or simulating with locally varying anisotropy is the number of dimensions to retain in multidimensional scaling. The methodology is demonstrated on a CO2 emissions data set for the United States in 2002 and shows an improvement in cross validation results as well as a visual reproduction of nonlinear features.  相似文献   

17.
Abstract

Automatic raingauge data often serve as an important input to hydrological and weather warning operations. They are not only fundamental in quantitative rainfall analysis, but also act as the ground truth in warning operation and forecast validation. Quality control is required before the data can be used quantitatively due to systematic and random errors. Extremely large random errors and unreasonably small or false zero values can hamper effective monitoring of heavy rain. Yet both are difficult to detect in real-time by objective means. In an attempt to address these problems, a rainfall data quality-control scheme based on radar-raingauge co-kriging analysis was developed. The important threshold values required in the data quality control of 60-min raingauge rainfall were determined from a detailed analysis of the distributions of rainfall residuals defined as the arithmetic difference and the logarithm of the ratio between a raingauge measurement and its co-kriging estimate. The scheme has been developed and is in real-time use in Hong Kong, a coastal city of about 1100 km2 area with more than 150 raingauges installed. Geographically, it is located in the subtropics and dominated by heavy convective rainfall in the summer. As a basis of the quality-control scheme, the co-kriging rainfall analysis was shown through a verification exercise to be superior to those obtained by the Barnes analysis and ordinary kriging of raingauge data. The performance of the quality-control algorithm was assessed using selected cases and controlled tests, and was found to be satisfactory, with a high error detection rate for the two targeted types of error. Limitations and operational issues identified during a real-time trial of the quality-control scheme are also discussed.
Citation Yeung, H.Y., Man, C., Chan, S.T., and Seed, A., 2014. Development of an operational rainfall data quality-control scheme based on radar-raingauge co-kriging analysis. Hydrological Sciences Journal, 59 (7), 1285–1299. http://dx.doi.org/10.1080/02626667.2013.839873  相似文献   

18.
Mapping geomorphic variables geostatistically, specifically by kriging, runs into difficulties when there is trend. The reason is that the variogram required for the kriging must be of residuals from any trend, which in turn cannot be estimated optimally by the usual method of trend surface analysis because the residuals are correlated. The difficulties can be overcome by the use of residual maximum likelihood (REML) to estimate both the trend and the variogram of the residuals simultaneously. We summarize the theory of REML as it applies to kriging in the presence of trend. We present the equations to show how estimates of the trend are combined with kriging of residuals to give empirical best linear unbiased predictions (E‐BLUPs). We then apply the method to estimate the height of the sub‐Upper‐Chalk surface beneath the Chiltern Hills of southeast England from 238 borehole data. The variogram of the REML residuals is substantially different from that computed by ordinary least squares (OLS) analysis. The map of the predicted surface is similar to that made from kriging with the OLS variogram. The variances, however, are substantially larger because (a) they derive from a variogram with a much larger sill and (b) they include the uncertainty of the estimate of the trend. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

19.
The assessment of potential volcanic eruptions is a critical aspect when evaluating the safety of populated areas. A stochastic approach has been developed for the analysis and simulation of data sampled at active volcanoes. This approach allows for the detection and quantification of time correlation, volcanic event forecasts using Cox model based simulations and volcanic tremor decomposition in order to identify potential precursors of major eruptions. The stochastic approach has been applied to data monitored at Stromboli volcano. Significant time correlation has been detected which makes Stromboli a volcano with a remarkable memory of its recent activity in comparison to other volcanoes. Forecasting of the number of strombolian events for the next few days has been performed by Monte Carlo simulations. Finally, kriging analysis of the tremor intensity has enabled time component estimation which could furnish additional monitoring variables for the forecast of paroxysmal phases at Stromboli.  相似文献   

20.
Kriging in the hydrosciences   总被引：1，自引：0，他引：1  
Most of the methods currently used in hydrosciences for interpolation and spatial averaging fail to quantify the accuracy of the estimates.The theory of regionalized variables enables one to point out the relationship between the spatial correlation of hydrometeorological or hydrogeological fields and the precision of interpolation, or determination of average values, over these fields.A new estimation method called kriging has proven to be quite well adapted to solving water resources problems. The author presents a series of case-studies in automatic contouring, data input for numerical models, estimation of average precipitation over a given catchment area, and measurement network design.  相似文献   

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