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.
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Precipitation is a key factor in the water cycle. At the same time, precipitation is the focus of study in meteorology and climatology, ecological environmental assessment, non-point source pollution and so on. Understanding the temporal-spatial variation and the corresponding factors of precipitation has become the object of hydrology and environmentology. Based on the annual precipitation data, we analyzed the spatial distribution of precipitation in Sichuan Province in China as well as the temporal-spatial variation and the corresponding influence factors involved. The results show that the amount of precipitation was abundant, but the spatial distribution was not consistent with it and the amount of precipitation gradually declined from the south-east to the north-west in Sichuan Province, China. Moreover, the spatial distribution was different throughout the years. The result of correlation analysis indicated that elevation, temperature and air pressure were three key factors affecting the amount and distribution of precipitation, and the correlation coefficients were −0.56, 0.38 and 0.45 respectively. Notably, the relationship between the slope of topography and precipitation were significantly negative and the average correlation coefficient was −0.28.
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A geostatistical approach for areal rainfall statistics assessment
Author: Th. Lebel; J. P. Laborde | Size: 865 KB | Format:PDF | Quality:Unspecified | Publisher: Stochastic Hydrology and Hydraulics(Springer) | Year: 1988 | pages: 245-261 | ISBN: --
Areal rainfall statistics are more relevant in flood hydrology and water resources management than point rainfall statistics when it comes to help designing dams or hydraulic structures. This paper presents a geostatistically based method to derive the areal statistics from point statistics. Assuming that the distribution models of point rainfall and areal belong to the same class of models and that the rainfall process is stationary, it is shown how the parameters of the areal distribution model can directly be computed from the parameters of the point distribution models in case of a non stationary process, an approximation is derived that yielded good results when applied to a mountainous region in Southern France. The method also allows the computation of the areal reduction factors in a very general form.
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Spatial rainfall estimation by linear and non-linear co-kriging of radar-rainfall and raingage data
Author: A. Azimi-Zonooz; W. F. Krajewski; D. S. Bowles; D. J. Seo | Size: 1 MB | Format:PDF | Quality:Unspecified | Publisher: Stochastic Hydrol.Hydraul (springer) | pages: 51-67 | ISBN: --
The feasibility of linear and nonlinear geostatistical estimation techniques for optimal merging of rainfall data from raingage and radar observations is investigated in this study by use of controlled numerical experiments. Synthetic radar and raingage data are generated with their hypothetical error structures
that explicitly account for sampling characteristics of the two sensors. Numerically simulated rainfall fields considered to be ground-truth fields on 4x4 km grids are used in the generation of radar and raingage observations. Ground-truth rainfall fields consist of generated rainfall fields with various climatic characteristics that preserve the space-time covariance function of rainfall events in extratropical cyclonic storms. Optimal mean areal precipitation estimates are obtained based on the minimum variance, unbiased property of kriging techniques under the second order homogeneity assumption of rainfall fields. The evaluation of estimated rainfall fields is done based on the refinement of spatial predictability over what would be provided from each sensor individually. Attention is mainly given to removal of measurement error and bias that are synthetically introduced to radar measurements. The influence of raingage network density on estimated rainfall fields is also examined.
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Multicriteria design of rain gauge networks for flash flood prediction in semiarid catchments with complex terrain
Author: Till H. M. Volkmann,Steve W. Lyon,Hoshin V. Gupta,Peter A. Troch | Size: 1.9 MB | Format:PDF | Quality:Unspecified | Publisher: wiley | Year: 2010 | pages: 1-16 | ISBN: --
Despite the availability of weather radar data at high spatial (1 km2) and temporal (5–15 min) resolution, ground-based rain gauges continue to be necessary for accurate estimation of storm rainfall input to catchments during flash flood events, especially in mountainous catchments. Given economical considerations, a long-standing problem in catchment hydrology is to establish optimal placement of a small number of rain gauges to acquire data on both rainfall depth and spatiotemporal variability of intensity during extreme storm events. Using weather radar observations and a dense network of 40 tipping bucket rain gauges, this study examines whether it is possible to determine a reliable “best” set of rain gauge locations for the Sabino Canyon catchment near Tucson, Arizona, USA, given its complex topography and dominant storm track pattern. High-quality rainfall data are used to evaluate all possible configurations of a “practical” network having from one to four rain gauges. A multicriteria design strategy is used to guide rain gauge placement, by simultaneously minimizing the residual percent bias and maximizing the coefficient of correlation between the estimated and true mean areal rainfall and minimizing the normalized spatial mean squared error between the estimated and true spatiotemporal rainfall distribution. The performance of the optimized rain gauge network was then compared against randomly designed network ensembles by evaluating the quality of streamflows predicted using the Kinematic Runoff and Erosion (KINEROS2) event-based rainfall-runoff model. Our results indicate that the multicriteria strategy provided a robust design by which a sparse but accurate network of rain gauges could be implemented for semiarid basins such as the one studied.
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Groundwater long-term monitoring (LTM) is a costly activity required at most subsurface remediation sites. Many existing LTM networks need to be optimized to reflect changes in site conditions and to increase their effectiveness in defining the plume. A spatial analysis method using Delaunay triangulation techniques was developed to eliminate redundant monitoring points and to locate new wells where additional data are needed. This method uses Delaunay triangulation of the monitoring network for site discretization and assesses the concentration estimation error at each monitoring location to judge its relative contribution to the spatial plume characterization. Locations where the concentration estimation error is small are considered redundant and become candidates for elimination. New monitoring locations are identified where the projected concentration estimation errors are high. Tests comparing the Delaunay method to a fate and transport analytical model illustrated the attributes and effectiveness of the method. Application to a benzene plume site demonstrated that results from Delaunay triangulation agree well with geostatistical approaches. Although the method is relatively less accurate, and lacks the resolution obtained with the geostatistical approach, it is computationally efficient and simple to implement by non-statisticians.
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Following some general remarks on the importance and unimportance of optimization in spatial network design, we take up, in modest detail, how one might exploit spatial autocorrelations and covariateinformation. We point out that spatial autocorrelations themselves require care in their estimation andthen proceed with two illustrations to show how probabilistic error calculations are made for mappingproblems using network station data. One illustration uses a quantitative mapping variable, and the otheruses a qualitative mapping variable.
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Cokriging is used to merge rain gage measurements and radar rainfall data. The cokriging estimators included are ordinary, universal, and disjunctive. To evaluate the estimators, two simulation experiments are performed. The first experiment assumes that high-quality radar rainfall fields are ground truth rainfall fields. From each ground truth rainfall field, multiple combinations of rain gage measurement field and radar rainfall field are artificially generated with varying gage network density and error characteristics of radar rainfall. The second experiment uses a stochastic space-time rainfall model to generate assumed ground truth rainfall fields of various characteristics. Due to the sparsity of rain gage measurements, the second-order statistics required for cokriging can only be estimated with large uncertainty. The adverse effects of this uncertainty, and the point sampling error of rain gage measurements are explicitly assessed by cokriging the ground truth rainfall data and the radar rainfall data with near perfectly known second-order statistics.
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A large number of hydrological phenomena may be regarded as realizations of space-time random functions. Most available hydrological data sets exhibit time-rich/space-poor characteristics, as well as, some form of temporal periodicity and spatial non-stationarity. To better understand the space-time structure of such hydrological variables, the observed values at each measurement site are considered as separate, but correlated time series. Moreover, it is assumed that the time series are realizations of a mixture of random functions, each associated with a different temporal scale, represented by a particular basic variogram. To preserve the observed temporal periodicities, the experimental direct and cross variograms are modelled as linear combinations of a number of hole function variograms. In a further step, the principal component analysis is used to determine groupings of measurement stations at different temporal scales. The proposed procedure is then applied to monthly piezometric data in a basin south of Paris, France. The temporal scales are determined to be the 12-month seasonal and the 12-year climatic cycles. At each temporal scale different spatial groupings are observed which are attributed to the contrast between the nearly steady state climatic variations versus the almost transient seasonal fluctuations.
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An entropy approach to data collection network design
Author: Donald H. Burn,Yujuin Yang | Size: 1.3 MB | Format:PDF | Quality:Unspecified | Publisher: Elsevier | Year: 1994 | pages: 307-324 | ISBN: --
A new methodology is developed for data collection network design. The approach employs a measure of the information flow between gauging stations in the network which is referred to as the directional information transfer. The information flow measure is based on the entropy of gauging stations and pairs of gauging stations. Non-parametric estimation is used to approximate the multivariate probability density functions required in the entropy calculations. The potential application of the approach is illustrated using extreme flow data from a collection of gauging stations located in southern Manitoba, Canada.
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