A simple approach for improving spatial interpolation of rainfall using ANN
Author: C. Sivapragasam; V. M. Arun; D. Giridhar | Size: 450 KB | Format:PDF | Quality:Unspecified | Publisher: Meteorology and Atmospheric Physics(Springer) | Year: 2010 | pages: 1-7 | ISBN: --
Interpolation of hydrological variables such as rainfall, ground water level, etc. is necessary to arrive at many engineering decisions. This study suggests an innovative and yet simple idea to effectively interpolate the rainfall at non-sampling locations using artificial neural network (ANN). The method has been demonstrated in the Tamirabarani basin of Tamil Nadu State (India), where rain gauge information for 18 rain gauge stations is available. With the help of land use map of the basin and also the proximity of rain gauge stations to each other in the neighbourhood, the most appropriate input variables for ANN are designed and used for training ANN to estimate rainfall in the unknown stations. It is also interesting to note that with appropriate selection of input variables for training ANN, one of the major lacunae of ANN (to have sufficiently lengthy training records) can be suitably addressed. ANN results are compared with Kriging method. Further, the proposed method is applied to improve the prediction of inflow to Ramanadhi reservoir in Tamirabarani basin, and the results seem to be very encouraging.
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Aspects of spatial and temporal rainfall variability and rainfall analysis in relation to some water management problems are surveyed and discussed. It is concluded that relevant modelling of hydrological processes in which the rainfall is a driving force is vital with respect to possibilities of finding solutions to increasing environmental problems following urbanization and industrialization. However, modern computer methods and our knowledge of the spatial and dynamic properties of rainfall fields are seldom used in practical engineering applications. This causes errors and uncertainties in the calculated output. Bridging the gaps between researchers and engineers may overcome some of these problems. It is also argued that experimental studies in a variety of climates and physiographical conditions using an interdisciplinary approach are needed in order to further investigate the scale and dynamics of spatial rainfall variability.
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Author: Phaedon C. Kyriakidis; André G. Journel | Size: 217 KB | Format:PDF | Quality:Unspecified | Publisher: Mathematical Geology(Springer) | Year: 1999 | pages: 651-684 | ISBN: --
Geostatistical space–time models are used increasingly for addressing environmental problems, such as monitoring acid deposition or global warming, and forecasting precipitation or stream flow. Each discipline approaches the problem of joint space–time modeling from its own perspective, a fact leading to a significant amount of overlapping models and, possibly, confusion. This paper attempts an annotated survey of models proposed in the literature, stating contributions and pinpointing shortcomings. Stochastic models that extend spatial statistics (geostatistics) to include the additional time dimension are presented with a common notation to facilitate comparison. Two conceptual viewpoints are distinguished: (1) approaches involving a single spatiotemporal random function model, and (2) approaches involving vectors of space random functions or vectors of time series. Links between these two viewpoints are then revealed; advantages and shortcomings are highlighted. Inference from space–time data is revisited, and assessment of joint space–time uncertainty via stochastic imaging is suggested.
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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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