Article

Geo-spatial grid-based transformations of precipitation estimates using spatial interpolation methods

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Abstract

Geo-spatial interpolation methods are often necessary in instances where the precipitation estimates available from multisensor source data on a specific spatial grid need to be transformed to another grid with a different spatial grid or orientation. The study involves development and evaluation of spatial interpolation or weighting methods for transforming hourly multisensor precipitation estimates (MPE) available in the form of 4×4km2 HRAP (hydrologic rainfall analysis project) grid to a Cartesian 2×2km2 radar (NEXt generation RADar:NEXRAD) grid. Six spatial interpolation weighting methods are developed and evaluated to assess their suitability for transformation of precipitation estimates in space and time. The methods use distances and areal extents of intersection segments of the grids as weights in the interpolation schemes. These methods were applied to transform precipitation estimates from HRAP to NEXRAD grids in the South Florida Water Management District (SFWMD) region in South Florida, United States. A total of 192 rain gauges are used as ground truth to assess the quality of precipitation estimates obtained from these interpolation methods. The rain gauge data in the SFWMD region were also used for radar data bias correction procedures. To help in the assessment, several error measures are calculated and appropriate weighting functions are developed to select the most accurate method for the transformation. Three local interpolation methods out of six methods were found to be competitive and inverse distance based on four nearest neighbors (grids) was found to be the best for the transformation of data.

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... Spatial interpolation is the generation of evaluation values or attributes for unsampled or missing locations within the area covered by existing measurements. It is most often applied as a precursor to creating contour or Comparison of Spatial Interpolation... isoline plots, the drawing of equal value lines to produce a realistic surface between measurement points [16,17]. ...
... The cross-validation was used to verify the accuracy of the different interpolation methods. To evaluate the goodness-of-fit, we calculated the mean absolute error (MAE), the mean relative error (MRE), and the root mean square error (RMSE) [3,16,28]. The MRE represents the percentage of error between the observed and predicted values, while the RMSE and MAE summarize the mean difference in the units of observed and predicted values [3]. ...
... The MAE, MRE, and RMSE are defined as follows: …where Z oi and Z ei represent the ith observation value and predicted value, and n denotes the number of rain gauges. Smaller values of these indicators indicate that the predicted value is closer to the observed one [16,28]. ...
Article
Accurate precipitation data are of great importance for environmental applications. Interpolation methods are usually applied to afford spatially distributed precipitation data. However, due to the scarcity of rain gauges, different spatial interpolation methods may result in deviations from the real spatial distribution of precipitation. In this study, three different interpolation methods were investigated with regard to their suitability for producing a spatial precipitation distribution on China's Tibetan Plateau. Precipitation data from 39 rain gauges were spatially interpolated using ordinary kriging, cokriging with covariates as elevation (Cok-elevation), and cokriging with covariates as tropical rainfall measuring mission (Cok-TRMM). The results showed that the mean absolute error (MAE), mean relative error (MRE), and root mean square error (RMSE) for Cok-TRMM amounted to 103.85 mm, 0.32, and 134.50 mm, respectively. These numbers were lower than the figures for ordinary kriging (MAE 111.01 mm, MRE 0.34, RMSE 144.86 mm) and Cok-elevation (MAE 111.43 mm, MRE 0.34, RMSE 144.35 mm). In addition, the correlation coefficient between observed and predicted values of Cok-TRMM (r(2) = 0.53) was higher than that for ordinary kriging (r(2) = 0.46) and Cok-elevation (r(2) = 0.46). Our results demonstrate that Cok-TRMM is more effective at producing a spatial precipitation distribution on the Tibetan Plateau and can serve as a new spatial interpolation method for precipitation in data-scarce regions.
... No entanto, para ambas as situações mencionadas, estimar os dados inexistentes de variáveis como a precipitação ainda é uma tarefa complexa devido à variabilidade espaço-temporal das chuvas e dos processos físicos inerentes ao ciclo hidrológico (Teegavarapu et al., 2012). ...
... Em vários destes estudos utilizam-se os métodos clássicos determinísticos e estocásticos, comumente apresentados na literatura como o inverso da distância, interpolação não linear e os diversos procedimentos de krigagem (Wanderley et al., 2012). No entanto, a aplicabilidade da Inteligência Artificial, como método preditor de dados inexistentes, vem apresentando resultados satisfatórios (Teegavarapu et al., 2009). ...
... Em estudo como o de Kim e Paxhepsky (2010), o coeficiente de determinação que apresentou melhor ajuste foi de r 2 = 0,81, obtido na interpolação de dados pluviométricos por redes neurais. Teegavarapu e Chandramouli (2005) encontraram coeficiente de correlação de r = 0,75 na tentativa de estimar dados de precipitação, e Teegavarapu et al. (2009) obtiveram coeficientes de correlação que variaram de r = 0,75 e 0,82 para r = 0,95 e 0,97, em função da proximidade das estações utilizadas para a interpolação da estação base, apresentando coeficientes maiores nas estações mais próximas da estação base. Vale ressaltar que coeficientes de determinação baixos e pouco significativos poderão influenciar no ajuste dos modelos estatísticos preditores, reduzindo sua dependência espacial. ...
Article
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A falta de informação quanto à distribuição da precipitação é um sério obstáculo para se compreender e modelar sua variabilidade, surgindo assim a necessidade de se obter informações para regiões que não apresentam estações de medição ou que apresentem falhas em seu banco de dados por meio da interpolação. Desta forma, o objetivo deste estudo consiste em utilizar Redes Neurais Artificiais (RNA's), propondo diferentes procedimentos para sua utilização, na interpolação espacial de dados pluviométricos no Estado de Alagoas. Para o estudo foram utilizadas 245 estações pluviométricas localizadas nos Estados de Alagoas e Pernambuco, das quais se usou as informações de latitude, longitude, altitude e precipitação das estações próxima à estação base que se desejou estimar a precipitação, como parâmetros de entrada das redes. A utilização de RNA´s, no preenchimento de falhas de dados pluviométricos, mostrou diferença estatística em apenas um procedimento adotado pelas redes. As estimativas realizadas para o mês de novembro apresentou resultados mais coerentes com os observados nas estações bases, devido a menor variabilidade espacial da precipitação neste mês.
... The kriging technique is mostly used in geostatistical interpolation (Figure 1). The study of interpolation techniques mainly works on the following two aspects: (1) interpolate meteorological elements in a region using different interpolation techniques, in an attempt to compare the accuracy of the techniques used and analyse the spatial and temporal variations of meteorological elements in the region (Zhuang & Wang 2003;Cai et al. 2006;Piazza et al. 2011;Bostan et al. 2012;Wagner et al. 2012;Teegavarapu et al. 2012); and (2) raised interpolation accuracy by improving the exiting interpolated methods but the improved interpolation methods are usually only fit for the specific study area not for other regions (Liu et al. 2004;Pan et al. 2004;Shi et al. 2011;Tang et al. 2012;Kilibarda et al. 2014). As a matter of fact, the variation of meteorological elements, especially at a large scale up to a region, could be very sophisticated. ...
... In recent years, a range of studies have been launched to regionalize the meteorological elements of north-eastern part of China (Zhuang & Wang 2003;Cai et al. 2006;Fu et al. 2009;He et al. 2013), though most of them employed only one interpolation technique and took the interpolation results as the input data for basic research works without the verification of accuracy, especially at the temporal scale. A few others worked to evaluate interpolation accuracy based on the comparisons of different interpolation techniques (Piazza et al. 2011;Bostan et al. 2012;Teegavarapu et al. 2012). Unfortunately, those studies have not sorted out a desired interpolation technique that can be applied in an accurate and universal manner. ...
Article
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An accurate gridded climatological temperature data-set can be a reliable basis for studying the issues that concern climate change, natural disasters, among others. In this study, the climate standard value data and annual observed data collected by 104 meteorological sites in Northeast China from 1971 to 2000 are used to interpolate the annual mean air temperature of the region with different spatial interpolation techniques. Efforts have also been made to verify the accuracy of the results generated by each interpolation method with error indicator, temperature characteristic value and temperature variation curves. The results show at the spatial scale, the partial thin-plate smoothing spline (PTPSS) scheme generates the most desirable temperature interpolations with a root-mean-square error at 0.34 °C and an average standard error at 0.52 °C. At the temporal scale, the PTPSS-based 1971–2000 temperature curves agree the best with the gridded temperature curves, with the correlation coefficients of means, minimums and maximums between the two being larger than 0.9. Meanwhile, the PTPSS produce the smallest error approaching zero among all the interpolation schemes tested in the study. In this context, the PTPSS scheme stands out as the most desirable interpolation method for the annual mean temperature in Northeast China.
... This study proposes an algorithm for repairing blank pixels during the orthorectification process to eliminate pixel discontinuity. The algorithm employs bilinear (BL) interpolation and distance-weighted allocation to obtain the gray values of all orthoimage pixels [4][5][6]. This study evaluates the results of the proposed algorithm by using a near-infrared band of the preliminary hyperspectral ima-ges, which were captured by a hyperspectral imager of plants and the environment [7,8]. ...
... This approach is similar to the Bilinear Interpolation (BL) approach for image pixel allocation. The two methods are described below [6]. The flowchart is shown in Figure 4. ...
... Three well-known rescale techniques available at ArcGIS software are applied in this study. NN, BI and CC are adopted to be used for rescaling the DEM (Keys 1981;Mitchell and Netravali 1988;Jordan 2003;Dragut et al. 2009;Teegavarapu et al. 2012). NN is an interpolation technique that uses the weight of only one cell (see Figure 2(a)). ...
Article
The accurate estimation of terrain characteristics is central in rainfall runoff modelling. In this study, influences of Digital Elevation Models (DEMs) obtained from different sources, resolutions and rescaling techniques are compared for Peak flow prediction in a large-scale watershed by the Topographic driven model (TOPMODEL). The comparison includes graphical representation and statistical assessments using daily time series data. As a result, DEM extracted from contour map (DEM-Con) showed better performance when DEM resolutions increased, but the Advanced Space-borne Thermal Emission and Reflection Radiometer (DEM-Aster) continued to achieve less Relative Error (RE) at low resolution. Moreover, better RE values were found at cubic convolution technique to predict the peaks followed by nearest-neighbor and bilinear. In addition, this study indicated that DEM resolution is more sensitive factor for TOPMODEL simulation compared to DEM sources and rescaling techniques for streamflow and peaks prediction.
... Three well-known rescale techniques available at ArcGIS software are applied in this study. NN, BI, and CC are adopted to be used for rescaling the DEM (Keys, 1981;Mitchell and Netravali, 1988;Jordan, 2003;Dragut et al., 2009;Teegavarapua et al., 2012). NN is an interpolation technique that uses the weight of only one cell (see Figure 2(a)). ...
... #1 and #10 represent the accuracy and efficiency of interpolation, with the wide application of spatial interpolation method, the accuracy and accuracy of spatial interpolation are becoming more and more important; The higher the interpolation accuracy is, the closer the spatial prediction is to the real situation. Wang [14] and Ramesh [15] respectively use computational grids to create continuous surface by spatial interpolation, which improves the computational efficiency and accuracy. ...
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In this paper, the literatures related to spatial interpolation between 1982 and 2017, which are included in the Web of Science core database, are used as data sources, and the visualization analysis is carried out according to the co-country network, co-category network, co-citation network, keywords co-occurrence network. It is found that spatial interpolation has experienced three stages: slow development, steady development and rapid development; The cross effect between 11 clustering groups, the main convergence of spatial interpolation theory research, the practical application and case study of spatial interpolation and research on the accuracy and efficiency of spatial interpolation. Finding the optimal spatial interpolation is the frontier and hot spot of the research. Spatial interpolation research has formed a theoretical basis and research system framework, interdisciplinary strong, is widely used in various fields.
... Another limitation was regarding the PAF estimation on a spatial scale based on two different grid resolutions of Pe and air pollutant concentration layer. Although, we used the resampling and interpolation technique in the raster algebra process [79], this may have produced some variation of grid and uncertainty from the estimation [66]. Further studies should employ a multi-spatial resolution approach [80,81] and/or consider the consistency of spatial resolution on air concentrations and the population of exposure distribution [48]. ...
Article
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Background Growing urbanisation and population requiring enhanced electricity generation as well as the increasing numbers of fossil fuel in Thailand pose important challenges to air quality management which impacts on the health of the population. Mortality attributed to ambient air pollution is one of the sustainable development goals (SDGs). We estimated the spatial pattern of mortality burden attributable to selected ambient air pollution in 2009 based on the empirical evidence in Thailand. Methods We estimated the burden of disease attributable to ambient air pollution based on the comparative risk assessment (CRA) framework developed by the World Health Organization (WHO) and the Global Burden of Disease study (GBD). We integrated geographical information systems (GIS)-based exposure assessments into spatial interpolation models to estimate ambient air pollutant concentrations, the population distribution of exposure and the concentration-response (CR) relationship to quantify ambient air pollution exposure and associated mortality. We obtained air quality data from the Pollution Control Department (PCD) of Thailand surface air pollution monitoring network sources and estimated the CR relationship between relative risk (RR) and concentration of air pollutants from the epidemiological literature. Results We estimated 650–38,410 ambient air pollution-related fatalities and 160–5,982 fatalities that could have been avoided with a 20 reduction in ambient air pollutant concentrations. The summation of population-attributable fraction (PAF) of the disease burden for all-causes mortality in adults due to NO2 and PM2.5 were the highest among all air pollutants at 10% and 7.5%, respectively. The PAF summation of PM2.5 for lung cancer and cardiovascular disease were 16.8% and 14.6% respectively and the PAF summations of mortality attributable to PM10 was 3.4% for all-causes mortality, 1.7% for respiratory and 3.8% for cardiovascular mortality, while the PAF summation of mortality attributable to NO2 was 7.8% for respiratory mortality in Thailand. Conclusion Mortality due to ambient air pollution in Thailand varies across the country. Geographical distribution estimates can identify high exposure areas for planners and policy-makers. Our results suggest that the benefits of a 20% reduction in ambient air pollution concentration could prevent up to 25% of avoidable fatalities each year in all-causes, respiratory and cardiovascular categories. Furthermore, our findings can provide guidelines for future epidemiological investigations and policy decisions to achieve the SDGs.
... Moreover, due to high spatial and temporal variability and precipitation uncertainty (Tustison et al., 2001;Hrachowitz & Weiler, 2009), satisfactory and continuously distributed precipitation data are difficult to obtain even if adopting spatial interpolation (Li & Heap, 2008;Teegavarapu et al., 2012;Plouffe et al., 2015). ...
Article
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With high spatiotemporal resolution and wide coverage, satellite-based precipitation products can potentially fill the deficiencies of traditional in situ gauge precipitation observations and provide an alternative data source for ungauged areas. However, due to the relatively poor accuracy and high uncertainty of satellite-based precipitation products, it remains necessary to assess the quality and applicability of the products for each investigated area. This study evaluated the accuracy and error of the latest Tropical Rainfall Measuring Mission (TRMM) Multi-satellites Precipitation Analysis (TMPA) 3B42-V7 satellite-based precipitation product and validated the applicability of the product for the Beijiang and Dongjiang River Basin, downstream of the Pearl River Basin in China. The study first evaluated the accuracy, error, and bias of the 3B42-V7 product during 1998-2006 at daily and monthly scale via comparison with in situ observations. The study further validated the applicability of the product via hydrologic simulation using the Variable Infiltration Capacity (VIC) hydrological model for three hydrological stations in the Beijiang River Basin, considering two scenarios: a streamflow simulation with gauge-calibrated parameters (scenario I) and a simulation after recalibration with the 3B42-V7 product (scenario II). The results revealed that: 1) the 3B42-V7 product produced acceptable accuracy both at the daily scale and high accuracy at the monthly scale, while generally tending to overestimate precipitation; 2) the product clearly overestimated the frequency of no rainfall events at the gridcell-scale and light rainfall (< 1 mm/day) events at the region-scale, and also overestimated the amount of heavy rain (25-50 mm/day) and hard rain (≥ 50 mm/day) events; 3) under scenario I, the 3B42-V7 product performed poorly at three stations with gauge-calibrated parameters; under scenario II, the recalibrated model provided significantly improved performance of streamflow simulation with the 3B42-V7 product; 4) the VIC model has the ability to reveal the hydrological characteristics of the karst landform in the Beijiang Basin when using the 3B42-V7 product.
... On the one hand, various spatialization methods for interpolating climate variables obtained from in situ station measurements have been developed (Daly et al., 1994(Daly et al., , 2008Steinacker et al., 2011b;Bica et al., 2007;Szentimrey et al., 2011;Teegavarapu et al., 2012;Frei, 2014;Gyasi-Agyei and Pegram, 2014;Hiebl and Frei, 2016;Boudevillain et al., 2016). Basically, these methods are based on statistical techniques for interpolating scattered station reports, integrating physical constraints, various additional measurements (e.g. ...
Article
The analysis of potential influencing factors that affect the likelihood of road accident occurrence has been of major interest for safety researchers throughout the recent decades. Even though steady methodological progresses were made over the years, several impediments pertaining to the statistical analysis of crash data remain. While issues related to methodological approaches have been subject to constructive discussion, uncertainties inherent to the most fundamental part of any analysis have been widely neglected: data. This paper scrutinizes data from various sources that are commonly used in road safety studies with respect to their actual suitability for applications in this area. Issues related to spatial and temporal aspects of data uncertainty are pointed out and their implications for road safety analysis are discussed in detail. These general methodological considerations are exemplary illustrated with data from Austria, providing suggestions and methods how to overcome these obstacles. Considering these aspects is of major importance for expediting further advances in road safety data analysis and thus for increasing road safety.
... Improvements were achieved in the estimation of precipitation data when the stations with lowest measurement uncertainty were selected in the interpolation process. Teegavarapu et al. (2011) Spatial interpolation for estimation of missing precipitation records 3 precipitation estimates from one grid to another. These methods use extents of spatial overlays as weights in nearest neighbour interpolation. ...
Article
New optimal proximity-based imputation, K-nearest neighbour (K-NN) classification and K-means clustering methods are proposed and developed for estimation of missing daily precipitation records. Mathematical programming formulations are developed to optimize the weighting, classification and clustering schemes used in these methods. Ten different binary and real-valued distance metrics are used as proximity measures. Two climatic regions, Kentucky and Florida, (temperate and tropical) in the USA, with different gauge density and network structure, are used as case studies to evaluate the new methods. A comprehensive exercise is undertaken to compare the performances of the new methods with those of several deterministic and stochastic spatial interpolation methods. The results from these comparisons indicate that the proposed methods performed better than existing methods. Use of optimal proximity metrics as weights, spatial clustering of observation sites and classification of precipitation data resulted in improvement of missing data estimates.Editor D. Koutsoyiannis; Associate editor C. Onof
... On the one hand, various spatialization methods for interpolating climate variables obtained from in situ station measurements have been developed (Daly et al., 1994(Daly et al., , 2008Steinacker et al., 2011b;Bica et al., 2007;Szentimrey et al., 2011;Teegavarapu et al., 2012;Frei, 2014;Gyasi-Agyei and Pegram, 2014;Boudevillain et al., 2016). Basically, these methods are based on statistical techniques for interpolating scattered station reports, integrating physical constraints, various additional measurements (e.g. ...
Thesis
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Road infrastructure networks are complex interconnected systems that serve as vital backbones of society. Therefore, upholding traffic safety and fluidity as well as network availability is of core importance, with implications derived therefrom affecting many spheres of life. In the face of climate change, extreme weather events are expected to increase in both intensity and frequency. Hence, ensuring reliability and resilience of road infrastructure is of particular importance during periods of inclement weather, since these conditions exert amplified strain to both infrastructure assets and traffic participants. In this thesis, selected aspects related to the impacts of adverse weather on road infrastructure networks in the Alps are analyzed using a data-driven approach. One statistical peculiarity that emerges across the multifaceted research aspects under consideration is that the quantities of interest, which are usually the target variables considered in statistical models, are related to extreme events. While extreme events are seldom by nature, they contain important information that is essential for any statistical analysis. This thesis comprises six articles on statistical modeling of extreme events, natural hazards and imbalanced data sets in the context of Alpine road networks. Four main research aspects are investigated. First, spatial and temporal uncertainties of road safety data are analyzed. Numerical and graphical illustrations reveal distinct patterns that emerge with respect to accident time and location, thereby highlighting the uncertainties inherent to commonly used data sources. Second, a comparative assessment framework for different approaches to extreme value analysis is proposed. Its core element is a novel model performance metric specifically tailored to the upper tail of the extreme value distribution, which may support diagnosis of the extreme value series. Third, landslide-transport network interactions in a changing climate are assessed in a quantitative way. On the one hand, this is achieved by investigating the development of potentially landslide-triggering rainfall events throughout the 21st century. On the other hand, the societal impacts of road network interruptions are analyzed by means of agent-based traffic simulation. The approach uses network interruptions based on a susceptibility map derived from historic landslide event data and geophysical properties of the area under consideration. Fourth, the potential of using high-resolution road safety data for accident prediction modeling is investigated. The major challenge of dealing with an extremely imbalanced data set was overcome by combining synthetic minority oversampling and maximum dissimilarity undersampling. Subsequently, a number of different machine learning classifiers were applied and contrasted with respect to their predictive performance. While statistical applications are demonstrated on the nexus between transportation and natural hazards, methodological innovations and approaches presented in this thesis are naturally transferable to various other domains of research beyond a geosciences context.
... Later, Teegavarapu (2012) has applied optimization methods to select rain gauges in the objective matter and delineated optimal clusters using quadrant-based method. Grid-based interpolation method of precipitation using geospatial information was also presented by Teegavarapu et al. (2012). ...
Article
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The gap filling is common practice to complete hydrological data series without missing values for environmental simulations and water resources modeling in a changing climate. However, gap filling processes are often cumbersome because physical constraints, such as complex terrain and density of weather stations, often limit the ability to improve the performance. Although several studies of gap filling methods have been developed and improved by researchers, it is still challenging to find the best gap filling method for broad applications. This research explores a gap filling method to improve climate data estimates (e.g., daily precipitation) using gamma distribution function with statistical correlation (GSC) in conjunction with cluster analysis (CA). The daily dataset at the source stations (SSs) is utilized to estimate missing values at the target stations (TSs) in the study area. Three standard gap filling methods, including Inverse Distance Weight (IDW), Ordinary Kriging (OK), and Gauge Mean Estimator (GME) are evaluated along with cluster analysis based on statistical measures (RMSE, MAE, R) and skill scores (HSS, PSS, CSI). The result indicates that cluster analysis can improve estimation performances regardless of the gap filling methods used. However, the GSC method associated with cluster analysis, in particular, outperformed other methods when the performance comparison task was conducted under rain and no-rain conditions in the study area. The proposed method, GSC, therefore, will be used as a case toward advancing gap filling methods in the field.
... From hydrological perspectives, a complete set of valid precipitation data is critical to simulate streamflow in rainfall-runoff models for various water resources decision making (e.g., reservoir operations, drought mitigation, and flood control). Hydrologists often estimate missing values using mathematical and statistical methods, such as the arithmetic mean (Mn), Inverse Distance Weighting (IDW), Regression-based analysis (RA) methods, Kriging Estimation (KE) Method, and Gamma distribution function (GDF) to fill gaps in missing values (Hubbard et al. 2005;Linsley et al. 1982;Mair and Fares 2011;Teegavarapu et al. 2009Teegavarapu et al. , 2011Westerberg et al. 2010;Teegavarapu 2014a, b). The IDW method, in particular, has been commonly used to estimate missing values in geographical sciences and hydrology because the result from IDW method shows good performances in filling missing values, especially for spatially dense networks (Ahrens 2006;Dirks et al. 1998;Garcia et al. 2008). ...
Article
Multiple missing levels are explored to quantify a threshold of missing values during gap filling processes in daily precipitation series. An autoregressive model was used to generate rainfall estimates and subsets of data are selected with four sampling windows (whole data, front, middle, and rear section) at different missing levels, including 5, 10, 15, 16, 17, and 18 %. The proposed threshold was found and evaluated based on statistical criteria, including coefficient of determination (R2) and its associated index termed “the R2 difference index (RDI).” The result indicates that about 15 % missing level of data is plausible to construct daily precipitation series for further hydrological analysis when the Gamma distribution function (GDF) is used as an estimation method. The threshold determined from this study will contribute to gap filling guidelines, especially for water managers and hydrologists to take advantage of skillful estimates for missing daily precipitation data.
... By considering that the computational complexity of a variogram is cubic in the size of the observed data [6], the variogram calculus, in this study, is sped-up by processing only the areas with information holes, rather than the global data. In [42], IDW and 1-nearest neighbors have been used to interpolate a grid of rainfall data and re-sample data at multiple resolutions. In [30], IDW is again investigated and formulated in an adaptive way which depends on the varying distance-decay relationship in the area under examination. ...
Article
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Ubiquitous sensor stations continuously measure several geophysical fields over large zones and long (potentially unbounded) periods of time. However, observations can never cover every location nor every time. In addition, due to its huge volume, the data produced cannot be entirely recorded for future analysis. In this scenario, interpolation, i.e., the estimation of unknown data in each location or time of interest, can be used to supplement station records. Although in GIScience there has been a tendency to treat space and time separately, integrating space and time could yield better results than treating them separately when interpolating geophysical fields. According to this idea, a spatiotemporal interpolation process, which accounts for both space and time, is described here. It operates in two phases. First, the exploration phase addresses the problem of interaction. This phase is performed on-line using data recorded froma network throughout a timewindow. The trend cluster discovery process determines prominent data trends and geographicallyaware station interactions in the window. The result of this process is given before a new data window is recorded. Second, the estimation phase uses the inverse distance weighting approach both to approximate observed data and to estimate missing data. The proposed technique has been evaluated using two large real climate sensor networks. The experiments empirically demonstrate that, in spite of a notable reduction in the volume of data, the technique guarantees accurate estimation of missing data.
... We used the inverse distance weighting (IDW) function, one of the most frequently used deterministic models in spatial interpolation (Chen & Liu 2012; Srivastava et al. 2012a; Srivastava et al. 2012b;Teegavarapu et al. 2012), to interpolate the spatial distribution of DO in the study area. IDW is relatively fast and easy to compute and straightforward to interpret. ...
Article
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Flood disasters are closely associated with an increased risk of infection, particularly from waterborne diseases. Most studies of waterborne diseases have relied on the direct determination of pathogens in contaminated water to assess disease risk. In contrast, this study aims to use an indirect assessment that employs a back propagation neural network (BPNN) for modelling diarrheal outbreaks using data from remote sensing and dissolved-oxygen (DO) measurements to reduce cost and time. Our study area is in Ayutthaya province, which was very severely affected by the catastrophic 2011 Thailand flood. BPNN was used to model the relationships among the parameters of the flood and the water quality and the risk of people becoming infected. Radarsat-2 scenes were utilized to estimate flood area and duration, while the flood water quality was derived from the interpolation of DO samples. The risk-ratio function was applied to the diarrheal morbidity to define the level of outbreak detection and the outbreak periods. Tests of the BPNN prediction model produced high prediction accuracy of diarrheal-outbreak risk with low prediction error and a high degree of correlation. With the promising accuracy of our approach, decision-makers can plan rapid and comprehensively preventive measures and countermeasures in advance.
... Cokriging uses direct and cross covariance functions that are computed in the sample of the observed data. Teegavarapu et al. (2012) use IDW and 1-Nearest Neighbor, in order to interpolate a grid of rainfall data and re-sample data at multiple resolutions. Lu and Wong (2008) formulate IDW in an adaptive way, by accounting for the varying distance-decay relationship in the area under examination. ...
Article
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Nowadays ubiquitous sensor stations are deployed worldwide, in order to measure several geophysical variables (e.g. temperature, humidity, light) for a growing number of ecological and industrial processes. Although these variables are, in general, measured over large zones and long (potentially unbounded) periods of time, stations cannot cover any space location. On the other hand, due to their huge volume, data produced cannot be entirely recorded for future analysis. In this scenario, summarization, i.e. the computation of aggregates of data, can be used to reduce the amount of produced data stored on the disk, while interpolation, i.e. the estimation of unknown data in each location of interest, can be used to supplement station records. We illustrate a novel data mining solution, named interpolative clustering, that has the merit of addressing both these tasks in time-evolving, multivariate geophysical applications. It yields a time-evolving clustering model, in order to summarize geophysical data and computes a weighted linear combination of cluster prototypes, in order to predict data. Clustering is done by accounting for the local presence of the spatial autocorrelation property in the geophysical data. Weights of the linear combination are defined, in order to reflect the inverse distance of the unseen data to each cluster geometry. The cluster geometry is represented through shape-dependent sampling of geographic coordinates of clustered stations. Experiments performed with several data collections investigate the trade-off between the summarization capability and predictive accuracy of the presented interpolative clustering algorithm.
... NN will take one nearest model point from observation coordinate so the possibility of same value between close points is relatively higher. On the other hand, BL uses four nearest points to calculate some value in observation coordinate [10]. ...
Article
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In production of climate change information, determining the best projection is a very important step. Missed projection can lead to loss of public trust in climate change. In some previous studies, most analyses were conducted on point approach due to the lack of observational data covering large spatial areas. In this study, rainfall data from 197 observation points are used to get correction coefficients by comparing it to monthly rainfall historical model from 1972-2005. Area of study is 110.89°E–116.27° E and 8.78°S–5.04°S. Two RCP scenarios (4.5 and 8.5) under CSIROMK3.6 RegCM4 BMKG SEA-Cordex are compared to get its ensemble weighting factor. Validation parameters used are mean absolute error and quartiles of error. Shifting correction is introduced in this study with some evidence based on visual analysis and high correction coefficients from the unshifted one. It is also shown that bilinear resampling gives better result than nearest neighbour. Ensemble weighting factors are then set 0.4 for RCP 8.5 and 0.6 for RCP 4.5. In next 10 years (2017-2026), dry condition average rainfall condition is expected to happen between May and October. Keywords: Projection, rainfall, correction coefficient, bilinear, shifting correction
... And according to Bargaoui and Chebbi (2009), "A full comparison of the accuracy of both methods (2-D, 3-D) using crossvalidation scheme, shows that the 3-D kriging leads to significantly lower prediction errors than the classical 2-D kriging." Teegavarapu et al. (2012) developed six spatial interpolation weighting methods to access their suitability for transformation of precipitation estimates in space and time. "The methods use distances and areal extents of intersection segments of the grids as weights in the interpolation schemes. ...
Chapter
Spatial interpolation is the process of estimating value of continuous target variable at unknown location based on available samples. At present, there are many interpolation techniques available, and each technique has its own pros and cons. Accuracy of interpolation mainly depends on (1) sampling pattern and number of samples, (2) interpolation model adopted, and (3) presence of co-variable if a number of sample points are less. There are certain sampling techniques available, namely, regular, random, stratified, cluster, etc. Due to complex topography of mountain ecosystem like the Himalaya, stratified sampling technique is supposed to give the best prediction. But due to high variability in elevation and remote locations in mountain regions, installation of automatic weather stations (AWS) as per stratified sampling method is very difficult. So mountain regions face lack of sufficient number of samples/observations for accurate prediction (Stahl et al. 2006). There are many interpolation techniques available, but they are mainly classified into two categories: deterministic and geostatistical techniques. Deterministic techniques are based on the geometric properties of the samples, whereas geostatistical techniques are based on geometric as well as spatial autocorrelation of the target variable. Some of the deterministic techniques are inverse distance weighted (IDW), spline, Thiessen polygon, and linear regression, and geostatistical techniques are simple kriging, ordinary kriging, universal kriging, co-kriging, regression kriging, indicator kriging, etc. Stationarity, isotropy, intrinsic hypothesis, and unbiasedness are the basic assumptions of geostatistical techniques (Sluiter 2009).
... Further on, the assumption of linear relationship between the observed rainfall and neighbouring stations by the conventional methods may not be true (Mwale et al., 2012, Dubey, 2013. Studies by Teegavarapu, 2014 andTeegavarapu et al., 2012 indicated the limitations of multiple regression method was negative estimates. Another issue in the inverse distance weighting method is the arbitrary selection of the neighbouring stations where the condition is not always true (Di Piazza et al., 2011). ...
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An incomplete rainfall data series could affect the reliability of related hydrological modelling. As Malaysia experiences a tropical climate with sensational variations, the availability of complete rainfall series is important for climate change assessments and water resources management. In this study, the estimation of missing rainfall data was carried out using the approach that covers an artificial neural network (ANN) and other conventional methods. These conventional methods were the inverse distance weighting method (IDW), the linear regression (LR) method, the normal ratio (NR) method and the ordinary kriging (OK) method. The performances of the estimation methods were evaluated by the goodness of fit tests, namely the mean absolute error (MAE), mean bias error (MBE), mean square error (MSE), scaled mean square error (SMSE) and the linear correlation coefficient (LCC). From the results, ANN was found to be the overall best estimation method. ANN resulted in lower values for MAE, MSE and SMSE, less biasedness for the MBE and the highest correlation for LCC. From the conventional method list, the OK was selected as the better option. Overall, ANN was more efficient approach to the estimation of missing rainfall data for the Kelantan River Basin in tropical Malaysia.
... Precipitation is a vital climate parameter, which has a wide range of applications in hydrological, meteorological and environmental research (Teegavarapu et al., 2012;Wagner et al., 2012). An accurate illustration of spatial rainfall distribution characteristics could depict convincible trends and hence improve the understanding of the precipitation behaviour for a specific region. ...
Article
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Accurate spatial distribution information of rainfall is essential to rainfall‐induced hazard predictions and statistical interpolation methods may serve as a useful tool to produce a detailed distribution from coarse data sources. Although numerous comparison studies about different interpolation methods have been conducted on irregular rain‐gauge networks, there is a need to perform such work on the increasingly available gridded rainfall data. Carried out in the Emilia‐Romagna region (Italy) from 2008 to 2018, this study aims to examine accurate and appropriate interpolation methods to produce finer rainfall surface maps based on the 0.25° × 0.25° ERA5 gridded precipitation datasets. Five interpolation techniques, namely Thiessen polygons, Inverse Distance Weighting (IDW), Thin Plate Spline (TPS), Ordinary Kriging (OK), and ordinary Co‐Kriging (CoK), have been selected and compared at different time scales (annual, monthly, and annual maximum daily precipitation). To assess the accuracy, the leave‐one‐out‐cross‐validation(LOOCV)test was used by using the indexes of Bias, Correlation coefficient (CC), the Nash‐Sutcliffe Efficiency (NSE), Root Mean Square Error (RMSE) and the Kling‐Gupta Efficiency (KGE). Additionally, visual inspections are employed to evaluate the plausibility of the interpolated maps. Results show: (1) All five interpolation methods have certain capabilities to improve spatial resolution, but they fail on accuracy at the daily scale. The OK generally outperforms the other four methods, while TPS shows better performance through the visual inspection at the monthly scale; (2) Unlike in the case of the interpolation using conventional point‐based rain‐gauge data, the multivariate method CoK is inferior to the univariate ones and the p‐power of the IDW also differs; (3) Winter and spring results are better than those of summer and autumn. This study has provided useful guidance on choosing suitable rainfall interpolation methods for gridded datasets, which can be expanded in other regions and data sources to explore the generality of the conclusions. This article is protected by copyright. All rights reserved.
... However, because of the limitation of having this equipment in all regions and the desired quantity, it allows the implementation of mathematical and statistical techniques to gain more and more importance as a practical and useful tool to determine the behavior of the pollutants in regions where it becomes indispensable to have some type of measurement of these agents [8]. Research on the development of tools and techniques to determine the level of contamination in a region includes Tegavarapu et al. [9] show in their study that geospatial interpolation methods can be applied as a faire as an accurate technique for predicting atmospheric variables. Beauchamp et al. [10] presented a geostatistical analysis based on the kriging method as a way of [11], used the land use regression (LUR) technique to estimate exposure to air pollution for epidemiological studies. ...
Article
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Given the global problem of high levels of pollutants in the atmosphere, it is essential to use tools to measure and determine these levels. Unfortunately, it is impossible to have devices that allow direct pollutants’ direct measurements in a place of interest. Due to this limitation, in this work, a computer tool was developed to predict contaminants’ behavior and their concentration levels in a reliable way. In this methodology, equations of the physics of motion were implemented to predict particles’ behavior in a given area and an interpolation technique based on the Kriging method. In the initial stage, a preliminary analysis of the pollution data of the city of Bogota, Colombia, downloaded from the Air quality monitoring network of Bogota, Colombia, was performed. In the next stage, the variables of most significant interest in the analysis were defined, and the data to be characterized is explored. Finally, the selected method’s calculation algorithm is implemented in Python, taking an ArcGIS library as a programming reference. From the results, it was possible to determine the contaminants’ levels for some regions of Bogota, Colombia, between values of 0.067 to a maximum weight of 0.4039 ¼g/m ³ , for January 2013.
... The method and resolution that has the highest correlation will be used in determining the threshold. The nearest neighbor scheme uses the one closest control point where the interpolation value is required, while the bilinear interpolation uses the four closest points [16]. Illustrations of both re-sample schemes are shown in Figure 2. Determination of the rainfall threshold that triggers landslides uses two methods: Cumulative Threshold (CT) method and Intensity-Duration (ID). ...
Article
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Landslide is one of the natural disasters that can cause a lot of loss, both material and fatalities. Banjarnegara Regency is one of Central Java Province regencies where landslides often occur due to the region's topography and high intensity rainfall.. Therefore, it is necessary to determine the threshold of rainfall that can trigger landslides to be used as an early warning for landslides. The rainfall data used for the threshold is daily and hourly rainfall intensity from remote sensing data that provides complete data but relatively rough resolution. So that remote sensing data need to be re-sampled. The remote sensing data used is CMORPH satellite data that has been re-sampled for detailing existing information of rainfall data. The resampling method used is the bilinear method and nearest neighbor by choosing between the two based on the highest correlation. Threshold calculation using Cumulative Threshold (CT) method resulted equation P 3 = 7.0354 - 1.0195P 15 and Intensity Duration (ID) method resulted equation I = 1.785D ⁻⁰³⁰⁵ . The peak rainfall intensity occurs at the threshold of 97-120 hours before a landslide occur.
... Interpolation is a standard method for estimating precipitation in areas with no rain gauge stations [53,54]. Figure 3 compares ground station precipitation, interpolated values, and satellite imagery results for 2017 for three different climatic zones. ...
Article
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The Tropical Rainfall Measuring Mission (TRMM) and Global Precipitation Mission (GPM) are the most important and widely used data sources in several applications-e.g., forecasting drought and flood, and managing water resources-especially in the areas with sparse or no other robust sources. This study explored the accuracy and precision of satellite data products over a span of 18 years (2000-2017) using synoptic ground station data for three regions in Iran with different climates, namely (a) humid and high rainfall, (b) semi-arid, and (c) arid. The results show that the monthly precipitation products of GPM and TRMM overestimate the rainfall. On average, they overestimated the precipitation amount by 11% in humid, by 50% in semi-arid, and by 43% in arid climate conditions compared to the ground-based data. This study also evaluated the satellite data accuracy in drought and wet conditions based on the standardized precipitation index (SPI) and different seasons. The results showed that the accuracy of satellite data varies significantly under drought, wet, and normal conditions and different timescales, being lowest under drought conditions , especially in arid regions. The highest accuracy was obtained on the 12-month timescale and the lowest on the 3-month timescale. Although the accuracy of the data is dependent on the season, the seasonal effects depend on climatic conditions.
... Furthermore, we used a simple grid-based spatial interpolation (Teegavarapu et al., 2012) to interpolate the GPS vertical displacement velocities (Pan et al., 2018) and to calculate the vertical displacement field of the TP. The process of interpolating the GPS velocities is mainly as follows. ...
Article
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The uplift state of the Tibetan Plateau (TP) is determined by tectonic displacement and hydrological load displacement. However, it is unknown how much the load effect contributes to the uplift of the plateau. Typically, the vertical displacement due to the mass load is calculated based on the Gravity Recovery and Climate Experiment (GRACE) data and the spherical harmonic analysis method. However, because the GRACE data are truncated at lower harmonic degrees and tectonic mass changes are contained in the GRACE-derived mass changes, the validity of using GRACE data to estimate the load displacement of the TP is questionable and needs further discussion. This study presents a reasonable approach to computing the loading effect by considering the global hydrological mass budget (seawater, lake, glacier, river, snow, soil water, canopy water, and groundwater). The TP’s mean vertical load displacement rate we obtained is 0.15 mm/yr, contributing to 16 percent of the average TP uplift rate. Comparing the hydrologically computed load displacements and the GRACE-derived load displacements indicates that the GRACE-derived displacement differs significantly from the real hydrological load displacement. That is, we found that the GRACE-derived load effect cannot be applied to correct the Global Positioning System (GPS) displacement, but the one computed with hydrological data works well. We claim that the load displacement effect for any GPS station should be calculated by Green’s function method based on global hydrological data. Finally, we present a distribution map of the valid load vertical displacement of the TP and the load displacement correction for all the collected GPS stations.
... The utilized interpolation method was the inverse distance weighting (IDW), reproducing the approach employed by Mingjin et al. (2011), Teegavarapu et al. (2012, and Tuo et al. (2016). After obtaining isohyets, the characteristic precipitations were determined by calculating the water precipitation heights. ...
Article
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Rainfall monitoring by using conventional rain gauges usually presents problems related to low pluviometric station densities, failures in historical series, difficult access to the precipitation station sites, and lack of people for operating equipment. In this context, remote sensing precipitation evaluation represents a useful alternative for rainfall characterization and precipitation volume determination. The present work analyzes the estimates of rainfall total values and indications of numbers of rainfall occurrence days by using data collected by the Tropical Rainfall Measuring Mission (TRMM) satellite for the Itapemirim River basin (Espirito Santo, Brazil). There were considered historical series corresponding to twenty (20) pluviometric stations and precipitation data produced by TRMM satellite (product 3B42, version 7) monitoring for a 25-km space network, for the period between 1998 and 2015. It is concluded that the values estimated for precipitation totals and rainfall occurrences for the study area are consistent, indicating that TRMM satellite monitoring may be an adequate alternative for the evaluation of precipitation characteristics in the Itapemirim basin and in other basins that present low rainfall monitoring station densities.
... Data penginderaan jauh hasil sampel ulang kemudian dikorelasikan dengan data curah hujan observasi untuk menemukan metode terbaik untuk setiap titik. Skema titik terdekat menggunakan satu titik kontrol yang paling dekat dengan titik di mana nilai interpolasi diperlukan dan interpolasi bilinear menggunakan empat titik terdekat (Teegavarapu, 2012).Secara teknis metode titik terdekat dan metode bilinear digambarkan oleh Gambar 2. Gambar 2. Skema Titik Terdekat (kanan) dan Skema Bilinear (Babo dan Devi, 2010) ...
Conference Paper
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Data penginderaan jauh memiliki peranan penting dalam analisis iklim maupun pengisian data kosong. Namun, data tersebut memiliki resolusi yang relatif kasar sehingga memberikan informasi dalam cakupan luasan yang besar. Oleh karena itu, dalam hipotesis dinyatakan perlu dilakukan sampel ulang (resampling) untuk memperinci informasi yang ada dan diharapkan dapat lebih sesuai dengan data pengamatan. Studi ini mencoba menguji hipotesis tersebut. Data acuan yang digunakan adalah data curah hujan bulanan dari 12 stasiun BMKG yang terletak di Provinsi Maluku dan Maluku Utara yang didapatkan dari data online BMKG. Adapun data penginderaan jauh yang digunakan adalah CMORPH. Periode yang dikaji adalah Maret 2005 sampai dengan Desember 2017. Metode sampel ulang yang digunakan adalah metode bilinear dan titik terdekat. Data diekstrak dan diolah menggunakan aplikasi R-statistics dengan memperkecil resolusi menjadi 0.20, 0.15, 0.10, 0.05 dan 0.01. Kemudian dihitung korelasi antara data observasi dengan data hasil sampel ulang secara keseluruhan maupun tiap titik. Titik Stasiun Meteorologi Pattimura menunjukkan korelasi tertinggi dengan nilai korelasi 0.912 yang diperoleh dengan metode titik terdekat. Korelasi terendah diperoleh di titik Stasiun Meteorologi Oesman Sadik dengan nilai korelasi 0.457. Pada resolusi 0.05 dan 0.01, metode sampel ulang bekerja dengan optimum di hampir semua titik. Dari nilai korelasi yang ada, metode sampel ulang titik terdekat memiliki performa lebih baik dibandingkan dengan metode bilinear. Meski metode sampel ulang di beberapa titik tidak memperbaiki data awal, setidaknya di titik Stasiun Meteorologi Namlea, Sultan Babulah, Oesman Sadik dan Geser, hasil sampel ulang menunjukkan peningkatan korelasi. Hal ini menunjukkan hasil sampel ulang dapat meningkatkan korelasi data penginderaan jauh dengan data pengamatan.
... In addition, the Kriging interpolation method leads to singular values in the western TP (Figures S7b), so the accuracy of interpolations from Kriging method cannot be guaranteed. To solve this problem, we applied the grid-distance weighted average method based on GPS observations ( Figures S6 and S7), which is improved from the Grid-based spatial interpolation method (Teegavarapu et al., 2012). Therefore, using the GPS observed vertical velocities of Pan et al. (2018) TP using the grid-distance weighted average method. ...
Article
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Abstract Since the mechanism of constructing the entire earth dam projects in terms of structure, shape and type of dam is somewhat the same, problems that dams would confront in the future could be due to the lack of a decent understanding of site geotechnical characteristics regarding penetration and improvement of their foundations. Sarroud Dam is located in the north of Khorasan Razavi Province in the city of Kalat. Being located in a fault zone, it is necessary to inject the cut-off wall. Using remote sensing techniques, geographic information system, Landsat satellite imagery and field observations in this research, it was specified that the dam has been located within the range of the Sarroud Fault. According to this, the foundation of axis, overflow shoot and the sides of the dam were evaluated in terms whether or not being affected by fault activities. It was divulged that the left side is more affected than the right. In addition, topographic maps and geological maps were prepared and faults were identified. Examining drill boreholes, the following were, therefore, evaluated; mechanical rock mass tests, permeability tests, statistical studies, rock mass quality and site behaviour. It was also exposed that the left side has more permeability than the right.According to the obtained information, the zonation of the cut-off wall based which the Geotechnical parameters & permeability tests in the Arc GIS was undertaken, was, subsequently, weighed & interpolated through the neighbor method. The outcome was preparation of the zonation maps of the injection/grouting? axis at the cut-off wall. Moreover, the zonation map for the most widely-injected areas was prepared using the Hierarchy Model (AHP). Keywords: Sarroud Dam, grout injection, Geotechnical parameters, permeability, cut-off wall zonation, AHP models
Chapter
Mean areal precipitation (MAP) estimate continues to serve as one of the essential inputs to lumped hydrologic simulation models. Accurate MAP estimates require error and gap-free precipitation measurements from rain gauge monitoring networks and bias-corrected weather radar and satellite-based quantitative precipitation estimates (QPEs). MAP estimation is one of the essential tasks that need to be completed before hydrologic simulation models can be calibrated and validated. Deterministic and stochastic weighting methods for MAP estimation that use both rain gauge-based measurements and QPEs are discussed in this chapter. Several issues related to errors associated with rain gauge measurements, monitoring network density, missing data, bias issues with QPEs that affect MAP estimation are also elaborated. The advantages and limitations of methods and recommendations for use of these methods in different physiographic and topographical settings are also provided.
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Triggering hydrological simulations with climate change gridded datasets is one of the prevailing approaches in climate change impact assessment at a river basin scale, with bias correction and spatio-temporal interpolation being functions routinely used on the datasets preprocessing. The research object is to investigate the dilemma arisen when climate datasets are used, and shed light on which process—i.e., bias correction or spatio-temporal interpolation—should go first in order to achieve the maximum hydrological simulation accuracy. In doing so, the fifth generation of the European Centre for Medium Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) temperature and precipitation products of 9 × 9 km spatial resolution, which are considered as the reference data, are initially compared with the same hindcast variables of a regional climate model of 12.5 × 12.5 km spatial resolution over a specific case study basin and for a 10-year period (1991–2000). Thereafter, the climate model’s variables are (a) bias corrected followed by their spatial interpolation at the reference resolution of 9 × 9 km with the use of empirical quantile mapping and spatio-temporal kriging methods respectively, and (b) spatially downscaled and then bias corrected by using the same methods as before. The derived outputs from each of the produced dataset are not only statistically analyzed at a climate variables level, but they are also used as forcings for the hydrological simulation of the river runoff. The simulated runoffs are compared through statistical performance measures, and it is established that the discharges attributed to the bias corrected climate data followed by the spatio-temporal interpolation present a high degree of correlation with the reference ones. The research is considered a useful roadmap for the preparation of gridded climate change data before being used in hydrological modeling.
Chapter
A PhotoVoltaic (PV) plant is a power station which converts sunlight energy into electric energy. In the last decade, PV plants have become ubiquitous in several countries of the European Union, due to a valuable policy of economic incentives (e.g., feed-in tariffs). Today, this ubiquity of PV plants has paved the way to the marketing of new smart systems, designed to monitor the energy production of a PV plant grid and supply intelligent services for customer and production applications. In this chapter, we start moving in this direction by fulfilling the urgent request of PV customers and PV companies to enjoy knowledge-based managing and monitoring services, integrated within a PV plant network. In particular, we illustrate a business intelligence solution developed to monitor the efficiency of the energy production of PV plants and a data mining solution for the fault diagnosis in PV plants.
Chapter
Ubiquitous sensor stations continuously measure several geophysical variables over large zones and long (potentially unbounded) periods of time. However, observations can cover neither every space location nor every time. Interpolation, i.e., the estimation of unknown data in each location or time of interest, can be used to supplement station records. Although in GIScience there has been a tendency to treat space and time separately, there is now great interest in analyzing data in both the domains. This suggests that integrating space and time would yield better results than treating them separately, when interpolating several geophysical fields. This chapter contributes to the investigation of spatiotemporal interpolators in a remote-sensing scenario. We describe two interpolation techniques, which use trend clusters to interpolate missing data. The former performs the estimation phase by using the Inverse Distance Weighting approach, while the latter uses Kriging. Both have been adapted to a sensor network scenario. The proposed techniques have been evaluated in a large air-climate sensor network. The empirical study compares the accuracy and efficiency of both techniques.
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Based on the SPOT/VEGETATION Normalized Difference Vegetation Index (NDVI) data and daily precipitation data of 357 meteorological stations, the spatial and temporal variability of vegetation cover, measured by NDVI, and precipitation as well as their relationships are investigated in Eastern China, which is portioned into three subregions (regions I, II, and III), for the period 1998-2010. The results show that high NDVI values appear mainly in Northeastern China and in August while high precipitation (PRETOT) occurs in Southeastern China and in July (June for Southern China). Extreme precipitation days (RD95p) and amount (EPRETOT) coincide well with PRETOT. Extreme precipitation intensity (RINTEN) has a similar spatial variability to PRETOT but with a smaller seasonal variation than PRETOT. Growing season NDVI is positively correlated with PRETOT in 11.7 % of the study area (mostly in arid to subhumid regions of Northern China), where precipitation is a limiting factor for vegetation growth. In contrast, a negative correlation between growing season NDVI and PRETOT is found in 4.8 % of the study area, mostly in areas around the Yangtze River and deep Northeastern China. No significant correlations between these two variables are found for the other regions because vegetation response to precipitation is affected by other factors such as temperature, radiation, and human disturbance. On a monthly scale, there is a positive correlation between NDVI and PRETOT in May (for region II) and September (all subregions except region I). NDVI variations lag 1 month behind PRETOT in June (for region I) and October. Correlations between NDVI and RD95p, EPRETOT are similar to that with PRETOT, but the relationships between NDVI and RINTEN are relatively weaker than with PRETOT. This study provides the technical basis for agriculture development and ecological construction in Eastern China.
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Several statistical downscaling models have been developed in the past couple of decades to assess the hydrologic impacts of climate change by projecting the station-scale hydrological variables from large-scale atmospheric variables simulated by general circulation models (GCMs). This paper presents and compares different statistical downscaling models that use multiple linear regression (MLR), positive coefficient regression (PCR), stepwise regression (SR), and support vector machine (SVM) techniques for estimating monthly rainfall amounts in the state of Florida. Mean sea level pressure, air temperature, geopotential height, specific humidity, U wind, and V wind are used as the explanatory variables/predictors in the downscaling models. Data for these variables are obtained from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) re-analysis dataset and the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled Global Climate Model, version 3 (CGCM3) GCM simulations. The principal component analysis (PCA) and fuzzy c-means clustering method (FCM) are used as part of downscaling model to reduce the dimensionality of the dataset and identify the clusters in the data, respectively. Evaluation of the performances of the models using different error and statistical measures indicates that the SVM-based model performed better than all the other models in reproducing most monthly rainfall statistics at 18 sites. Output from the third-generation CGCM3 GCM for the A1B scenario was used for future projections. For the projection period 2001–10, MLR was used to relate variables at the GCM and NCEP grid scales. Use of MLR in linking the predictor variables at the GCM and NCEP grid scales yielded better reproduction of monthly rainfall statistics at most of the stations (12 out of 18) compared to those by spatial interpolation technique used in earlier studies.
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Precipitation is considered a crucial component in the hydrological cycle and changes in its spatial pattern directly influence the water resources. We compare different interpolation techniques in predicting the spatial distribution pattern of precipitation in Chongqing. Six interpolation methods, i.e., Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Diffusion Interpolation with Barrier (DIB), Kernel Interpolation with Barrier (KIB), Ordinary Kriging (OK) and Empirical Bayesian Kriging (EBK), were applied to estimate different rainfall patterns. Annual mean, rainy season and dry-season precipitation was calculated from the daily precipitation time series of 34 meteorological stations with a time span of 1991 to 2019, based on Leave-One-Out Cross-Validation (LOOCV), Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Symmetric Mean Absolute Percentage Error (SMAPE) and Nash–Sutcliffe Efficiency coefficient (NSE) as validation indexes of the applied models for calculating the error degree and accuracy. Correlation test and Spearman coefficient was performed on the estimated and observed values. A method combining Entropy Weight and Technique for Order Preference by Similarity to Ideal Solution (Entropy-Weighted TOPSIS) was introduced to rank the performance of six interpolation methods. The results indicate that interpolation technique performs better in estimating during periods of low precipitation (i.e., dry season, relative to rainy season and mean annual). The performance priorities of the six methods under the combined multiple precipitation distribution patterns are KIB > EBK > OK > RBF > DIB > IDW. Among them, KIB method has the highest accuracy which maps more accurate precipitation surfaces, with the disadvantage that estimation error is prone to outliers. EBK method is the second highest, and IDW method has the lowest accuracy with a high degree of error. This paper provides information for the application of interpolation methods in estimating rainfall spatial pattern and for water resource management of concerned regions.
Article
This study focuses on the assessment of biases from infilling missing precipitation data on the detection of long-term change using parametric and non-parametric statistical techniques. Long-term historical precipitation data available for almost 100 years at 53 rain gages in south Florida, USA, with gages having varying lengths of missing data are used for the study. Precipitation data with gaps and time series with spatial interpolated data are analyzed. Chronologically complete datasets are often used in climate variability studies by analyzing data in multiple temporal windows. The temporal windows selected in this work coincide with Atlantic multi-decadal oscillation (AMO) cool and warm phases that strongly influence precipitation extremes and characteristics in the study region. Selection of these windows has helped in evaluating the extremes derived based on infilled and unfilled data. The frequency of occurrence of precipitation extremes over a pre-specified threshold is also analyzed. Results indicate that infilled precipitation data introduce large biases in the statistical trends and over and under-estimate low and high extremes respectively. Evaluation of three extreme precipitation indices (i.e. Rx1day, R25mm and R50mm) indicates that bias increases with increase in amount of missing data. Nonparametric hypothesis tests indicate that statistical distributions of data of infilled and unfilled data are different when the data infilled is more than 5% of the entire data. Infilled data also introduced high variability in precipitation extremes in AMO cool and warm phases along with the changes in the frequency of occurrence of extreme events over a threshold.
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Crop production vulnerability to climate change in Northwest China depends upon multiple socio-ecological factors. Knowledge regarding the specific indicators and methods suitable for assessing crop production vulnerability is limited that address spatiotemporal variations across large and diverse zones. We propose an integrated assessment framework to quantify the vulnerability of crop production derived from crop yield sensitivity, exposure, and adaptive consequences across 338 counties in Northwest Chinac during 1995–2014. Maps on these indices were generated using climatic and socioeconomic data with spatial mapping method. Different clusters of crop production vulnerability were then identified by a k-means cluster method to assess the heterogeneity of vulnerability at a regional scale. Results show that the vulnerability of crop production in 338 counties varies significantly in both geographical and socioeconomic aspects, specifically, vulnerability indicators are generally higher in Minhe, Menyuan, Hualong, and Ledu, and Xayar had the lowest value of vulnerability. This indicates that adaptation strategies for regional crop production need to focus on several levels, from the improvement of adaptive ability to crop yield fluctuation by promoting irrigation agriculture and optimizing limited water resources in typical arid areas, to agriculture-related financial policies incentivizing the capital investment and technology upgrade of crop production on traditional farming regions. This study provides convincing evidence that the factors related to socioeconomic policies are particularly alarming when a crop’s risk is compared to precipitation fluctuations. We recommend these findings be used to facilitate regional agriculture planning to reduce crop production vulnerability and ensure sustainable food security in specific regions.
Chapter
The analysis of spatial data involves different procedures that typically include model estimation, spatial prediction, and simulation. Model estimation or model inference refers to determining a suitable spatial model and the “best” values for the parameters of the model. Parameter estimation is not necessary for certain simple deterministic models (e.g., nearest neighbor method), since such models do not involve any free parameters. Model selection is then used to choose the “optimal model” (based on some specified statistical criterion) among a suite of candidates.
Chapter
Flooding is the leading cause of water-related morbidity and mortality in most monsoon areas frequently facing floods.
Article
A comprehensive understanding of the thermal environment of building spaces is essential to the improvement of building energy-saving design and human comfort. However, current measurements of the thermal environment are limited by testing instruments, measurement points, etc., and only the parameters of a given measurement point can be considered rather than those of a plane covering the entire space. Besides, there are few studies on the spatial visualization of indoor thermal environment. To solve these problems, this paper proposes a method that combines point measurement and spatial interpolation to generate a spatial temperature distribution map. The exhibition hall of an office building in Shanghai was selected as an example. Eleven spatial interpolation methods (SIMs) were applied by Surfer to obtain contour maps after inputting the coordinates and air temperature of every measurement point. By comparing the root mean square errors (RMSEs) of 11 SIMs, it was found that the SIM with the smallest error was inverse distance to a power method, whose RMSE reached 0.87 °C on rainy days and 0.80 °C on sunny days. Therefore, the inverse distance to a power method was finally applied to generate a visual stacked temperature distribution map that serves as a basis for spatial design and retrofitting. The proposed method aims to improve the limitations in terms of accuracy and efficiency in the post-occupancy evaluation and make architects accurately analyse the indoor temperature distribution, which provides architects with data-based support for applying passive design strategies, thus facilitating reasonable energy-saving planning, designing, or retrofitting.
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The response of a watershed due to changes in its physical environment might result in floods, river erosions and siltations, subsequently affecting humans and biotas. Evaluating land-use changes is crucial for better assessment of hydrological conditions in a watershed system. The remote sensing imagery, field data collection, and land change modelling were used to produce the land-use maps of different spatiotemporal scale from 1989 to 2039. The generated maps are integrated into Hydrological Simulation Program-Fortran (HSPF) model, to evaluate the hydrological changes in Skudai River watershed in Malaysia. Total runoff is expected to account for 57% of the rainfall influx by 2039, a change of 2% from 1989 land-use, an indication of the low response of runoff to change in land-use. As built-up land increase by 3.39 %, the average streamflow will increase by 0.05 m3/s. It will further reduce actual evapotranspiration (AET) by 0.39%, groundwater by 0.34% and change in storage by 0.38%. The sensitivity analysis of the hydrological elements to the land-use changes indicates that AET being the most sensitive then change in storage, and total runoff showing the lowest sensitivity. The result of the study provides information on the long-term impact of land-use on the hydrology of the tropical watershed, and it can be a useful tool in the planning and management of a watershed in a different perspective.
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Surface modeling with very large data sets is challenging. An efficient method for modeling massive data sets using the high accuracy surface modeling method (HASM) is proposed, and HASM_Big is developed to handle very large data sets. A large data set is defined here as a large spatial domain with high resolution leading to a linear equation with matrix dimensions of hundreds of thousands. An augmented system approach is employed to solve the equality-constrained least squares problem (LSE) produced in HASM_Big, and a block row action method is applied to solve the corresponding very large matrix equations. A matrix partitioning method is used to avoid information redundancy among each block and thereby accelerate the model. Experiments including numerical tests and real-world applications are used to compare the performances of HASM_Big with its previous version, HASM. Results show that the memory storage and computing speed of HASM_Big are better than those of HASM. It is found that the computational cost of HASM_Big is linearly scalable, even with massive data sets. In conclusion, HASM_Big provides a powerful tool for surface modeling, especially when there are millions or more computing grid cells.
Article
To evaluate the accuracy and applicability of the TMPA 3B42-V7 precipitation product for the Lancang River basin, we used different statistical indices to explore the performance of the product in comparison to gauge data. Then, we performed a hydrologic simulation using the Variable Infiltration Capacity (VIC) hydrological model with two scenarios (Scenario I: streamflow simulation using gauge-calibrated parameters; Scenario II: streamflow simulation using 3B42-V7-recalibrated parameters) to verify the applicability of the product. The results of the precipitation analysis show good accuracy of the V7 precipitation data. The accuracy increases with the increase of both space and time scales, while time scale increases cause a stronger effect. The satellite can accurately measure most of the precipitation but tends to misidentify non-precipitation events as light precipitation events (<1 mm/day). The results of the hydrologic simulation show that the VIC hydrological model has good applicability for the Lancang River basin. However, 3B42-V7 data did not perform as well under Scenario I with the lowest Nash–Sutcliffe coefficient of efficiency (NSCE) of 0.42; Scenario II suggests that the error drops significantly and the NSCE increases to 0.70 or beyond. In addition, the simulation accuracy increases with increased temporal scale.
Article
Spatial interpolation of precipitation data is an essential input for hydrological modelling. At present, the most frequently used spatial interpolation methods for precipitation are based on the assumption of stationary in spatial autocorrelation and spatial heterogeneity. As climate change is altering the precipitation, stationary in spatial autocorrelation and spatial heterogeneity should be first analysed before spatial interpolation methods are applied. This study aims to propose a framework to understand the spatial patterns of autocorrelation and heterogeneity embedded in precipitation using Moran’s I, Getis–Ord test, and semivariogram. Variations in autocorrelation and heterogeneity are analysed by the Mann–Kendall test. The indexes and test methods are applied to the 7-day precipitation series which are corresponding to the annual maximum 7-day flood volume (P-AM7FV) upstream of the Changjiang river basin. The spatial autocorrelation of the P-AM7FV showed a statistically significant increasing trend over the whole study area. Spatial interpolation schemes for precipitation may lead to better estimation and lower error for the spatial distribution of the areal precipitation. However, owing to the changing summer monsoons, random variation in the spatial heterogeneity analysis shows a significant increasing trend, which reduces the reliability of the distributed hydrological model with the input of local or microscales.
Article
This study investigates how assimilation of surface soil moisture jointly retrieved by multiple microwave satellites affects flood simulation and forecasting based on the experiments of simulation (Sim), Open Loop (OL), and Ensemble Kalman Filter (EnKF) in small and medium-sized watersheds without gauged soil moisture. We developed a framework for data assimilation (DA) of satellite soil moisture into the WRF-Hydro model based on the EnKF algorithm. Three statistical metrics to evaluate the impacts of DA, including net error reduction, normalized error reduction, and effectiveness criterion, are all positive values (>6.0%), indicating that DA gains reduced errors. Meanwhile, the deterministic coefficients of the EnKF experiment are also greater than those of the OL experiment. It is obvious that multi-satellite retrieved soil moisture and DA technology can improve the accuracy of flood simulation and forecasting in ungauged regions and play an important and positive role in hydrological forecasting.
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Interpolating precipitation data is of prime importance to hydrological design, modeling, and water resource management. Various models have been developed that estimate spatial precipitation patterns. The purpose of this study is to analyze different precipitation interpolation schemes at different time scales in order to improve the accuracy of discharge simulations. The study was carried out in the upstream area of the Changjiang River basin. The performance of all selected methods was assessed using cross-validation schemes, with the mixed methods ultimately displaying the best performance at all three time scales. However, the differences in performance between the spatial interpolation methods decreased with increasing time scales. The unifying catchment Soil and Water Assessment Tool (SWAT), ‘abcd’, and the Budyko equation were employed at the daily, monthly, and annual scales, respectively, to simulate discharge. The performance of the discharge simulation at the monthly and annual time scales was consistent with their ranks of spatial precipitation estimation. For coarse, or long period, precipitation, there were no significant differences. However, the mixed methods performed better than the single model for the daily, or short, time scale with respect to the accuracy of the discharge simulation.
Article
With the release of Global Precipitation Measurement Integrated Multi-satellitE Retrievals for GPM products, hydrologists can obtain precipitation data with higher resolution and wider coverage. However, great uncertainties still exist in the accuracy and hydrological utility of these data in alpine and gorge regions with sparse gauge stations. In this study, the Lancang River Basin in China was used as an example, and near real-time products (IMERG-E and IMERG-L) and post-processed products (IMERG-F and TMPA 3B42-V7) were evaluated. Different indexes and methods were applied to evaluate the accuracy of these products. The variable infiltration capacity hydrological model was adopted to evaluate their hydrological utility. The following findings were obtained: (1) Compared with observed precipitation data, the near real-time products tend to underestimate, while the post-processed products tend to overestimate precipitation. The performance of the four products in winter is poor. (2) IMERG products offer improvements in two aspects: first, the near real-time products achieve good accuracy and second, the detectability and the accuracy in gorge areas have been greatly improved. (3) The near real-time products have the potential for hydrological applications. The best simulation result was obtained based on IMERG-F, followed by 3B42-V7, IMERG-E, and IMERG-L. (4) The four products can provide reliable precipitation data for the hydrological application over the Lancang River Basin.
Article
Strata in red bed areas have typical characteristics of soft-hard interbedding and high sensitivity to water. Under the comprehensive action of internal stratigraphic structure and external hydrological factors, red bed landslides have highly complex spatiotemporal characteristics, presenting significant challenges to the prevention and control of landslide disasters in red bed areas, especially for slope and tunnel engineering projects. In this study, we applied an interdisciplinary approach combining small baseline subset interferometric synthetic aperture radar (SBAS-InSAR), deep displacement monitoring, and engineering geological surveying to identify the deformation mechanisms and spatiotemporal characteristics of the Abi landslide, an individual landslide that occurred in the red bed area of Western Yunnan, China. Surface deformation time series indicated that a basic deformation range developed by March 2020. Based on InSAR results and engineering geological analysis, the landslide surface could be divided into three zones: an upper sliding zone (US), a lower uplifted zone (LU), and a toe zone (Toe). LU was affected by the structure of the sliding bed with variable inclination. Using deep displacement curves combined with the geological profile, a set of sliding surfaces were identified between different lithology. The groundwater level standardization index (GLSI) and deformation normalization index (DNI) showed different quadratic relationships between US and LU. Verification using the Pearson correlation analysis shows that the correlation coefficients between model calculated results and measured data are 0.7933 and 0.7577, respectively, indicating that the DNI-GLSI models are applicable. A fast and short-lived deformation sub stage (ID-Fast) in the initial deformation stage was observed, and ID-Fast was driven by concentrated rainfall.
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Distributed physics-based hydrology integrates a range of disciplines from soil science to radar hydrology within a geographic information system framework.
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The demand for climatological precipitation fields on a regular grid is growing dramatically as ecological and hydrological models become increasingly linked to geographic information systems that spatially represent and manipulate model output. This paper presents an analytical model that distributes point measurements of monthly and annual precipitation to regularly spaced grid cells in midlatitude regions. PRISM (Precipitation-elevation Regressions on Independent Slopes Model) brings a combination of climatological and statistical concepts to the analysis of orographic precipitation. PRISM exhibited the lowest cross-validation bias and absolute error when compared to kriging, detrended kriging, and cokriging in the Willamette River basin, Oregon. PRISM was also applied to northern Oregon and to the entire western United States; detrended kriging and cokriging could not be used, because there was no overall relationship between elevation and precipitation. Cross-validation errors in these applications were confined to relatively low levels because PRISM continually adjusts its frame of reference by using localized precipitation-DEM elevation relationships. -from Authors
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Various estimation procedures using ordinary, universal, and disjunctive cokriging are evaluated in merging rain gage measurements and radar rainfall data. The estimation procedures and the simulation experiments were described in part 1 (Seo et al., this issue) of this two-part work. In this part, the experiments are described in detail. An objective comparison scheme, devised to compare a large number of estimators, is also described. The results are presented focusing upon (1) the potential of radar-gage estimation using cokriging over radar-only estimation and gage-only estimation under widely varying conditions of gage network density and the error characteristics of radar rainfall, (2) the potential for using universal or disjunctive cokriging over ordinary cokriging, (3) how the uncertain second-order statistics affect the estimators, due to lack of rain gage measurements, and (4) how the statistical characteristics of ground truth rainfall affect the estimators.
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The demand for spatial climate data in digital form has risen dramatically in recent years. In response to this need, a variety of statistical techniques have been used to facilitate the production of GIS-compatible climate maps. However, observational data are often too sparse and unrepresentative to directly support the creation of high-quality climate maps and data sets that truly represent the current state of knowledge, An effective approach is to use the wealth of expert knowledge on the spatial patterns of climate and their relationships with geographic features, termed 'geospatial climatology', to help enhance, control, and parameterize a statistical technique. Described here is a dynamic knowledge-based framework that allows for the effective accumulation, application, and refinement of climatic knowledge, as expressed in a statistical regression model known as PRISM (parameter-elevation regressions on independent slopes model). The ultimate goal is to develop an expert system capable of reproducing the process a knowledgeable climatologist would use to create high-quality climate maps, with the added benefits of consistency and repeatability. However, knowledge must first be accumulated and evaluated through an ongoing process of model application; development of knowledge prototypes, parameters and parameter settings; testing; evaluation; and modification. This paper describes the current state of a knowledge-based framework for climate mapping and presents specific algorithms from PRISM to demonstrate how this framework is applied and refined to accommodate difficult climate mapping situations. A weighted climate-elevation regression function acknowledges the dominant influence of elevation on climate. Climate stations are assigned weights that account for other climatically important factors besides elevation. Aspect and topographic exposure, which affect climate at a variety of scales, from hill slope to windward and leeward sides of mountain ranges, are simulated by dividing the terrain into topographic facets. A coastal proximity measure is used to account for sharp climatic gradients near coastlines. A 2-layer model structure divides the atmosphere into a lower boundary layer and an upper free atmosphere layer, allowing the simulation of temperature inversions, as well as mid-slope precipitation maxima. The effectiveness of various terrain configurations at producing orographic precipitation enhancement is also estimated. Climate mapping examples are presented.
Article
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The South Florida Water Management District (SFWMD) relies on a network of nearly 300 rain gauges in order to provide rainfall data for use in operations, modeling, water supply planning, and environmental projects. However, the prevalence of convective and tropical disturbances in South Florida during the wet season presents a challenge in that the current rain gauge network may not fully capture rain events that demonstrate high spatial variability. Next Generation Radar (NEXRAD) technology offers the advantage of providing a spatial account of rainfall, although the quality of radar-rainfall measurements remains largely unknown. The comparison of rainfall estimates from a gauge-adjusted, NEXRAD-based product developed by the OneRain Company with precipitation measurements from SFWMD rain gauges was performed for the Upper and Lower Kissimmee River Basins over a four-year period from 2002 to 2005. Overall, NEXRAD was found to underestimate rainfall with respect to the rain gauges for the study period, demonstrating a radar to gauge ratio of 0.95. Further investigation of bias revealed the tendency for NEXRAD to overestimate small rainfall amounts and underestimate large rainfall amounts relative to the gauge network. The nature of bias present in the data led to the development of a radar-rain gauge relationship to predict radar precipitation estimates as a function of rain gauge measurements. The intent of this paper is to demonstrate the importance of identifying systematic offsets which may be present in radar-rainfall data before application in hydrologic analysis.
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In order to estimate rainfall magnitude at unmeasured locations, this entry to the Spatial Interpolation Comparison of 1997 (SIC'97) used 2-dimensional, anisotropic, inverse-distance weighting interpolator (IDW), with cross-validation as a method of optimizing the interpolator's parameters. A jackknife resampling was then used to reduce bias of the predictions and estimate their uncertainty. The method is easy to programme, "data driven", and fully automated. It provides a realistic estimate of uncertainty for each predicted location, and could be readily extended to 3-dimentional cases. For SIC97 purposes, the IDW was set to be an exact interpolator (smoothing parameter was set to zero), with the search radius set at the maximum extend of data. Other parameters were optimized as follows: exponent = 4, anisotropy ratio = 4.5 and anisotropy angle = 40°. The results predicted by the IDW interpolator were later compared with the actual values measured at the same locations. The overall root-mean-squared-error (RMSE) between predicted and observed rainfall for all 367 unknown locations was 6.32 mm of rain. The method was successful in predicting 50% and 65% of the exact locations of the twenty highest and lowest measurements respectively. Of the measured values, 65% (238 out of 367 data points) fell within jackknife-predicted 95% confidence intervals, uniquely constructed for each predicted location.
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Indicator cokriging (Journel 1983) is examined as a tool for real-time estimation of rainfall from rain gage measurements. The approach proposed in this work obviates real-time estimation of real-time statistics of rainfall by using ensemble or climatological statistics exclusively, and reduces computational requirements attendant to indicator cokriging by employing only a few auxiliary cutoffs in estimation of conditional probabilities. Due to unavailability of suitable rain gage measurements, hourly radar rain fall data were used for both indicator covariance estimation and a comparative evaluation. Preliminary results suggest that the indicator cokriging approach is clearly superior to its ordinary kriging counterpart, whereas the indicator kriging approach is not. The improvement is most significant in estimation of light rainfall, but drops off significantly for heavy rainfall. The lack of predictability in spatial estimation of heavy rainfall is borne out in the integral scale of indicator correlation: peaking to its maximum for cutoffs near the median, indicator correlation scale becomes increasingly smaller for larger cutoffs of rainfall depth. A derived-distribution analysis, based on the assumption that radar rainfall is a linear sum of ground-truth and a random error, suggests that, at low cutoffs, indicator correlation scale of ground-truth can significantly differ from that of radar rainfall, and points toward inclusion of rainfall intermittency, for example, within the framework proposed in this work.
Book
R. S. GOVINDARAJU and ARAMACHANDRA RAO School of Civil Engineering Purdue University West Lafayette, IN. , USA Background and Motivation The basic notion of artificial neural networks (ANNs), as we understand them today, was perhaps first formalized by McCulloch and Pitts (1943) in their model of an artificial neuron. Research in this field remained somewhat dormant in the early years, perhaps because of the limited capabilities of this method and because there was no clear indication of its potential uses. However, interest in this area picked up momentum in a dramatic fashion with the works of Hopfield (1982) and Rumelhart et al. (1986). Not only did these studies place artificial neural networks on a firmer mathematical footing, but also opened the dOOf to a host of potential applications for this computational tool. Consequently, neural network computing has progressed rapidly along all fronts: theoretical development of different learning algorithms, computing capabilities, and applications to diverse areas from neurophysiology to the stock market. . Initial studies on artificial neural networks were prompted by adesire to have computers mimic human learning. As a result, the jargon associated with the technical literature on this subject is replete with expressions such as excitation and inhibition of neurons, strength of synaptic connections, learning rates, training, and network experience. ANNs have also been referred to as neurocomputers by people who want to preserve this analogy.
Article
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.
Article
Traditional error measures (e.g. mean squared error, mean relative error) are often used in the field of water resources to evaluate the performance of models developed for modeling various hydrological processes. However, these measures may not always provide a comprehensive assessment of the performance of the model intended for a specific application. A new error measure is proposed and developed in this paper to fill the gap left by existing traditional error measures for performance evaluation. The measure quantifies the error that corresponds to the hydrologic condition and model application under consideration and also facilitates selection of the best model whenever multiple models are available for that application. FUZZY set theory is used to model the modeler's perceptions of predictive accuracy in specific applications. The development of the error measure is primarily intended for use with models that provide hydrologic time series predictions. Hypothetical and real-life examples are used to illustrate and evaluate this measure. Results indicate that use of this measure is rational and meaningful in the selection process of an appropriate model from a set of competing models
Conference Paper
The use of radar (NEXRAD) estimated rainfall data for providing information about the extreme rainfall amounts resulting from storms, hurricanes and tropical depressions is common today. Often corrections are applied to the RADAR generated rainfall data-based on what was actually measured on the ground by rain gages. Understanding and modeling the relationships between RADAR and rain gage data are essential tasks to confirm the accuracy and reliability of the former surrogate method of rainfall measurement. Conventional regression models are often used to capture these highly variant non-linear spatial and temporal relationships. This study aims to understand and model the relationships between radar (NEXRAD) estimated rainfall data and the data measured by conventional rain gages. This study proposes to investigate the use of emerging computational data modeling (inductive) techniques and develop optimal functional approximation methods for this purpose. The radar based rainfall data and rain gage data will also be analyzed to understand spatio-temporal associations. The study areas selected from upper and lower Kissimmee basins of south Florida form the test-bed for the proposed approaches and ensure the testing of the validity and operational applicability of these approaches.
Conference Paper
Deterministic and stochastic weighting methods are the most frequently used methods for infilling rainfall values at a gage based on values recorded at all other available recording gages or other sources. Radar (NEXRAD) data is also commonly used for infilling of rainfall data. Several issues that affect the infilling methods include: the historical rain gage and radar data, spatial and temporal variability of rainfall, radar-rain gage relationships, selection of spatial extent of radar data. The current study evaluates the influence of spatial and temporal variability of rainfall processes on the performance of spatial interpolation algorithms. Seasonal variation of rainfall, rainfall areas that are delineated based on physical processes affecting the genesis and morphology of rainfall processes, and other factors may affect the performance of infilling methods. All these issues are important for south Florida which experiences wide variability in rainfall in space and time. In the current study, data from several rain gages and radar (NEXRAD) data in the south Florida region are used to evaluate the influence of spatial and temporal variability of rainfall processes on the performance of methods used for infilling rain gage data.
Conference Paper
The South Florida Water Management District is responsible for managing water resources in a 46,439 square-kilometer (17,930 square-mile) region. The area extends from Orlando to Key West and from the Gulf Coast to the Atlantic Ocean and contains the country’s second largest lake. The area is also the site of a major environmental restoration project. The District operates 2,898 kilometers (1,800 miles) of canals, 22 major pump stations and 2,200 water control structures. Rainfall-based management plans are becoming more prevalent in operation of these pumps and structures. The District uses a network of over 300 active raingage stations that cover the more populated and environmentally sensitive areas under its management and provide data for this purpose. Five NEXRAD (Next Generation Weather Radar) sites operated by the National Weather Service cover the region. NEXRAD data have been used for several years at the District for weather reporting that targets operational issues. However, their use has been largely limited to visual interpretation of data by the staff as opposed to quantitative analysis. In July 2002 the District, in conjunction with three of the other four water management districts in Florida, began to acquire NEXRAD data coverage and develop a corporate database and methods for data access. Corporate access of 15-minute, raingage-adjusted NEXRAD data was a major objective of the acquisition. Four major uses of the NEXRAD data at the District were identified: operations; modeling; planning and analysis; and reporting. Each use had unique datastorage and access needs. This paper details the database design; integration with the corporate database, DBHYDRO; access methods established, including those for GIS and modeling applications; data QA/QC; data verification; and applications of the NEXRAD database.
Article
Traditional approaches to spatially weigh rainfall totals such as Thiessen polygons or inverse distance squared do not always produce an accurate estimation of the total volume of water falling over a particular area. Recent advances in weather radar technology have allowed for the estimation of rainfall rates on a rainfall grid as small as 2 km by 2 km, in 15-minute time increments. When the radar data are adjusted with the local rain gage network, volume estimates over the areas of interest have been greatly improved. Gage-adjusted radar rainfall data has numerous applications in operations and water resources management. The data are currently being used for real-time local flood prediction and large-scale operations management. The data will be useful for real-time water allocation decision support and dam operation.
Article
An ordinary cokriging procedure has been developed to optimally merge rainfall data from radars and standard rain gages. The radar-rainfall data are given in digitized form. The covariance matrices required to perform cokriging are computed from single realization data, using the ergodicity assumption. Since the ground truth and the error structure of the radar data are unknown, parameterization of the covariance between radar data and the true rainfall is required. The sensitivity of the procedure to that parameterization is analyzed within a controlled simulation experiment. The experiment is based on a hypothesized error structure for the rainfall measurements. The effect of measurement noise and network density is examined. The usefulness of the procedure to remove the bias in radar is tested. Daily data are used.
Article
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.
Article
Deterministic and stochastic weighting methods are the most frequently used methods for estimating missing rainfall values. These methods may not always provide accurate estimates due to their inability to completely characterize the spatial and temporal variability of rainfall. A new association rule mining (ARM) based spatial interpolation approach is proposed, developed and investigated in the current study to estimate missing precipitation values at a gauging station. As an integrated approach this methodology combines the power of data mining techniques and spatial interpolation approaches. Data mining concepts are used to extract and formulate rules based on spatial and temporal associations among observed precipitation data series. The rules are then used to improve the precipitation estimates obtained from spatial interpolation methods. A stochastic spatial interpolation technique and three deterministic weighting methods are used as interpolation methods in the current study. Historical daily precipitation data obtained from 15 rain gauging stations from a temperate climatic region (Kentucky, USA) are used to test this approach and derive conclusions about its efficacy for estimating missing precipitation data. Results suggest that the use of association rule mining in conjunction with a spatial interpolation technique can improve the precipitation estimates.
Article
Recent advances in geographic information systems have resulted in precision spatial analysis, with map features being geographically referenced with connected spatial data. The new GIS technology has established a link between map-based and quantitative analysis. Hypotheses of spatial patterns can be formulated and verified, removing the subjective component. This book introduces the quantitative methods associated with GIS-based spatial analysis. Chapters 1 to 3 present the basic concepts specific to GIS and spatial analysis. The specific techniques and procedures are the focus of chapters 4 to 10; single layer operations, multiple layer operations, point pattern analysis, network analysis, spatial modeling, surface analysis and grid analysis. The last chapter provides quidelines for the selection of the most appropriate method. The glossary contains definitions of GIS, spatial analysis and statistics terminology.
Article
Several point rainfall estimation techniques including the conventionally used arithmatic average and normal ratio methods, inverse-distance method, modified normal ratio method, and method of using linear programming model are applied to the Sierra-Nevada mountainous region. In the study area, the elevation difference between the rain gages range from 70 ft to 1750 ft (21m to 534m) and the distance from 10 miles to 35 miles (18km to 63km). It is found that the recently advocated inverse-distance method fails to provide a desirable result. A method is proposed which takes into account the effect of topographic elevation variation for the region. Also, the issue about the number of index stations to be used in the estimation procedure is explored and discussed.
Article
The use of precipitation data as input for conceptual hydrologic models has enhanced the need for measurements more representative of ‘true’ precipitation. Precipitation input to continuous watershed models is generally some form of mean basin precipitation estimate based on point measurements. Each point measurement can have large catch deficiencies due to wind, especially for solid precipitation. A brief review is made of past results from studies concerned with these deficiencies. New curves based on current studies are presented for wind-caused gage catch deficiencies for both rain and snow. The results of using gage catch correction factors to adjust precipitation input to a conceptual hydrologic model are presented.
Article
Climatic data are an essential input for the determination of crop water requirements. The density and location of weather stations are the important design variables for obtaining the required degree of accuracy of weather data. The planning of weather station networks should include economic considerations, and a mixture of full and partial weather stations could be a cost-effective alternative. A ‘full’ weather station is defined here as one in which all the weather variables used in the modified Penman equation are measured, and a ‘partial’ weather station is one in which some, but not all, weather variables are measured. The accuracy of reference evapotranspiration (Etr) estimates for sites located some distance from surrounding stations is dependent on measurement error, error of the estimation equation, and interpolation error. The interpolation error is affected by the spatial correlation structure of weather variables and method of interpolation. A case-study data set of 2 years of daily climatic data (1989–1990) from 17 stations in the states of Nebraska, Kansas, and Colorado was used to compare alternative network designs and interpolation methods. Root mean squared interpolation error (RMSIE) values were the criteria for evaluating Etr estimates and network performance. The kriging method gave the lowest RMSIE, followed by the inverse distance square method and the inverse distance method. Co-kriging improved the estimates still further. For a given level of performance, a mixture of full and partial weather stations would be more economical than full stations only.
Article
Two widely used procedures for optimally combining rada r- and gauge - derived rainfall are those by the OneRain Corporation and the National Weather Service (NWS). This paper statistical ly compar es values from the two schemes. We consider the area of the South Florida Water Management District (SFWMD) d uring the 2005 calendar year . Comparison s are presented f or yearly , monthly, and seasonal intervals and during Hurricane Wilma . In addition, differences between the two schemes based on h ourly precipitation data are compared with those from 6 hourly and daily accumulations which often are used in hydrologic mode ls. In summary, the paper describe s the ext ent to which the OneRain and NWS products can be used interchangeably, i.e., those situations when differences are expected to be small or
Article
This paper forms the second part of the series on application of artificial neural networks (ANNs) in hydrology. The role of ANNs in various branches of hydrology has been examined here. It is found that ANNs are robust tools for modeling many of the nonlinear hydrologic processes such as rainfall-runoff, stream flow, ground-water management, water quality simulation, and precipitation. After appropriate training, they are able to generate satisfactory results for many prediction problems in hydrology. A good physical understanding of the hydrologic process being modeled can help in selecting the input vector and designing a more efficient network. However, artificial neural networks tend to be very data intensive, and there appears to be no established methodology for design and successful implementation. For this emerging technique to find application in engineering practice, there are still some questions about this technique that must be further studied, and important aspects such as physical interpretation of ANN architecture, optimal training data set, adaptive learning, and extrapolation must be explored further. The merits and limitations of ANN applications have been discussed, and potential research avenues have been explored briefly.
Book
This book, and the associated software, have grown out of the author’s work in the field of local regression over the past several years. The book is designed to be useful for both theoretical work and in applications. Most chapters contain distinct sections introducing methodology, computing and practice, and theoretical results. The methodological and practice sections should be accessible to readers with a sound background in statistical meth- ods and in particular regression, for example at the level of Draper and Smith (1981). The theoretical sections require a greater understanding of calculus, matrix algebra and real analysis, generally at the level found in advanced undergraduate courses. Applications are given from a wide vari- ety of fields, ranging from actuarial science to sports. The extent, and relevance, of early work in smoothing is not widely appre- ciated, even within the research community. Chapter 1 attempts to redress the problem. Many ideas that are central to modern work on smoothing: local polynomials, the bias-variance trade-off, equivalent kernels, likelihood models and optimality results can be found in literature dating to the late nineteenth and early twentieth centuries. The core methodology of this book appears in Chapters 2 through 5. These chapters introduce the local regression method in univariate and multivariate settings, and extensions to local likelihood and density estima- tion. Basic theoretical results and diagnostic tools such as cross validation are introduced along the way. Examples illustrate the implementation of the methods using the locfit software. The remaining chapters discuss a variety of applications and advanced topics: classification, survival data, bandwidth selection issues, computa- vi tion and asymptotic theory. Largely, these chapters are independent of each other, so the reader can pick those of most interest. Most chapters include a short set of exercises. These include theoretical results; details of proofs; extensions of the methodology; some data analysis examples and a few research problems. But the real test for the methods is whether they provide useful answers in applications. The best exercise for every chapter is to find datasets of interest, and try the methods out! The literature on mathematical aspects of smoothing is extensive, and coverage is necessarily selective. I attempt to present results that are of most direct practical relevance. For example, theoretical motivation for standard error approximations and confidence bands is important; the reader should eventually want to know precisely what the error estimates represent, rather than simply asuming software reports the right answers (this applies to any model and software; not just local regression and loc- fit!). On the other hand, asymptotic methods for boundary correction re- ceive no coverage, since local regression provides a simpler, more intuitive and more general approach to achieve the same result. Along with the theory, we also attempt to introduce understanding of the results, along with their relevance. Examples of this include the discussion of non-identifiability of derivatives (Section 6.1) and the problem of bias estimation for confidence bands and bandwidth selectors (Chapters 9 and 10).
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In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface. These irregularly-spaced locations, hence referred to as “data points,” may have diverse meanings: in meterology, weather observation stations; in geography, surveyed locations; in city and regional planning, centers of data-collection zones; in biology, observation locations. It is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point. In order to display these data in some type of contour map or perspective view, to compare them with data for the same region based on other data points, or to analyze them for extremes, gradients, or other purposes, it is extremely useful, if not essential, to define a continuous function fitting the given values exactly. Interpolated values over a fine grid may then be evaluated. In using such a function it is assumed that the original data are without error, or that compensation for error will be made after interpolation.
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A comparison of 13 different methods of estimating mean areal rainfall was made on two areas in New Mexico, U.S.A., and one area in Great Britain. Daily, monthly and yearly rainfall data were utilized. All methods, in general, yielded comparable estimates, especially for yearly values. This suggested that a simpler method would be preferable for estimating mean areal rainfall in these areas.
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Complete monthly series of precipitation data have been generated for 932 stations run by the Instituto Nacional de Meteorología (INM) in Andalusia (Andalucía, southern region of Spain) and some adjacent areas for the period 1961–2000 using a new method for the estimation of missing data. The proposed method fills in the gaps in the climatological series for a target station using precipitation data from neighbouring stations with a similar precipitation pattern. Particular emphasis is made in the consideration of the precipitation data uncertainty. A set of possible estimates for the missing data are obtained assuming a linear relationship between the target station and the selected neighbour stations. The final imputed value is the median of the previously evaluated estimates distribution. This approach also provides the uncertainty of the missing data estimate. As an application, the suggested approach is used to obtain a precipitation map of Andalusia, as well as the average annual series for the examined period. Copyright © 2008 Royal Meteorological Society
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Long-term daily climatological data are important to study forest damage and simulate tree growth, but they are scarce in forested areas because observational records are often scarce. At the eight Bavarian forest sites, we examined six interpolation methods and established empirical transfer functions relating observed forest climate data to the climate data of German weather stations. Based on our comparisons, a technique is developed and used to reconstruct 31-year daily forest climatological data at six forest sites. The reconstructed climate data were then used to calculate four meteorological stress factors which are of importance to forest studies. Finally, the uncertainties, temporal and spatial variation of these stress factors were discussed.
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One of the problems which often arises in engineering hydrology is to estimate data at a given site because either the data are missing or the site is ungaged. Such estimates can be made by spatial interpolation of data available at other sites. A number of spatial interpolation techniques are available today with varying degrees of complexity. It is the intent of this paper to compare the applicability of various proposed interpolation techniques for estimating annual precipitation at selected sites. The interpolation techniques analyzed include the commonly used Thiessen polygon, the classical polynomial interpolation by least-squares or Lagrange approach, the inverse distance technique, the multiquadric interpolation, the optimal interpolation and the Kriging technique. Thirty years of annual precipitation data at 29 stations located in the Region II of the North Central continental United States have been used for this study. The comparison is based on the error of estimates obtained at five selected sites. Results indicate that the Kriging and optimal interpolation techniques are superior to the other techniques. However, the multiquadric technique is almost as good as those two. The inverse distance interpolation and the Thiessen polygon gave fairly satisfactory results while the polynomial interpolation did not produce good results.