Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

Abstract

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naïve approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Teegavarapu, R.S.V., 2012. Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records. Hydrological Sciences Journal, 57 (3), 383–406.     

Evaluation of nonlinear models for precipitation forecasting

Prediction of factors affecting water resources systems is important for their design and operation. In hydrology, wavelet analysis (WA) is known as a new method for time series analysis. In this study, WA was combined with an artificial neural network (ANN) for prediction of precipitation at Varayeneh station, western Iran. The results obtained were compared with the adaptive neural fuzzy inference system (ANFIS) and ANN. Moreover, data on relative humidity and temperature were employed in addition to rainfall data to examine their influence on precipitation forecasting. Overall, this study concluded that the hybrid WANN model outperformed the other models in the estimation of maxima and minima, and is the best at forecasting precipitation. Furthermore, training and transfer functions are recommended for similar studies of precipitation forecasting.     

Effective probability distribution approximation for the reconstruction of missing data

Stochastic Environmental Research and Risk Assessment - Spatially distributed processes can be modeled as random fields. The complex spatial dependence is then incorporated in the joint probability...     

Comparative study of fuzzy evidential reasoning and fuzzy rule-based approaches: an illustration for water quality assessment in distribution networks

This paper presents the use of two multi-criteria decision-making (MCDM) frameworks based on hierarchical fuzzy inference engines for the purpose of assessing drinking water quality in distribution networks. Incommensurable and uncertain water quality parameters (WQPs) at various sampling locations of the water distribution network (WDN) are monitored. Two classes of WQPs including microbial and physicochemical parameters are considered. Partial, incomplete and subjective information on WQPs introduce uncertainty to the water quality assessment process. Likewise, conflicting WQPs result in a partially reliable assessment of the quality associated with drinking water. The proposed methodology is based on two hierarchical inference engines tuned using historical data on WQPs in the WDN and expert knowledge. Each inference engine acts as a decision-making agent specialized in assessing one aspect of quality associated with drinking water. The MCDM frameworks were developed to assess the microbial and physicochemical aspects of water quality assessment. The MCDM frameworks are based on either fuzzy evidential or fuzzy rule-based inference. Both frameworks can interpret and communicate the relative quality associated with drinking water, while the second is superior in capturing the nonlinear relationships between the WQPs and estimated water quality. More comprehensive rules will have to be generated prior to reliable water quality assessment in real-case situations. The examples presented here serve to demonstrate the proposed frameworks. Both frameworks were tested through historical data available for a WDN, and a comparison was made based on their performance in assessing levels of water quality at various sampling locations of the network.     

Statistical corrections of spatially interpolated missing precipitation data estimates

Spatial interpolation methods used for estimation of missing precipitation data generally under and overestimate the high and low extremes, respectively. This is a major limitation that plagues all spatial interpolation methods as observations from different sites are used in local or global variants of these methods for estimation of missing data. This study proposes bias‐correction methods similar to those used in climate change studies for correcting missing precipitation estimates provided by an optimal spatial interpolation method. The methods are applied to post‐interpolation estimates using quantile mapping, a variant of equi‐distant quantile matching and a new optimal single best estimator (SBE) scheme. The SBE is developed using a mixed‐integer nonlinear programming formulation. K‐fold cross validation of estimation and correction methods is carried out using 15 rain gauges in a temperate climatic region of the U.S. Exhaustive evaluation of bias‐corrected estimates is carried out using several statistical, error, performance and skill score measures. The differences among the bias‐correction methods, the effectiveness of the methods and their limitations are examined. The bias‐correction method based on a variant of equi‐distant quantile matching is recommended. Post‐interpolation bias corrections have preserved the site‐specific summary statistics with minor changes in the magnitudes of error and performance measures. The changes were found to be statistically insignificant based on parametric and nonparametric hypothesis tests. The correction methods provided improved skill scores with minimal changes in magnitudes of several extreme precipitation indices. The bias corrections of estimated data also brought site‐specific serial autocorrelations at different lags and transition states (dry‐to‐dry, dry‐to‐wet, wet‐to‐wet and wet‐to‐dry) close to those from the observed series. Bias corrections of missing data estimates provide better serially complete precipitation time series useful for climate change and variability studies in comparison to uncorrected filled data series. Copyright © 2013 John Wiley & Sons, Ltd.     

华北地区降水事件变化和暴雨事件减少原因分析

使用北京、天津、河北、山西的37个气象观测站的1961~2008年逐日降水资料和NCEP、EC环流资料,对华北降水事件和暴雨事件减少原因进行分析.结果表明,华北地区盛夏暴雨事件对夏季降水量和全年降水量变化有重要影响,近50年盛夏暴雨事件呈显著线性减少趋势,这与东亚夏季风减弱使得从南边界进入华北的水汽通量大量减少以及副热带高压位置南移有关.此外,盛夏暴雨事件减少还与印度对流减弱和菲律宾对流加强、125°E越赤道气流减弱和145°E越赤道气流加强有很好的对应关系.这为认识华北降水减少变化提供了科学依据.     

A multi-sensor evaluation of precipitation uncertainty for landslide-triggering storm events

Extreme precipitation can have profound consequences for communities, resulting in natural hazards such as rainfall-triggered landslides that cause casualties and extensive property damage. A key challenge to understanding and predicting rainfall-triggered landslides comes from observational uncertainties in the depth and intensity of precipitation preceding the event. Practitioners and researchers must select from a wide range of precipitation products, often with little guidance. Here we evaluate the degree of precipitation uncertainty across multiple precipitation products for a large set of landslide-triggering storm events and investigate the impact of these uncertainties on predicted landslide probability using published intensity–duration thresholds. The average intensity, peak intensity, duration, and NOAA-Atlas return periods are compared ahead of 177 reported landslides across the continental United States and Canada. Precipitation data are taken from four products that cover disparate measurement methods: near real-time and post-processed satellite (IMERG), radar (MRMS), and gauge-based (NLDAS-2). Landslide-triggering precipitation was found to vary widely across precipitation products with the depth of individual storm events diverging by as much as 296 mm with an average range of 51 mm. Peak intensity measurements, which are typically influential in triggering landslides, were also highly variable with an average range of 7.8 mm/h and as much as 57 mm/h. The two products more reliant upon ground-based observations (MRMS and NLDAS-2) performed better at identifying landslides according to published intensity–duration storm thresholds, but all products exhibited hit ratios of greater than 0.56. A greater proportion of landslides were predicted when including only manually verified landslide locations. We recommend practitioners consider low-latency products like MRMS for investigating landslides, given their near-real time data availability and good performance in detecting landslides. Practitioners would be well-served considering more than one product as a way to confirm intense storm signals and minimize the influence of noise and false alarms.     

电离层三维层析成像的自适应联合迭代重构算法

在电离层层析成像过程中,联合迭代重构算法是一种常用的反演算法.然而,该算法迭代收敛较慢,反演结果精度不高.为此,本文发展了一种自适应的联合迭代重构算法,该算法利用上一轮的电离层电子密度反演结果,自适应地调整松弛因子和加权参数.通过模拟数据和实测数据对该算法的反演结果进行了验证,并将得到的反演结果与电离层测高仪数据进行了比较,结果表明,该算法能够有效地反演电离层电子密度,且反演结果精度优于常用的联合迭代重构算法.     

Artificial neural network models for forecasting monthly precipitation in Jordan

Forecasting precipitation in arid and semi-arid regions, in Jordan in the Middle East for example, has particular importance since precipitation is the unique source of water in such regions. In this study, 1-month ahead precipitation forecasts are made using artificial neural network (ANN) models. Feed forward back propagation (FFBP), radial basis function (RBF) and generalized regression type ANNs are used and compared with a simple multiple linear regression (MLR) model. The models are tested on monthly total precipitation recorded at three meteorological stations (Baqura, Amman and Safawi) from different climatological regions in Jordan. For the three stations, it is found that the best calibrated model is FFBP with respect to all performance criteria used in the study, including determination coefficient, mean square error, mean absolute error, the slope and the intercept in the best-fit linear line of the scatter diagram. In the validation stage, FFBP is again the best model in Baqura and Amman. However, in Safawi, the driest station, not only FFBP but also RBF and MLR perform equally well depending on the performance criterion under consideration.     

Earthquake hazard assessment in the Zagros Orogenic Belt of Iran using a fuzzy rule-based model

Producing accurate seismic hazard map and predicting hazardous areas is necessary for risk mitigation strategies. In this paper, a fuzzy logic inference system is utilized to estimate the earthquake potential and seismic zoning of Zagros Orogenic Belt. In addition to the interpretability, fuzzy predictors can capture both nonlinearity and chaotic behavior of data, where the number of data is limited. In this paper, earthquake pattern in the Zagros has been assessed for the intervals of 10 and 50 years using fuzzy rule-based model. The Molchan statistical procedure has been used to show that our forecasting model is reliable. The earthquake hazard maps for this area reveal some remarkable features that cannot be observed on the conventional maps. Regarding our achievements, some areas in the southern (Bandar Abbas), southwestern (Bandar Kangan) and western (Kermanshah) parts of Iran display high earthquake severity even though they are geographically far apart.     

Cluster-based fuzzy models for groundwater flow in the unsaturated zone

In this paper fuzzy models are used as an alternative to describe groundwater flow in the unsaturated zone. The core of these models consists of a fuzzy rule-based model of the Takagi–Sugeno type. Various fuzzy clustering algorithms are compared in the data-driven identification of these Takagi–Sugeno models. The performance of the resulting fuzzy models is evaluated on the training surface on which they were identified, and on time series measurements of water content values obtained through an experiment carried out by the non-vegetated terrain (NVT) workgroup of the European Microwave Signature Laboratory (EMSL) (see [Mancini M, Hoeben R, Troch PA. Multifrequency radar observations of bare surface soil moisture content: a laboratory experiment. Water Resour Res 1999;35(6):1827–38] and [Hoeben R, Troch PA. Assimilation of active microwave observation data for soil moisture profile estimation. Water Resour Res 2000;36(10):2805–19]). Despite higher errors at the borders of high water content values in the training surface, good results are obtained on the simulation of the time series.     

Entropy inference of recurrence models for variability analysis of extreme events

A complete methodology is developed to analyze the recurrence of extreme environmental events and its variability as time without further events elapses. Firstly we investigate the conditioned recurrence inference problem consisting in the selection of a probability model for the interarrival time between extreme events, given a contexto-factual evidence conditioned by the time elapsed since the last of such events. Two ways to include this condition can be considered, which yield alternative conditioned evidences and convert the former problem into two distinct ones, thus giving rise to a possible consistency violation. These problems are formalized within the logical probability framework, in a plausible logic language that allows a suitable expression of the available observational data. They are solved using the REF relative entropy method with fractile constraints, and their solutions are compared at all inference levels. It is concluded that the two conditioning ways are not really mutually exclusive and that a unique global solution to the conditioned inference can be obtained using this procedure. An example illustrates an application of the methodology to the variability analysis of the recurrence time between historical inundations of the Guadalquivir river in Spain, as time elapses with no new floods.Acknowledgments. Support for this work was provided by DGI of Spain as the grant REN2000-2988-E/CLI and the research project REN2002-01337/CLI.     

Comparison of SDSM and LARS-WG for simulation and downscaling of extreme precipitation events in a watershed

Future climate projections of Global Climate Models (GCMs) under different emission scenarios are usually used for developing climate change mitigation and adaptation strategies. However, the existing GCMs have only limited ability to simulate the complex and local climate features, such as precipitation. Furthermore, the outputs provided by GCMs are too coarse to be useful in hydrologic impact assessment models, as these models require information at much finer scales. Therefore, downscaling of GCM outputs is usually employed to provide fine-resolution information required for impact models. Among the downscaling techniques based on statistical principles, multiple regression and weather generator are considered to be more popular, as they are computationally less demanding than the other downscaling techniques. In the present study, the performances of a multiple regression model (called SDSM) and a weather generator (called LARS-WG) are evaluated in terms of their ability to simulate the frequency of extreme precipitation events of current climate and downscaling of future extreme events. Areal average daily precipitation data of the Clutha watershed located in South Island, New Zealand, are used as baseline data in the analysis. Precipitation frequency analysis is performed by fitting the Generalized Extreme Value (GEV) distribution to the observed, the SDSM simulated/downscaled, and the LARS-WG simulated/downscaled annual maximum (AM) series. The computations are performed for five return periods: 10-, 20-, 40-, 50- and 100-year. The present results illustrate that both models have similar and good ability to simulate the extreme precipitation events and, thus, can be adopted with confidence for climate change impact studies of this nature.     

Formation of homogeneous regions for regional frequency analysis of extreme precipitation events in the Czech Republic

Extreme high precipitation amounts are among environmental events with the most disastrous consequences for human society. This paper deals with the identification of ‘homogeneous regions’ according to statistical characteristics of precipitation extremes in the Czech Republic, i.e. the basic and most important step toward the regional frequency analysis. Precipitation totals measured at 78 stations over 1961–2000 are used as an input dataset. Preliminary candidate regions are formed by the cluster analysis of site characteristics, using the average-linkage clustering and Ward’s method. Several statistical tests for regional homogeneity are utilized, based on the 10-yr event and the variation of L-moment statistics. In compliance with results of the tests, the area of the Czech Republic has been divided into four homogeneous regions. The findings are supported by simulation experiments proposed to evaluate stability of the test results. Since the regions formed reflect also climatological differences in precipitation regimes and synoptic patterns causing high precipitation amounts, their future application may not be limited to the frequency analysis of extremes.     

Comparison of transfer functions in statistical downscaling models for daily temperature and precipitation over Canada

This study compares three linear models and one non-linear model, specifically multiple linear regression (MLR) with ordinary least squares (OLS) estimates, robust regression, ridge regression, and artificial neural networks (ANNs), to identify an appropriate transfer function in statistical downscaling (SD) models for the daily maximum and minimum temperatures (T_max and T_min) and daily precipitation occurrence and amounts (P_occ and P_amount). This comparison was made over twenty-five observation sites located in five different Canadian provinces (British Columbia, Saskatchewan, Manitoba, Ontario, and Québec). Reanalysis data were employed as atmospheric predictor variables of SD models. Predictors of linear transfer functions and ANN were selected by linear correlations coefficient and mutual information, respectively. For each downscaled case, annual and monthly models were developed and analysed. The monthly MLR, annual ANN, annual ANN, and annual MLR yielded the best performance for T_max, T_min, P_occ and P_amont according to the modified Akaike information criterion (AICu). A monthly MLR is recommended for the transfer functions of the four predictands because it can provide a better performance for the T_max and as good performance as the annual MLR for the T_min, P_occ, and P_amount. Furthermore, a monthly MLR can provide a slightly better performance than an annual MLR for extreme events. An annual MLR approach is also equivalently recommended for the transfer functions of the four predictands because it showed as good a performance as monthly MLR in spite of its mathematical simplicity. Robust and ridge regressions are not recommended because the data used in this study are not greatly affected by outlier data and multicollinearity problems. An annual ANN is recommended only for the T_min, based on the best performance among the models in terms of both the RMSE and AICu.     

An adaptive hybrid EnKF-OI scheme for efficient state-parameter estimation of reactive contaminant transport models

Reactive contaminant transport models are used by hydrologists to simulate and study the migration and fate of industrial waste in subsurface aquifers. Accurate transport modeling of such waste requires clear understanding of the system’s parameters, such as sorption and biodegradation. In this study, we present an efficient sequential data assimilation scheme that computes accurate estimates of aquifer contamination and spatially variable sorption coefficients. This assimilation scheme is based on a hybrid formulation of the ensemble Kalman filter (EnKF) and optimal interpolation (OI) in which solute concentration measurements are assimilated via a recursive dual estimation of sorption coefficients and contaminant state variables. This hybrid EnKF-OI scheme is used to mitigate background covariance limitations due to ensemble under-sampling and neglected model errors. Numerical experiments are conducted with a two-dimensional synthetic aquifer in which cobalt-60, a radioactive contaminant, is leached in a saturated heterogeneous clayey sandstone zone. Assimilation experiments are investigated under different settings and sources of model and observational errors. Simulation results demonstrate that the proposed hybrid EnKF-OI scheme successfully recovers both the contaminant and the sorption rate and reduces their uncertainties. Sensitivity analyses also suggest that the adaptive hybrid scheme remains effective with small ensembles, allowing to reduce the ensemble size by up to 80% with respect to the standard EnKF scheme.