Selecting best mapping strategies for storm runoff modeling in a mountainous semi‐arid area

Accurate runoff and soil erosion modeling is constrained by data availability, particularly for physically based models such as OpenLISEM that are data demanding, as the processes are calculated on a cell‐by‐cell basis. The first decision when using such models is to select mapping units that best reflect the spatial variability of the soil and hydraulic properties in the catchment. In environments with limited data, available maps are usually generic, with large units that may lump together the values of the soil properties, affecting the spatial patterns of the predictions and output values in the outlet. Conversely, the output results may be equally acceptable, following the principle of equifinality. To studyhow the mapping method selected affects the model outputs, four types of input maps with different degrees of complexity were created: average values allocated to general soil map units (ASG1), average values allocated to detailed map units (ASG2), values interpolated by ordinary kriging (OK) and interpolated by kriging with external drift (KED). The study area was Ribeira Seca, a 90 km² catchment located in Santiago Island, Cape Verde (West Africa), a semi‐arid country subject to scarce but extreme rainfall during the short tropical summer monsoon. To evaluate the influence of rainfall on runoff and erosion, two storm events with different intensity and duration were considered. OK and KED inputs produced similar results, with the latter being closer to the observed hydrographs. The highest soil losses were obtained with KED (43 ton ha^{? 1} for the strongest event). To improve the results of soil loss predictions, higher accurate spatial information on the processes is needed; however, spatial information of input soil properties alone is not enough in complex landscapes. The results demonstrate the importance of selecting the appropriate mapping strategy to obtain reliable runoff and erosion estimates. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimating threshold-exceeding probability maps of environmental variables with Markov chain random fields

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

Copula-based geostatistical modeling of continuous and discrete data including covariates

It is common in geostatistics to use the variogram to describe the spatial dependence structure and to use kriging as the spatial prediction methodology. Both methods are sensitive to outlying observations and are strongly influenced by the marginal distribution of the underlying random field. Hence, they lead to unreliable results when applied to extreme value or multimodal data. As an alternative to traditional spatial modeling and interpolation we consider the use of copula functions. This paper extends existing copula-based geostatistical models. We show how location dependent covariates e.g. a spatial trend can be accounted for in spatial copula models. Furthermore, we introduce geostatistical copula-based models that are able to deal with random fields having discrete marginal distributions. We propose three different copula-based spatial interpolation methods. By exploiting the relationship between bivariate copulas and indicator covariances, we present indicator kriging and disjunctive kriging. As a second method we present simple kriging of the rank-transformed data. The third method is a plug-in prediction and generalizes the frequently applied trans-Gaussian kriging. Finally, we report on the results obtained for the so-called Helicopter data set which contains extreme radioactivity measurements.     

Spatial variability of liquefaction potential in regional mapping using CPT and SPT data

Cone penetration test (CPT) and standard penetration test (SPT) are widely used for the site specific evaluation of liquefaction potential and are getting increased use in the regional mapping of liquefaction hazard. This paper compares CPT and SPT-based liquefaction potential characterizations of regional geologic units using the liquefaction potential index (LPI) across the East Bay of the San Francisco Bay, California, USA and examines the statistical and spatial variability of LPI across and within geologic units. Overall, CPT-based LPI characterizations result in higher hazard than those derived from the SPT. This bias may result from either mis-classifications of soil type in the CPT or a bias in the CPT simplified procedure for liquefaction potential. Regional mapping based on cumulative distribution of LPI values show different results depending on which dataset is used. For both SPT and CPT-based characterizations, the geologic units in the area have broad LPI distributions that overlap between units and are not distinct from the population as a whole. Regional liquefaction classifications should therefore give a distribution, rather than a single hazard rating that does not provide for variability within the area. The CPT-based LPI values have a higher degree of spatial correlation and a lower variance over a greater distance than those estimated from SPTs. As a result, geostatistical interpolation can provide a detailed map of LPI when densely sampled CPT data are available. The statistical distribution of LPI within specific geologic units and interpolated maps of LPI can be used to understand the spatial variability of liquefaction potential.     

Towards generic real-time mapping algorithms for environmental monitoring and emergency detection

Real-time analysis of data reported by environmental monitoring networks poses a number of challenges, one of which is the conversion of point measurements of phenomena that display some spatial dependence into maps. This is the case for the many variables that cannot be monitored efficiently over large regions by satellites. Environmental pollutants, radiation levels, rainfall fields and seismic activity are but a few of these variables that are usually interpolated for the production of maps. These maps will then further serve as an essential support for decision-making. Ideally, in order to allow real-time assessments and minimize human intervention in case of hazards and emergencies that are frequently linked to the above mentioned variables (e.g. air pollution peaks, nuclear accidents, flash-floods, earthquakes), these maps should be established in near real time and thus automatically. The ability of real-time mapping systems running in the routine mode to be able to cope with extreme events is not straightforward, and few systems are today used automatically for both monitoring the environment and triggering early warnings in case of necessity. Alternatively, adopting a decision-centered view of environmental monitoring and mapping systems allows us to re-formulate their final objective as a classification problem that consists of discriminating routine against emergency conditions, or background information against outliers. It is the purpose of this paper to give an overview of the main challenges for developing and evaluating automatic mapping systems for critical environmental variables, as well as to discuss steps toward the development of generic real-time mapping algorithms.     

A P-spline ANOVA type model in space-time disease mapping

One of the main objectives in disease mapping is the identification of temporal trends and the production of a series of smoothed maps from which spatial patterns of mortality risks can be monitored over time. When studying rare diseases, conditional autoregressive models have been commonly used for smoothing risks. In this work, a P-spline ANOVA type model is used instead. The model is anisotropic and explicitly considers different smooth terms for space, time, and space-time interaction avoiding, in addition, model identifiability problems. The mean squared error of the log-risk predictor is derived accounting for the variability associated to the estimation of the smoothing parameters. The procedure is illustrated analyzing Spanish prostate cancer mortality data in the period 1975–2008.     

Wavelet analysis residual kriging vs. neural network residual kriging

 This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method – wavelet analysis residual kriging (WARK) – is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses artificial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.     

一种综合地学数据的矿产资源潜力制图方法

研究适应信息化时代特征的矿产资源潜力制图新技术、新方法对推动矿产资源评价理论与技术的发展具有重要的意义.笔者把GIS技术、图像分类算法和空间统计学理论进行有机集成,在空间统计学的空间结构分析技术和遥感图像纹理分类算法的基础上,提出了一种以综合地学数据（地质、地球物理、地球化学和遥感图像数据等）为基本数据源的矿产资源潜力自动制图方法.该方法的技术流程为：①数据准备,即对地球物理和地球化学勘探数据进行预处理,生成一个物化遥综合图像文件;②图像空间结构性分析和纹理图像生成,以综合地学图像为研究对象,用空间统计学的结构分析技术研究地学数据综合图像的空间结构性,生成纹理图像;③纹理图像多元分类,用实验变差函数纹理分类方法对研究区进行多元分类,生成分类专题图;④分类后处理,用叠置分析修正空间分类结果,生成区域矿产资源潜力分布图.     

Space–time forecasting of groundwater level using a hybrid soft computing model

Forecasting of space–time groundwater level is important for sparsely monitored regions. Time series analysis using soft computing tools is powerful in temporal data analysis. Classical geostatistical methods provide the best estimates of spatial data. In the present work a hybrid framework for space–time groundwater level forecasting is proposed by combining a soft computing tool and a geostatistical model. Three time series forecasting models: artificial neural network, least square support vector machine and genetic programming (GP), are individually combined with the geostatistical ordinary kriging model. The experimental variogram thus obtained fits a linear combination of a nugget effect model and a power model. The efficacy of the space–time models was decided on both visual interpretation (spatial maps) and calculated error statistics. It was found that the GP–kriging space–time model gave the most satisfactory results in terms of average absolute relative error, root mean square error, normalized mean bias error and normalized root mean square error.     

A comparison of methods for spatial relative risk mapping of human neural tube defects

Birth defects are a major cause of infant mortality and disability in many parts of the world. Yet the etiology of neural tube defects (NTDs), the most common types of birth defects, is still unknown. The construction and analysis of maps of disease incidence data can help explain the geographical distribution of NTDs and can point to possible environmental causes of these birth defects. We compared two methods of mapping spatial relative risk of NTDs: (1) hierarchical Bayesian model, and (2) Spatial filtering method. Heshun county, which has the highest rate of NTDs in China, was selected as the region of interest. Both methods were used to produce a risk map of NTDs for rural Heshun for 1998–2001. Hierarchical Bayesian model estimated the relative risk for any given village in Heshun by “borrowing” strength from other villages in the study region. It did not remove all the random spatial noise in the rude disease rate. There were several areas of high incidence scattered around its risk map with no readily apparent pattern. The spatial filtering method calculated the relative risk for all villages based on a series of circulars. The risk map from the spatial filtering method revealed some spatial clusters of NTDs in Heshun. These two methods differed in their ability to map the spatial relative risk of NTDs. Distributional assumption of relative risk and the target of the risk assessment should be taken into consideration when choosing which method to use.     

Investigating hydrogeomorphic floodplain mapping performance with varying DTM resolution and stream order

Hydrogeomorphic models allow parsimonious, fast and effective floodplain extent mapping using topographic data as the main input. Hydrogeomorphic approaches enforce the principle that floodplains are well-distinguished and unique landscape features within river corridors. We investigated the sensitivity of a hydrogeomorphic floodplain delineation algorithm, based on a hydrological power law, relating flow depth to contributing area, digital terrain model (DTM) resolution and river network hierarchy. In addition, we compared the results to other common floodplain mapping methods using standard flood-hazard maps as a reference. Taking the Arno River Basin, Italy, as a case study, our results show a dependency between the optimal power law parameters and DTM resolution, with larger parameter values required to reach optimal consistency with flood-hazard maps as DTM resolution increased. Floodplain mapping performance was also found to depend on stream order. We further tested the model consistency at a larger scale to evaluate its performance with respect to inundation maps in Hungary, Italy, Spain and the UK. Our study suggests that pre-defined power law parameters can be assumed, considering DTM resolution and stream order, supporting the use of the presented hydrogeomorphic model for large-scale floodplain mapping in ungauged basins where reference flood-hazard maps are not available.     

Geostatistical simulation of random fields with bivariate isofactorial distributions by adding mosaic models

This work deals with the geostatistical simulation of a family of stationary random field models with bivariate isofactorial distributions. Such models are defined as the sum of independent random fields with mosaic-type bivariate distributions and infinitely divisible univariate distributions. For practical applications, dead leaf tessellations are used since they provide a wide range of models and allow conditioning the realizations to a set of data via an iterative procedure (simulated annealing). The model parameters can be determined by comparing the data variogram and madogram, and enable to control the spatial connectivity of the extreme values in the realizations. An illustration to a forest dataset is presented, for which a negative binomial model is used to characterize the distribution of coniferous trees over a wooded area.     

Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations

An approach is presented for identifying statistical characteristics of stratigraphies from borehole and hydraulic data. The approach employs a Markov-chain based geostatistical framework in a stochastic inversion. Borehole data provide information on the stratigraphy while pressure and flux data provide information on the hydraulic performance of the medium. The use of Markov-chain geostatistics as opposed to covariance-based geostatistics can provide a more easily interpreted model geologically and geometrically. The approach hinges on the use of mean facies lengths (negative inverse auto-transition rates) and mean transition lengths (inverse cross-transition rates) as adjustable parameters in the stochastic inversion. Along with an unconstrained Markov-chain model, simplifying constraints to the Markov-chain model, including (1) proportionally-random and (2) symmetric spatial correlations, are evaluated in the stochastic inversion. Sensitivity analyses indicate that the simplifying constraints can facilitate the inversion at the cost of spatial correlation model generality. Inverse analyses demonstrate the feasibility of this approach, indicating that despite some low parameter sensitivities, all adjustable parameters do converge for a sufficient number of ensemble realizations towards their “true” values. This paper extends the approach presented in Harp et al. (doi:, 2008) to (1) statistically characterize the hydraulic response of a geostatistical model, thereby incorporating an uncertainty analysis directly in the inverse method, (2) demonstrate that a gradient-based optimization strategy is sufficient, thereby providing relative computational efficiency compared to global optimization strategies, (3) demonstrate that the approach can be extended to a 3-D analysis, and (4) introduce the use of mean facies lengths and mean transition lengths as adjustable parameters in a geostatistical inversion, thereby allowing the approach to be extended to greater than two category Markov-chain models.     

Precipitation regional extreme mapping as a tool for ungauged areas and the assessment of climate changes

The spatial‐temporal characteristics of mean annual daily maximum precipitation events in the upper Yangtze River basin in China are examined using a framework termed precipitation regional extreme mapping (PREM). The framework consists of regional analyses and mapping methods, which have the capability to assess the presence or absence of climate change. The findings confirm the homogeneous regions identified by Wang (2002) using a heterogeneity measure, where all three regions have heterogeneity less than 1.0. The Pearson type III (PE3) distribution was found to be acceptable for all three regions, while the generalized extreme‐value distribution performs better than PE3 for Region I (eastern portion of the upper Yangtze basin). Two indices, root mean square error and mean bias, were used to access the performance of the extreme map, and the results show that the map of extreme can predict precipitation for ungauged regions with acceptable accuracy. The regional frequency maps were used in conjunction with the Student's t‐test to identify the statistical significance of changes of extremes in precipitation. Results indicate that there have been no significant changes in maximum daily precipitation magnitudes over the past four decades, a finding that is valuable for the safe planning of major hydraulic projects and the management and planning of water resources in the upper Yangtze River basin. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison of ordinary kriging and artificial neural network for spatial mapping of arsenic contamination of groundwater

In this technical note, we investigate the hypothesis that ‘non-linearity matters in the spatial mapping of complex patterns of groundwater arsenic contamination’. The spatial mapping pertained to data-driven techniques of spatial interpolation based on sampling data at finite locations. Using the well known example of extensive groundwater contamination by arsenic in Bangladesh, we find that the use of a highly non-linear pattern learning technique in the form of an artificial neural network (ANN) can yield more accurate results under the same set of constraints when compared to the ordinary kriging method. One ANN and a variogram model were used to represent the spatial structure of arsenic contamination for the whole country. The probability for successful detection of a well as safe or unsafe was found to be atleast 15% larger than that by kriging under the country-wide scenario. The probability of false hopes, which is a serious issue in public health monitoring was found to be significantly lower (by more than 10%) than that by kriging.     

Radial basis function neural network for hydrologic inversion: an appraisal with classical and spatio-temporal geostatistical techniques in the context of site characterization

This paper investigates three techniques for spatial mapping and the consequential hydrologic inversion, using hydraulic conductivity (or transmissivity) and hydraulic head as the geophysical parameters of concern. The data for the study were obtained from the Waste Isolation and Pilot Plant (WIPP) site and surrounding area in the remote Chihuahuan Desert of southeastern New Mexico. The central technique was the Radial Basis Function algorithm for an Artificial Neural Network (RBF-ANN). An appraisal of its performance in light of classical and temporal geostatistical techniques is presented. Our classical geostatistical technique of concern was Ordinary Kriging (OK), while the method of Bayesian Maximum Entropy (BME) constituted an advanced, spatio-temporal mapping technique. A fusion technique for soft or inter-dependent data was developed in this study for use with the neural network. It was observed that the RBF-ANN is capable of hydrologic inversion for transmissivity estimation with features remaining essentially similar to that obtained from kriging. The BME technique, on the other hand, was found to reveal an ability to map localized lows and highs that were otherwise not as apparent in OK or RBF-ANN techniques.     

Spatial correlation of shear-wave velocity in the San Francisco Bay Area sediments

Ground motions recorded within sedimentary basins are variable over short distances. One important cause of the variability is that local soil properties are variable at all scales. Regional hazard maps developed for predicting site effects are generally derived from maps of surficial geology; however, recent studies have shown that mapped geologic units do not correlate well with the average shear-wave velocity of the upper 30 m, V_s(30). We model the horizontal variability of near-surface soil shear-wave velocity in the San Francisco Bay Area to estimate values in unsampled locations in order to account for site effects in a continuous manner. Previous geostatistical studies of soil properties have shown horizontal correlations at the scale of meters to tens of meters while the vertical correlations are on the order of centimeters. In this paper we analyze shear-wave velocity data over regional distances and find that surface shear-wave velocity is correlated at horizontal distances up to 4 km based on data from seismic cone penetration tests and the spectral analysis of surface waves. We propose a method to map site effects by using geostatistical methods based on the shear-wave velocity correlation structure within a sedimentary basin. If used in conjunction with densely spaced shear-wave velocity profiles in regions of high seismic risk, geostatistical methods can produce reliable continuous maps of site effects.     

Macrobenthos habitat mapping in a tidal flat using remotely sensed data and a GIS-based probabilistic model

This paper proposes and tests a method of producing macrofauna habitat potential maps based on a weights-of-evidence model (a probabilistic approach) for the Hwangdo tidal flat, Korea. Samples of macrobenthos were collected during field work, and we considered five mollusca species for habitat mapping. A weights-of-evidence model was used to calculate the relative weights of 10 control factors that affect the macrobenthos habitat. The control factors were compiled as a spatial database from remotely sensed data combined with GIS analysis. The relative weight of each factor was integrated as a species potential index (SPI), which produced habitat potential maps. The maps were compared with the surveyed habitat locations, revealing a strong correlation between the potential maps and species locations. The combination of a GIS-based weights-of-evidence model and remote sensing techniques is an effective method in determining areas of macrobenthos habitat potential in a tidal flat setting.     

Spatial mapping of drought in Zambia using regional frequency analysis

Regional frequency analysis based on L-moments was applied to assess the spatial extent of meteorological droughts in tandem with their return periods in Zambia. Weather station monthly rainfall data were screened to form homogeneous sub-regions-, validated by a homogeneity criterion and fitted by a generalized extreme value distribution using goodness-of-fit test statistics. Predictor equations at regional scale for L-moment ratios and mean annual precipitation were developed to generate spatial maps of meteorological drought recurrences. The 80% of normal rainfall level and two thresholds of 60% and 70% were synonymous with moderate and severe droughts, respectively. Droughts were more severe in the south than in the north of Zambia. The return periods for severe and moderate droughts showed an overlapping pattern in their occurrence at many locations, indicating that in certain years droughts can affect the entire country. The extreme south of Zambia is the most prone to drought.     

Hierarchical spatial modeling of the presence of Chagas disease insect vectors in Argentina. A comparative approach

We modeled the spatial distribution of the most important Chagas disease vectors in Argentina, in order to obtain a predictive mapping method for the probability of presence of the vector species. We analyzed both the binary variable of presence-absence of Chagas disease and the vector species richness in Argentina, in combination with climatic and topographical covariates associated to the region of interest. We used several statistical techniques to produce distribution maps of presence–absence for the different insect species as well as species richness, using a hierarchical Bayesian framework within the context of multivariate geostatistical modeling. Our results show that the inclusion of covariates improves the quality of the fitted models, and that there is spatial interaction between neighboring cells/pixels, so mapping methods used in the past, which assumed spatial independence, are not adequate as they provide unreliable results.