Stochastic analysis of spatiotemporal solute content measurements using a regression model

A regression model is used to study spatiotemporal distributions of solute content ion concentration data (calcium, chloride and nitrate), which provide important water contamination indicators. The model consists of three random and one deterministic components. The random space/time component is assumed to be homogeneous/stationary and to have a separable covariance. The purely spatial and the purely temporal random components are assumed to have homogenous and stationary increments, respectively. The deterministic component represents the space/time mean function. Inferences of the random components involve maximum likelihood and semi-parametric methods under some restrictions on the data configuration. Computational advantages and modelling limitations of the assumptions underlying the regression model are discussed. The regression model leads to simplifications in the space/time kriging and cokriging systems used to obtain space/time estimates at unobservable locations/instants. The application of the regression model in the study of the solute content ions was done at a global scale that covers the entire region of interest. The variability analysis focuses on the calculation of the spatial direct and cross-variograms and the evaluation of correlations between the three solute content ions. The space/time kriging system is developed in terms of the space direct and cross-variograms, and allows the separate estimation of the regression model components. Maps of these components are then obtained for each one of the three ions. Using the estimates of the purely spatial component, spatial dependencies between the ions are studied. Physical causes and consequences of the space/time variability are discussed, and comparisons are made with previous analyses of the solute content dataset.     

Spatiotemporal estimation of snow depth using point data from snow stakes,digital terrain models,and satellite data

Snow availability in Alpine catchments plays an important role in water resources management. In this paper, we propose a method for an optimal estimation of snow depth (areal extension and thickness) in Alpine systems from point data and satellite observations by using significant explanatory variables deduced from a digital terrain model. It is intended to be a parsimonious approach that may complement physical‐based methodologies. Different techniques (multiple regression, multicriteria analysis, and kriging) are integrated to address the following issues: We identify the explanatory variables that could be helpful on the basis of a critical review of the scientific literature. We study the relationship between ground observations and explanatory variables using a systematic procedure for a complete multiple regression analysis. Multiple regression models are calibrated combining all suggested model structures and explanatory variables. We also propose an evaluation of the models (using indices to analyze the goodness of fit) and select the best approaches (models and variables) on the basis of multicriteria analysis. Estimation of the snow depth is performed with the selected regression models. The residual estimation is improved by applying kriging in cases with spatial correlation. The final estimate is obtained by combining regression and kriging results, and constraining the snow domain in accordance with satellite data. The method is illustrated using the case study of the Sierra Nevada mountain range (Southern Spain). A cross‐validation experiment has confirmed the efficiency of the proposed procedure. Finally, although it is not the scope of this work, the snow depth is used to asses a first estimation of snow water equivalent resources.     

Seismic-impedance inversion with fuzzy clustering constraints: an example from the Carlin Gold District,Nevada, USA

The seismic reflection method provides high-resolution data that are especially useful for discovering mineral deposits under deep cover. A hindrance to the wider adoption of the seismic reflection method in mineral exploration is that the data are often interpreted differently and independently of other geophysical data unless common earth models are used to link the methods during geological interpretation. Model-based inversion of post-stack seismic data allows rock units with common petrophysical properties to be identified and permits increased bandwidth to enhance the spatial resolution of the acoustic-impedance model. However, as seismic reflection data are naturally bandlimited, any inversion scheme depends upon an initial model, and must deal with non-unique solutions for the inversion. Both issues can be largely overcome by using constraints and integrating prior information. We exploit the abilities of fuzzy c-means clustering to constrain and to include prior information in the inversion. The use of a clustering constraint for petrophysical values pushes the inversion process to select models that are primarily composed of several discrete rock units and the fuzzy c-means algorithm allows some properties to overlap by varying degrees. Imposing the fuzzy clustering techniques in the inversion process allows solutions that are similar to the natural geologic patterns that often have a few rock units represented by distinct combinations of petrophysical characteristics. Our tests on synthetic models, with clear and distinct boundaries, show that our methodology effectively recovers the true model. Accurate model recovery can be obtained even when the data are highly contaminated by random noise, where the initial model is homogeneous, or there is minimal prior petrophysical information available. We demonstrate the abilities of fuzzy c-means clustering to constrain and to include prior information in the acoustic-impedance inversion of a challenging magnetotelluric/seismic data set from the Carlin Gold District, USA. Using fuzzy c-means guided inversion of magnetotelluric data to create a starting model for acoustic-impedance proved important in obtaining the best result. Our inversion results correlate with borehole data and provided a better basis for geological interpretation than the seismic reflection images alone. Low values of the acoustic impedance in the basement rocks were shown to be prospective by geochemical analysis of rock cores, as would be predicted for later gold mineralization in weak, decalcified rocks.     

Artificial intelligence for identifying hydrologically homogeneous regions: A state‐of‐the‐art regional flood frequency analysis

Due to the severity related to extreme flood events, recent efforts have focused on the development of reliable methods for design flood estimation. Historical streamflow series correspond to the most reliable information source for such estimation; however, they have temporal and spatial limitations that may be minimized by means of regional flood frequency analysis (RFFA). Several studies have emphasized that the identification of hydrologically homogeneous regions is the most important and challenging step in an RFFA. This study aims to identify state‐of‐the‐art clustering techniques (e.g., K ‐means, partition around medoids, fuzzy C‐means, K ‐harmonic means, and genetic K ‐means) with potential to form hydrologically homogeneous regions for flood regionalization in Southern Brazil. The applicability of some probability density function, such as generalized extreme value, generalized logistic, generalized normal, and Pearson type 3, was evaluated based on the regions formed. Among all the 15 possible combinations of the aforementioned clustering techniques and the Euclidian, Mahalanobis, and Manhattan distance measures, the five best were selected. Several watersheds' physiographic and climatological attributes were chosen to derive multiple regression equations for all the combinations. The accuracy of the equations was quantified with respect to adjusted coefficient of determination, root mean square error, and Nash–Sutcliffe coefficient, whereas, a cross‐validation procedure was applied to check their reliability. It was concluded that reliable results were obtained when using robust clustering techniques based on fuzzy logic (e.g., K ‐harmonic means), which have not been commonly used in RFFA. Furthermore, the probability density functions were capable of representing the regional annual maximum streamflows. Drainage area, main river length, and mean altitude of the watershed were the most recurrent attributes for modelling of mean annual maximum streamflow. Finally, an integration of all the five best combinations stands out as a robust, reliable, and simple tool for estimation of design floods.     

Regionalization of precipitation characteristics in the Canadian Prairie Provinces using large-scale atmospheric covariates and geophysical attributes

Observed data at most stations are often inadequate to obtain reliable estimates of many hydro-meteorological variables that not only define water availability across a region but also the vulnerability of social infrastructure to climatic extremes. To overcome this, data from neighboring sites with similar statistical characteristics are often pooled. The pooling process is based on partitioning of a larger region into smaller sub-regions with homogeneous features of interest. The established approaches rely heavily on statistics computed from observed precipitation data rather than the covariates that play a significant role in modulating the regional and local climate patterns at various temporal and spatial scales. In this study, a new approach for identifying homogeneous regions for regionalization of precipitation characteristics is proposed for the Canadian Prairie Provinces. This approach incorporates information about large-scale atmospheric covariates, teleconnection indices and geographical site attributes that impact spatial patterns of precipitation in order to delineate homogeneous precipitation regions through combined use of multivariate approaches—principal component analysis, canonical correlation analysis and fuzzy C-means clustering. Results of the analyses suggest that the study area can be partitioned into five homogeneous regions. These partitions are validated independently for homogeneity using statistics computed from monthly and seasonal precipitation totals, and seasonal extremes from a network of observation stations. Furthermore, based on the identified regions, precipitation magnitude-frequency relationships of warm and cold season single- and multi-day precipitation extremes, developed through regional frequency analysis, are mapped spatially. Such estimates are important for numerous water resources related activities.     

Development of spatial regression models for predicting summer river temperatures from landscape characteristics: Implications for land and fisheries management

There is increasing demand for models that can accurately predict river temperature at the large spatial scales appropriate to river management. This paper combined summer water temperature data from a strategically designed, quality controlled network of 25 sites, with recently developed flexible spatial regression models, to understand and predict river temperature across a 3,000 km² river catchment. Minimum, mean and maximum temperatures were modelled as a function of nine potential landscape covariates that represented proxies for heat and water exchange processes. Generalised additive models were used to allow for flexible responses. Spatial structure in the river network data (local spatial variation) was accounted for by including river network smoothers. Minimum and mean temperatures decreased with increasing elevation, riparian woodland and channel gradient. Maximum temperatures increased with channel width. There was greater between‐river and between‐reach variability in all temperature metrics in lower‐order rivers indicating that increased monitoring effort should be focussed at these smaller scales. The combination of strategic network design and recently developed spatial statistical approaches employed in this study have not been used in previous studies of river temperature. The resulting catchment scale temperature models provide a valuable quantitative tool for understanding and predicting river temperature variability at the catchment scales relevant to land use planning and fisheries management and provide a template for future studies.     

On the estimation of continuous 24-h precipitation maxima

Extreme value analysis of precipitation is of great importance for several types of engineering studies and policy decisions. For return level estimation of extreme 24-h precipitation, practitioners often use daily measurements (usually 08:00–08:00 local time) since high-frequency measurements are scarce. Annual maxima of daily series are smaller or equal to continuous 24-h precipitation maxima such that the resulting return levels may be systematically underestimated. In this paper we use a rule, derived earlier, on the conversion of the generalized extreme value (GEV) distribution of daily to 24-h maxima. We develop an estimator for the conversion exponent by combining daily maxima and high-frequency sampled 24-h maxima in one joint log-likelihood. Once the conversion exponent has been estimated, GEV-parameters of 24-h maxima can be obtained at sites where only daily data is available. The new methodology has been extended to spatial regression models.     

渤海常见土类剪切波速与埋深关系分析

土层的剪切波速是岩土地震工程中重要的物理量,本文利用多年来在渤海海域地震安全性评价中积累的资料,研究了渤海常见土类剪切波速和埋深的关系。利用非线性最小二乘法,采用指数函数、一次函数、二次函数、幂函数、"幂函数+常数函数"、"幂函数+一次函数" 6种回归模型对各类土的剪切波速和埋深的关系进行了回归分析,以拟合优度以及最小二乘拟合的误差平方和为评价指标对比了各种模型拟合效果的优劣。结果表明,"幂函数+一次函数"回归模型的拟合效果最好。此外,本文给出了该海域常见的7类土在此回归模型下的拟合公式的系数,以供工程中参考。     

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.     

Topographic,pedologic and climatic interactions influencing streamflow generation at multiple catchment scales

Dominant flow pathways (DFPs) in mesoscale watersheds are poorly characterized and understood. Here, we make use of a conservative tracer (Gran alkalinity) and detailed information about climatic conditions and physical properties to examine how temporally and spatially variable factors interact to determine DFPs in 12 catchments draining areas from 3.4 to 1829.5 km² (Cairngorms, Scotland). After end‐member mixing was applied to discriminate between near surface and deep groundwater flow pathways, variation partitioning, canonical redundancy analyses and regression models were used to resolve: (i) What is the temporal variability of DFPs in each catchment?; (ii) How do DFPs change across spatial scales and what factors control the differences in hydrological responses?; and (iii) Can a conceptual model be developed to explain the spatiotemporal variability of DFPs as a function of climatic, topographic and soil characteristics? Overall, catchment characteristics were only useful to explain the temporal variability of DFPs but not their spatial variation across scale. The temporal variability of DFPs was influenced most by prevailing hydroclimatic conditions and secondarily soil drainability. The predictability of active DFPs was better in catchments with soils supporting fast runoff generation on the basis of factors such as the cumulative precipitation from the seven previous days, mean daily air temperature and the fractional area covered by Rankers. The best regression model R² was 0.54, thus suggesting that the catchments’ internal complexity was not fully captured by the factors included in the analysis. Nevertheless, this study highlights the utility of combining tracer studies with digital landscape analysis and multivariate statistical techniques to gain insights into the temporal (climatic) and spatial (topographic and pedologic) controls on DFPs. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation of coalbed methane reservoirs from geophysical log data using an improved fuzzy comprehensive decision method and a homologous neural network

The evaluation of coalbed methane reservoirs using log data is an important approach in the exploration and development of coalbed methane reservoirs. Most commonly, regression techniques, fuzzy recognition and neural networks have been used to evaluate coalbed methane reservoirs. It is known that a coalbed is an unusual reservoir. There are many difficulties in using regression methods and empirical qualitative recognition to evaluate a coalbed, but fuzzy recognition, such as the fuzzy comprehensive decision method, and neural networks, such as the back-propagation (BP) network, are widely used. However, there are no effective methods for computing weights for the fuzzy comprehensive decision method, and the BP algorithm is a local optimization algorithm, easily trapped in local minima, which significantly affect the results. In this paper, the recognition method for coal formations is developed; the improved fuzzy comprehensive decision method, which uses an optimization approach for computing weighted coefficients, is developed for the qualitative recognition of coalbed methane reservoirs. The homologous neural network, using a homologous learning algorithm, which is a global search optimization, is presented for the quantitative analysis of parameters for coalbed methane reservoirs. The applied procedures for these methods and some problems related to their application are also discussed. Verification of the above methods is made using log data from the coalbed methane testing area in North China. The effectiveness of the methods is demonstrated by the analysis of results for real log data.     

Quantifying geographic variations in associations between alcohol distribution and violence: a comparison of geographically weighted regression and spatially varying coefficient models

Past studies consistently indicate measurable local associations between alcohol distribution and the incidence of violence. These results, coupled with measurements of spatial correlation, reveal the importance of spatial analysis in the study of the interaction of alcohol and violence. While studies increasingly incorporate spatial correlation among model residuals to improve precision and reduce bias, to date, most analyses assume associations that are constant and independent of location, an assumption coming under increasing scrutiny in the quantitative geography literature. In this paper, we review and contrast two approaches for the estimation of and inference for spatially heterogeneous effects (i.e., associative factors whose impacts on the outcome of interest vary throughout geographic space). Specifically, we provide an in-depth comparison of “geographically weighted regression” models (allowing covariate effects to vary in space but only allowing relatively ad hoc inference) with “variable coefficient” models (allowing varying effects via spatial random fields and providing model-based estimation and inference, but requiring more advanced computational techniques). We compare the approaches with respect to underlying conceptual structures, computational implementation, and inferential output. We apply both approaches to violent crime, illegal drug arrest, and alcohol distribution data from Houston, Texas and compare results in light of the differing methodological structures of the two approaches.     

Fuzzy model identification based on cluster estimation for reservoir inflow forecasting

Fuzzy theory appears to be extremely effective at handling dynamic, non‐linear and noisy data, especially when the underlying physical relationships are not fully understood. Since hydrologists are still uncertain about many of the aspects of the physical processes in the watershed, fuzzy theory has proved to be a very attractive tool enabling them to investigate such problems. The effectiveness of the fuzzy model lies in the identification of the antecedent membership function (MF), which is generally addressed through a fuzzy clustering approach. Most of the applications of fuzzy computing in hydrology seem to have selected the clustering algorithm quite arbitrarily. However, it is apparent that, as the antecedent parameters are based solely on the identified clusters, the method used for clustering should certainly have an impact on the overall performance of the model. This paper presents the results of a study conducted to investigate the impact of choice of clustering algorithm on the overall performance of a fuzzy‐based hydrologic model. The research is illustrated through a case study of developing a Takagi–Sugeno fuzzy model for reservoir inflow forecasting in the Narmada basin, India. The model was developed using two popular clustering techniques, namely Gustafson–Kessel (GK) and subtractive clustering (SC), and was extensively evaluated for performance based on various statistical indices. The results show that the model performance is comparable at a 1 h lead forecast. However, it is observed that the GK approach results in a better performance than the SC approach in computing forecasts at higher lead times. The analysis suggest that the GK method clusters the input space based on the actual pattern, since it uses a membership‐grade weighted‐distance measure as the measure of closeness, whereas the SC method classifies the input space more logically according to the magnitude of flow available in the data set. Copyright © 2007 John Wiley & Sons, Ltd.     

A comparision of interpolation methods for producing digital elevation models at the field scale

Digital elevation models have been used in many applications since they came into use in the late 1950s. It is an essential tool for applications that are concerned with the Earth's surface such as hydrology, geology, cartography, geomorphology, engineering applications, landscape architecture and so on. However, there are some differences in assessing the accuracy of digital elevation models for specific applications. Different applications require different levels of accuracy from digital elevation models. In this study, the magnitudes and spatial patterning of elevation errors were therefore examined, using different interpolation methods. Measurements were performed with theodolite and levelling. Previous research has demonstrated the effects of interpolation methods and the nature of errors in digital elevation models obtained with indirect survey methods for small‐scale areas. The purpose of this study was therefore to investigate the size and spatial patterning of errors in digital elevation models obtained with direct survey methods for large‐scale areas, comparing Inverse Distance Weighting, Radial Basis Functions and Kriging interpolation methods to generate digital elevation models. The study is important because it shows how the accuracy of the digital elevation model is related to data density and the interpolation algorithm used. Cross validation, split‐sample and jack‐knifing validation methods were used to evaluate the errors. Global and local spatial auto‐correlation indices were then used to examine the error clustering. Finally, slope and curvature parameters of the area were modelled depending on the error residuals using ordinary least regression analyses. In this case, the best results were obtained using the thin plate spline algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

A comparative analysis of three habitat suitability models for commercial yield estimation of Tapes philippinarum in a North Adriatic coastal lagoon (Sacca di Goro,Italy)

Habitat Suitability (HS) models have been extensively used by conservation planners to estimate the spatial distribution of threatened species and of species of commercial interest. In this work we compare three HS models for the estimation of commercial yield potential and the identification of suitable sites for Tapes philippinarum rearing in the Sacca di Goro lagoon (Italy) on the basis of six environmental factors. The habitat suitability index (HSI) is based on expert opinion while the habitat suitability conditional (HSC) is calibrated on observational data. The habitat suitability mixed (HSM) model is a two-part model combining expert knowledge and regression analysis: the first component of the model uses logistic regression to identify the areas in which clams are likely to be present; the second part applies the same parameter-specific suitability functions of the HSI model only in the areas previously identified as productive by the logistic component.The HS models were validated on an independent data set and estimates of potential yield of the Goro lagoon were compared. The effectiveness of the three approaches is then discussed in terms of predicted yield and identification of suitable sites for farming.     

A comparative analysis of three habitat suitability models for commercial yield estimation of Tapes philippinarum in a North Adriatic coastal lagoon (Sacca di Goro, Italy)

Habitat Suitability (HS) models have been extensively used by conservation planners to estimate the spatial distribution of threatened species and of species of commercial interest. In this work we compare three HS models for the estimation of commercial yield potential and the identification of suitable sites for Tapes philippinarum rearing in the Sacca di Goro lagoon (Italy) on the basis of six environmental factors. The habitat suitability index (HSI) is based on expert opinion while the habitat suitability conditional (HSC) is calibrated on observational data. The habitat suitability mixed (HSM) model is a two-part model combining expert knowledge and regression analysis: the first component of the model uses logistic regression to identify the areas in which clams are likely to be present; the second part applies the same parameter-specific suitability functions of the HSI model only in the areas previously identified as productive by the logistic component. The HS models were validated on an independent data set and estimates of potential yield of the Goro lagoon were compared. The effectiveness of the three approaches is then discussed in terms of predicted yield and identification of suitable sites for farming.     

基于多元线性回归方法的砌体结构加固费用估算模型研究

为建立适用于砌体结构的加固费用快速估算模型,对中国陕西、山西、四川等地砌体结构建筑物的历史加固费用及相关建筑参数进行统计,建立涵盖35栋砌体结构建筑物加固费用估算模型的回归与验证数据库,同时对影响加固费用的各建筑参数作显著性分析,并基于后向消去的多元线性回归方法,利用SPSS统计分析软件对已采集的加固数据进行回归,得到4个费用估算模型;按照相应评价准则分别对各模型进行评价,提出一套最优的砌体结构加固费用快速估算模型,并对该回归模型进行验证分析。回归得到的费用估算模型满足精度要求,具有一定的工程应用价值。     

A comparative analysis of three habitat suitability models for commercial yield estimation of Tapes philippinarum in a North Adriatic coastal lagoon (Sacca di Goro, Italy)

Habitat Suitability (HS) models have been extensively used by conservation planners to estimate the spatial distribution of threatened species and of species of commercial interest. In this work we compare three HS models for the estimation of commercial yield potential and the identification of suitable sites for Tapes philippinarum rearing in the Sacca di Goro lagoon (Italy) on the basis of six environmental factors. The habitat suitability index (HSI) is based on expert opinion while the habitat suitability conditional (HSC) is calibrated on observational data. The habitat suitability mixed (HSM) model is a two-part model combining expert knowledge and regression analysis: the first component of the model uses logistic regression to identify the areas in which clams are likely to be present; the second part applies the same parameter-specific suitability functions of the HSI model only in the areas previously identified as productive by the logistic component.The HS models were validated on an independent data set and estimates of potential yield of the Goro lagoon were compared. The effectiveness of the three approaches is then discussed in terms of predicted yield and identification of suitable sites for farming.     

模糊数学方法在地震综合预报中的应用

本文的目的,是把模糊数学中发展起来的模糊识别的直接方法与间接方法,试用于地震综合预报.模糊识别的直接方法,就是直接由前兆指标的从属函数来估计地震危险性并进行预报,其效果依赖于建立前兆指标的从属函数的技巧.文中以地下水氡含量、视电阻率、波速等前兆资料为基础,提出了一种主要依据前兆变化速率及相关系数,并使用其它途径来建立从属函数的具体方法与公式.使用这样的从属函数之后,可以更好地识别出前兆异常,并且更容易区分出异常的起始、终结或发生明显转折的时期.模糊识别的间接方法,本文中采用的是模糊聚类分析方法,它与选取表示型类区别的相似系数或距离有关.我们这里采用的是基于模糊等价关系的聚类分析方法.此方法包括以下步骤:将一系列样本按彼此间的相似程度建立一个模糊相容关系;通过合成运算把这个模糊相容关系改造为一个模糊等价关系;选择一个适当的参数的数值,并对原始样本进行分类.选取某一给定地区的地震活动性的一些统计指标,或者选取由多手段单台或单手段多台得出的一些前兆数据(地形变、地下水氡含量、视电阻率等等),就可以使用上述模糊聚类分析方法来进行地震综合预报.作为说明此方法的例子,文中给出了对我国西部强震及中强震得出的一些初步结果.由所得结果可以看出,利用模      

Moment and Bayesian wavelet regression from spatially correlated functional data

A new wavelet-based estimation methodology, in the context of spatial functional regression, is proposed to discriminate between small-scale and large scale variability of spatially correlated functional data, defined by depth-dependent curves. Specifically, the discrete wavelet transform of the data is computed in space and depth to reduce dimensionality. Moment-based regression estimation is applied for the approximation of the scaling coefficients of the functional response. While its wavelet coefficients are estimated in a Bayesian regression framework. Both regression approaches are implemented from the empirical versions of the scaling and wavelet auto-covariance and cross-covariance operators, characterizing the correlation structure of the spatial functional response. Weather stations in ocean islands display high spatial concentration. The proposed estimation methodology overcomes the difficulties arising in the estimation of ocean temperature field at different depths, from long records of ocean temperature measurements in these stations. Data are collected from The World-Wide Ocean Optics Database. The performance of the presented approach is tested in terms of 10-fold cross-validation, and residual spatial and depth correlation analysis. Additionally, an application to soil sciences, for prediction of electrical conductivity profiles is also considered to compare this approach with previous related ones, in the statistical analysis of spatially correlated curves in depth.