Comparison of Volterra Model and Artificial Neural Networks for Rainfall–Runoff Simulation

This study evaluates the performances of two distinct linear and non-linear models for simulating non-linear rainfall–runoff processes and their applications to flood forecasting in the Navrood River basin, Iran. Due to the excellent capacity of the artificial neural networks [multilayer perceptron (MLP)] and Volterra model, these models were used to approximate arbitrary non-linear rainfall–runoff processes. The MLP model was trained using two different training algorithms. The Volterra model was applied as a linear model [the first-order Volterra (FOV) model] and solved using the traditional ordinary least-square (OLS) method. Storm events within the Navrood River basin were used to verify the suitability of the two models. The models’ performances were evaluated and compared using five performance criteria namely coefficient of efficiency, root mean square error, error of total volume, relative error of peak discharge, and error of time for peak to arrive. Results indicated that the non-linear MLP models outperform the linear FOV model. The latter was ineffective because of the non-linearity of the rainfall–runoff process. Moreover, the OLS method is inefficient when the FOV model has many parameters that must be estimated.     

2-D or 3-D interpretation of conductivity anomalies: example of the Rhine-Graben conductivity anomaly

Summary. Evidence of a conductivity anomaly in the Rhine-Graben was first given about 15 years ago and consequently led to the definition of various models of induction in the region for periods ranging from a few minutes to a few hours. These models reflect two antagonistic ways of explaining the observed anomalous variations of the magnetic field: direct induction in a two-dimensional (2-D) structure or static distortion of telluric currents by the resistive crystalline Vosges (France) and Schwarzwalde (Germany) massifs. We discuss the two approaches using a simple formalism. In particular, we show that the self-induction related to the anomalous currents flowing in the Rhine-Graben is negligible for periods larger than 1000 s, and that, even though the static distortion of telluric currents does account for the observed anomaly, 2-D models can explain some of its features. We also show how the channelled currents are induced in the large sedimentary basins surrounding the area under study.
An experimental verification of this result is given.     

Non-linear inversion using general measures of data misfit and model structure

We investigate the use of general, non- l ₂ measures of data misfit and model structure in the solution of the non-linear inverse problem. Of particular interest are robust measures of data misfit, and measures of model structure which enable piecewise-constant models to be constructed. General measures can be incorporated into traditional linearized, iterative solutions to the non-linear problem through the use of an iteratively reweighted least-squares (IRLS) algorithm. We show how such an algorithm can be used to solve the linear inverse problem when general measures of misfit and structure are considered. The magnetic stripe example of Parker (1994 ) is used as an illustration. This example also emphasizes the benefits of using a robust measure of misfit when outliers are present in the data. We then show how the IRLS algorithm can be used within a linearized, iterative solution to the non-linear problem. The relevant procedure contains two iterative loops which can be combined in a number of ways. We present two possibilities. The first involves a line search to determine the most appropriate value of the trade-off parameter and the complete solution, via the IRLS algorithm, of the linearized inverse problem for each value of the trade-off parameter. In the second approach, a schedule of prescribed values for the trade-off parameter is used and the iterations required by the IRLS algorithm are combined with those for the linearized, iterative inversion procedure. These two variations are then applied to the 1-D inversion of both synthetic and field time-domain electromagnetic data.     

Exploring space-time models for West Nile virus mosquito abundance data

This paper explores variant space-time models for log-transformed West Nile virus (WNv) mosquito data, which explicitly account for both local environmental conditions and complex dependent structures. Four space-time models take various forms to accommodate correlated structure in space and time, nested data, and nonstationarity. The average WNv mosquito abundance is captured by a global trend across all four models, but different model assumptions are imposed on the stochastic component of the proposed models: a simple multivariate linear regression model with independent and identical errors, a site-specific linear mixed model with temporally correlated errors, a week-specific linear mixed model with spatially correlated errors, and a local space-time kriging model. In a case study, the predictive performance of the four models was assessed using data collected in 2007 and 2008 for the Greater Toronto Area by the mosquito surveillance program of Ontario Ministry of Health and Long-term Care: the local space-time kriging model outperforms others, but closely followed by a site-specific linear mixed model with temporal correlation. Our findings suggest that the predictive accuracy of space-time WNv mosquito abundance models can be enhanced by explicitly taking into account spatiotemporal correlation, nonstationarity, and the data collection procedure, such as surveillance design, based on sound understanding of mosquito behavior and population dynamics.     

Context in Human Geography: A Multilevel Approach to Study Human–Environment Interactions∗

One of the shortcomings of quantitative methods in human geography is an overreliance on models that can only account for the average outcomes of spatial events. Although methodological advancements in the form of multilevel models now allow human geographers to account for average outcomes as well as deviations about average outcomes of spatial events, it is not without question that such models can fully account for the cultural, political, and social contexts that affect human behavior. In this article I argue for the adoption of a multilevel approach to the study of human behavior to address some of the criticisms of quantitative methods in human geography. Using a transportation geography research agenda as an example, I discuss how a multilevel approach can complement qualitative methods. Such mixed research methods offer human geographers the opportunity to identify the appropriate role for quantitative methods and explore how context affects behavior.     

QUADRATIC PLS REGRESSION

We treat here an extension of linear PLS regression to include regression on quadratic PLS components.The quadratic regression can be viewed as a natural extension of linear PLS regression to quadratic PLSaccording to the H-principle of mathematical modelling.The numerical implementation is treated indetail.It is shown that this approach can be used for models with large numbers of variables.Somemodelling strategies are discussed depending on the purpose of the modelling.Applications of thisapproach are treated.     

青海湖环湖地区草地植被生物量遥感监测模型

利用青海湖环湖地区2000年陆地卫星TM遥感图像数据和同期野外实测的34处样方产草量数据,分析了遥感植被指数与草地植被生物量之间的相关关系,进而分别建立了遥感植被指数与草地植被生物量的一元线性回归模型和非线性回归模型。研究表明,遥感植被指数与草地生物量之间存在较好的相关性,但不同遥感植被指数与草地植被生物量相关性程度存在一定差别。此外,所建遥感植被指数与草地植被生物量的非线性回归模型在拟合精度上优于一元线性回归模型,且由三次方程得到的非线性回归模型最适用于监测青海湖环湖地区的草地植被生物量。     

DETECTING AND ADJUSTING FOR NON-LINEARITIES IN CALIBRATION OF NEAR-INFRARED DATA USING PRINCIPAL COMPONENTS

A new regression method for non-linear near-infrared spectroscopic data is proposed.The technique isbased on a model which is linear in the principal components and simple functions(squares and products)of them.Added variable plots are used to determine which squares and products to incorporate into themodel.The regression coefficients are estimated by a Stein estimate which shrinks towards the estimatedetermined by the first several principal components and the selected non-linear terms.The technique isnot computationally intensive and is appropriate for routine predictions of chemical concentrations.Themethod is tested on three data sets and in all cases gives more accurate predictions than does linearprincipal components regression.     

Benefits and drawbacks of two modelling approaches for a generalist carnivore: can models predict where Wile E. Coyote will turn up next?

Wildlife ecologists frequently make use of limited information on locations of a species of interest in combination with readily available GIS data to build models to predict space use. In addition to a wide range of statistical data models that are more commonly used, machine learning approaches provide another means to develop predictive spatial models. However, comparison of output from these two families of models for the same data set is not often carried out. It is important that wildlife managers understand the pitfalls and limitations when a single set of models is used with limited GIS data to try to predict and understand species distribution. To illustrate this, we carried out two sets of models (generalized linear mixed models (GLMMs) and boosted regression trees (BRTs)) to predict geographic occupancy of the eastern coyote (Canis latrans) on the island of Newfoundland, Canada. This exercise is illustrative of common spatial questions in wildlife research and management. Our results show that models vary depending on the approach (GLMM vs. BRT) and that, overall, BRT had higher predictive ability. Although machine learning has been criticized because it is not explicitly hypothesis-driven, it has been used in other areas of spatial modelling with success. Here, we demonstrate that it may be a useful approach for predicting wildlife space use and to generate hypotheses when data are limited. The results of this comparison can help to improve other models for species distributions and also guide future sampling and modelling initiatives.     

The Relationship between Carbon Dioxide Emission Intensity and Economic Growth in China: Cointegration,Linear and Nonlinear Granger Causality

This study is to use cointegration, linear and non-linear Granger causality test to investigate the relationship between carbon dioxide (CO₂) emissionand economic growth (GDP) in China for the period 1961-2010. Our analysis shows that CO₂ emission and GDP are balanced in the long-run. The results suggest that there is evidence that economic development can improve environmental degradation in the long-run. Moreover, the result of linear and non-linear Granger causality test indicates a long-run unidirectional causality running from GDP to CO₂ emissions. The study suggests that in the long run, economic growth may have an adverse effect on the CO₂ emissions in China. Government should take into account the environment in their current policies, which may be of great importance for policy decision-makers to develop economic policies to preserve economic growth while curbing of carbon emissions.     

Non-linear crustal corrections in high-resolution regional waveform seismic tomography

We compare 3-D upper mantle anisotropic structures beneath the North American continent obtained using standard and improved crustal corrections in the framework of Non-linear Asymptotic Coupling Theory (NACT) applied to long period three component fundamental and higher mode surface waveform data. Our improved approach to correct for crustal structure in high-resolution regional waveform tomographic models goes beyond the linear perturbation approximation, and is therefore more accurate in accounting for large variations in Moho topography within short distances as observed, for instance, at ocean–continent margins. This improved methodology decomposes the shallow-layer correction into a linear and non-linear part and makes use of 1-D sensitivity kernels defined according to local tectonic structure, both for the forward computation and for the computation of sensitivity kernels for inversion. The comparison of the 3-D upper mantle anisotropic structures derived using the standard and improved crustal correction approaches shows that the model norm is not strongly affected. However, significant variations are observed in the retrieved 3-D perturbations. The largest differences in the velocity models are present below 250 km depth and not in the uppermost mantle, as would be expected. We suggest that inaccurate crustal corrections preferentially map into the least constrained part of the model and therefore accurate corrections for shallow-layer structure are essential to improve our knowledge of parts of the upper mantle where our data have the smallest sensitivity.     

Spatial Pair-Copula Modeling of Grade in Ore Bodies: A Case Study

A real-world mining application of pair-copulas is presented to model the spatial distribution of metal grade in an ore body. Inaccurate estimation of metal grade in an ore reserve can lead to failure of a mining project. Conventional kriged models are the most commonly used models for estimating grade and other spatial variables. However, kriged models use the variogram or covariance function, which produces a single average value to represent the spatial dependence for a given distance. Kriged models also assume linear spatial dependence. In the application, spatial pair-copulas are used to appropriately model the non-linear spatial dependence present in the data. The spatial pair-copula model is adopted over other copula-based spatial models since it is better able to capture complex spatial dependence structures. The performance of the pair-copula model is shown to be favorable compared to a conventional lognormal kriged model.     

Additive models in mining and exploration

In this paper we present the use of additive models (AMs) for geostatistical applications. AMs are generalizations of linear regression models which hold the central place in the toolbox of applied statisticians. Generally speaking, the linear relationship between response and predictors is replaced with a general functional form. Recently such models were introduced in geostatistics. Especially, we give an approach for binary data. In this case we get generalized additive models (GAMs). Logistic regression is quite popular in medical and biological research. Using logit links also in GAMs we get so called additive logistic models. An application for geostatistical data is introduced. In a second approach we use AMs for spatial prediction and surface modelling. In both cases an advantage of multivariate data can be taken. The proposed applications can be used in the development of exploration strategies, especially in the early stage of exploration     

土地利用变化的多尺度空间自相关分析——以内蒙古翁牛特旗为例

用传统统计学方法模拟和解释土地利用变化的前提条件是研究分析的数据在统计上必须独立且均匀分布。但是空间数据相互之间通常具有依赖性 (即空间自相关),某一变量的值随着测定距离的缩小而变得更相似或更为不同。由于经典线性回归方法未能抓住数据的空间自相关特征,而空间自相关包含一些有用的信息,为了克服这一缺点,利用Moran的I系数自相关图来描述研究区土地利用变化的空间自相关,并且建立了不仅考虑回归而且又考虑空间自相关的混合回归-空间自相关回归模型 (即空间滞后模型)。研究得到：① 研究区土地利用变化模型中不但自变量之间而且因变量之间存在空间正自相关,这表明土地利用变化数据的空间自相关很强;② Moran的I系数随着尺度的变粗而减小,这是由于数据平均时的滤波特性和Moran的I系数对距离的非线性特征造成的;③ 经典线性回归模型的残差也表现出正相关,这表明标准的多元线性回归模型未能考虑土地利用数据所存在的空间依赖性;④ 混合回归-空间自相关回归模型 (即空间滞后模型) 的残差未存在空间自相关,并且有更好的拟合度;⑤ 相对于经典线性回归模型,混合回归-空间自相关回归模型 (即空间滞后模型) 对于存在空间自相关性的数据来说有着统计上的合理性,而经典线性回归模型未能考虑这些因素。     

PREDICTIVE ABILITY OF REGRESSION MODELS.PART Ⅰ:STANDARD DEVIATION OF PREDICTION ERRORS (SDEP)

The standard deviation of prediction errors(SDEP)is used to evaluate and compare the predictive abilityof some regression models,namely MLR,ACE and linear and non-linear PLS,the last being the bestone.The parameter is determined by a cross-validation approach as an average of several runs obtainedon forming groups in a random way.The variation in SDEP with the number of latent variables in PLSis also discussed.     

Handbook of applied spatial analysis: software tools,methods and applications,edited by M.M. Fischer and A. Getis

With the rising oil prices, climate change, and the ever increasing burden of nutrition-related disease, food security is of growing research interest in academic disciplines spanning agronomy to epidemiology to urban planning. Some governments have developed progressive policies encouraging individuals to consume locally produced foods in order to support local economies, improve agricultural sustainability and community access to food, and to plan and prepare for adverse environmental impacts on food security. However, fundamental methods are lacking for conducting research on food security across these various disciplines. In this article, we first present a method to measure agricultural self-sufficiency, which we refer to as our self-sufficiency index (SSI) for the province of British Columbia, Canada. We then present a Bayesian autoregressive framework utilizing readily available agricultural data to develop predictive smoothing models for the SSI. We find that regional capital investment in agriculture and cropland acreage is the strong predictor of SSI. To accommodate spatial variability, we compare linear regression models with spatially correlated errors to less traditional spatially varying coefficient models, and find that the former class results in better model fit. The smoothed maps suggest that relatively strong self-sufficiency exists only in subset clusters in the Okanagan, Peace River, and lower mainland regions. In spite of policy to promote local food, the existing local agricultural system is insufficient to support a large-scale shift to local diets. Our approach to estimating neighborhood-based self-sufficiency with a predictive model can be extended for use in other regions where limited data are available to directly assess local agriculture and benefit from explicit consideration of spatial structure in the local food system.     

Assessment of the importance of moderate spatial resolution cloud climatology data in solar radiation modeling

Improving solar radiation models is critical for supporting the increase in solar energy usage and modeling ecosystem dynamics. However, coarse spatial resolutions of solar radiation models overlook the impacts resulting from spatial variability of clouds at meso- and micro-scales. To address this problem, Moderate Resolution Imaging Spectroradiometer (MODIS) cloud climatology developed by the National Severe Storms Laboratory was used to relate cloudiness to surface solar radiation observations. We developed a linear regression model between the surface solar radiation and MODIS cloud climatology and used the model to estimate average radiation across Oklahoma. Furthermore, the study compared the average error and coefficient of determination to measured ground radiation. Error analysis of the regression model showed that the differences between observed radiation and estimated radiation were spatially autocorrelated for the Aqua MODIS satellite scan. This suggests cloudiness alone is not sufficient to predict surface solar radiation. This study found that simple cloud datasets alone can account for approximately 50% of the variation in observed solar radiation at 250-m spatial resolution, but additional datasets such as optical depth, elevation, and slope are needed to accurately explain spatial distributions of incoming shortwave radiation.     

Evaluation of paleohydrologic models for terrestrial inverted channels: Implications for application to martian sinuous ridges

Fluvial systems can be preserved in inverted relief on both Earth and Mars. Few studies have evaluated the applicability of various paleohydrological models to inverted fluvial systems. The first phase of this investigation focused on an extensive (spanning  12 km) inverted paleochannel system that consists of four sandstone-capped, carbonate-cemented, sinuous ridges within the Early Cretaceous Cedar Mountain Formation located southwest of Green River, Utah. Morphologic and sedimentologic observations of the exhumed paleochannels were used to evaluate multiple numerical models for reconstructing paleofluvial hydrological parameters. Another objective of the study was to determine whether aerial or orbital observations yield model results that are consistent with those constrained by field data. The models yield an envelope of plausible dominant discharge values (100–500 m³/s), reflecting the limitations of the approach, and no single model can be used to reliably estimate paleodischarge. On Mars, landforms with attributes consistent with inverted channels have been identified. In spite of differences in the formation history between these martian landforms and the terrestrial analog described here, including potential differences in cement composition and the erosional agent that was responsible for relief inversion, these numerical models can be applied (with modification) to the martian landforms and yield an envelope of plausible values for dominant discharge.     

On the density distribution within the Earth

The distribution of density as a function of position within the Earth is much less well constrained than the seismic velocities. The primary information comes from the mass and moment of inertia of the Earth and this information alone requires that there be a concentration of mass towards the centre of the globe. Additional information is to be found in the frequencies of the graver normal modes of the Earth which are sensitive to density through self-gravitation effects induced in deformation.
  The present generation of density models has been constructed using linearized inversion techniques from earlier models, which ultimately relate back to models developed by Bullen and based in large part on physical arguments. A number of experiments in non-linear inversion have been conducted using the PREM reference model, with fixed velocity and attenuation, but with the density model constrained to lie within fixed bounds on both density and density gradient. A set of models is constructed from a uniform probability density within the bound and slope constraints. Each of the resultant density models is tested against the mass and moment of inertia of the Earth, and for successful models a comparison is made with observed normal mode frequencies. From the misfit properties of the ensemble of models the robustness of the density profile in different portions of the Earth can be assessed, which can help with the design of parametrization for future reference models. In both the lower mantle and the outer core it would be desirable to allow a more flexible representation than the single cubic polynomial employed in PREM.     

On the prediction error variance of three common spatial interpolation schemes

Three forms of linear interpolation are routinely implemented in geographical information science, by interpolating between measurements made at the endpoints of a line, the vertices of a triangle, and the vertices of a rectangle (bilinear interpolation). Assuming the linear form of interpolation to be correct, we study the propagation of error when measurement error variances and covariances are known for the samples at the vertices of these geometric objects. We derive prediction error variances associated with interpolated values at generic points in the above objects, as well as expected (average) prediction error variances over random locations in these objects. We also place all the three variants of linear interpolation mentioned above within a geostatistical framework, and illustrate that they can be seen as particular cases of Universal Kriging (UK). We demonstrate that different definitions of measurement error in UK lead to different UK variants that, for particular expected profiles or surfaces (drift models), yield weights and predictions identical with the interpolation methods considered above, but produce fundamentally different (yet equally plausible from a pure data standpoint) prediction error variances.