Analyzing explanatory factors of urban pluvial floods in Shanghai using geographically weighted regression

In the context of climate change and rapid urbanization, urban pluvial floods pose an increasing threat to human wellbeing and security in the cities of China. A valuable aid to managing this problem lies in understanding the roles of environmental factors in influencing the occurrence of pluvial floods. This study presents a spatial analysis of records of inundated streets in the inner city of Shanghai during 1997–2013. A geographically weighted regression (GWR) is employed to examine the spatially explicit relationships between inundation frequency and spatial explanatory factors, and an ordinary least squares regression (OLS) is used to validate the GWR results. Results from the GWR model show that the inundation frequency is negatively related to elevation, pipeline density, and river density, and is positively related to road/square ratio and shantytown ratio. The green ratio is another significant explanatory factor for inundation frequency, and its coefficients range from ?1.11 to 0.81. In comparison with the OLS model, the GWR model has better performance as it has higher R², and lower corrected Akaike information criterion and mean square error values, as well as insignificant spatial autocorrelation of the model residuals. Additionally, the GWR model reveals detailed site-specific roles of the related factors in influencing street inundation. These findings demonstrate that the GWR model is a useful tool for investigating spatially explicit causes of disasters. The results also provide guidance for policy makers aiming to mitigate urban pluvial flood risks.     

Estimating the provincial environmental Kuznets curve in China: a geographically weighted regression approach

This study estimates the environmental Kuznets curve (EKC) relationship at the province level in China. We apply empirical methods to test three industrial pollutants—SO₂ emission, wastewater discharge, and solid waste production—in 29 Chinese provinces in 1994–2010. We use the geographically weighted regression (GWR) approach, wherein the model can be fitted at each spatial location in the data, weighting all observations by a function of distance from the regression point. Hence, considering spatial heterogeneity, the EKC relationship can be analyzed region-specifically through this approach, rather than describing the average relationship over the entire area examined. We also investigate the spatial stratified heterogeneity to verify and compare risk factors that affect regional pollution with statistical models. This study finds that the GWR model, aimed at considering spatial heterogeneity, outperforms the OLS model; it is more effective at explaining the relationships between environmental performance and economic growth in China. The results indicate a significant variation in the existence of the EKC relationship. Such spatial patterns suggest province-specific policymaking to achieve balanced growth in those provinces.     

Declustering experimental variograms by global estimation with fourth order moments

The variogram is a key parameter for geostatistical estimation and simulation. Preferential sampling may bias the spatial structure and often leads to noisy and unreliable variograms. A novel technique is proposed to weight variogram pairs in order to compensate for preferential or clustered sampling . Weighting the variogram pairs by global kriging of the quadratic differences between the tail and head values gives each pair the appropriate weight, removes noise and minimizes artifacts in the experimental variogram. Moreover, variogram uncertainty could be computed by this technique. The required covariance between the pairs going into variogram calculation, is a fourth order covariance that must be calculated by second order moments. This introduces some circularity in the calculation whereby an initial variogram must be assumed before calculating how the pairs should be weighted for the experimental variogram. The methodology is assessed by synthetic and realistic examples. For synthetic example, a comparison between the traditional and declustered variograms shows that the declustered variograms are better estimates of the true underlying variograms. The realistic example also shows that the declustered sample variogram is closer to the true variogram.     

Using geographically weighted regression to explore the spatially heterogeneous spread of bovine tuberculosis in England and Wales

An understanding of the factors that affect the spread of endemic bovine tuberculosis (bTB) is critical for the development of measures to stop and reverse this spread. Analyses of spatial data need to account for the inherent spatial heterogeneity within the data, or else spatial autocorrelation can lead to an overestimate of the significance of variables. This study used three methods of analysis—least-squares linear regression with a spatial autocorrelation term, geographically weighted regression (GWR) and boosted regression tree (BRT) analysis—to identify the factors that influence the spread of endemic bTB at a local level in England and Wales. The linear regression and GWR methods demonstrated the importance of accounting for spatial differences in risk factors for bTB, and showed some consistency in the identification of certain factors related to flooding, disease history and the presence of multiple genotypes of bTB. This is the first attempt to explore the factors associated with the spread of endemic bTB in England and Wales using GWR. This technique improves on least-squares linear regression approaches by identifying regional differences in the factors associated with bTB spread. However, interpretation of these complex regional differences is difficult and the approach does not lend itself to predictive models which are likely to be of more value to policy makers. Methods such as BRT may be more suited to such a task. Here we have demonstrated that GWR and BRT can produce comparable outputs.     

Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor

In this study, we link and compare the geographically weighted regression (GWR) model with the kriging with an external drift (KED) model of geostatistics. This includes empirical work where models are performance tested with respect to prediction and prediction uncertainty accuracy. In basic forms, GWR and KED (specified with local neighbourhoods) both cater for nonstationary correlations (i.e. the process is heteroskedastic with respect to relationships between the variable of interest and its covariates) and as such, can predict more accurately than models that do not. Furthermore, on specification of an additional heteroskedastic term to the same models (now with respect to a process variance), locally-accurate measures of prediction uncertainty can result. These heteroskedastic extensions of GWR and KED can be preferred to basic constructions, whose measures of prediction uncertainty are only ever likely to be globally-accurate. We evaluate both basic and heteroskedastic GWR and KED models using a case study data set, where data relationships are known to vary across space. Here GWR performs well with respect to the more involved KED model and as such, GWR is considered a viable alternative to the more established model in this particular comparison. Our study adds to a growing body of empirical evidence that GWR can be a worthy predictor; complementing its more usual guise as an exploratory technique for investigating relationships in multivariate spatial data sets.     

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.     

Defining probability of saturation with indicator kriging on hard and soft data

In humid, well-vegetated areas, such as in the northeastern US, runoff is most commonly generated from relatively small portions of the landscape becoming completely saturated, however, little is known about the spatial and temporal behavior of these saturated regions. Indicator kriging provides a way to use traditional water table data to quantify probability of saturation to evaluate predicted spatial distributions of runoff generation risk, especially for the new generation of water quality models incorporating saturation excess runoff theory. When spatial measurements of a variable are transformed to binary indicators (i.e., 1 if above a given threshold value and 0 if below) and the resulting indicator semivariogram is modeled, indicator kriging produces the probability of the measured variable to exceed the threshold value. Indicator kriging gives quantified probability of saturation or, consistent with saturation excess runoff theory, runoff generation risk with depth to water table as the variable and the threshold set near the soil surface. The probability of saturation for a 120 m × 180 m hillslope based upon 43 measurements of depth to water table is investigated with indicator semivariograms for six storm events. The indicator semivariograms show high spatial structure in saturated regions with large antecedent rainfall conditions. The temporal structure of the data is used to generate interpolated (soft) data to supplement measured (hard) data. This improved the spatial structure of the indicator semivariograms for lower antecedent rainfall conditions. Probability of saturation was evaluated through indicator kriging incorporating soft data showing, based on this preliminary study, highly connected regions of saturation as expected for the wet season (April through May) in the Catskill Mountain region of New York State. Supplementation of hard data with soft data incorporates physical hydrology of the hillslope to capture significant patterns not available when using hard data alone for indicator kriging. With the need for water quality models incorporating appropriate runoff generation risk estimates on the rise, this manner of data will lay the groundwork for future model evaluation and development.     

Spatial prediction on river networks: comparison of top‐kriging with regional regression

Top‐kriging is a method for estimating stream flow‐related variables on a river network. Top‐kriging treats these variables as emerging from a two‐dimensional spatially continuous process in the landscape. The top‐kriging weights are estimated by regularising the point variogram over the catchment area (kriging support), which accounts for the nested nature of the catchments. We test the top‐kriging method for a comprehensive Austrian data set of low stream flows. We compare it with the regional regression approach where linear regression models between low stream flow and catchment characteristics are fitted independently for sub‐regions of the study area that are deemed to be homogeneous in terms of flow processes. Leave‐one‐out cross‐validation results indicate that top‐kriging outperforms the regional regression on average over the entire study domain. The coefficients of determination (cross‐validation) of specific low stream flows are 0.75 and 0.68 for the top‐kriging and regional regression methods, respectively. For locations without upstream data points, the performances of the two methods are similar. For locations with upstream data points, top‐kriging performs much better than regional regression as it exploits the low flow information of the neighbouring locations. Copyright © 2012 John Wiley & Sons, Ltd.     

A first arrival picking method of microseismic data based on single time window with window length independent

First arrival picking is a key factor which affects the precision of microseismic data analysis. Here, we propose a new method, which employs the maximum eigenvalue to constraint the Maeda-Akaike Information Criterion (Maeda-AIC) algorithm. First, aims at addressing the pick result affected by signal-to-noise ratio (SNR) of microseismic data, maximum eigenvalue method based on polarization analysis is applied, and the maximum eigenvalue is calculated firstly, as for three component (3C) microseismic data, the maximum eigenvalue is calculated with corresponding covariance matrix, a time window need to be set in the process of building the covariance matrix, and it is the only time window set in the method proposed in this paper, so the method is called single window Maeda-AIC (SWM-AIC), to the single component (1C) microseismic data, the variance of the data is taken as the maximum eigenvalue. Then, to reduce the effect of time window and increase the automation of the algorithm, Maeda-AIC method which is a non-window-based first arrival picking method is applied. Maeda-AIC values in preliminary window are calculated, and the preliminary window is the sequence before the largest eigenvalue of the 3C or 1C data. We validate the developed method with both synthetic and field microseismic data, using a range of signal-to-noise ratios. The developed method is compared with some basic methods, specifically STA/LTA, Maeda-AIC, and the maximum eigenvalue method. The results demonstrate that the new method is much better at identifying first arrival times than basic methods when the data have a low signal-to-noise ratio, and is even faster than the STA/LTA method with 1C data. In contrast to other improved methods, threshold value is not required for this method, and the only time window used in this method is just for maximum eigenvalue calculation, through test in the paper, its length has almost no effect on the first arrival picking.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Generation of runoff series at ungauged locations using empirical orthogonal functions in combination with kriging

The method of Empirical Orthogonal Functions (EOF method) is combined with an objective interpolation technique, kriging, to generate runoff series at ungauged locations. In a case study the results are compared to series interpolated by a combination of EOF analysis and regression using catchment characteristics as independent variables. The results are also compared to linear weighting of an existing runoff series, a commonly used method for spatial interpolation. The influence of altitude on the runoff is studied comparing kriging based on 2 and 3 coordinates. The study showed that the capacity of EOF analysis combined with kriging is as good as the traditionally used linear weighting. The results, when altitude is included in the kriging, are improved.     

基于离心窗倾角扫描的曲率属性提取

体曲率属性作为三维地震资料构造解释的重要工具,在识别地层弯曲、地层不连续性,以及裂缝预测方面呈现了不可或缺的作用,因此如何高质量的提取该属性成为一个需要关注的问题.体曲率属性提取质量的关键在于倾角扫描的精度,本文提出了一种基于离心窗的倾角扫描方法,该离心窗是在空间为中心偏离分析点的四个旋转窗口,时间上为包含分析点的五个纵向滑动窗口,通过变换不同的窗口进行高精度倾角估计,并采用最小二乘拟合插值求取真实倾角.该方法避免了多窗扫描对小断层构造的忽略以及噪声的过大影响,同时在处理中对倾角数据进行中值滤波,去掉噪点影响.将由离心窗倾角扫描方法所计算的倾角数据体应用到曲率属性的计算中,在恢复构造细节和提高信噪比方面均展现了较好的效果.     

A general weighted total Kalman filter algorithm with numerical evaluation

An applicable algorithm for Total Kalman Filter (TKF) approach is proposed. Meanwhile, we extend it to the case in which we can consider arbitrary weight matrixes for the observation vector, the random design matrix and possible correlation between them. Also the updated dispersion matrix of the predicted unknown is given. This approach makes use of condition equations and straightforward variance propagation rules. It is applicable to data fusion within a dynamic errors-in-variables (DEIV) model, which usually appears in the determination of the position and attitude of mobile sensors. Then, we apply for the first time the TKF algorithm and its extended version named WTKF to a DEIV model and compare the results. The results show the efficiency of the proposed WTKF algorithm. In particular in the case of large weights, WTKF shows approximately 25% improvement in contrast to TKF approach.     

Comparison between the indirect approach and kriging with samples of different support for estimation using samples of different length

In this paper we compare two estimation methods to deal with samples of different support: (1) the indirect approach using accumulation and (2) kriging with samples of different support. These two methods were tested in a simple example. The estimates of the two methods were compared against a benchmark scenario. The benchmark consisted of kriging using a complete set of samples on the same support. The effects of the nugget effect, variogram range and type on the weight of long samples, the estimate, and the error variance were assessed. Kriging with samples of different support led to lower error variance and to estimates closer to the estimates of the benchmark scenario. Furthermore, in the case of spatially continuous attributes (low nugget effect), the indirect approach assigns greater weight to long samples than kriging with samples of different support. A cross validation study comparing the two methods with a database from a bauxite deposit was performed. The results of the cross validation study showed that kriging with samples of different support resulted in more precise estimates.     

Geostatistical prediction of a local geometric geoid - kriging and cokriging with the use of EGM2008 geopotential model

We investigate prediction abilities of different variants of kriging and different combinations of data in a local geometric (GNSS/leveling based) geoid modeling. In order to generate local geoid models, we have used GNSS/leveling data and EGM2008 geopotential model. EGM2008 has been used twofold. Firstly, it was used as a basic long wave-length trend to be removed from geoid undulation data to generate a residual field of geoid heights modeled later by kriging (remove-restore technique). Secondly, EGM2008-based undulations were used as a secondary variable in a cokriging prediction procedure (as pseudo-observations). Besides the use of EGM2008, the kriging-based local geometric geoid models were generated only on the basis of raw undulations data. Kriging itself was used in two variants, i.e. ordinary kriging and universal kriging for univariate and bivariate cases (cokriging). The quality of kriging-based prediction for all its variants and all data combinations have been investigated on one fixed validation dataset consisting of 86 points and three training data sets characterized by a different density of sampling. Results of this study indicate that incorporation of EGM08 as a long wave-length trend in kriging prediction procedure outperforms cokriging strategy based on incorporation of EGM08 as a secondary spatially correlated variable.     

基于压缩感知的加权MCA地震数据重构方法

地震数据规则化重构是地震资料处理十分重要的基础性工作.压缩感知理论打破了香农采样定理的制约,利用信号在某个变换域的稀疏特性重构出完整的信号,在地震数据重构领域得到了很好的应用.深反射地震剖面大都布置在地质构造比较复杂的区段,复杂的地质构造使深反射地震剖面上的波阻特征复杂,采用单一稀疏变换不能最有效地表征数据的内部结构特征.MCA（形态成分分析）方法将信号分解为几种形态特征区别明显的分量来逼近数据的内部复杂结构,但是对各成分简单的叠加仍然无法有效地描述复杂构造数据的各种特征.结合两种方法的优点,本文提出了一种新的基于压缩感知的重构算法框架,在MCA方法的基础上对各稀疏字典进行加权,在迭代中不断更新各个稀疏字典的权值系数,对信号内部的各种特征进行最优描述,从而实现对信号的高质量重构.模型测试和实际资料处理结果表明：基于压缩感知的加权MCA方法不仅可以对地质构造复杂的地震数据进行高效的插值重建,而且可以很好的消除空间假频.

     

带窗洞的加气混凝土砌块砌体墙抗震性能分析

为了研究设窗洞的蒸压加气混凝土砌块砌体承重墙的抗震性能,运用ABAQUS有限元分析软件对其进行了非线性分析。首先将有限元模型的计算结果与足尺试件的试验结果进行了对比验证,在此基础上,通过改变墙体的竖向压应力、水平配筋和开洞大小,研究了这些参数对墙体抗震性能的影响。研究表明:随着竖向压应力的增大,墙体水平承载力提高,而极限变形能力则有降低趋势;水平配筋可以提高墙体的承载力和变形性能;增大洞口水平尺寸导致极限承载力明显降低,而对其相应位移的影响则小得多。     

Map plotting with weighted average on the surface of a circular disc

Summary The weighted averaging on the surface of a circular disc as a method of the transformation of a data system measured in random points to grid points is discussed using the concepts of filter theory. The transfer functions of various weighting functions are computed. The transformation is illustrated by practical examples.     

Mapping gamma radiation and its uncertainty from weathering products in a Tasmanian landscape with a proximal sensor and random forest kriging

The radionuclides of potassium (⁴⁰ K), uranium (²³⁸U) and thorium (²³²Th) emit from the land surface gamma radiation that is characteristic of the underlying rocks and the distribution of their weathering products in the landscape. We measured the radiation along widely separated transects using a mobile proximal sensor over a 10 000‐ha region of Tasmania. We supplemented the transect data with information from soil and geological maps and dense data from LandSat and SPOT imagery, a digital elevation model and terrain attributes on a grid at 30‐m intervals so as to map the radionuclides. We used a sequence of steps, starting with a spatial bootstrap and random forests to predict emissions across the study area and at sampling points excluded from the bootstrap samples. The predictions at the sampling points were compared with the observed values to obtain residuals, which were then used to krige them at all points on the 30 m grid. We combined the random forest and kriging predictions on the 30‐m grid to obtain our random forest kriging predictions. Repeating the procedure 100 times provided confidence limits on our results and predictions. The resulting maps of the radionuclides accord well with what we know of the soil, lithology and topography of the region from other sources. Alluvial deposits with large amounts of potassium extend from the foot slopes of the Great Western Tiers and along the flood plains of the Meander River, providing evidence of previous widespread weathering and deposition of the material. The fertile Red Ferrosols (roughly equivalent to Ferralic Nitisols in the World reference base (WRB) classification) on the extensive Tertiary basalt plateau emit little gamma radiation as a result of deep weathering and of potassium movement and accumulation down its talus slopes. The maps show the complexity of the region in terms of soil, lithology and terrain, and they show the merits of gamma radiometry for mapping and understanding the distribution of materials in such regions. Copyright © 2013 John Wiley & Sons, Ltd.