基于时空窗口改进的时空加权回归分析——以湖北省黄石市住房价格为例

针对地理加权回归(GWR)模型不能有效处理样本数据空间自相关性这一问题,构造局部时空窗口统计量,尝试改进时空加权回归(GTWR)模型。定义多时空窗口的概念,给出其选取、计算和验证方法;计算时空窗口包含的各样本点的被解释变量平均值,与样本拟合点的被解释变量值的比值,作为新的解释变量,构建改进的时空加权回归(IGTWR)模型。以土地稀缺、多中心、资源型城市——湖北省黄石市为例,收集2007~2012年商品住宅成交价格1.93万个数据和398个楼栋样本点,选取小区等级、绿化率、楼栋总层数、容积率、距区域中心距离和销售年份6个解释变量,分别利用常规线性回归(OLS)、GWR、GTWR和IGTWR方法进行回归分析。模型结果表明：计算Moran’s I指数和分析时间序列的自相关性,能确定时空窗口的大小和数量的选取;IGTWR模型和各变量的回归统计均通过0.05的显著性水平检验,有关解释变量的系数估计值在空间分布上能合理解释;GWR拟合结果优于OLS,GTWR优于GWR,而IGTWR拟合精度最好。与GTWR模型分析相比, IGTWR模型R²从0.877提升到0.919,而AICc、残差方(RSS)和均方差(MSE)分别从6 226、49 996 201和354.427下降到6 206、32 327 472和284.969。案例研究表明：IGTWR能够表达一定时空范围的时空自相关特征,减小了估计误差,提高了回归拟合精度。     

GWR模型在土壤重金属高光谱预测中的应用

目前土壤重金属高光谱反演模型大多忽视了重金属与光谱变量间相关关系的空间异质性,这与实际情况不相吻合,而地理权重回归（GWR）模型能有效地揭示变量间关系的空间异质性。本文以福州市土壤重金属Cd、Cu、Pb、Cr、Zn、Ni为对象,构建土壤重金属预测的GWR高光谱模型,并将预测结果与普通最小二乘法回归（OLS）结果进行比较分析,探讨GWR模型在土壤重金属高光谱预测中的适用性及局限性。结果表明：① GWR模型在土壤重金属高光谱预测中适用与否取决于重金属对光谱变量影响的空间异质性程度：对于Cr、Cu、Zn、Pb等对光谱变量影响空间异质性大的元素,其GWR预测精度较OLS提高明显,表现为GWR模型的调节R²较OLS模型有了明显提高,分别为OLS模型的2.69倍、2.01倍、1.87倍和1.53倍;而AIC值以及残差平方和较OLS模型却明显降低,AIC值减少量均大于3个单位,残差平方和则仅分别为OLS模型的25.33%、30.09%、47.22%和86.84%;对于Cd和Ni等对光谱变量影响空间异质性小的元素,相较于OLS模型,GWR模型的调节R²分别提高了0.015和0.007,残差平方和分别减少了5.97%和4.18%,但AIC值却分别增加了2.737和2.762,GWR预测效果改善不明显;② 光谱变换可以有效增强土壤重金属的光谱特征,其中以光谱的倒数变换效果最好,而且该变换及其微分形式可以很好地提高模型的预测效果;③ GWR模型的应用前提是变量间关系的空间非平稳性,适合在与土壤光谱变量间关系具有显著空间异质性的重金属高光谱预测中推广。     

黄土高原地区NDVI与气候因子空间尺度依存性及非平稳性研究

基于MODIS传感器的植被指数产品(MOD13Q1)及50年气候数据,通过地理加权回归与普通最小二乘回归模型对比,对中国黄土高原地区NDVI与气候因子间的空间尺度依存性及非平稳性进行研究,以期准确建立二者间关系.结果表明:① 研究区域内,NDVI与气候因子间存在很强的空间尺度依存关系,相同空间尺度下,年均降水较年均温对NDVI影响的波动性更大;② 与普通最小二乘回归模型相比,地理加权回归模型能够更准确地展现二者间关系;③气候因子对该地区NDVI的影响差异明显,降水存在直接正向影响,而温度的影响则较复杂;④ NDVI与气候因子间沿东北--西南的分布格局体现出区域内不同植被--气候区差异特征.二者间的异质情况还反映出除气候外,人类活动,地形等其他因素对NDVI的影响.     

基于地理加权回归的漫湾库区景观破碎化及影响因子分析

应用地理加权回归模型分析漫湾库区景观破碎化指数——有效筛网大小与相关因子之间的空间关系。选取的解释变量分别是距道路的距离、距乡村的距离、距河流的距离、坡度。结果表明：大坝修建后4种解释变量与有效筛网大小呈现较显著的正相关性。与线性回归模型相比,地理加权回归模型的拟合效果显著提高。1974~1988年,有效筛网大小对各影响因子最敏感的区域面积呈现显著的时空变化这为确定水电站建设及其他因素对景观破碎化影响的大小,并进一步改善库区景观破碎化的现状提供了依据。     

A comment on geographically weighted regression with parameter-specific distance metrics

A recent paper in this journal proposed a form of geographically weighted regression (GWR) that is termed parameter-specific distance metric geographically weighted regression (PSDM GWR). The central focus of the PSDM generalization of the GWR framework is that it allows the kernel function that weights nearby data to be specified with a distinct distance metric. As with the recent paper on Multiscale GWR (MGWR), the PSDM framework presents a form of GWR that also allows for parameter-specific bandwidths to be computed. As a result, a secondary focus of the PSDM GWR framework is to reduce the computational overhead associated with searching a massive parameter space to find a set of optimal parameter-specific bandwidths and parameter-specific distance metrics. In this comment, we discuss several concerns with the PSDM GWR framework in terms of model interpretability, complexity, and computational efficiency. We also recommend some best practices when using these models, suggest how to more holistically assess model variations, and set out an agenda to constructively focus future research endeavors.     

基于3种地理加权回归方法的安徽省土壤pH空间预测制图对比研究

基于安徽省140个采样点的土壤pH数据,综合考虑土壤、地形、气候、生物等因子对土壤pH的影响,采用地理加权回归(Geographically Weighted Regression, GWR)、主成分地理加权回归(Principal Component Geographically Weighted Regression, PCA-GWR)和混合地理加权回归(Mixed Geographically Weighted Regression, M-GWR)3种模型对安徽省土壤pH空间分布进行建模预测,揭示环境因子对土壤pH的影响在空间上的差异,最后以多元线性回归模型(Multiple Linear Regression, MLR)为基准比较3种GWR模型的精度。研究表明：(1)安徽省土壤pH具有空间异质性,且集聚特征明显。(2) 3种GWR模型中M-GWR模型略优,GWR、PCA-GWR和M-GWR的建模集调整后决定系数(R_adj²)分别为0.59、0.62和0.63;对比MLR模型,3种GWR模型的R_adj^2<...     

Climatic Changes Dominant Interannual Trend in Net Primary Productivity of Alpine Vulnerable Ecosystems

The Three-River Headwaters (TRH), which is the source area of Yangtze River, Yellow River and Lancang River, is vulnerable and sensitive, and its alpine ecosystem is considered an important barrier for China’s ecological security. Understanding the impact of climate changes is essential for determining suitable measures for ecological environmental protection and restoration against the background of global climatic changes. However, different explanations of the interannual trends in complex alpine ecosystems have been proposed due to limited availability of reliable data and the uncertainty of the model itself. In this study, the remote sensing-process coupled model (GLOPEM-CEVSA) was used to estimate the net primary productivity (NPP) of vegetation in the TRH region from 2000 to 2012. The estimated NPP significantly and linearly correlated with the above-ground biomass sampled in the field (the multiple correlative coefficient R² = 0.45, significant level P < 0.01) and showed better performance than the MODIS productivity product, i.e. MOD17A3, (R² = 0.21). The climate of TRH became warmer and wetter during 1990-2012, and the years 2000 to 2012 were warmer and wetter than the years1990-2000. Responding to the warmer and wetter climate, the NPP had an increasing trend of 13.7 g m^-2 (10 yr)^-1 with a statistical confidence of 86% (P = 0.14). Among the three basins, the NPP of the Yellow River basin increased at the fastest rate of 17.44 g m^-2 (10 yr)^-1 (P = 0.158), followed by the Yangtze River basin, and the Lancang River, which was the slowest with a rate of 12.2 g m^-2 (10 yr)^-1 and a statistical confidence level of only 67%. A multivariate linear regression with temperature and precipitation as the independent variables and NPP as the dependent variable at the pixel level was used to analyze the impacts of climatic changes on the trend of NPP. Both temperature and precipitation can explain the interannual variability of 83% in grassland NPP in the whole region, and can explain high, medium and low coverage of 78%, 84% and 83%, respectively, for grassland in the whole region. The results indicate that climate changes play a dominant role in the interannual trend of vegetation productivity in the alpine ecosystems on Qinghai-Tibetan Plateau. This has important implications for the formulation of ecological protection and restoration policies for vulnerable ecosystems against the background of global climate changes.     

基于MODIS数据的青藏高原气温与增温效应估算

利用2001-2007 年MODIS地表温度数据、137 个气象观测台站数据和ASTERGDEM数据, 采用普通线性回归分析方法(OLS)及地理加权回归分析方法(GWR), 研究了高原月均地表温度与气温的相关关系, 最终选择精度较高的GWR分析方法, 建立了高原气温与地表温度、海拔高度的回归模型。各月气温GWR回归模型的决定系数(Adjusted R²) 都达到了0.91 以上(0.91~0.95), 标准误差(RMSE) 介于1.16~1.58℃;约70%以上的台站各月残差介于-1.5~1.5℃之间, 80%以上的台站的残差介于-2~2℃之间。根据该模型, 估算了青藏高原气温, 并在此基础上, 将高原及周边地区7 月份月均气温转换到4500 m和5000 m海拔高度上, 对比分析高原内部相对于外围地区的增温效应。研究结果表明:(1) 利用GWR方法, 结合地面台站的观测数据和MODIS Ts、DEM等, 对高原气温估算的精度高于以往普通回归分析模型估算的精度(RMSE=2~3℃), 精度可以提高到1.58℃;(2) 高原夏半年海拔5000 m左右的高山区气温能达到0℃以上, 尤其是7 月份, 海拔4000~5500 m的高山区的气温仍能达到10℃左右, 为山地森林的发育提供了温度条件, 使高原成为北半球林线分布最高的地方;(3) 高原的增温效应非常突出, 初步估算, 在相同的海拔高度上高原内部气温要比外围地区高6~10℃。     

干旱区大尺度土壤盐度信息环境建模——以新疆天山南北中低海拔冲积平原为例

区域空间信息有助于决策者针对特定潜在和既定的土壤盐渍化区域制定改良和优化政策,以避免灌区水土资源的不合理配置和干旱区土地生态系统持续性退化。然而现存区域尺度土壤盐度数据以矢量方式留存,多边形内部土壤属性无空间变异性,缺乏实时更新,对当下实际指导作用具有一定的局限性。随着人类活动的加剧,土壤及其结构性退化正加速危害土壤质量和健康。对此,急需更新或升级,用于刻画干旱区生态系统中土壤盐度数据,以辅助制定相关政策,减缓土壤盐渍化的危害。针对此问题,本文基于代表性等级的采样设计方法（Integrative Hierarchical Sampling Strategy, IHSS）,获取少量典型样点,结合土壤—环境推理模型（soil land inference model, SoLIM）,尝试推理区域尺度土壤盐分含量信息。研究以新疆天山南北中低海拔冲积平原为案例,仅以23个代表性样本,推理陆表（0~10 cm）土壤盐分含量,源自3个典型绿洲94个野外样本的验证数据显示,依据评判标准,预测结果与实际情况较为相符,与线性回归模型相比,具备处理土壤与环境变量之间非线性关系的SoLIM,推理精度更高。所以,研究认为模糊隶属度加权平均的方法（IHSS-SoLIM）可以通过较小的建模点得到更好的预测效果,可作为区域尺度土壤盐度推理的备选方案。     

基于MODIS的青海草地产草量变化遥感分析

青海省属于全国四大牧区之一,及时监测草地植被长势、准确估算牧草产量对青海牧区可持续发展与生态保护具有重要意义。草地产草量遥感估算主要基于植被指数与地面实测数据的统计关系,但是估算涉及植被指数、统计模型和建模指标等因素,不同组合建立的估算模型的精度不同。本文基于青海省MODIS数据与地面实测产草量数据,选择了6种植被指数（NDVI、EVI、RVI、DVI、RDVI、MSAVI）、5种统计模型（简单线性模型、二次多项式模型、幂函数模型、指数函数模型、对数函数模型）以及3种建模指标（植被指数年度最大值VI_max、植被指数生长季累积值VI_season-cum、植被指数年度累积值VI_annual-cum）,研究不同组合下估算模型的精度差异,并从中选出最优产草量估算模型,用于估算青海省2015年和2016年的产草量。结果表明：（1）6种植被指数中,基于NDVI的产草量估算精度最高;非线性模型的估算精度高于线性模型,尤其是指数模型,适用于大多数草地类型产草量的估算;基于NDVI年度最大值的估算模型对大多数草地类型都具有最高的决定系数（R²）。（2）从干重来看,高产草量区（>1 200 kg·hm^-2）主要位于青海东部的高寒草原,中等产草量区（600~1 200 kg·hm^-2）位于青海南部和东部的高寒草原和禾草草原,低产草量区（<600 kg·hm^-2）位于青海西部和北部的高寒草甸、高寒草原、高寒荒漠和盐生草甸。（3）与2015年相比,2016年青海省干草总产量减少31.60×10⁴ t,减幅为1.36%。其中,禾草草原和高寒草甸的减产幅度最大,而荒漠草原和盐生草甸的产量则有所增加。本文可为草地产草量遥感估算的研究和实践提供参考。     

省域经济增长与电力消费的局域空间计量经济分析

中国各个地区经济发展对电力消费需求量大且存在地域差异,不同区域间的电力需求与经济增长之间的关系十分复杂,并非能由常系数的普通最小二乘回归分析所解释.采用电力消费模型,利用局域空间计量经济学模型方法--空间变系数的地理加权回归模型,对中国省域电力消费与经济增长之间的关系进行了局域空间计量经济分析.结果发现,中国大陆30个省域的电力消费和经济增长之间表现为一种非均衡的联动关系和局域性特征,制定差异化的区域电力消费调控政策是非常必要的.     

基于改进土壤冻融水循环的Biome-BGC模型估算青藏高原草地NPP

Biome-BGC模型被广泛用于估算植被净初级生产力（Net Primary Productivity, NPP）,但是该模型未考虑冻土区土壤冻融水循环过程对植被生长的影响。本文基于Biome-BGC模型,改进冻土区活动层土壤冻融水循环,估算了2000—2018年青藏高原高寒草地NPP。通过比较原模型和改进后的模型,并对NPP模拟结果的时空特征进行了分析,结果表明：① 增加冻融循环提高了NPP估算精度,青藏高原草地NPP均值由114.68 gC/(m²·a)提高到128.02 gC/(m²·a)。② 原模型和改进后NPP的空间分布差异较大,时间变化趋势差异不明显。③ 青藏高原草地NPP总量为253.83 TgC/a,呈东南向西北递减的空间格局,年均增速为0.21gC/(m²·a)（P=0.023）,显著增加的占17.85%,主要分布在羌塘高寒草原地带的大部分地区和藏南山地灌木草原地带的西部。④ 该冻融水循环改进方法简单可靠,具有在其他多年冻土区推广的价值。     

中国省域犯罪率影响因素的空间非平稳性分析

收入差距和流动人口是影响犯罪率的两个重要因素, 以往研究基于OLS模型, 在假设地域空间为均质的前提下分析其对犯罪率的影响, 但现实世界的空间单元往往难以满足“均质”的假设, 多数表现为“空间异质”。以OLS计量空间异质会造成计量结果出现偏差, 同时无法了解不同空间单元的不同影响。而地理加权回归模型通过将空间结构嵌入线性回归模型中, 很好的解决了空间异质的计量问题。利用地理加权回归模型研究2008 年中国大陆省域单元犯罪率的影响因素, 结果表明:① 犯罪率的影响因素表现出空间非平稳性, 流动人口与犯罪率显著相关, 但各个省份相关程度并不相同, 影响关系随空间位置变化而变化;② 地理加权回归模型的计量精度和拟合度比OLS模型有大幅提高     

内蒙古高原等地湖泊表层沉积物孢粉与植被覆盖度定量关系研究

过去植被覆盖度重建在长尺度气候模拟和陆地生态环境演变机制研究等方面具有重要意义。基于现代过程的孢粉—植被覆盖度转换函数研究,可为利用孢粉地层数据重建过去植被覆盖度变化提供一条新的途径。以内蒙古高原等地39个湖泊和7个水库中心的表层沉积物孢粉组合与归一化植被指数(NDVI)为研究对象,利用加权平均偏最小二乘法(WA-PLS)、局部加权加权平均法(LWWA)和最佳类比法(MAT)分别建立了孢粉—NDVI转换函数;通过留一交叉检验法、自助法和空间自相关性等检验,筛选出最优模型并应用于古地层孢粉数据,实现定量重建过去植被覆盖度变化。结果表明:MAT和WA-PLS模型均受到空间自相关性的显著影响,而LWWA模型则是建立孢粉—NDVI转换函数的最优模型。与已有类似转换函数表现能力的对比表明,本研究建立的转换函数具有较强的可靠性和应用潜力。基于本研究转换函数重建的内蒙古辉腾锡勒(HTL)区域全新世植被覆盖变化与孢粉重建的植被变化具有很好的一致性,进一步印证了本研究转换函数的较强潜力,均表现出对降水变化的响应更为显著。     

西藏NPP时空格局与气候因子的关系

根据2000-2012年1 km MOD17A3 NPP遥感数据和气温、降水等气象资料,在GIS支撑下,结合多种统计计算方法,对西藏NPP时空格局与气候因子的关系进行研究。结果表明:2000-2012年间西藏陆地植被的NPP为119.3～148.4 g·m^-2·a^-1,平均为135.2 g·m^-2·a^-1;近年来西藏NPP呈不显著上升趋势,NPP总体上由东南向西北逐渐变小。13年来西藏NPP在总体不变(面积占61.11%)的基础上略有增加(面积占10.7%);不同植被类型中阔叶林的NPP最大,为1 185.2～1 430.2 g·m^-2·a^-1,其次是混交林,为535.1～741.2 g·m^-2·a^-1,其后依次是稀树草原、针叶林、农用地、草地和灌丛;西藏NPP与气温、降水因子分别有较好的正、负相关性。所有植被类型都与年均气温呈正相关,其中草地的NPP与年均气温的相关系数达0.88,其次是针叶林为0.76,相关性最差为热带稀树草原0.13;与年降水量的相关性,除了热带稀树草原正相关(0.26),其余都负相关,草地、针叶林的相关系数分别为-0.79、-0.73。     

Computational improvements to multi-scale geographically weighted regression

ABSTRACT

Geographically Weighted Regression (GWR) has been broadly used in various fields to model spatially non-stationary relationships. Multi-scale Geographically Weighted Regression (MGWR) is a recent advancement to the classic GWR model. MGWR is superior in capturing multi-scale processes over the traditional single-scale GWR model by using different bandwidths for each covariate. However, the multiscale property of MGWR brings additional computation costs. The calibration process of MGWR involves iterative back-fitting under the additive model (AM) framework. Currently, MGWR can only be applied on small datasets within a tolerable time and is prohibitively time-consuming to run with moderately large datasets (greater than 5,000 observations). In this paper, we propose a parallel implementation that has crucial computational improvements to the MGWR calibration. This improved computational method reduces both memory footprint and runtime to allow MGWR modelling to be applied to moderate-to-large datasets (up to 100,000 observations). These improvements are integrated into the mgwr python package and the MGWR 2.0 software, both of which are freely available to download.     

Geographically neural network weighted regression for the accurate estimation of spatial non-stationarity

ABSTRACT

Geographically weighted regression (GWR) is a classic and widely used approach to model spatial non-stationarity. However, the approach makes no precise expressions of its weighting kernels and is insufficient to estimate complex geographical processes. To resolve these problems, we proposed a geographically neural network weighted regression (GNNWR) model that combines ordinary least squares (OLS) and neural networks to estimate spatial non-stationarity based on a concept similar to GWR. Specifically, we designed a spatially weighted neural network (SWNN) to represent the nonstationary weight matrix in GNNWR and developed two case studies to examine the effectiveness of GNNWR. The first case used simulated datasets, and the second case, environmental observations from the coastal areas of Zhejiang. The results showed that GNNWR achieved better fitting accuracy and more adequate prediction than OLS and GWR. In addition, GNNWR is applicable to addressing spatial non-stationarity in various domains with complex geographical processes.     

Responses of Grassland Net Primary Productivity to Environmental Variables in Northern China

Various environmental factors affect net primary productivity (NPP) of grassland ecosystem. Extensive reports on the effects of environmental variables on NPP can be found in literature. However, the agreement on the relative importance of various factors in shaping the spatial pattern of grassland NPP has not yet been reached. Here a grassland in situ NPP database comprising 602 samples in northern China for 1980-1999 was developed based on a literature review of published biomass and forage yield field measurements. Correlation analyses and dominance analysis were used to quantify the separate and combined effects of environmental variables (climate, topography and soil) on spatial variation in NPP separately. Grassland NPP ranged from 4.76 g C m^-2a^-1 to 975.94 g C m^-2a^-1, showing significant variations in space. NPP increased with annual precipitation and declined with annual mean temperature significantly. Specifically, precipitation had the greatest impact on deserts, followed by steppes and meadows. Grassland NPP decreased with increasing altitude because of water limitation, and positively correlated with slope, but weakly correlated with aspect. Soil quality showed positive effects on NPP. Annual precipitation was the dominant factor affecting the spatial variability of net primary productivity, followed by elevation.     

MODIS和Landsat时空融合影像在土壤盐渍化监测中的适用性研究——以渭干河—库车河三角洲绿洲为例

土壤盐渍化的遥感监测依赖于高时空分辨率影像,但受经费预算、卫星回访周期及天气的影响,高时空分辨率的遥感影像较难获取,这就限制了根据采样时间来获取对应时期遥感影像进行土壤盐渍化监测反演的应用。为此,提出融合MODIS和Landsat影像生成高时空分辨率影像来提取土壤盐渍化信息,为时空影像进行土壤盐渍化监测研究提供数据参考。以渭干河—库车河绿洲为研究区,利用增强型时空自适应融合率反射模型（Enhanced spatial and temporal adaptive reflectance fusion model,ESTARFM）和灵活的时空融合模型（Flexible spatiotemporal data fusion,FSDAF）,对MODIS和Landsat影像进行时空融合,并基于融合影像数据构建了关于土壤电导率（EC）的随机森林（RF）预测模型,对比分析时空融合影像应用于土壤盐渍化遥感监测的适用性。结果表明：ESTARFM融合影像的特征波段反射率与Landsat验证影像对应波段反射率一致性决定系数R²（Red）=0.8066、R²（SWIR2）=0.8444;FSDAF融合影像的特征波段与Landsat验证影像对应波段反射率一致性决定系数R²（Red）=0.6999、R²（SWIR2）=0.7493;基于ESTARFM融合影像构建的EC值预测模型精度最高,R²=0.9268,基于FSDAF融合影像构建的EC值预测模型精度良好,R²=0.8987,基于验证影像构建的EC值预测模型R²=0.9103; ESTARFM模型的融合精度高于FSDAF模型,并且基于融合影像构建的EC值预测模型效果良好。     

Exploring Spatially Non-stationary Relationships in the Determinants of Mineralization in 3D Geological Space

Exploring the spatial relationships between various geological features and mineralization is not only conducive to understanding the genesis of ore deposits but can also help to guide mineral exploration by providing predictive mineral maps. However, most current methods assume spatially constant determinants of mineralization and therefore have limited applicability to detecting possible spatially non-stationary relationships between the geological features and the mineralization. In this paper, the spatial variation between the distribution of mineralization and its determining factors is described for a case study in the Dingjiashan Pb–Zn deposit, China. A local regression modeling technique, geological weighted regression (GWR), was leveraged to study the spatial non-stationarity in the 3D geological space. First, ordinary least-squares (OLS) regression was applied, the redundancy and significance of the controlling factors were tested, and the spatial dependency in Zn and Pb ore grade measurements was confirmed. Second, GWR models with different kernel functions in 3D space were applied, and their results were compared to the OLS model. The results show a superior performance of GWR compared with OLS and a significant spatial non-stationarity in the determinants of ore grade. Third, a non-stationarity test was performed. The stationarity index and the Monte Carlo stationarity test demonstrate the non-stationarity of all the variables throughout the area. Finally, the influences of the degree of non-stationary of all controlling factors on mineralization are discussed. The existence of significant non-stationarity of mineral ore determinants in 3D space opens up an exciting avenue for research into the prediction of underground ore bodies.