On the use of dimensioned measures of error to evaluate the performance of spatial interpolators

Spatial cross‐validation and average‐error statistics are examined with respect to their abilities to evaluate alternate spatial interpolation methods. A simple cross‐validation methodology is described, and the relative abilities of three, dimensioned error statistics—the root‐mean‐square error (RMSE), the mean absolute error (MAE), and the mean bias error (MBE)—to describe average interpolator performance are examined. To illustrate our points, climatologically averaged weather‐station temperatures were obtained from the Global Historical Climatology Network (GHCN), Version 2, and then alternately interpolated spatially (gridded) using two spatial‐interpolation procedures. Substantial differences in the performance of our two spatial interpolators are evident in maps of the cross‐validation error fields, in the average‐error statistics, as well as in estimated land‐surface‐average air temperatures that differ by more than 2°C. The RMSE and its square, the mean‐square error (MSE), are of particular interest, because they are the most widely reported average‐error measures, and they tend to be misleading. It (RMSE) is an inappropriate measure of average error because it is a function of three characteristics of a set of errors, rather than of one (the average error). Our findings indicate that MAE and MBE are natural measures of average error and that (unlike RMSE) they are unambiguous.     

Prediction of Blast-induced Air Over-pressure in Open-Pit Mine: Assessment of Different Artificial Intelligence Techniques

Air over-pressure (AOp) is one of the products of blasting operations for rock fragmentation in open-pit mines. It can cause structural vibration, smash glass doors, adversely affect the surrounding environment, and even be fatal to humans. To assess its dangerous effects, seven artificial intelligence (AI) methods for predicting specific blast-induced AOp have been applied and compared in this study. The seven methods include random forest, support vector regression, Gaussian process, Bayesian additive regression trees, boosted regression trees, k-nearest neighbors, and artificial neural network (ANN). An empirical technique was also used to compare with AI models. The degree of complexity and the performance of the models were compared with each other to find the optimal model for predicting blast-induced AOp. The Deo Nai open-pit coal mine (Vietnam) was selected as a case study where 113 blasting events have been recorded. Indicators used for evaluating model performances include the root-mean-square error (RMSE), determination coefficient (R²), and mean absolute error (MAE). The results indicate that AI techniques provide better performance than the empirical method. Although the relevance of the empirical approach was acceptable (R²?=?0.930) in this study, its error (RMSE?=?7.514) is highly significant to guarantee the safety of the surrounding environment. In contrast, the AI models offer much higher accuracies. Of the seven AI models, ANN was the most dominant model based on RMSE, R², and MAE. This study demonstrated that AI techniques are excellent for predicting blast-induced AOp in open-pit mines. These techniques are useful for blasters and managers in controlling undesirable effects of blasting operations on the surrounding environment.

     

A Novel Hunger Games Search Optimization-Based Artificial Neural Network for Predicting Ground Vibration Intensity Induced by Mine Blasting

Innovation efforts in developing soft computing models (SCMs) of researchers and scholars are significant in recent years, especially for problems in the mining industry. So far, many SCMs have been proposed and applied to practical engineering to predict ground vibration intensity (BIGV) induced by mine blasting with high accuracy and reliability. These models significantly contributed to mitigate the adverse effects of blasting operations in mines. Despite the fact that many SCMs have been introduced with promising results, but ambitious goals of researchers are still novel SCMs with the accuracy improved. They aim to prevent the damages caused by blasting operations to the surrounding environment. This study, therefore, proposed a novel SCM based on a robust meta-heuristic algorithm, namely Hunger Games Search (HGS) and artificial neural network (ANN), abbreviated as HGS–ANN model, for predicting BIGV. Three benchmark models based on three other meta-heuristic algorithms (i.e., particle swarm optimization (PSO), firefly algorithm (FFA), and grasshopper optimization algorithm (GOA)) and ANN, named as PSO–ANN, FFA–ANN, and GOA–ANN, were also examined to have a comprehensive evaluation of the HGS–ANN model. A set of data with 252 blasting operations was collected to evaluate the effects of BIGV through the mentioned models. The data were then preprocessed and normalized before splitting into individual parts for training and validating the models. In the training phase, the HGS algorithm with the optimal parameters was fine-tuned to train the ANN model to optimize the ANN model's weights. Based on the statistical criteria, the HGS–ANN model showed its best performance with an MAE of 1.153, RMSE of 1.761, R² of 0.922, and MAPE of 0.156, followed by the GOA–ANN, FFA–ANN and PSO–ANN models with the lower performances (i.e., MAE?=?1.186, 1.528, 1.505; RMSE?=?1.772, 2.085, 2.153; R²?=?0.921, 0.899, 0.893; MAPE?=?0.231, 0.215, 0.225, respectively). Based on the outstanding performance, the HGS–ANN model should be applied broadly and across a swath of open-pit mines to predict BIGV, aiming to optimize blast patterns and reduce the environmental effects.

     

RFE2.0遥感降水数据在新疆的适用性评价

结合新疆的65个气象观测站日降水数据,采用连续验证统计方法、分类验证统计方法对RFE2.0遥感降水数据在新疆的适用性进行了评估。结果表明：（1）通过连续验证统计分析,新疆地区平均偏差MBE （Mean Bias Error）总体对日降水量高估,均值为0.4 mm,在0.5 mm内的站点超过70%。RFE2.0遥感降水数据与地面观测站的日降水量之间相关系数R的平均值为0.4,表现为较低的相关性。从偏离真实值情况来说,东疆模拟值和观测值最接近。（2）分类验证统计方法对降水事件FBI （Frequency Bias Index）有所高估。按片区来说,降水事件高估的小值区主要在北疆,高估程度低于全疆平均水平。北疆的正确率POD （Probability of Detection）大于南疆、东疆,同时北疆发生空报率FAR （False Alarm Rate）的可能性也小于南疆、东疆。（3）通过实例验证了RFE2.0在北疆、南疆、东疆的可靠性。以上规律可为RFE2.0在新疆的应用提供科学依据。     

基于贝叶斯最大熵的甘肃省多年平均降水空间化研究

 贝叶斯最大熵方法可以对具有一定不确定性的“软数据”和认为没有误差的“硬数据”进行插值。对甘肃省1961—1990年52个气象站点的多年平均降水数据进行空间化研究。通过比较普通克里格、共协克里格、三元回归建模后残差插值以及基于贝叶斯最大熵的3种不同软硬数据参与情况下的插值结果,发现考虑降水30 a时间序列不完整性以及辅助变量经验模型不确定性的插值结果的MAE和RMSE,比直接使用多年平均降水数据直接插值的MAE和RMSE小,表明贝叶斯最大熵方法通过对不确定性的考虑可以有效降低预测结果的绝对误差。从降水的空间分布来看,考虑辅助变量DEM的插值结果能相对较好的体现高程对降水的地形影响,尤其分区将辅助变量转换为软数据可以有效体现不同区域高程对降水的不同影响问题。综合误差评价以及降水插值结果的空间分布,认为BME插值过程中可以考虑数据本身以及辅助数据利用的不确定性,使降水空间化的结果更加真实客观,同时为合理利用辅助信息提供了一个新思路。     

中国土壤温度的空间插值方法比较

利用中国698个气象站点1971~2000年的地面气候资料,采用三种不同方法预测中国0cm、20cm和40cm深度年均土壤温度的空间分布,其中普通克里格和泛克里格法直接以年均土壤温度数据为源数据、回归克里格法以中国年均气温数据和中国DEM数据为源数据进行预测。预测结果的准确性通过平均绝对误差(MAE)和均方根误差(RMSE)值来评价。结果表明回归克里格法预测的MAE值和RMSE值均为最小,说明其预测结果的准确性最好、预测的极端误差也最小;其次为泛克里格法;普通克里格法预测的效果最差。回归克里格法预测结果由于采用了中国DEM数据进行修正,在空间特征表达方面能够更好地表达复杂地形地区的局部变异,其平滑效应明显小于泛克里格法和普通克里格法的预测结果。     

Application and comparison of two prediction models for groundwater levels: A case study in Western Jilin Province,China

Evaluation and prediction of groundwater levels through specific model(s) helps in forecasting of groundwater resources. Among the different robust tools available, the Integrated Time Series (ITS) and Back-Propagation Artificial Neural Network (BPANN) models are commonly used to empirically forecast hydrological variables. Here, we discuss the modeling process and accuracy of these two methods in assessing their relative advantages and disadvantages based on Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and coefficient of efficiency (CE). The arid and semi-arid areas of western Jilin province of China were chosen as study area owing to the decline of groundwater levels during the past decade mainly due to overexploitation. The simulation results indicated that both ITS and BPANN are accurate in reproducing (fitting) the groundwater levels and the CE are 0.98 and 0.97, respectively. In the validation phase, the comparison of the prediction accuracy of the BPANN and ITS models indicated that the BPANN models is superior to the ITS in forecasting the groundwater levels time series in term of the RMSE, MAE and CE.     

Kriging方法在区域土壤水分估值中的应用

土壤水分的观测对于地表参数化的发展以及气候变化的研究有着重要的作用。本文对大尺度区域土壤水分的估值进行了尝试:采用1987年中国102个气象站点1米土层四个季节的土壤水分值作为样本,运用KRIGING方法,通过对半变异函数的计算和分析,得出了所研究7个采集日的拟合函数,发现均符合球状模型,对模型有关的参数进行了拟合。并将插值结果与距离反比法进行了对比性检验,同时给出了KRIGING方法的估值精度。检验结果表明平均相对误差和标准偏差均以距离反比法较小,以样本量较大的f时段为例对检验结果进行了深入分析。由此得出了KRIGING方法内插估值的优势和不足,简要给出了提高估值精度的可能方案。最后对中国东半部f时段的土壤水分值进行内插成图。     

喀斯特地区春季土壤水分空间插值方法对比

以杨眉河小流域为研究区,通过土壤水分采样,选取辅助变量,采用普通克里金、协同克里金、回归克里金3种地统计学方法对土壤水分数据进行空间插值。结果表明：1）回归克里金对研究区土壤水分估算误差最小,其次为协克里金,普通克里金的误差最大;2）普通克里金生成的土壤水分表面最为平滑,而回归克里金最大程度反映了研究区实际的土壤水分空间变化;3）对于协同克里金,以湿度指数（WI）样点数据作为辅助变量的估算误差小于将WI栅格数据作为辅助变量的估算误差。总之,在可获得有效辅助变量的条件下,回归克里金对研究区土壤水分估算的效果优于协同克里金与普通克里金。     

一种改进的生成区域日降水场的方法及精度分析

利用全国687个气象站点11年的日降水数据,对基于地理特征和统计回归的函数拟合类模型DAYMET生成中国区域日降水场的能力进行了验证。交叉验证表明,DAYMET模型估计日降水累计得到的年降水量的绝对偏差11年平均为29.8%,年降水总量估计偏差低于20％的站点占48.3％。鉴于中国陆地区域降水深受季风的影响,不同方位气象站点对插值点的影响也有所不同,引入了站点不同方位对插值的影响权重,对DAYMET模型进行了改进,改进后年降水量的绝对偏差降为27%。与梯度距离平方反比法相比,该方法具有较高的区域降水插值精度。还以无定河流域降水插值为例,说明降水插值精度的高低与区域内雨量站点的多寡紧密相联。     

基于机器学习模型的海河北系干旱预测研究

提高干旱预测精度能为流域干旱应对及风险防范提供可靠数据支撑,构建比选合适的干旱模型是当前研究的热点。研究以4个时间尺度（3、6、9、12月）标准化降水指数（SPI）为表征指标,利用小波神经网络（WNN）、支持向量回归（SVR）、随机森林（RF）三种机器学习算法分别构建了海河北系干旱预测模型,利用Kendall、K-S、MAE三种检验方法判定模型表现及其稳定性。研究表明：（1） WNN、SVR模型呈现结果在不同时间尺度SPI存在差异,WNN最适合12个月尺度SPI干旱预测;SVR最适合6个月尺度SPI干旱预测。（2） 对3、12个月尺度SPI,RF预测性能最优（Kendall>0.898,MAE<0.05）;对6、9个月尺度SPI,SVR预测性能最优（Kendall>0.95,MAE<0.04）。（3） 模型预测性能稳定性存在区别,RF预测稳定性最高,其次为SVR。（4） 构建的三种模型表现异同主要是因为SVR转为凸优化问题解决了WNN易陷入局部最优解的不足,从而提高了模型预测性能,RF集成多样化回归树,降低了弱学习器的负面影响,提高了模型预测准确率及稳定性,同时,RF处理包含噪声的降水数据的能力更强。     

Modeling Aboveground Biomass Using MODIS Images and Climatic Data in Grasslands on the Tibetan Plateau

Accurate quantification of aboveground biomass of grasslands in alpine regions plays an important role in accurate quantification of global carbon cycling. The monthly normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), mean air temperature (Ta), ≥5℃ accumulated air temperature (AccT), total precipitation (TP), and the ratio of TP to AccT (TP/AccT) were used to model aboveground biomass (AGB) in grasslands on the Tibetan Plateau. Three stepwise multiple regression methods, including stepwise multiple regression of AGB with NDVI and EVI, stepwise multiple regression of AGB with Ta, AccT, TP and TP/AccT, and stepwise multiple regression of AGB with NDVI, EVI, Ta, AccT, TP and TP/AccT were compared. The mean absolute error (MAE) and root mean squared error (RMSE) values between estimated AGB by the NDVI and measured AGB were 31.05 g m^-2 and 44.12 g m^-2, and 95.43 g m^-2 and 131.58 g m^-2 in the meadow and steppe, respectively. The MAE and RMSE values between estimated AGB by the AccT and measured AGB were 33.61g m^-2 and 48.04 g m^-2 in the steppe, respectively. The MAE and RMSE values between estimated AGB by the vegetation index and climatic data and measured AGB were 28.09 g m^-2 and 42.71 g m^-2, and 35.86 g m^-2 and 47.94 g m^-2, in the meadow and steppe, respectively. The study finds that a combination of vegetation index and climatic data can improve the accuracy of estimates of AGB that are arrived at using the vegetation index or climatic data. The accuracy of estimates varied depending on the type of grassland.     

ECMWF高分辨率模式对陕西2017年7月高温预报的检验及订正

2017年7月陕西累计出现26 d日最高气温≥35℃的高温天气,其中14 d日最高气温突破40℃,7月7～14日和17～27日出现2次区域性持续高温天气。利用陕西99个国家站的最高气温逐时观测和ECMWF高分辨率模式的定时最高气温预报资料,检验ECMWF高分辨率模式对2017年7月陕西极端高温天气的预报能力和一元线性回归方法对气温预报的订正能力。结果表明:144 h之前模式较好地预报出了陕西2次区域性持续高温天气,但是高温日数的预报值在陕西大部分地区较观测值偏少,漏报了陕南大部分地区的高温日,与14:00～17:00时段最高气温的预报值在陕西大部分地区较观测值偏低,其中陕南地区的预报平均绝对误差明显大于其他地区有关。一元线性回归方法对168 h之前的最高气温预报为正订正效果,订正后陕西大部分地区最高气温的预报准确率上升,平均绝对误差减小,日最高气温≥35℃或≥40℃的高温预报较订正前更接近实况。     

模糊坡位信息在精细土壤属性空间推测中的应用

坡位的空间渐变特征影响着小流域及坡面尺度上的土壤、水文、地貌等现象和过程,因此对精细尺度下的地理建模(如土壤空间信息推理)有重要作用。虽然目前已有多种模糊坡位信息定量提取方法,但所得到的模糊坡位信息还缺乏实际应用。本文以精细尺度下的土壤属性空间分布推测为例,对此展开探索。应用模型假设:(1)在小流域内,地形因素主导着土壤属性空间分布的变化;(2)典型坡位上对应分布着典型的土壤属性值,土壤属性与坡位之间存在协同变化关系。据此建立以模糊坡位信息对各类典型坡位上土壤样点属性值的加权平均模型,推测土壤属性的空间分布。模型应用于黑龙江省嫩江流域一个地形平缓的小区(面积约60 km²),通过一个以坡位典型位置作为原型的模糊坡位定量方法提取5类坡位(山脊、坡肩、背坡、坡脚、沟谷)的空间渐变信息,对土壤表层有机质含量的空间分布进行推测。推测结果通过研究区70个土壤采样点进行评价,以推测结果与评价样点集之间的相关系数、平均绝对误差、均方根误差作为定量评价指标,与使用常用地形属性的多元线性回归模型推测结果进行对比。评价结果表明,仅使用极少建模点的加权平均模型的推测结果优于多元线性回归模型的推测结果。     

黄土丘陵小流域土壤水分空间预测的统计模型

在6个土层和10次土壤含水量测定的基础上,利用土地利用与地形等6类20个环境因子变量,建立了黄土丘陵区小流域土壤水分空间预测的6种多元线性回归模型,并提出了5类13个指标对模型进行了评价与比较。研究表明,各模型组之间的差异较大,以直接回归模型组为最优,PCA线性转换回归模型组次之,DCA非线性转换回归模型组最差。在每一组内,模型之间的差异相对较小,以变量全部入选模型稍优于变量逐步筛选模型。6种模型中,通用多元线性回归模型的拟合性最好、预测精度最高,但模型结构最为复杂、需要的环境因子最多;多元线性逐步回归模型不仅拟合性和无偏性方面很好,而且结构最为简单、需要的环境变量最少,因而为最优模型     

SPATIAL AND TEMPORAL DISTRIBUTIONS OF ATMOSPHERIC MOISTURE IN A SMALL MIDWESTERN CITY

Location, timing, and intensities of urban atmospheric moisture anomalies in the relatively small city of Lawrence, Kansas are mapped, explained, and compared with previously studied cities. Forty-five urban-rural dew point distributions were obtained during mornings, afternoons, and evenings in August, September, and October. A meteorologically-equipped auto was used to traverse an 88.5-km route through the major land uses in the city and surrounding countryside. Rural dew points exceeded urban values much more frequently than the reverse. On several dates, a reversal of the urban-rural dew point relationship occurred; in the afternoon, rural dew points were greater than urban values, but at night urban values exceeded those in rural areas. Lowest values often corresponded with the most developed sections of the city, and the central business district exerted the most consistent influence on dew points. Greatest gradients developed on the periphery of the developed area. Pattern complexity was generally at a maximum in the afternoon and was least complex during morning hours. Results compare and contrast with previous urban-rural humidity studies.     

基于Sentinel-1A数据在广东省近海海面风场反演应用

采用基于风条纹提取风向的方式,利用地球物理模式函数,基于Sentinel-1A数据,通过CMOD5模型反演2017年3、5、7、12月份广东省近海海域风场。将反演结果与实测数据对比,风速普遍比实测风速大,风速反演的平均绝对误差为1.98 m/s,均方根误差为2.74 m/s,相关系数为0.8。其中3、5、7月的风速较为接近,且平均绝对误差和均方根误差都＜2 m/s,而12月份平均风速＞8 m/s,实测数据与卫星过境时间不完全匹配,导致平均绝对误差和均方根误差都偏大。哨兵一（Sentinel-1A）影像反演结果整体上与实测数据相一致,验证了COMD5反演模型适用于广东省近海高分辨率海洋风场反演,可为下一步估算广东省风能资源储量提供可能。     

气象要素空间插值方法优化

在区域水土平衡模型的研究中 ,空间插值可提供每个计算栅格的气象要素资料。本文运用反距离加权法 (IDW )和梯度距离反比法 (GIDW ) ,对 196 1～ 2 0 0 0年甘肃省及其周围85个气象站点的多年平均温度与降雨量进行了内插。交叉验证结果表明 :对于IDW和GIDW ,二者温度插值的平均绝对误差 (MAE)分别为 2 2 8℃和 0 73℃ ,平均相对误差(MRE)分别为 2 9 0 2 %和 9 4 1% ,降雨插值的MAE值依次为 5 5 2mm和 4 90mm ,MRE值分别为 19 4 3%和 17 80 % ,GIDW明显优于IDW。需要指出的是 :对于降雨 ,当其经纬度和海拔高程的复相关系数大于 0 80时 ,GIDW插值结果优于IDW ;否则相反     

基于GIS的新疆气温数据栅格化方法研究

以新疆99个气象台站1971-2010年年平均气温为数据源,采用多元回归结合空间插值的方法对新疆区域气温数据进行栅格化研究。建立了年平均气温与台站经纬度和海拔高度的多元回归模型,对于残差数据的插值采用了反距离权重法(IDW) 、普通克立格法 (Kriging)和样条函数法(Spline)3种目前应用广泛的空间插值方法,针对于这3种方法进行了基于MAE和RMSIE的交叉验证和对比分析,结果表明在新疆的年平均气温的GIS插值方案中,IDW方法精度总体要高于其他两种插值方法。     

近32 a中亚地区气温时空格局分析

中亚地区生态环境脆弱,生态系统对于气候变化的响应非常敏感,但其气候变化的时空格局并不清楚。该区域气象站点分布稀疏、高精度气象数据缺乏,利用单一数据源研究气候变化具有极大的不确定性。因此,结合站点数据和再分析数据探索中亚五国气候变化时空格局具有重要的研究价值。选取31个气象站点数据（OBS）、CRU气象插值数据和CFSR、ERA-Interim和MERRA三套高精度的再分析数据,对中亚地区1980-2011年的年、四季气温的时空格局变化进行分析。研究结果表明：（1） 近32 a中亚年均气温显著升高,增温速率为0.36～0.47 ℃·（10 a）^-1,即过去的近32 a中亚地区平均气温升高1.15～1.50 ℃。（2）四季气温变化中春季的增温速率最快（0.71～0.93 ℃·（10 a）^-1）,而冬季气温无显著性的变化。（3）中亚中部、南部、西南部、西部地区显著增温,尤其是在1990s后期至2000s前期经历了显著性地增温过程,而中亚其它地区气温无显著变化。