Application of spatial filter theory to kriging

Data-processing requirements for remotely sensed, digital images include spatial filtering to suppress image noise, enhance edges/contacts, and improve image clarity. Spatial filter theory demonstrates that the addition of a high-pass filtered image to a low-pass filtered image yields the original digital image. Application of this principle in kriging can be accomplished by using the same covariance matrix to solve for two weighting vectors to yield a result analogous to low- and high-pass filtering. The addition of kriged estimates calculated using both weighting vectors is analogous to summing high-, and low-pass filtered digital images. This modified method of kriging yields estimates associated with less smoothing compared to ordinary kriging. Statistical moments of original sample data are better preserved through estimation by this method.     

PM2.5浓度插值中不同空间插值方法对比

针对不同插值方法对于重点大气颗粒物污染源PM_(2.5)大区域内整体分布情况的插值效果和精度存在差异性的问题,该文以石家庄市赵县100个点的PM_(2.5)的数据作为样本点,利用反距离权重法、普通克里格插值法和协同克里格插值法,分别进行PM_(2.5)浓度的空间插值。利用研究区内另外20个PM_(2.5)的数据点进行插值精度的检验。研究结果表明:协同克里格插值的精度最高,但可视化效果不如其他两种方法。     

Estimation of rainfall distribution for the southwestern region of Saudi Arabia

Abstract

Rainfall is the most important input parameter for water resource planning and hydrological studies because flood risk assessment, rainfall harvesting and runoff estimation depend on the rainfall distribution within a region. Due to practical and economic factors, it is not possible to site rainfall stations everywhere, so representative rainfall stations are sited at specific locations. Rainfall distribution is then estimated from such stations. In this study, rainfall distribution in the southwestern region of Saudi Arabia was estimated using kriging, co-kriging and inverse distance weighted (IDW) methods. Historical records of rainfall from 47 stations for the period 1965–2010 and the altitude of these stations were used. The study shows that co-kriging is a better interpolator than the kriging and IDW methods, with a better correlation between actual and estimated monthly average rainfall for the region.     

Relating hydrograph components to rainfall and streamflow: a case study from northern Taiwan

Abstract

This study investigates the characteristics of hydrograph components from a watershed in Taiwan. Hydrograph components were modelled by using a model of three serial reservoirs with one parallel reservoir. Mean rainfall was calculated by using the block kriging method. The model parameters for 38 events were calibrated by using the shuffled complex evolution optimization algorithm. The model verification was made using 18 events. Based on the study results, the following findings were obtained: (1) for single-peak events, times to peak of hydrograph components are an increasing power function of the peak time of rainfall; (2) peak discharges of hydrograph components are linearly proportional to that of total runoff, and the ratios of quick and slow runoff are approximately 83% and 17% of total runoff, respectively; and (3) the total volume of quick runoff component is 52% of total runoff and that of slow runoff is 27%.

Editor D. Koutsoyiannis

Citation Li, Y.-J., Cheng, S.-J. Pao, T.-L. and Bi, Y.-J., 2012. Relating hydrograph components to rainfall and streamflow: a case study from northern Taiwan. Hydrological Sciences Journal, 57 (5), 861–877.     

ANNUAL ACCUMULATION OVER THE GREENLAND ICE SHEET INTERPOLATED FROM HISTORICAL AND NEWLY COMPILED OBSERVATION DATA

The estimation of ice/snow accumulation is of great significance in quantifying the mass balance of ice sheets and variation in water resources. Improving the accuracy and reducing uncertainty has been a challenge for the estimation of annual accumulation over the Greenland ice sheet. In this study, we kriged and analyzed the spatial pattern of accumulation based on an observation data series including 315 points used in a recent research, plus 101 ice cores and snow pits and newly compiled 23 coastal weather station data. The estimated annual accumulation over the Greenland ice sheet is 31.2 g cm^?2 yr^?1, with a standard error of 0.9 g cm^?2 yr^?1. The main differences between the improved map developed in this study and the recently published accumulation maps are in the coastal areas, especially southeast and southwest regions. The analysis of accumulations versus elevation reveals the distribution patterns of accumulation over the Greenland ice sheet.     

福州晋安河沿岸区域地表径流中氮磷污染物的空间分布特征及来源分析

以福州市晋安河沿线区域为研究对象,采集区内地表径流样品,通过分析径流水样中全氮、全磷浓度,采用普通克里格法分析了地表径流中全氮、全磷的空间分布特征.结果表明,全氮是地表径流的主要污染物质,全磷除少部分地段超标外,总体上不构成污染;全氮、全磷的半方差函数用球状模型拟合的最好,其空间分布表现为各向同性;地表径流中全氮污染主要集中于管理条件落后的居民区、餐饮业集中的娱乐场所以及非城市主干道路.地表径流中的全磷主要分布在餐饮业集中区域及管理落后的住宅小区.福州城市地表径流的氮磷污染主要来自于居民的日常生活排污.     

Spatial Interpolation of Daily Precipitation in China: 1951--2005

Climate research relies heavily on good quality instrumental data; for modeling efforts gridded data are needed. So far, relatively little effort has been made to create gridded climate data for China. This is especially true for high-resolution daily data. This work, focuses on identifying an accurate method to produce gridded daily precipitation in China based on the observed data at 753 stations for the period 1951--2005. Five interpolation methods, including ordinary nearest neighbor, local polynomial, radial basis function, inverse distance weighting, and ordinary kriging, have been used and compared. Cross-validation shows that the ordinary kriging based on seasonal semi-variograms gives the best performance, closely followed by the inverse distance weighting with a power of 2. Finally the ordinary kriging is chosen to interpolate the station data to a 18 km×18 km grid system covering the whole country. Precipitation for each 0.5o×0.5o latitude-longitude block is then obtained by averaging the values at the grid nodes within the block. Owing to the higher station density in the eastern part of the country, the interpolation errors are much smaller than those in the west (west of 100oE). Excluding 145 stations in the western region, the daily, monthly, and annual relative mean absolute errors of the interpolation for the remaining 608 stations are 74%, 29%, and 16%, respectively. The interpolated daily precipitation has been made available on the internet for the scientific community.     

基于克里格回归分析和机器学习算法的日本福岛县土地价格估算与制图的比较分析

Finding accurate methods for estimating and mapping land prices at the macro-scale based on publicly accessible and low-cost spatial data is an essential step in producing a meaningful reference for regional planners.This asset would assist them in making economically justified decisions in favor of key investors for development projects and post-disaster recovery efforts.Since 2005,the Ministry of Land,Infrastructure,and Transport of Japan has made land price data open to the public in the form of observations at dispersed locations.Although this data is useful,it does not provide complete information at every site for all market participants.Therefore,estimating and mapping land prices based on sound statistical theories is required.This paper presents a comparative study of spatial prediction of land prices in 2015 in Fukushima prefecture based on geostatistical methods and machine learning algorithms.Land use,elevation,and socioeconomic factors,including population density and distance to railway stations,were used for modeling.Results show the superiority of the random forest algorithm.Overall,land prices are distributed unevenly across the prefecture with the most expensive land located in the western region characterized by flat topography and the availability of well-connected and highly dense economic hotspots.     

Kriging with Inequality Constraints

A Gaussian random field with an unknown linear trend for the mean is considered. Methods for obtaining the distribution of the trend coefficients given exact data and inequality constraints are established. Moreover, the conditional distribution for the random field at any location is calculated so that predictions using e.g. the expectation, the mode, or the median can be evaluated and prediction error estimates using quantiles or variance can be obtained. Conditional simulation techniques are also provided.