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Concept: Kriging


Many spatial interpolation methods perform well for gentle terrains when producing spatially continuous surfaces based on ground point data. However, few interpolation methods perform satisfactorily for complex terrains. Our objective in the present study was to analyze the suitability of several popular interpolation methods for complex terrains and propose an optimal method. A data set of 153 soil water profiles (1 m) from the semiarid hilly gully Loess Plateau of China was used, generated under a wide range of land use types, vegetation types and topographic positions. Four spatial interpolation methods, including ordinary kriging, inverse distance weighting, linear regression and regression kriging were used for modeling, randomly partitioning the data set into 2/3 for model fit and 1/3 for independent testing. The performance of each method was assessed quantitatively in terms of mean-absolute-percentage-error, root-mean-square-error, and goodness-of-prediction statistic. The results showed that the prediction accuracy differed significantly between each method in complex terrain. The ordinary kriging and inverse distance weighted methods performed poorly due to the poor spatial autocorrelation of soil moisture at small catchment scale with complex terrain, where the environmental impact factors were discontinuous in space. The linear regression model was much more suitable to the complex terrain than the former two distance-based methods, but the predicted soil moisture changed too sharply near the boundary of the land use types and junction of the sunny (southern) and shady (northern) slopes, which was inconsistent with reality because soil moisture should change gradually in short distance due to its mobility in soil. The most optimal interpolation method in this study for the complex terrain was the hybrid regression kriging, which produced a detailed, reasonable prediction map with better accuracy and prediction effectiveness.

Concepts: Regression analysis, Linear regression, Statistics, Forecasting, Interpolation, Landform, Kriging, Multivariate interpolation


Most studies examining the temperature-mortality association in a city used temperatures from one site or the average from a network of sites. This may cause measurement error as temperature varies across a city due to effects such as urban heat islands. We examined whether spatiotemporal models using spatially resolved temperatures produced different associations between temperature and mortality compared with time series models that used non-spatial temperatures. We obtained daily mortality data in 163 areas across Brisbane city, Australia from 2000 to 2004. We used ordinary kriging to interpolate spatial temperature variation across the city based on 19 monitoring sites. We used a spatiotemporal model to examine the impact of spatially resolved temperatures on mortality. Also, we used a time series model to examine non-spatial temperatures using a single site and the average temperature from three sites. We used squared Pearson scaled residuals to compare model fit. We found that kriged temperatures were consistent with observed temperatures. Spatiotemporal models using kriged temperature data yielded slightly better model fit than time series models using a single site or the average of three sites' data. Despite this better fit, spatiotemporal and time series models produced similar associations between temperature and mortality. In conclusion, time series models using non-spatial temperatures were equally good at estimating the city-wide association between temperature and mortality as spatiotemporal models.

Concepts: Regression analysis, Fundamental physics concepts, Temperature, Thermodynamics, Heat, Interpolation, Urban heat island, Kriging


Rainfall is one the main drivers of soil erosion. The erosive force of rainfall is expressed as rainfall erosivity. Rainfall erosivity considers the rainfall amount and intensity, and is most commonly expressed as the R-factor in the USLE model and its revised version, RUSLE. At national and continental levels, the scarce availability of data obliges soil erosion modellers to estimate this factor based on rainfall data with only low temporal resolution (daily, monthly, annual averages). The purpose of this study is to assess rainfall erosivity in Europe in the form of the RUSLE R-factor, based on the best available datasets. Data have been collected from 1541 precipitation stations in all European Union (EU) Member States and Switzerland, with temporal resolutions of 5 to 60min. The R-factor values calculated from precipitation data of different temporal resolutions were normalised to R-factor values with temporal resolutions of 30min using linear regression functions. Precipitation time series ranged from a minimum of 5years to a maximum of 40years. The average time series per precipitation station is around 17.1years, the most datasets including the first decade of the 21st century. Gaussian Process Regression (GPR) has been used to interpolate the R-factor station values to a European rainfall erosivity map at 1km resolution. The covariates used for the R-factor interpolation were climatic data (total precipitation, seasonal precipitation, precipitation of driest/wettest months, average temperature), elevation and latitude/longitude. The mean R-factor for the EU plus Switzerland is 722MJmmha(-1)h(-1)yr(-1), with the highest values (>1000MJmmha(-1)h(-1)yr(-1)) in the Mediterranean and alpine regions and the lowest (<500MJmmha(-1)h(-1)yr(-1)) in the Nordic countries. The erosivity density (erosivity normalised to annual precipitation amounts) was also the highest in Mediterranean regions which implies high risk for erosive events and floods.

Concepts: European Union, Precipitation, Climate, Soil, Europe, Italy, Interpolation, Kriging


Hospitals are merging to become more cost-effective. Mergers are often complex and difficult processes with variable outcomes. The aim of this study was to analyze the effect of mergers on long-term sickness absence among hospital employees.

Concepts: Regression analysis, Statistics, Econometrics, Multivariate statistics, Random effects model, Interpolation, Kriging


Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R(2)) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial-proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001-2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.

Concepts: Regression analysis, Agriculture, Numerical analysis, Interpolation, Polynomial interpolation, Kriging, Spline, Multivariate interpolation


Relative to terrestrial plants, and despite similarities in life history characteristics, the potential for corals to exhibit intra-reef local adaptation in the form of genetic differentiation along an environmental gradient has received little attention. The potential for natural selection to act on such small scales is likely increased by the ability of coral larval dispersal and settlement to be influenced by environmental cues. Here, we combine genetic, spatial, and environmental data for a single patch reef in Kāne'ohe Bay, O'ahu, Hawai'i, USA in a landscape genetics framework to uncover environmental drivers of intra-reef genetic structuring. The genetic dataset consists of near-exhaustive sampling (n = 2352) of the coral, Pocillopora damicornis at our study site and six microsatellite genotypes. In addition, three environmental parameters - depth and two depth-independent temperature indices - were collected on a 4 m grid across 85 locations throughout the reef. We use ordinary kriging to spatially interpolate our environmental data and estimate the three environmental parameters for each colony. Partial Mantel tests indicate a significant correlation between genetic relatedness and depth while controlling for space. These results are also supported by multi-model inference. Furthermore, spatial Principle Component Analysis indicates a statistically significant genetic cline along a depth gradient. Binning the genetic dataset based on size-class revealed that the correlation between genetic relatedness and depth was significant for new recruits and increased for larger size classes, suggesting a possible role of larval habitat selection as well as selective mortality in structuring intra-reef genetic diversity. That both pre- and post-recruitment processes may be involved points to the adaptive role of larval habitat selection in increasing adult survival. The conservation importance of uncovering intra-reef patterns of genetic diversity is discussed.

Concepts: Genetics, Natural selection, Evolution, Statistics, Population genetics, Artificial selection, Adaptation, Kriging


Land use regression (LUR) is widely used for estimating within-urban variability in air pollution. While LUR has recently been extended to national and continental scales, these models are typically for long-term averages. Here we present NO2 surfaces for the continental United States with excellent spatial resolution (~100-m) and monthly-average concentrations for one decade. We investigate multiple potential data sources (e.g., satellite column and surface estimates, high- and standard-resolution satellite data, and a mechanistic model [WRF-Chem]), approaches to model building (e.g., one model for the whole country versus having separate models for urban and rural areas; monthly LURs versus temporal scaling of a spatial LUR), and spatial interpolation methods for temporal scaling factors (e.g., kriging versus inverse distance weighted). Our core approach uses NO2 measurements from U.S. EPA monitors (2000 - 2010) to build a spatial LUR and to calculate spatially-varying temporal scaling factors. The model captures 82% of the spatial and 76% of the temporal variability (population-weighted average) of monthly-mean NO2 concentrations from U.S. EPA monitors with low average bias (21%) and error (2.4 ppb). Model performance in absolute terms is similar near versus far from monitors, and in urban, suburban, and rural locations (mean absolute error: 2-3 ppb); since low-density locations generally experience lower concentrations, model performance in relative terms is better near monitors than far from monitors (mean bias: 3% versus 40%) and is better for urban and suburban locations (1%-6%) than for rural locations (78%, reflecting the relatively clean conditions in many rural areas). We apply our approach to all U.S. Census blocks in the contiguous United States to provide 132 months of publicly available, high-resolution NO2 concentration estimates.

Concepts: United States, Concentration, Arithmetic mean, United States Environmental Protection Agency, Air pollution, Interpolation, Kriging, Contiguous United States


To evaluate the influence of vancomycin dose, serum trough concentration, and dosing strategy on the evolution of acute kidney injury in critically ill patients.

Concepts: Regression analysis, Statistics, Retrospective, Interpolation, Kriging


Multivariate regression models for age estimation are a powerful tool for assessing abnormal brain morphology associated to neuropathology. Age prediction models are built on cohorts of healthy subjects and are built to reflect normal aging patterns. The application of these multivariate models to diseased subjects usually results in high prediction errors, under the hypothesis that neuropathology presents a similar degenerative pattern as that of accelerated aging. In this work, we propose an alternative to the idea that pathology follows a similar trajectory than normal aging. Instead, we propose the use of metrics which measure deviations from the mean aging trajectory. We propose to measure these deviations using two different metrics: uncertainty in a Gaussian process regression model and a newly proposed age weighted uncertainty measure. Consequently, our approach assumes that pathologic brain patterns are different to those of normal aging. We present results for subjects with autism, mild cognitive impairment and Alzheimer’s disease to highlight the versatility of the approach to different diseases and age ranges. We evaluate volume, thickness, and VBM features for quantifying brain morphology. Our evaluations are performed on a large number of images obtained from a variety of publicly available neuroimaging databases. Across all features, our uncertainty based measurements yield a better separation between diseased subjects and healthy individuals than the prediction error. Finally, we illustrate differences in the disease pattern to normal aging, supporting the application of uncertainty as a measure of neuropathology.

Concepts: Alzheimer's disease, Regression analysis, Epidemiology, Disease, Statistics, Normal distribution, Interpolation, Kriging


Aerosol is an important component of the atmosphere that affects the environment, climate, and human health. Remote sensing is an efficient observation method for monitoring global aerosol distribution and changes over time. The daily Moderate Resolution Imaging Spectroradiometer (MODIS) level-2 aerosol optical depth (AOD) (Collection 6) product (10 km resolution) is often used to study climate change and air pollution. However, the product is prone to yielding large amounts of data gaps due to the unfeasibility of retrieving reliable estimates under cloudy conditions, and these data gaps inevitably affect the results and analysis of the product’s application. In this study, a geostatistical data interpolation framework based on the spatiotemporal kriging method was implemented to interpolate satellite AOD products in Beijing, China. Compared to the ordinary kriging method for filling data gaps, the spatiotemporal interpolation not only utilizes spatial autocorrelation but also considers the temporal and spatiotemporal autocorrelations between different locations. In the study region, the completeness of the spatiotemporal-interpolated AOD product reaches 67.73%, which is significantly superior to the completeness of the original MODIS product (14.27%) and that of the spatial kriging-interpolated AOD product (33.3%). The cross-validation results show that the mean absolute error of the spatiotemporal kriging results (0.07) is lower than that of the ordinary kriging (0.09).

Concepts: Regression analysis, Climate, Linear interpolation, Atmosphere, Numerical analysis, Interpolation, Kriging, Multivariate interpolation