Kriging With External Drift Research Articles

The Precision of C Stock Estimation in the Ludhikola Watershed Using Model-Based and Design-Based Approaches

In this study, two sampling protocols using a model-based and a design-based framework were juxtaposed to evaluate their precision in the estimation of C stock in the Ludikhola watershed, Nepal. The model-based approach exploits the spatial dependencies in the sampled variable and may therefore be attractive over the design-based approach as it reduces the substantial costs of survey and effort required in the latter. Scales of spatial variability for C stock which resulted in a grid resolution of 10,000 m2 were determined using a reconnaissance variogram. Akaike information criterion was used for the selection of the best linear model of feature space for use in kriging with external drift (KED). Among the five tested covariates, distance, elevation, and aspect were statistically significant, with the best model of feature space accounting for 87.7% variability of C stock. An ANOVA established significance differences in mean C stocks (P = 0.00017). KED using the best model of feature space was found to be more precise, (9.89 ± 0.17) sqrt mg C/ha, than a pure-based approach of ordinary kriging and the design-based approach, (9.91 ± 0.8) sqrt mg C/ha. The confidence bounds of the two estimators showed that their confidence intervals will overlap 99.7% of the time, with both confidence intervals falling within the 95% confidence bounds of each other. There is less uncertainty around the mean C stock estimated using the model-based approach than the mean C stock estimated using the design-based approach. The model-based approach is a prospective option for the REDD framework.

A Geostatistical Approach to Estimate Soil Moisture as a Function of Geophysical Data and Soil Attributes

Successful implementation of site-specific irrigation requires an understanding of within-field-variability of soil parameters. These parameters can be estimated by direct sampling or by indirect surveying using geophysical data. The geophysical outputs are quite sensitive to soil water content; therefore, they can be used as covariates in soil water content (SWC) estimation.The objectives of this study were to use geophysical and soil data as auxiliary variables in the estimation of soil water content through geostatistical techniques.The surveys were carried out in a test site at the agricultural experimental farm located in south-eastern Italy in dry and wet soil conditions. The plot was surveyed with an EMI sensor and two different mono-static GPR systems, one with central frequencies of 600/1600MHz and the other with a central frequency of 250MHz. Forty-eight soil cores were collected for laboratory analysis of textural properties. One hundred and sixteen soil samples up to 0.30m-depth were collected to measure the SWC with gravimetric method. Kriging with external drift (KED), a non-stationary geostatistical technique, was used to estimate SWC with EMI, GPR and soil data as covariates. Cross-validation test was used to assess the goodness of the estimates and compare KED with ordinary kriging.The results showed that the approach using the auxiliary variables can be preferred to univariate kriging in terms of correlation between true and estimated values and capability of interpretation of spatial variability. Kriging with external drift proved to be a valid tool in sensor data fusion and could be effectively applied in Precision Irrigation.

A methodology for digital soil mapping in poorly-accessible areas

Effective soil management requires knowledge of the spatial patterns of soil variation within the landscape to enable wise land use decisions. This is typically obtained through time-consuming and costly surveys. The aim of this study was to develop a cost-efficient methodology for digital soil mapping in poorly-accessible areas. The methodology uses a spatial model calibrated on the basis of limited soil sampling and explanatory covariables related to soil-forming factors, developed from readily available secondary information from accessible areas. The model is subsequently applied in the poorly-accessible areas. This can only be done if the environmental conditions in the poorly-accessible areas are also found in the accessible areas in which the model is developed. This study illustrates the methodology in an exercise to predict soil organic carbon (SOC) concentration in the Limpopo National Park, Mozambique. Readily-available secondary data was used as explanatory variables representing the soil-forming factors. Conditions in the accessible and poorly-accessible areas corresponded sufficiently to allow the extrapolation of the spatial model into the latter. The spatial variation of SOC in the accessible area was mostly described by the sampling cluster (71.5%) and the landscape unit (46.3%). Therefore ordinary (punctual) kriging (OK) and kriging with external drift (KED) based on the landscape unit were used to predict SOC. A linear regression (LM) model using only landscape stratification was used as control. All models were independently validated with test sets collected in both accessible and poorly-accessible areas. In the former the root mean squared error of prediction (RMSEP) was 0.42–0.50% SOC. The ratio between the RMSEP in the poorly-accessible and accessible areas was 0.67–0.72, showing that the methodology can be applied to predict SOC in poorly-accessible areas as successful as in accessible areas. The methodology is thus recommended for areas with similar access problems, especially for baseline studies and for sample design in two-stage surveys.

Data Transformation and Uncertainty in Geostatistical Combination of Radar and Rain Gauges

AbstractGeostatistics provides a popular framework for deriving high-resolution quantitative precipitation estimates (QPE) by combining radar and rain gauge data. However, the skewed and heteroscedastic nature of precipitation is in contradiction to assumptions of classical geostatistics. This study examines the potential of trans-Gaussian kriging to overcome this contradiction. Combination experiments are undertaken with kriging with external drift (KED) using several settings of the Box–Cox transformation. Hourly precipitation data in Switzerland for the year 2008 serve as test bed to compare KED with and without transformation. The impact of transformation is examined with regard to compliance with model assumptions, accuracy of the point estimate, and reliability of the probabilistic estimate. Data transformation improves the compliance with model assumptions, but some level of contradiction remains in situations with many dry gauges. Very similar point estimates are found for KED with untransformed and appropriately transformed data. However, care is needed to avoid excessive transformation (close to log) because this can introduce a positive bias. Strong benefits from transformation are found for the probabilistic estimate, which is rendered positively skewed, sensitive to precipitation amount, and quantitatively more reliable. Without transformation, 44% of all precipitation observations larger than 5 mm h−1 are considered as extremely unlikely by the probabilistic estimate in the test application. Transformation reduces this rate to 4%. Although transformation cannot fully remedy the complications for geostatistics in radar–gauge combination, it seems a useful procedure if realistic and reliable estimation uncertainties are desired, such as for the stochastic simulation of QPE ensembles.

Incorporating elevation in rainfall interpolation in Tunisia using geostatistical methods

This paper compares the performance of three geostatistical algorithms, which integrate elevation as an auxiliary variable: kriging with external drift (KED); kriging combined with regression, called regression kriging (RK) or kriging after detrending; and co-kriging (CK). These three methods differ by the way by in which the secondary information is introduced into the prediction procedure. They are applied to improve the prediction of the monthly average rainfall observations measured at 106 climatic stations in Tunisia over an area of 164 150 km2 using the elevation as the auxiliary variable. The experimental sample semivariograms, residual semivariograms and cross-variograms are constructed and fitted to estimate the rainfall levels and the estimation variance at the nodes of a square grid of 20 km × 20 km resolution and to develop corresponding contour maps. Contour diagrams for KED and RK were similar and exhibited a pattern corresponding more closely to local topographic features when (a) the network is sparse and (b) the rainfall–elevation correlation is poor, while CK showed a smooth zonal pattern. Smaller prediction variances are obtained for the RK algorithm. The cross-validation showed that the RMSE obtained for CK gave better results than for KED or RK. Editor D. Koutsoyiannis; Associate editor C. Onof Citation Feki, H., Slimani, M., and Cudennec, C., 2012. Incorporating elevation in rainfall interpolation in Tunisia using geostatistical methods. Hydrological Sciences Journal, 57 (7), 1294–1314.

Spatial interpolation of monthly climate data for Finland: comparing the performance of kriging and generalized additive models

The Finnish Meteorological Institute has calculated statistics for the new reference period of 1981–2010. During this project, the grid size has been reduced from 10 to 1 km, the evaluation of the interpolation has been improved, and comparisons between different methods has been performed. The climate variables of interest were monthly mean temperature and mean precipitation, for which the spatial variability was explained using auxiliary information: mean elevation, sea percentage, and lake percentage. We compared three methods for spatial prediction: kriging with external drift (KED), generalized additive models (GAM), and GAM combined with residual kriging (GK). Every interpolation file now has attached statistical key figures describing the bias and the normality of the prediction error. According to the cross-validation results, GAM was the best method for predicting mean temperatures, with only very small differences relative to the other methods. For mean precipitation, KED produced the most accurate predictions, followed by GK. In both cases, there was notable seasonal variation in the statistical skill scores. For the new reference period and future interpolations, KED was chosen as the primary method due to its robustness and accuracy.

Spatiotemporal interpolation of elevation changes derived from satellite altimetry for Jakobshavn Isbræ, Greenland

Estimation of ice sheet mass balance from satellite altimetry requires interpolation of point‐scale elevation change (dH/dt) data over the area of interest. The largest dH/dtvalues occur over narrow, fast‐flowing outlet glaciers, where data coverage of current satellite altimetry is poorest. In those areas, straightforward interpolation of data is unlikely to reflect the true patterns ofdH/dt. Here, four interpolation methods are compared and evaluated over Jakobshavn Isbræ, an outlet glacier for which widespread airborne validation data are available from NASA's Airborne Topographic Mapper (ATM). The four methods are ordinary kriging (OK), kriging with external drift (KED), where the spatial pattern of surface velocity is used as a proxy for that of dH/dt, and their spatiotemporal equivalents (ST‐OK and ST‐KED). KED assumes a linear relationship between spatial gradients of velocity anddH/dt, which is confirmed for both negative (Pearson's correlation ρ < −0.85) and, to a lesser degree, positive (ρ = 0.73) dH/dtvalues. When compared to ATM data, KED and ST‐KED yield more realistic spatial patterns and higher thinning rates (over 20 m yr−1 as opposed to 7 m yr−1for OK). Spatiotemporal kriging smooths inter‐annual variability and improves interpolation in periods with sparse data coverage and we conclude, therefore, that ST‐KED produces the best results. Using this method increases volume loss estimates from Jakobshavn Isbræ by up to 20% compared to those obtained by OK. The proposed interpolation method will improve ice sheet mass balance reconstructions from existing and past satellite altimeter data sets, with generally poor sampling of outlet glaciers.

Spatial assessment of soil salinity in the Harran Plain using multiple kriging techniques

The Harran Plain is located in the southeastern part of Turkey and has recently been developed for irrigation agriculture. It already faces soil salinity problems causing major yield losses. Management of the problem is hindered by the lack of information on the extent and geography of the salinization problem. A survey was carried out to delineate the spatial distribution of salt-affected areas by randomly selecting 140 locations that were sampled at two depths (0 to 30 and 30 to 60 cm) and analyzed for soil salinity variables: soil electrical conductivity (EC), soluble cations (Ca(2+,) Mg(2+), Na(+), and K(+)), soluble anions (SO (4) (2-) , Cl(-)), exchangeable Na(+) (me 100 g(-1)) and exchangeable sodium percentage. Terrain attributes (slope, topographical wetness index) were extracted from the digital elevation model of the study area. Variogram analyses after log transformation and ordinary kriging (OK) were applied to map spatial patterns of soil salinity variables. Multivariate geostatistical methods-regression kriging (RK) and kriging with external drift (KED)-were used using elevation and soil electrical conductivity data as covariates. Performances of the three estimation methods (OK, RK, and KED) were compared using independent validation samples randomly selected from the main dataset. Soils were categorized into salinity classes using disjunctive kriging (DK) and ArcGIS, and classification accuracy was tested using the kappa statistic. Results showed that soil salinity variables all have skewed distribution and are poorly correlated with terrain indices but have strong correlations among each other. Up to 65 % improvement was obtained in the estimations of soil salinity variables using hybrid methods over OK with the best estimations obtained with RK using EC(0-30) as covariate. DK-ArcGIS successfully classified soil samples into different salinity groups with overall accuracy of 75 % and kappa of 0.55 (p < 0.001).

Integrating geophysical and geostatistical techniques to map the spatial variation of clay

The development of subsoil models represents an important aspect of land resource evaluation, because they can provide an accurate description of the spatial variability in soil properties. Although direct soil sampling provides the best information in terms of soil properties, sample density is rarely adequate to accurately describe the horizontal and vertical variability of the physical properties of soil. Geophysical methods, such as Ground Penetrating Radar (GPR) and electromagnetic induction (EMI) sensors, provide rapid, non-invasive and exhaustive ways for subsoil characterization. Moreover, geophysical methods can be integrated with geostatistics to map soil properties.This study investigates the capability of geostatistics to incorporate auxiliary geoelectrical information for the prediction of soil properties. The prediction model of clay content used was kriging with external drift (KED) with EMI and GPR data as auxiliary information. Soil clay contents were computed for a 1×1m grid maps at two depths (0–0.20m and 0.20–0.40m). The spatial trend map and the standard error maps were shown separately. Maps of the clay content at the two depths were compared with the ordinary kriging estimates through cross-validation. The results showed that the model using the auxiliary variables can be preferred to univariate kriging in terms of correlation between true and estimated values and capability of interpretation of spatial variability.

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

Abstract. Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation period. It is found that both methods yield merged fields of better quality than the original radar field or fields obtained by OK of gauge data. The newly suggested KED formulation is shown to be beneficial, in particular in mountainous regions where the quality of the Swiss radar composite is comparatively low. An analysis of the Kriging variances shows that none of the methods tested here provides a satisfactory uncertainty estimate. A suitable variable transformation is expected to improve this.

Performance evaluation of interpolation methods for incorporating rain gauge measurements into NEXRAD precipitation data: a case study in the Upper Guadalupe River Basin

AbstractHigh spatial and temporal resolution of precipitation data is critical input for hydrological budget estimation and flash flood modelling. This study evaluated four methods [Bias Adjustment (BA), Simple Kriging with varying Local Means (SKlm), Kriging with External Drift (KED), and Regression Kriging (RK)] for their performances in incorporating gauge rainfall measurements into Next Generation Weather Radar (NEXRAD) multi‐sensor precipitation estimator (MPE; hourly and 4 × 4 km2). Measurements from a network of 50 gauges at the Upper Guadalupe River Basin, central Texas and MPE data for the year 2004 were used in the study. We used three evaluation coefficients percentage bias (PB), coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE) to examine the performance of the four methods for preserving regional‐ and local‐scale characteristics of observed precipitation data. The results show that the two Kriging‐based methods (SKlm and RK) are in general better than BA and KED and that the PB and NSE criteria are better than theR2criterion in assessing the performance of the four methods. It is also worth noting that the performance of one method at regional scale may be different from its performance at local scale. Critical evaluation of the performance of different methods at local or regional scale should be conducted according to the different purposes. The results obtained in this study are expected to contribute to the development of more accurate spatial rainfall products for hydrologic budget and flash flood modelling. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Using Digital Elevation Model to Improve Soil pH Prediction in an Alpine Doline

Among spatial interpolation techniques, geostatistics is generally preferred because it takes into account the spatial correlation between neighbouring observations in order to predict attribute values at unsampled locations. A doline of approximately 15 000 m 2 at 1 900 m above sea level (North Italy) was selected as the study area to estimate a digital elevation model (DEM) using geostatistics, to provide a realistic distribution of the errors and to demonstrate whether using widely available secondary data provided more accurate estimates of soil pH than those obtained by univariate kriging. Elevation was measured at 467 randomly distributed points that were converted into a regular DEM using ordinary kriging. Further, 110 pits were located using spatial simulated annealing (SSA) method. The interpolation techniques were multi-linear regression analysis (MLR), ordinary kriging (OK), regression kriging (RK), kriging with external drift (KED) and multi-collocated ordinary cokriging (CKmc). A cross-validation test was used to assess the prediction performances of the different algorithms and then evaluate which methods performed best. RK and KED yielded better results than the more complex CKmc and OK. The choice of the most appropriate interpolation method accounting for redundant auxiliary information was strongly conditioned by site specific situations.

Spatial interpolation of hourly rainfall – effect of additional information, variogram inference and storm properties

Abstract. Hydrological modelling of floods relies on precipitation data with a high resolution in space and time. A reliable spatial representation of short time step rainfall is often difficult to achieve due to a low network density. In this study hourly precipitation was spatially interpolated with the multivariate geostatistical method kriging with external drift (KED) using additional information from topography, rainfall data from the denser daily networks and weather radar data. Investigations were carried out for several flood events in the time period between 2000 and 2005 caused by different meteorological conditions. The 125 km radius around the radar station Ummendorf in northern Germany covered the overall study region. One objective was to assess the effect of different approaches for estimation of semivariograms on the interpolation performance of short time step rainfall. Another objective was the refined application of the method kriging with external drift. Special attention was not only given to find the most relevant additional information, but also to combine the additional information in the best possible way. A multi-step interpolation procedure was applied to better consider sub-regions without rainfall. The impact of different semivariogram types on the interpolation performance was low. While it varied over the events, an averaged semivariogram was sufficient overall. Weather radar data were the most valuable additional information for KED for convective summer events. For interpolation of stratiform winter events using daily rainfall as additional information was sufficient. The application of the multi-step procedure significantly helped to improve the representation of fractional precipitation coverage.

Improved interpolation of meteorological forcings for hydrologic applications in a Swiss Alpine region

This paper presents a comparative study on the mapping of temperature and precipitation fields in complex Alpine terrain. Its relevance hinges on the major impact that inadequate interpolations of meteorological forcings bear on the accuracy of hydrologic predictions regardless of the specifics of the models, particularly during flood events. Three flood events measured in the Swiss Alps are analyzed in detail to determine the interpolation methods which best capture the distribution of intense, orographically-induced precipitation. The interpolation techniques comparatively examined include: Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and Kriging with External Drift (KED). Geostatistical methods rely on a robust anisotropic variogram for the definition of the spatial rainfall structure. Results indicate that IDW tends to significantly underestimate rainfall volumes whereas OK and KED methods capture spatial patterns and rainfall volumes induced by storm advection. Using numerical weather forecasts and elevation data as covariates for precipitation, we provide evidence for KED to outperform the other methods. Most significantly, the use of elevation as auxiliary information in KED of temperatures demonstrates minimal errors in estimated instantaneous rainfall volumes and provides instantaneous lapse rates which better capture snow/rainfall partitioning. Incorporation of the temperature and precipitation input fields into a hydrological model used for operational management was found to provide vastly improved outputs with respect to measured discharge volumes and flood peaks, with notable implications for flood modeling.

Combining geostatistical models and remotely sensed data to improve tropical tree richness mapping

Information on the spatial distribution and composition of biological communities is essential in designing effective strategies for biodiversity conservation and management. Reliable maps of species richness across the landscape can be useful tools for these purposes. Acquiring such information through traditional survey techniques is costly and logistically difficult. The kriging interpolation method has been widely used as an alternative to predict spatial distributions of species richness, as long as the data are spatially dependent. However, even when this requirement is met, researchers often have few sampled sites in relation to the area to be mapped. Remote sensing provides an inexpensive means to derive complete spatial coverage for large areas and can be extremely useful for estimating biodiversity. The aim of this study was to combine remotely sensed data with kriging estimates (hybrid procedures) to evaluate the possibility of improving the accuracy of tree species richness maps. We did this through the comparison of the predictive performance of three hybrid geostatistical procedures, based on tree species density recorded in 141 sampling quadrats: co-kriging (COK), kriging with external drift (KED), and regression kriging (RK). Reflectance values of spectral bands, computed NDVI and texture measurements of Landsat 7 TM imagery were used as ancillary variables in all methods. The R 2 values of the models increased from 0.35 for ordinary kriging to 0.41 for COK, and from 0.39 for simple regression estimates to 0.52 and 0.53 when using simple KED and RK, respectively. The R 2 values of the models also increased from 0.60 for multiple regression estimates to 0.62 and 0.66 when using multiple KED and RK, respectively. Overall, our results demonstrate that these procedures are capable of greatly improving estimation accuracy, with multivariate RK being clearly superior, because it produces the most accurate predictions, and because of its flexibility in modeling multivariate relationships between tree richness and remotely sensed data. We conclude that this is a valuable tool for guiding future efforts aimed at conservation and management of highly diverse tropical forests.

Geostatistical modeling of riparian forest microclimate and its implications for sampling

Predictive models of microclimate under various site conditions in forested headwater stream – riparian areas are poorly developed, and sampling designs for characterizing underlying riparian microclimate gradients are sparse. We used riparian microclimate data collected at eight headwater streams in the Oregon Coast Range to compare ordinary kriging (OK), universal kriging (UK), and kriging with external drift (KED) for point prediction of mean maximum air temperature (Tair). Several topographic and forest structure characteristics were considered as site-specific parameters. Height above stream and distance to stream were the most important covariates in the KED models, which outperformed OK and UK in terms of root mean square error. Sample patterns were optimized based on the kriging variance and the weighted means of shortest distance criterion using the simulated annealing algorithm. The optimized sample patterns outperformed systematic sample patterns in terms of mean kriging variance mainly for small sample sizes. These findings suggest methods for increasing efficiency of microclimate monitoring in riparian areas.

Influence of spatial interpolation methods for climate variables on the simulation of discharge and nitrate fate with SWAT

Abstract. For ecohydrological modeling climate variables are needed on subbasin basis. Since they usually originate from point measurements spatial interpolation is required during preprocessing. Different interpolation methods yield data of varying quality, which can strongly influence modeling results. Four interpolation methods to be compared were selected: nearest neighbour, inverse distance, ordinary kriging, and kriging with external drift (Goovaerts, 1997). This study presents three strategies to evaluate the influence of the interpolation method on the modeling results of discharge and nitrate load in the river in a mesoscale river catchment (~1000 km2) using the Soil and Water Assessment Tool (SWAT, Neitsch et al., 2005) model: I. Automated calibration of the model with a mixed climate data set and consecutive application of the four interpolated data sets. II. Consecutive automated calibration of the model with each of the four climate data sets. III. Random generation of 1000 model parameter sets and consecutive application of the four interpolated climate data sets on each of the 1000 realisations, evaluating the number of realisations above a certain quality criterion threshold. Results show that strategies I and II are not suitable for evaluation of the quality of the interpolated data. Strategy III however proves a significant influence of the interpolation method on nitrate modeling. A rank order from the simplest to the most sophisticated method is visible, with kriging with external drift (KED) outperforming all others. Responsible for this behaviour is the variable temperature, which benefits most from more sophisticated methods and at the same time is the main driving force for the nitrate cycle. The missing influence of the interpolation methods on discharge modeling is explained by a much higher measuring network density for precipitation than for all other climate variables.

Using landscape characteristics to define an adjusted distance metric for improving kriging interpolations

Interpolation of point measurements using geostatistical techniques such as kriging can be used to estimate values at non-sampled locations in space. Traditional geostatistics are based on the spatial autocorrelation concept that nearby things are more related than distant things. In this study, additional information was used to modify the traditional Euclidean concept of distance into an adjusted distance metric that incorporates similarity in terms of quantifiable landscape characteristics such as topography or land use. This new approach was tested by interpolating soil moisture content, pH and carbon-to-nitrogen (C:N) ratio measured in both the mineral and the organic soil layers at a field site in central Sweden. Semivariograms were created using both the traditional distance metrics and the proposed adjusted distance metrics to carry out ordinary kriging (OK) interpolations between sampling points. In addition, kriging with external drift (KED) was used to interpolate soil properties to evaluate the ability of the adjusted distance metric to incorporate secondary data into interpolations. The new adjusted distance metric typically lowered the nugget associated with the semivariogram, thereby better representing small-scale variability in the measured data compared to semivariograms based on the traditional distance metric. The pattern of the resulting kriging interpolations using KED and OK based on the adjusted distance metric were similar because they represented secondary data and, thus, enhanced small-scale variability compared to traditional distance OK. This created interpolations that agreed better with what is expected for the real-world spatial variation of the measured properties. Based on cross-validation error, OK interpolations using the adjusted distance metric better fit observed data than either OK interpolations using traditional distance or KED.

Mapping soil organic matter using the topographic wetness index: A comparative study based on different flow-direction algorithms and kriging methods

Terrain attributes derived from digital elevation models have been used widely for mapping soil organic matter (SOM). Among these attributes, the topographic wetness index (TWI), an index for quantitatively indicating the balance between water accumulation and drainage conditions at the local scale, has been shown to correlate with SOM. However, TWIs used in most studies are calculated using a single-flow-direction (SFD) algorithm, which assumes that all water from a grid cell flows into only one neighboring cell. This assumption is not always valid, especially in areas with low relief where movement of water may be divergent. To overcome this SFD limitation, a multiple-flow-direction (MFD) algorithm has been developed, which distributes flow from a grid cell to several downslope neighbors. In this study we compared the effect of TWI Calculations based on SFD and MFD in predictive mapping of SOM by incorporating them into different kriging methods over a 51.76 km(2) area in Nenjiang County of northeastern China. We found that the MFD-based TWI was better correlated with SOM than was the SFD-based index. We then compared the accuracies of SOM maps which were derived from MFD-based TWI and SFD-based TWI incorporated by ordinary kriging (OK), simple kriging with varying local means (SKlm), kriging with external drift (KED) and collocated cokriging (CC). The MFD-based TWI, used as a secondary variable in SKlm and CC, outperforms the SFD-based TWI. For the different kriging methods, CC (incorporating either MFD-based TWI or SFID-based TWI) showed the best performance, and OK generated a better result than SKlm and KED. Both the MFD-based TWI and SFD-based TWI proved to be incompatible with KED and SKlm due to their numerical instability caused by the rough TWI surfaces. Among all predictive methods, CC incorporating the MFD-based TWI produced the best results. This is because: (1) the MFD-based TWI is best able to indicate quantitatively soil moisture and therefore has the strongest correlation with SOM; (2) CC is capable of utilizing effectively the spatial auto-correlation of SOM and the cross-correlation between SOM and the MFD-based TWI. (C) 2009 Elsevier Ltd. All rights reserved.

GIS‐Based Spatial Precipitation Estimation: A Comparison of Geostatistical Approaches1

Abstract: As one of the primary inputs that drive watershed dynamics, the estimation of spatial variability of precipitation has been shown to be crucial for accurate distributed hydrologic modeling. In this study, a Geographic Information System program, which incorporates Nearest Neighborhood (NN), Inverse Distance Weighted (IDW), Simple Kriging (SK), Ordinary Kriging (OK), Simple Kriging with Local Means (SKlm), and Kriging with External Drift (KED), was developed to facilitate automatic spatial precipitation estimation. Elevation and spatial coordinate information were used as auxiliary variables in SKlm and KED methods. The above spatial interpolation methods were applied in the Luohe watershed with an area of 5,239 km2, which is located downstream of the Yellow River basin, for estimating 10 years’ (1991‐2000) daily spatial precipitation using 41 rain gauges. The results obtained in this study show that the spatial precipitation maps estimated by different interpolation methods have similar areal mean precipitation depth, but significantly different values of maximum precipitation, minimum precipitation, and coefficient of variation. The accuracy of the spatial precipitation estimated by different interpolation methods was evaluated using a correlation coefficient, Nash‐Sutcliffe efficiency, and relative mean absolute error. Compared with NN and IDW methods that are widely used in distributed hydrologic modeling systems, the geostatistical methods incorporated in this GIS program can provide more accurate spatial precipitation estimation. Overall, the SKlm_EL_X and KED_EL_X, which incorporate both elevation and spatial coordinate as auxiliary into SKlm and KED, respectively, obtained higher correlation coefficient and Nash‐Sutcliffe efficiency, and lower relative mean absolute error than other methods tested. The GIS program developed in this study can serve as an effective and efficient tool to implement advanced geostatistics methods that incorporate auxiliary information to improve spatial precipitation estimation for hydrologic models.