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DOI	10.5194/hess-23-1633-2019
	Geostatistical interpolation by quantile kriging
	Lebrenz H.; Bárdossy A.
发表日期	2019
ISSN	1027-5606
起始页码	1633
结束页码	1648
卷号	23 期号:3
英文摘要	The widely applied geostatistical interpolation methods of ordinary kriging (OK) or external drift kriging (EDK) interpolate the variable of interest to the unknown location, providing a linear estimator and an estimation variance as measure of uncertainty. The methods implicitly pose the assumption of Gaussianity on the observations, which is not given for many variables. The resulting "best linear and unbiased estimator" from the subsequent interpolation optimizes the mean error over many realizations for the entire spatial domain and, therefore, allows a systematic under-(over-)estimation of the variable in regions of relatively high (low) observations. In case of a variable with observed time series, the spatial marginal distributions are estimated separately for one time step after the other, and the errors from the interpolations might accumulate over time in regions of relatively extreme observations. Therefore, we propose the interpolation method of quantile kriging (QK) with a two-step procedure prior to interpolation: We firstly estimate distributions of the variable over time at the observation locations and then estimate the marginal distributions over space for every given time step. For this purpose, a distribution function is selected and fitted to the observed time series at every observation location, thus converting the variable into quantiles and defining parameters. At a given time step, the quantiles from all observation locations are then transformed into a Gaussian-distributed variable by a 2-fold quantile-quantile transformation with the beta- A nd normal-distribution function. The spatio-temporal description of the proposed method accommodates skewed marginal distributions and resolves the spatial non-stationarity of the original variable. The Gaussian-distributed variable and the distribution parameters are now interpolated by OK and EDK. At the unknown location, the resulting outcomes are reconverted back into the estimator and the estimation variance of the original variable. As a summary, QK newly incorporates information from the temporal axis for its spatial marginal distribution and subsequent interpolation and, therefore, could be interpreted as a space-time version of probability kriging. In this study, QK is applied for the variable of observed monthly precipitation from raingauges in South Africa. The estimators and estimation variances from the interpolation are compared to the respective outcomes from OK and EDK. The cross-validations show that QK improves the estimator and the estimation variance for most of the selected objective functions. QK further enables the reduction of the temporal bias at locations of extreme observations. The performance of QK, however, declines when many zero-value observations are present in the input data. It is further revealed that QK relates the magnitude of its estimator with the magnitude of the respective estimation variance as opposed to the traditional methods of OK and EDK, whose estimation variances do only depend on the spatial configuration of the observation locations and the model settings. © 2019 Author(s).
语种	英语
scopus关键词	Distribution functions; Interpolation; Location; Normal distribution; Time series; Distribution parameters; External drift kriging; Geostatistical interpolation; Marginal distribution; Measure of uncertainty; Spatial configuration; Spatial non-stationarity; Spatio-temporal description; Spatial distribution; Gaussian method; geostatistics; interpolation; kriging; optimization; probability; spatial distribution; South Africa
来源期刊	Hydrology and Earth System Sciences
文献类型	期刊论文
条目标识符	http://gcip.llas.ac.cn/handle/2XKMVOVA/159719
作者单位	Lebrenz, H., University of Applied Sciences and Arts-Northwestern Switzerland, Institute of Civil Engineering, Muttenz, Switzerland, University of Stuttgart, Institute for Modelling Hydraulic and Environmental Systems, Stuttgart, Germany; Bárdossy, A., University of Stuttgart, Institute for Modelling Hydraulic and Environmental Systems, Stuttgart, Germany
推荐引用方式 GB/T 7714	Lebrenz H.,Bárdossy A.. Geostatistical interpolation by quantile kriging[J],2019,23(3).
APA	Lebrenz H.,&Bárdossy A..(2019).Geostatistical interpolation by quantile kriging.Hydrology and Earth System Sciences,23(3).
MLA	Lebrenz H.,et al."Geostatistical interpolation by quantile kriging".Hydrology and Earth System Sciences 23.3(2019).