Numerical stochastic modelling of spatial and spatio-temporal fields of the wind chill index in the South of Western Siberia

The paper presents the results of comparison of various methods of spatial interpolation of the wind chill index in two regions located in the South of Western Siberia (Russia). It is shown that stochastic interpolation provides the least interpolation error in the considered regions. The results of modelling the spatial and spatio-temporal fields of the considered bioclimatic index on a regular grid are presented.

High Space-Time Resolution Observation of Extreme Orographic Rain Gradients in a Pacific Island Catchment

In the vicinity of orographic barriers, interactions between mountains and prevailing winds can enhance rainfall and generate strong spatial gradients of precipitation. Orographic rainfall is still poorly quantified despite being an important driver of headwater catchment hydrology, in particular when considered at high space-time resolution. In this paper, we propose a complete framework for the observation and quantification of orographic rainfall gradients at the local scale. This framework, based on the stochastic interpolation of drop-counting rain gauge observations, provides reconstructions of local rain fields at high space-time resolution. It allows us to capture the life-cycle of individual rain cells, which typically occurs at a spatial scale of approximately 1–5 km and a temporal scale of approximately 5–15 min over our study area. In addition, the resulting rain estimates can be used to investigate how rainfall gradients develop during rain storms, and to provide better input data to drive hydrological models. The proposed framework is presented in the form of a proof-of-concept case study aimed at exploring orographic rain gradients in Mānoa Valley, on the leeward side of the Island of Oʻahu, Hawaiʻi, USA. Results show that our network of eight rain gauges captured rainfall variations over the 6 × 5 km2 study area, and that stochastic interpolation successfully leverages these in-situ data to produce rainfall maps at 200 m × 1 min resolution. Benchmarking against Kriging shows better performance of stochastic interpolation in reproducing key statistics of high-resolution rain fields, in particular rain intermittency and low intensities. This leads to an overall enhancement of rain prediction at ungauged locations.

A Stochastic Interpolation-Based Fractal Model for Vulnerability Diagnosis of Water Supply Networks Against Seismic Hazards

Historical seismic events show that water supply networks are increasingly vulnerable to seismic damage, especially in a violent earthquake, which leads to an unprecedented level of risk. Evaluation of vulnerability to seismic hazards can be considered as one of the first steps of risk management and mitigation. This paper presents a stochastic interpolation-based fractal model for assessing the physical vulnerability of urban water supply pipelines. Firstly, based on the formation mechanism of natural disaster risk and the concept of seismic vulnerability, the most representative factors were selected as the vulnerability evaluation indices, and the classification criterion of each index was teased out according to the earthquake damage investigations and researches on the aseismatic behavior of water supply pipelines. Secondly, considering the randomness of vulnerability to earthquake hazards, the test data set was produced by way of stochastic interpolation according to the uniform distribution, on the basis of the classification criterion. The fractal dimensions of all of the indices were calculated based on the test data set. The fractal interpolation diagnosis function for identifying the vulnerability levels of pipelines to earthquake disasters was established. Finally, the application of the proposed model to a real water supply network and its comparative analysis showed that the water supply network was basically in a medium vulnerability level. Through the case study verification, we could find that the model was theoretically and practically feasible. This study helps to gain a better understanding of the extents of potential vulnerability levels of water supply pipelines. It can provide technical support for disaster prevention plans of urban water supply networks.

Hydro-stochastic interpolation coupling with the Budyko approach for prediction of mean annual runoff

The hydro-stochastic interpolation method based on traditional block Kriging has often been used to predict mean annual runoff in river basins. A caveat in such a method is that the statistic technique provides little physical insight into relationships between the runoff and its external forcing, such as the climate and land cover. In this study, the spatial runoff is decomposed into a deterministic trend and deviations from it caused by stochastic fluctuations. The former is described by the Budyko method (Fu's equation) and the latter by stochastic interpolation. This coupled method is applied to spatially interpolate runoff in the Huaihe River basin of China. Results show that the coupled method significantly improves the prediction accuracy of the mean annual runoff. The error of the predicted runoff by the coupled method is much smaller than that from the Budyko method and the hydro-stochastic interpolation method alone. The determination coefficient for cross-validation, Rcv2, from the coupled method is 0.87, larger than 0.81 from the Budyko method and 0.71 from the hydro-stochastic interpolation. Further comparisons indicate that the coupled method has also reduced the error in overestimating low runoff and underestimating high runoff suffered by the other two methods. These results confirm that the coupled method offers an effective and more accurate way to predict the mean annual runoff in river basins.

Stochastic Interpolation

Spatial analysis includes an expanding array of methods which address different spatial issues, ranging from remote sensing to spatial error uncertainty. Each of these methods focuses on geographically raw data correlated by statistical methods. In general, spatial interpolation and stochastic Kriging, in particular, will be addressed in this chapter. Ordinary Kriging (OK) foundations are presented in the first section which encompasses eight sub-sections (in accordance with the eight myGeoffice© options). Section two introduces Kriging with Trend (KT but sometimes known as Universal Kriging) including five sub-sections: Geocomputation of KT, estimation mapping, the cross-validation procedure, validation using an extra dataset and KT versus OK comparison. Finally, Indicator Kriging (IK) is explored in section three together with nine sub-sections: First and second cutoff definition, first and second probabilistic interpolation maps, construction of the conditional cumulative distribution function, entropy of Shannon, E-type spatial estimation (including misclassification risks and economic classification), morphologic geostatistics and probabilistic interval mapping.