Abstract Geospatial data are often spatially varying but measured sparsely in a two-dimensional (2D) plane. Therefore, spatial interpolation methods, such as Kriging, are frequently used to estimate values at locations without measurement and quantify the associated uncertainty. However, Kriging generally requires extensive measurements to effectively divide non-stationary geospatial data into a deterministic trend and stationary residuals (i.e., detrending) and to estimate semi-variogram parameters from the detrended residuals (i.e., semi-variogram fitting). When measurements are limited, a scenario often encountered in practice, detrending might be challenging, and the estimated semi-variogram parameters inevitably contain statistical uncertainty. The statistical uncertainty may significantly affect the subsequent Kriging interpolation, but it is often ignored in practical applications of Kriging. This study develops a 2D Kriging method (SR-Kriging) that is featured by a sparse representation of covariance function from a Bayesian perspective and explicitly models both spatial variability and statistical uncertainty for interpolation of 2D geospatial data directly from sparse measurements. The proposed method requires neither detrending nor semi-variogram fitting. Both simulated and real data are used to illustrate and validate the proposed method. Results demonstrate that the proposed method directly interpolates 2D geospatial data from limited measurements, with quantified interpolation uncertainty, and explicitly accounts for statistical uncertainty. Ignorance of statistical uncertainty may lead to an underestimation of Kriging interpolation uncertainty.

Abstract In addition to prolonged conflict and political instability, recurrent drought has severely affected Afghanistan’s rural populations and agriculture. As agriculture remains the primary source of livelihood in the country, repeated drought events have significantly constrained agricultural production, increased water stress, and weakened the national economy. A comprehensive assessment of recurring droughts risk for the agriculture system in Afghanistan is a task that remains missing to prepare and mitigate such impacts. Our study addresses this gap by assessing drought risk for agriculture using an index-based framework that integrates hazard, exposure, and vulnerability indicators. The results reveal that drought occurs frequently across the country, albeit with varying intensities and patterns. Over the past two decades (2003–2023), all provinces have experienced drought episodes, with severe events observed in 2001–2002, 2008, 2011, 2018, and consecutively from 2021 to 2023. The exposure and vulnerability of the agriculture system to recurring droughts vary substantially, with particularly high levels observed in the northern, southwestern, and western zones. Likewise, agricultural systems in most provinces of these zones face moderate to high drought risks, exacerbating agricultural challenges in these regions. These findings provide spatially explicit insights into the patterns and underlying drivers of drought risk for agriculture in Afghanistan, which can support decision-making for drought mitigation and adaptation strategies. Graphical abstract

Abstract The regional flood frequency analysis (RFFA) technique is widely used to estimate design floods in ungauged catchments. This study presents development and testing of an ordinary kriging based RFFA technique using peaks-over-threshold (POT) model. Ordinary kriging offers significant advantages in RFFA by providing unbiased, optimal interpolation of spatial data, leading to more accurate flood quantile estimation. This study uses flood and catchment characteristics data from 419 stream gauging stations in eastern Australia. It has been found that the median relative error values are found to be in the range of 29 and 33%, which is more accurate than regression based RFFA models recommended in Australian Rainfall and Runoff (national guideline). The POT based kriging model is found to provide more accurate design flood estimates in coastal areas than the inner part of Australia. Further study should focus on developing a bias correction method to minimize tendency of over-estimation by the new kriging based RFFA model.

This study investigates the spatial and spatio-temporal prediction of significant wave height (SWH) and corresponding wave power analysis in the seas surrounding the Korean Peninsula using fixed rank kriging (FRK). Using both reanalysis data and observational data, the analysis addresses the non-stationary and non-Gaussian characteristics inherent in SWH data, and refines the SWH data to a finer spatial resolution for conducting a more detailed wave power analysis. In this study, two different modeling scenarios were investigated: seasonal spatial modeling and daily spatio-temporal modeling. The first scenario explores seasonal patterns of SWH, identifying the offshore waters along the eastern coast of the Korean Peninsula in winter as the region with the highest wave power potential. The second scenario captures daily variations through a moving window approach, incorporating temporal dependencies for more accurate short-term predictions. To handle the non-Gaussian nature of the data, we considered Gaussian, Inverse Gaussian, and Gamma distributions, with the Gamma distribution consistently yielding the best predictive performance across all scenarios. The FRK framework demonstrated effective predictive capability over large spatio-temporal scales. The results provide practical insights into optimal site selection for wave power generation and highlight the feasibility of using wave energy as a renewable energy source in South Korea.