An Embedded Model Estimator for Non-Stationary Random Functions Using Multiple Secondary Variables

An algorithm for non-stationary spatial modelling using multiple secondary variables is developed herein, which combines geostatistics with quantile random forests to provide a new interpolation and stochastic simulation. This paper introduces the method and shows that its results are consistent and similar in nature to those applying to geostatistical modelling and to quantile random forests. The method allows for embedding of simpler interpolation techniques, such as kriging, to further condition the model. The algorithm works by estimating a conditional distribution for the target variable at each target location. The family of such distributions is called the envelope of the target variable. From this, it is possible to obtain spatial estimates, quantiles and uncertainty. An algorithm is also developed to produce conditional simulations from the envelope. As they sample from the envelope, realizations are therefore locally influenced by relative changes of importance of secondary variables, trends and variability.

Geostatistical modeling of “lethal coconut palm crown atrophy”, a new disease in the State of Pará

’Lethal Coconut Palm Crown Atrophy’ (LCCA) is a rapidly spreading disease in Brazil, capable of quickly killing coconut trees and threatening the commercial exploration of this plant. The objective of this work was to characterize the spatial and temporal distribution pattern of LCCA in green dwarf coconut commercial plantation areas, located the municipality of Santa Izabel, mesoregion of Northeastern Pará, Brazil. Surveys were carried out at monthly intervals between January 2014 and December 2018, checking for plants with LCCA-characteristic symptoms. Geostatistics was applied to perform spatial-temporal disease estimates based on semivariogram modeling and preparation of ordinary kriging maps. These spatial estimates are conducted through interpolations that characterize data variability in the area. The spherical model yielded the best fit to the spatial distribution of the disease, as it presented the best coefficient of determination (R²), with the range varying between 14m and 45m. The Spatial Dependence Index (SDI) was moderate in the evaluations carried out between 2014 and 2017 (in the 0.26-0.64 range), but not in 2018, when it was strong (0.23). The values of the clustering intensity of LCCA-symptomatic plants were estimated in non-sampled points. The spherical fit model of the data indicates an aggregated distribution pattern, shown by aggregation patches in the plantation, graded by values of dissemination intensity. The kriging maps allowed the observation that the disease expands between plants in the same line, suggesting the possibility of the presence of a short-range vector.

Monitoring the Daily Evolution and Extent of Snow Drought

Snow droughts are commonly defined as below average snowpack at a point in time, typically 1 April in the western United States (wUS). This definition is valuable for interpreting the state of the snowpack but obscures the temporal evolution of snow drought. Borrowing from dynamical systems theory, we applied phase diagrams to visually examine the evolution of snow water equivalent (SWE) and accumulated precipitation conditions in maritime, intermountain, and continental snow climates in the wUS using station observations as well as spatially distributed estimates of SWE and precipitation. Using a percentile-based drought definition phase diagrams of daily observed SWE and precipitation highlighted decision-relevant aspects of snow drought such as onset, evolution, and termination. The phase diagram approach can be used in tandem with spatially distributed estimates of daily SWE and precipitation to reveal variability in snow drought type and extent. When combined streamflow or other data, phase diagrams and spatial estimates of snow drought conditions can help inform drought monitoring and early warning and help link snow drought type and evolution impacts on ecosystems, water resources, and recreation. A web tool is introduced allowing users to create real-time or historic snow drought phase diagrams.

Comparison of radon mapping methods for the delineation of radon priority areas – an exercise

Background: Many different methods are applied for radon mapping depending on the purpose of the map and the data that are available. In addition, the definitions of radon priority areas (RPA) in EU Member States, as requested in the new European EURATOM BSS (1), are diverse. Objective: 1) Comparison of methods for mapping geogenic and indoor radon, 2) the possible transferability of a mapping method developed in one region to other regions and 3) the evaluation of the impact of different mapping methods on the delineation of RPAs. Design: Different mapping methods and several RPA definitions were applied to the same data sets from six municipalities in Austria and Cantabria, Spain. Results: Some mapping methods revealed a satisfying degree of agreement, but relevant differences were also observed. The chosen threshold for RPA classification has a major impact, depending on the level of radon concentration in the area. The resulting maps were compared regarding the spatial estimates and the delineation of RPAs. Conclusions: Not every mapping method is suitable for every available data set. Data robustness and harmonisation are the main requirements, especially if the used data set is not designed for a specific technique. Different mapping methods often deliver similar results in RPA classification. The definition of thresholds for the classification and delineation of RPAs is a guidance factor in the mapping process and is as relevant as harmonising mapping methods depending on the radon levels in the area.

Global hotspots for the occurrence of compound events

Compound events (CEs) are weather and climate events that result from multiple hazards or drivers with the potential to cause severe socio-economic impacts. Compared with isolated hazards, the multiple hazards/drivers associated with CEs can lead to higher economic losses and death tolls. Here, we provide the first analysis of multiple multivariate CEs potentially causing high-impact floods, droughts, and fires. Using observations and reanalysis data during 1980–2014, we analyse 27 hazard pairs and provide the first spatial estimates of their occurrences on the global scale. We identify hotspots of multivariate CEs including many socio-economically important regions such as North America, Russia and western Europe. We analyse the relative importance of different multivariate CEs in six continental regions to highlight CEs posing the highest risk. Our results provide initial guidance to assess the regional risk of CE events and an observationally-based dataset to aid evaluation of climate models for simulating multivariate CEs.

Spatial estimates for Kelvin–Voigt finite elasticity with nonlinear viscosity: Well behaved solutions in space

We provide some spatial estimates for the nonlinear partial differential equation governing anti-plane motions in a nonlinear viscoelastic theory of Kelvin–Voigt type when the viscosity is a function of the strain rate. The spatial estimates we prove are an alternative of Phragmen–Lindelöf type. These estimates are possible when a precise balance between the elastic and viscoelastic nonlinearities holds.