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Pedometricians have spent a lot of effort on mapping soil types and basic soil properties. However, end‐users typically need a more elaborate soil quality index for land management. Soil quality indices are typically derived from multiple individual soil properties by evaluating whether specific criteria are met. If this is based on individually mapped soil properties, then an important consequence is that cross‐correlations between soil properties are ignored. This makes it impossible to quantify the uncertainties associated with the mapped indices. The objective of this study was to map a soil potential multifunctionality index for agriculture (Agri‐SPMI) over a 12,125 km2 study region located along the French Mediterranean coast to help urban planners preserve soils of the highest quality. The index considered the ability of soils to fulfil four functions under five land use scenarios. A binary map represented each soil function fulfilment for a given scenario. The final soil quality index map was the sum of the 20 binary maps. A regression cokriging model was developed to map the basic soil properties first individually from legacy soil data and spatial soil covariates using a random forest algorithm, and next, interpolate the residuals using cokriging and the linear model of coregionalisation. The mapping uncertainties of soil properties were propagated by calculating the soil quality index over 300 stochastic simulations of soil properties derived from the linear models of coregionalisation. Results showed a poor prediction accuracy of the quality index, mainly because some soil properties were poorly predicted (notably available water capacity and coarse fragments) and used in combination with extreme thresholds that defined land suitability. Overall, the uncertainty was correctly quantified because the stochastic simulations reproduced the width of the observed distribution well, but the shapes of the distributions differed considerably from those of the observations. We envisage some ways for improvement, such as creating probability maps instead of the mean from simulations, and changing the prediction support from point to area. Highlights: The study mapped a soil quality index (Agri‐SPMI) to help preserve soils of highest quality along the French Mediterranean coast.The Agri‐SPMI considered the ability of soils to fulfill four functions under five land use scenarios, derived from multiple individual soil properties.A regression cokriging model was developed to map the basic soil properties, followed by interpolating the residuals using cokriging and the linear model of coregionalisation.The study accurately quantified mapping uncertainties using stochastic simulations, but the soil quality index prediction accuracy was poor, with suggestions for improvement. [ABSTRACT FROM AUTHOR]

To better manage the risks of destructive natural disasters, impact models can be fed with simulations of extreme scenarios to study the sensitivity to temporal and spatial variability. We propose a semi-parametric stochastic framework that enables simulations of realistic spatio-temporal extreme fields using a moderate number of observed extreme space-time episodes to generate an unlimited number of extreme scenarios of any magnitude. Our framework draws sound theoretical justification from extreme value theory, building on generalized Pareto limit processes arising as limits for event magnitudes exceeding a high threshold. Specifically, we exploit asymptotic stability properties by decomposing extreme event episodes into a scalar magnitude variable (that is resampled), and an empirical profile process representing space-time variability. For illustration on hourly gridded precipitation data in Mediterranean France, we calculate various risk measures using extreme event simulations for yet unobserved magnitudes, and we highlight contrasted behavior for different definitions of the magnitude variable. [ABSTRACT FROM AUTHOR]

In this paper we formulate a dynamic model expressing the human life table data by using the first- passage-time theory for a stochastic process. The model is derived analytically and then is applied to the mortality data in Belgium and France. A stochastic simulation is also performed for the `health state function' proposed and the related stochastic paths. Furthermore the implications of the proposed model and the results derived for pension funds and option theory are discussed. [ABSTRACT FROM AUTHOR]

Despite intensive explorations by speleologists, karstic systems remain only partially described as many conduits are not accessible to humans. The classical exploration techniques produce sparse data, leading to various uncertainties about the conduit dimensions, essential parameters for flow simulations. Stochastic simulations offer a possibility to better assess these uncertainties. In this paper, we propose different methods to stochastically simulate the properties (size and shape anisotropy) of karstic conduits on already existing skeletons. These approaches, based on Sequential Gaussian Simulations (SGS), allow taking different conditioning data into account, while respecting the intricacy of the networks. To infer the input parameters, we perform a statistical study of the conduit dimensions of 49 explored karstic networks, focusing on their equivalent radius and width-height ratio. Thanks to the definition of 1D-curvilinear variograms, we demonstrate the existence of a spatial correlation along the networks, which is even higher when considering independently each conduit. Finally, using ad hoc algorithms implemented for computing both a conduit hierarchy inside karstic networks and a relative position regarding outputs, we find no evidence of an obvious link between these two entities and the studied metrics. The simulation methods are then demonstrated on the karstic network of Arrestelia (Pyrénées-Atlantiques, France), and show the consistency of the proposed approach with the observations made on the explored natural systems. • Statistical study of the conduit dimensions of 49 explored karstic networks • Analysis of the spatial variability by using 1D-curvilinear variograms • Analysis of the conduit dimension hierarchy inside the networks • Stochastic simulation of the properties (size and anisotropy) of karstic conduits [ABSTRACT FROM AUTHOR]

Simple Summary: In order to study the efficiency of countermeasures used against the Covid-19 pandemic at the scale of a country, we designed a model and developed an efficient simulation program based on a well known discrete stochastic simulation framework along with a standard, coarse grain, spatial localisation extension. Our particular approach allows us also to implement deterministic continuous resolutions of the same model. We applied it to the Covid-19 epidemic in France where lockdown countermeasures were used. With the stochastic discrete method, we found good correlations between the simulation results and the statistics gathered from hospitals. In contrast, the deterministic continuous approach lead to very different results. We proposed an explanation based on the fact that the effects of discretisation are high for small values, but low for large values. When we add stochasticity, it can explain the differences in behaviour of those two approaches. This system is one more tool to study different countermeasures to epidemics, from lockdowns to social distancing, and also the effects of mass vaccination. It could be improved by including the possibility of individual reinfection. Many methods have been used to model epidemic spreading. They include ordinary differential equation systems for globally homogeneous environments and partial differential equation systems to take into account spatial localisation and inhomogeneity. Stochastic differential equations systems have been used to model the inherent stochasticity of epidemic spreading processes. In our case study, we wanted to model the numbers of individuals in different states of the disease, and their locations in the country. Among the many existing methods we used our own variant of the well known Gillespie stochastic algorithm, along with the sub-volumes method to take into account the spatial localisation. Our algorithm allows us to easily switch from stochastic discrete simulation to continuous deterministic resolution using mean values. We applied our approaches on the study of the Covid-19 epidemic in France. The stochastic discrete version of Pandæsim showed very good correlations between the simulation results and the statistics gathered from hospitals, both on day by day and on global numbers, including the effects of the lockdown. Moreover, we have highlighted interesting differences in behaviour between the continuous and discrete methods that may arise in some particular conditions. [ABSTRACT FROM AUTHOR]