Spatial Uncertainty Propagation Analysis with the spup R Package

Abstract

Many environmental and geographical models, such as those used in land degradation, agroecological and climate studies, make use of spatially distributed inputs that are known imperfectly. The R package spup provides functions for examining the uncertainty propagation from input data and model parameters onto model outputs via the environmental model. The functions include uncertainty model specification, stochastic simulation and propagation of uncertainty using Monte Carlo (MC) techniques. Uncertain variables are described by probability distributions. Both numerical and categorical data types are handled. The package also accommodates spatial auto-correlation within a variable and cross-correlation between variables. The MC realizations may be used as input to the environmental models written in or called from R. This article provides theoretical background and three worked examples that guide users through the application of spup.Uncertainty propagation aims to analyse how uncertainty (e.g. from measurement error, sampling, or interpolation) in spatial data, combined with modeling uncertainty (e.g. in model parameters and structure) propagate through the model . Many environmental and geographical phenomena of interest are spatial in nature and often have strong spatial correlations imposed by the physics and dynamics of the natural systems, making uncertainty evaluation difficult.A common approach to uncertainty propagation analysis makes use of MC stochastic simulation (Hammersley and Handscomb, 1979; Lewis and Orav, 1989). The MC approach is very flexible and can reach an arbitrary level of accuracy, and is therefore generally preferred over analytical methods such as the Taylor series method (Heuvelink et al., 1989). The MC method for uncertainty propagation analysis consists of the following main steps: (i) uncertainty about the variables is expressed by probability distribution functions (pdfs); (ii) many sets of possible uncertain inputs are generated from their marginal or joint probability distribution using a pseudo-random number generator; (iii) the model is run for each of the simulated input sets; (iv) the set of model outputs forms a random sample from the output pdf, so that the parameters of the output distribution, such as the mean, standard deviation and quantiles, can be estimated from the sample. In other words, the spread in the model outputs characterises how uncertainty about the model inputs has propagated to the model output. Note that the above ignores uncertainty in model parameters and model structure, but these can easily be included if available as pdfs. For example, these might have been obtained through Bayesian calibration (Van Oijen et al., 2005). The above four steps are described in detail further below.

Progress in the R ecosystem for representing and handling spatial data

“…Modelling and analysis packages demonstrate the considerable range of implementations now available and are often supported with additional code provided as supplementary material to journal articles, for example in the Journal of Statistical Software spatial statistics special issue (Pebesma et al 2015). The availability of software and scripts provides a helpful mechanism supporting reproducible research and hands-on reviewing in which readers can read the code and scripts used in calculating the results presented in published work (see, for example, Sawicka et al 2018;Lovelace and Ellison 2018;Evangelista and Beskow 2018, in one issue of the R Journal).…”

Temporal uncertainty propagation analysis : A contribution towards sustainable urban water management

“…There is no software that can do all that is needed for UP analysis in such a complex case. Although important contributions have been made, e.g., the UncertWeb framework (Bastin et al, 2013) and the R-package spup (Sawicka et al, 2017), there still is a need for tools for temporal, spatial and spatio-temporal UP accounting for change of support across multiple scales.…”

“…Spatial uncertainty propagation has been addressed in several fields, such as in hydrological and water quality modelling (Hengl et al, 2010;Hamel and Guswa, 2015;Muthusamy et al, 2017), in scenario analysis (Rauch et al, 2017), and in soil pollution and nutrient modelling (Leopold et al, 2006;Nol et al, 2010;Vanguelova et al, 2016). However, it is recognised that there is not a universal software tool for performing uncertainty propagation tasks (Sawicka et al, 2017).…”

“…Regarding software tools developed for uncertainty propagation analysis, Sawicka et al (2017) list different tools available for spatial and non-spatial uncertainty propagation and uncertainty assessment. Among the listed tools, there is free software, such as Open-TURNS (Andrianov et al, 2007), DAKOTA (Adams et al, 2009),and DUE (Brown and Heuvelink, 2007), commercial software, such as COSSAN (Schueller and Pradlwarter, 2006), and free software written for licensed software, e.g., SAFE (Pianosia et al, 2015) and UQLab (Marelli and Sudret, 2014) toolboxes for MATLAB (MathWorks, Natick, MA, USA).…”

“…We recognise that spup (Sawicka et al, 2017) addresses spatial UP as well, both for continuous and categorical variables. Although there are similarities between spup and stUPscales, there are meaningful differences too.…”