stUPscales: An R-Package for Spatio-Temporal Uncertainty Propagation across Multiple Scales with Examples in Urban Water Modelling

Abstract

Integrated environmental modelling requires coupling sub-models at different spatial and temporal scales, thus accounting for change of support procedures (aggregation and disaggregation). We introduce the R-package spatio-temporal Uncertainty Propagation across multiple scales, stUPscales, which constitutes a contribution to state-of-the-art open source tools that support uncertainty propagation analysis in temporal and spatio-temporal domains. We illustrate the tool with an uncertainty propagation example in environmental modelling, specifically in the urban water domain. The functionalities of the class setup and the methods and functions MC.setup, MC.sim, MC.analysis and Agg.t are explained, which are used for setting up, running and analysing Monte Carlo uncertainty propagation simulations, and for spatio-temporal aggregation. We also show how the package can be used to model and predict variables that vary in space and time by using a spatio-temporal variogram model and space-time ordinary kriging. stUPscales takes uncertainty characterisation and propagation a step further by including temporal and spatio-temporal auto-and cross-correlation, resulting in more realistic (spatio-)temporal series of environmental variables. Due to its modularity, the package allows the implementation of additional methods and functions for spatio-temporal disaggregation of model inputs and outputs, when linking models across multiple space-time scales.

Multivariate autoregressive modelling and conditional simulation for temporal uncertainty analysis of an urban water system in Luxembourg

“…uncertain constants). In our study, we sampled the time series of dynamic inputs using an implementation in stUPscales (Torres-Matallana et al, 2019;Torres-Matallana et al, 2018a). Diaz-Fierros T et al (2002), in a study in the city of Santiago de Compostela (northwestern Spain; population about 100 000 inhabitants), where a combined sewer system feeds to a grossly undersized wastewater treatment plant, reported an event mean concentration (Diaz-Fierros T et al, 2002;Table 4) for the output variables C COD, Sv, av and C NH 4 , Sv, av of 329.1 and 8.7 mg L −1 , respectively.…”

EmiStatR: A Simplified and Scalable Urban Water Quality Model for Simulation of Combined Sewer Overflows

“…Level 1 indicates the parallel computation done inside EmiStatR. Level 2 indicates the parallel computation done outside of EmiStatR, for example, MC simulations or optimisation, in other R packages such as dream [49] or stUPscales ( [59]; under review, to be published in this issue) packages.…”