@article{BaroniTarantola2014,
  author    = {Baroni, Gabriele and Tarantola, S.},
  title     = {A general probabilistic framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study},
  series = {Environmental modelling \& software with environment data news},
  volume    = {51},
  journal   = {Environmental modelling \& software with environment data news},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {1364-8152},
  doi       = {10.1016/j.envsoft.2013.09.022},
  pages     = {26 -- 34},
  year      = {2014},
  abstract  = {The present study proposes a General Probabilistic Framework (GPF) for uncertainty and global sensitivity analysis of deterministic models in which, in addition to scalar inputs, non-scalar and correlated inputs can be considered as well. The analysis is conducted with the variance-based approach of Sobol/Saltelli where first and total sensitivity indices are estimated. The results of the framework can be used in a loop for model improvement, parameter estimation or model simplification. The framework is applied to SWAP, a 113 hydrological model for the transport of water, solutes and heat in unsaturated and saturated soils. The sources of uncertainty are grouped in five main classes: model structure (soil discretization), input (weather data), time-varying (crop) parameters, scalar parameters (soil properties) and observations (measured soil moisture). For each source of uncertainty, different realizations are created based on direct monitoring activities. Uncertainty of evapotranspiration, soil moisture in the root zone and bottom fluxes below the root zone are considered in the analysis. The results show that the sources of uncertainty are different for each output considered and it is necessary to consider multiple output variables for a proper assessment of the model. Improvements on the performance of the model can be achieved reducing the uncertainty in the observations, in the soil parameters and in the weather data. Overall, the study shows the capability of the GPF to quantify the relative contribution of the different sources of uncertainty and to identify the priorities required to improve the performance of the model. The proposed framework can be extended to a wide variety of modelling applications, also when direct measurements of model output are not available.},
  language  = {en}
}
@article{WeissHuisinga2011,
  author    = {Weiss, Andrea Y. and Huisinga, Wilhelm},
  title     = {Error-controlled global sensitivity analysis of ordinary differential equations},
  series = {Journal of computational physics},
  volume    = {230},
  journal   = {Journal of computational physics},
  number    = {17},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2011.05.011},
  pages     = {6824 -- 6842},
  year      = {2011},
  abstract  = {We propose a novel strategy for global sensitivity analysis of ordinary differential equations. It is based on an error-controlled solution of the partial differential equation (PDE) that describes the evolution of the probability density function associated with the input uncertainty/variability. The density yields a more accurate estimate of the output uncertainty/variability, where not only some observables (such as mean and variance) but also structural properties (e.g., skewness, heavy tails, bi-modality) can be resolved up to a selected accuracy. For the adaptive solution of the PDE Cauchy problem we use the Rothe method with multiplicative error correction, which was originally developed for the solution of parabolic PDEs. We show that, unlike in parabolic problems, conservation properties necessitate a coupling of temporal and spatial accuracy to avoid accumulation of spatial approximation errors over time. We provide convergence conditions for the numerical scheme and suggest an implementation using approximate approximations for spatial discretization to efficiently resolve the coupling of temporal and spatial accuracy. The performance of the method is studied by means of low-dimensional case studies. The favorable properties of the spatial discretization technique suggest that this may be the starting point for an error-controlled sensitivity analysis in higher dimensions.},
  language  = {en}
}