Can hydrological model identifiability be improved? Stress-testing the concept of stochastic calibration

<p>Hydrological calibrations with historical data are often deemed insufficient for deducing safe estimations about a model structure that imitates, as closely as possible, the anticipated catchment behaviour. Ιn order to address this issue, we investigate a promising strategy, using as drivers synthetic time series, which preserve the probabilistic properties and dependence structure of the observed data. The key idea is calibrating a model on the basis of synthetic rainfall-runoff data, and validating against the full observed data sample. To this aim, we employed a proof of concept on few representative catchments, by testing several lumped conceptual hydrological models with alternative parameterizations and across two time-scales, monthly and daily. Next, we attempted to reinforce the validity of the recommended methodology by employing monthly stochastic calibrations in 100 MOPEX catchments. As before, a number of different hydrological models were used, for the purpose of proving that calibration with stochastic inputs is independent of the chosen model. The results highlight that in most cases the new approach leads to stronger parameter identifiability and stable predictive capacity across different temporal windows, since the model is trained over much extended hydroclimatic conditions.</p>

A mixed ℓ1 regularization approach for sparse simultaneous approximation of parameterized PDEs

We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a jointly sparse reconstruction problem through the reformulation of the standard basis pursuit denoising, where the set of jointly sparse vectors is infinite. To achieve global reconstruction of sparse solutions to parameterized elliptic PDEs over both physical and parametric domains, we combine the standard measurement scheme developed for compressed sensing in the context of bounded orthonormal systems with a novel mixed-norm based ℓ1 regularization method that exploits both energy and sparsity. In addition, we are able to prove that, with minimal sample complexity, error estimates comparable to the best s-term and quasi-optimal approximations are achievable, while requiring only a priori bounds on polynomial truncation error with respect to the energy norm. Finally, we perform extensive numerical experiments on several high-dimensional parameterized elliptic PDE models to demonstrate the superior recovery properties of the proposed approach.

Efficient Uncertainty Assessment in EM Problems via Dimensionality Reduction of Polynomial-Chaos Expansions

The uncertainties in various Electromagnetic (EM) problems may present a significant effect on the properties of the involved field components, and thus, they must be taken into consideration. However, there are cases when a number of stochastic inputs may feature a low influence on the variability of the outputs of interest. Having this in mind, a dimensionality reduction of the Polynomial Chaos (PC) technique is performed, by firstly applying a sensitivity analysis method to the stochastic inputs of multi-dimensional random problems. Therefore, the computational cost of the PC method is reduced, making it more efficient, as only a trivial accuracy loss is observed. We demonstrate numerical results about EM wave propagation in two test cases and a patch antenna problem. Comparisons with the Monte Carlo and the standard PC techniques prove that satisfying outcomes can be extracted with the proposed dimensionality-reduction technique.