This chapter makes a review, in a complete methodological framework, of various global sensitivity analysis methods of model output. Numerous statistical and probabilistic tools (regression, smoothing, tests, statistical learning, Monte Carlo, …) aim at determining the model input variables which mostly contribute to an interest quantity depending on model output. This quantity can be for instance the variance of an output variable. Three kinds of methods are distinguished: the screening (coarse sorting of the most influential inputs among a large number), the measures of importance (quantitative sensitivity indices) and the deep exploration of the model behaviour (measuring the effects of inputs on their all variation range). A progressive application methodology is illustrated on a scholar application. A synthesis is given to place every method according to several axes, mainly the cost in number of model evaluations, the model complexity and the nature of brought information.

A Review on Global Sensitivity Analysis Methods

Data assimilation (DA) holds considerable potential for improving hydrologic predictions as demonstrated in numerous research studies. However, advances in hydrologic DA research have not been adequately or timely implemented in operational forecast systems to improve the skill of forecasts for better informed real-world decision making. This is due in part to a lack of mechanisms to properly quantify the uncertainty in observations and forecast models in real-time forecasting situations and to conduct the merging of data and models in a way that is adequately efficient and transparent to operational forecasters. The need for effective DA of useful hydrologic data into the forecast process has become increasingly recognized in recent years. This motivated a hydrologic DA workshop in Delft, the Netherlands in November 2010, which focused on advancing DA in operational hydrologic forecasting and water resources management. As an outcome of the workshop, this paper reviews, in relevant detail, the current status of DA applications in both hydrologic research and operational practices, and discusses the existing or potential hurdles and challenges in transitioning hydrologic DA research into cost-effective operational forecasting tools, as well as the potential pathways and newly emerging opportunities for overcoming these challenges. Several related aspects are discussed, including (1) theoretical or mathematical aspects in DA algorithms, (2) the estimation of different types of uncertainty, (3) new observations and their objective use in hydrologic DA, (4) the use of DA for real-time control of water resources systems, and (5) the development of community-based, generic DA tools for hydrologic applications. It is recommended that cost-effective transition of hydrologic DA from research to operations should be helped by developing community-based, generic modeling and DA tools or frameworks, and through fostering collaborative efforts among hydrologic modellers, DA developers, and operational forecasters.

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Advancing data assimilation in operational hydrologic forecasting: progresses, challenges, and emerging opportunities

https://cronfa.swan.ac.uk/Record/cronfa21107/Download/0021107-10052016114550.pdf

Global sensitivity analysis in hydrological modeling: Review of concepts, methods, theoretical framework, and applications

We commonly refer to state estimation theory in geosciences as data assimilation (DA). This term encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and dynamical information (such as a dynamical evolution model), provides an estimate of its state. DA is standard practice in numerical weather prediction, but its application is becoming widespread in many other areas of climate, atmosphere, ocean, and environment modeling; in all circumstances where one intends to estimate the state of a large dynamical system based on limited information. While the complexity of DA, and of the methods thereof, stands on its interdisciplinary nature across statistics, dynamical systems, and numerical optimization, when applied to geosciences, an additional difficulty arises by the continually increasing sophistication of the environmental models. Thus, in spite of DA being nowadays ubiquitous in geosciences, it has so far remained a topic mostly reserved to experts. We aim this overview article at geoscientists with a background in mathematical and physical modeling, who are interested in the rapid development of DA and its growing domains of application in environmental science, but so far have not delved into its conceptual and methodological complexities.

Data assimilation in the geosciences: An overview of methods, issues, and perspectives

Sensitivity analysis provides users of mathematical and simulation models with tools to appreciate the dependency of the model output from model input and to investigate how important is each model input in determining its output. All application areas are concerned, from theoretical physics to engineering and socio-economics. This introductory paper provides the sensitivity analysis aims and objectives in order to explain the composition of the overall “Sensitivity Analysis” chapter of the Springer Handbook. It also describes the basic principles of sensitivity analysis, some classification grids to understand the application B. Iooss ( ) Industrial Risk Management Department, EDF RD biooss@yahoo.fr A. Saltelli Centre for the Study of the Sciences and the Humanities (SVT), University of Bergen (UIB), Bergen, Norway Institut de Ciencia i Tecnologia Ambientals (ICTA), Universitat Autonoma de Barcelona (UAB), Barcelona, Spain e-mail: andrea.saltelli@svt.uib.no; andrea.saltelli@jrc.ec.europa.eu © Springer International Publishing Switzerland 2015 R. Ghanem et al. (eds.), Handbook of Uncertainty Quantification, DOI 10.1007/978-3-319-11259-6_31-1 1 2 B. Iooss and A. Saltelli ranges of each method, a useful software package, and the notations used in the chapter papers. This section also offers a succinct description of sensitivity auditing, a new discipline that tests the entire inferential chain including model development, implicit assumptions, and normative issues and which is recommended when the inference provided by the model needs to feed into a regulatory or policy process. For the “Sensitivity Analysis” chapter, in addition to this introduction, eight papers have been written by around twenty practitioners from different fields of application. They cover the most widely used methods for this subject: the deterministic methods as the local sensitivity analysis, the experimental design strategies, the sampling-based and variance-based methods developed from the 1980s, and the new importance measures and metamodelbased techniques established and studied since the 2000s. In each paper, toy examples or industrial applications illustrate their relevance and usefulness.

Introduction to Sensitivity Analysis

https://hal.inria.fr/hal-00172943/document

A reduced-order strategy for 4D-Var data assimilation

Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thore basin and used as a relatively simple (synthetic observations) but didactic application case. It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting.

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F.-X. Le Dimet

Papers

A reduced-order strategy for 4D-Var data assimilation

Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods

Retrieving ocean surface current by 4-D variational assimilation of sea surface temperature images