EN FR
EN FR


Section: Scientific Foundations

Consideration and management of uncertainties in integrated models

Uncertainty arises at different levels; it ranges from imprecisions and inaccuracies in data until the absence of scientific knowledge on certain processes under consideration. Until now, this range of difficulties has practically not been fully taken into account in our target domain of integrated socio-economic and environmental models. Taking into account uncertainties is crucial in our opinion, for various reasons. First, it is essential to understand the propagation of errors and its impact on final obtained results. In this respect, it is necessary to carry out a deep analysis of sources of error/uncertainty and of the sensitivity of different model variables or indicators (An indicator is a piece of information computed a posteriori from the model's output variables. This information may be more or less quantitative. It can be represented by numbers but may also take the form of tendencies ...) relative to errors in the input data and the estimated parameters. This analysis should allow to ensure that the output variables' values or the indicators are meaningful with respect to uncertainties present. In other words, the objective is to guarantee the robustness of conclusions drawn by analysts (...who use output variables and indicators as building blocks for their own analysis.). To our knowledge, existing modeling works are, besides a few exceptions, limited to providing deterministic results without an evaluation of the confidence in these results.

Let us remind here that it is important to distinguish at least two error sources, which together impact results. First, errors in input data, whose influence on the final results is due to structural aspects of a model, related to stability and robustness. Second, errors introduced by the model itself, due to the model being only an approximation of reality. An analysis of the latter is as crucial as one of the former and touches upon the problem of model validation. The literature on this is extremely scarce; only few works propose ideas and elements of actual methodologies.

While a sensitivity analysis allows to assess if it is possible to draw significant conclusions based on an implemented model, such an analysis also enables to determine the main "drivers" of the model: the parameters that have a strong impact on the model's dynamics. The identification of these "drivers" is of utmost importance for decision makers, in their search for leveraging solutions.

Sensitivity analyses are also very useful, e.g. in order to gain insight into the level of precision in input data and parameters that would guarantee a model's validity. Such prior knowledge is important for the technician who has to set up a model in practice. It allows to not waste energy in the production of ultra-precise data that eventually would not have a great impact. Reciprocally, such knowledge enables the concentration of efforts on sensitive data. Finally, as mentioned previously, sensitivity analyses constitute precious tools allowing to reduce the number of parameters to be optimized during the model's calibration phase (by only keeping parameters with strong impact).

Independently of all this, it is worthwhile and indeed essential to take into account uncertainties on data already at the calibration stage. We propose to do so in a similar fashion to what is done in data assimilation. By encapsulating the above errors in the calibration algorithm itself, one may limit their propagation. Likewise, it is important to automatically detect and possibly to correct wrong data during the calibration process. Finally, it is mandatory to consider a specificity of socio-economic and environmental models such as those considered by our team, namely the importance (unavoidability) of scenarios. In some cases, these scenarios concern control aspects (in the mathematical sense of control theory) or very large uncertainties. For instance, it is usual to use scenarios corresponding to different political decisions whose impact one is to assess; such scenarios concern control aspects. Also, in the present time, climatic scenarios are considered quasi-systematically; those scenarios refer rather to uncertainties. Let us stress the fact that this type of important uncertainties lacks in physical and geophysical models. It is quite specific to socio-economic models and, to our knowledge, has not been formally studied yet. This type of uncertainties can not be handled in the same way as "noise" in input data or errors due to approximations done by a model. Still, any sensitivity analysis of data and parameters, as well as calibration methods, ought to be robust to these uncertainties, which is why we plan to work on these aspects.