Sequential aggregation with uncertainty estimation

Participants : Jean Thorey, Vivien Mallet, Christophe Chaussin [EdF R&D] .

In the context of ensemble forecasting, one goal is to combine an ensemble of forecasts in order to produce an improved probabilistic forecast. We previously designed a new approach to predict a probability density function or cumulative distribution function, from a weighted ensemble of forecasts. The procedure aims at forecasting the cumulative distribution function of the observation which is simply a Heaviside function centered at the observed value. Our forecast is the weighted empirical cumulative distribution function based on the ensemble of forecasts. Each forecast of the ensemble is attributed a weight which is updated whenever new observations become available. The performance of the forecast is given by the continuous ranked probability score (CRPS), which is the square of the two-norm of the discrepancy between the forecast and the observed cumulative distribution functions. The method guarantees that, in the long run, the forecast cumulative distribution function has a continuous ranked probability score at least as good as the best weighted empirical cumulative function with weights constant in time.

The CRPS computed from an ensemble of forecasts is subject to a bias. We proposed a new way to compute the CRPS in order to mitigate the bias and obtain better aggregation performance.

The work was applied to the forecast of photovoltaics production, both at EDF production sites and for global France production.

Sensitivity analysis of air quality simulations at urban scale

Participants : Vivien Mallet, Louis Philippe, Fabien Brocheton [Numtech] , David Poulet [Numtech] .

We carried out a sensitivity analysis of the urban air quality model Sirane. We carried out dimension reduction on both inputs and outputs of the air quality model. This designed a reduced-order model, which we then emulated. We sampled the (reduced) inputs to the reduced model, and emulated the response surface of the reduced outputs. A metamodel was derived by the combination of the dimension reduction and the statistical emulation. This metamodel performs as well as the original model, compared to field observations. It is also extremely fast, which allowed us to compute Sobol' indices and carry out a complete sensitivity analysis.

Sensitivity analysis of road traffic simulations and corresponding emissions

Participants : Ruiwei Chen [École des Ponts ParisTech] , Vivien Mallet, Vincent Aguiléra [Cerema] , Fabien Brocheton [Numtech] , David Poulet [Numtech] , Florian Cohn [Numtech] .

This work deals with the simulation of road traffic at metropolitan scale. We compared state-of-the-art static traffic assignment and dynamic traffic assignment, which better represents congestion. The work was applied in Clermont-Ferrand and its surrounding region, for a time period of two years, and using about 400 traffic loop counters for evaluation. The dynamic model showed similar overall performance as the static model.

We developed an open source software for the computation of the emissions of traffic. It computes the emissions of the main air pollutants, according the vehicle fleet.

For both traffic assignment and pollutant emissions, we carry out sensitivity tests with respect to limit speed, roads capacities or fleet composition. A complete sensitivity analysis is out of reach with the complete, computational intensive, traffic assignment model. Hence further work has been engaged with the metamodeling of the traffic assignment model. Preliminary results are encouraging and tend to show that a very fast metamodel can perform as well as the complete model.

Ensemble variational data assimilation

Participants : Julien Brajard, Isabelle Herlin, Marc Bocquet [CEREA] , Jérôme Sirven [LOCEAN] , Olivier Talagrand [LMD, ENS] , Sylvie Thiria [LOCEAN] .

The general objective of ensemble data assimilation is to produce an ensemble of analysis from observations and a numerical model which is representative of the uncertainty of the system. In a bayesian framework, the ensemble represents a sampling of the state vector probability distribution conditioned to the available knowledge of the system, denoted the a-posteriori probability distribution.

Ensemble variational data assimilation (EnsVar) consists in producing such an ensemble by perturbating N times the observations according to their error law, and run a standard variationnal assimilation for each perturbation. An ensemble of N members is then produced. In the case of linear models, there is a theoretical guarantee that this ensemble is a sampling of the a-posteriori probability. But there is no theoretical result in the non-linear case.

The objective of this work is to study the ability of EnsVar to produce "good" ensemble (i.e. that sampled the a posteriori probablility) on a shallow-water model. Statistical properties of the ensemble are evaluated, and the sensitivity to the main features of the assimilation system (number, distribution of observations, size of the assimilation window, ...) are also studied.