Stéphane Vannitsem

Postprocessing of Ensemble Precipitation Predictions with Extended Logistic Regression Based on Hindcasts

AbstractExtended logistic regression is used to calibrate areal precipitation forecasts over two small catchments in Belgium computed with the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) between 2006 and 2010. The parameters of the postprocessing are estimated from the hindcast database, characterized by a much lower number of members (5) than the EPS (51). Therefore, the parameters have to be corrected for predictor uncertainties. They have been fitted on the 51-member EPS ensembles, on 5-member subensembles drawn from the same EPS, and on the 5-member hindcasts. For small ensembles, a simple “regression calibration” method by which the uncertain predictors are corrected has been applied. The different parameter sets have been compared, and the corresponding extended logistic regressions have been applied to the 51-member EPS. The forecast probabilities have then been validated using rain gauge data and compared with the raw EPS. In addition, the calibrated...

Accounting for Model Error in Variational Data Assimilation: A Deterministic Formulation

In data assimilation, observations are combined with the dynamics to get an estimate of the actual state of a natural system. The knowledge of the dynamics, under the form of a model, is unavoidably incomplete and model error affects the prediction accuracy together with the error in the initial condition. The variational assimilation theory provides a framework to deal with model error along with the uncertainties coming from other sources entering the state estimation. Nevertheless, even if the problem is formulated as Gaussian, accounting for model error requires the estimation of its covariances and correlations, which are difficult to estimate in practice, in particular because of the large system dimension and the lack of enough observations. Model error has been therefore either neglected or assumed to be an uncorrelated noise. In the present work, an approach to account for a deterministic model error in the variational assimilation is presented. Equations for its correlations are first derived along with an approximation suitable for practical applications. Based on these considerations, a new four-dimensional variational data assimilation (4DVar) weak-constraint algorithm is formulated and tested in the context of a linear unstable system and of the three-component Lorenz model, which has chaotic dynamics. The results demonstrate that this approach is superior in skill to both the strong-constraint and a weak-constraint variational assimilation that employs the uncorrelated noise model error assumption.

Statistical and dynamical properties of covariant lyapunov vectors in a coupled atmosphere-ocean model—multiscale effects, geometric degeneracy, and error dynamics

We study a simplified coupled atmosphere-ocean model using the formalism of covariant Lyapunov vectors (CLVs), which link physically-based directions of perturbations to growth/decay rates. The model is obtained via a severe truncation of quasi-geostrophic equations for the two fluids, and includes a simple yet physically meaningful representation of their dynamical/thermodynamical coupling. The model has 36 degrees of freedom, and the parameters are chosen so that a chaotic behaviour is observed. One finds two positive Lyapunov exponents (LEs), sixteen negative LEs, and eighteen near-zero LEs. The presence of many near-zero LEs results from the vast time-scale separation between the characteristic time scales of the two fluids, and leads to nontrivial error growth properties in the tangent space spanned by the corresponding CLVs, which are geometrically very degenerate. Such CLVs correspond to two different classes of ocean/atmosphere coupled modes. The tangent space spanned by the CLVs corresponding to the positive and negative LEs has, instead, a non-pathological behaviour, and one can construct robust large deviations laws for the finite time LEs, thus providing a universal model for assessing predictability on long to ultra-long scales along such directions. It is somewhat surprising to find that the tangent space of the unstable manifold has strong projection on both atmospheric and oceanic components. Our results underline the difficulties in using hyperbolicity as a conceptual framework for multiscale chaotic dynamical systems, whereas the framework of partial hyperbolicity seems better suited, possibly indicating an alternative definition for the chaotic hypothesis. Our results suggest the need for accurate analysis of error dynamics on different time scales and domains and for a careful set-up of assimilation schemes when looking at coupled atmosphere-ocean models.

Stochastic parametrization of subgrid‐scale processes in coupled ocean–atmosphere systems: benefits and limitations of response theory

A stochastic subgrid-scale parameterization based on the Ruelles response theory and proposed inWouters and Lucarini (2012) is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes are considered as unresolved. A natural separation of the phase-space into an invariant set and its complement allows for an analytical derivation of the different terms involved in the parameterization, namely the average, the fluctuation and the long memory terms. In this case, the fluctuation term is an additive stochastic noise. Its application to the loworder system reveals that a considerable correction of the low-frequency variability along the invariant subset can be obtained, provided that the coupling is sufficiently weak. This new approach of scale separation opens new avenues of subgrid-scale parameterizations in multiscale systems used for climate forecasts.

The role of the ocean mixed layer on the development of the North Atlantic Oscillation: A dynamical system's perspective

The development of the low-frequency variability (LFV) in the atmosphere at multidecadal timescales is investigated in the context of a low-order coupled ocean-atmosphere model designed to emulate the interaction between the ocean mixed layer (OML) and the atmosphere at midlatitudes, both subject to seasonal variations of the Suns radiative input. When no seasonal dependences are present, a LFV is emerging from the chaotic background for sufficiently large wind stress forcing (WSF). The period of this LFV is strongly controlled by the depth of the OML, with a shorter period for a deeper layer. In the seasonally dependent case, a similar LFV is developing that persists throughout the year. Remarkably, the emergence of this LFV occurs for smaller values of the WSF coefficient and is strongly related to the small thickness of the OML in summer, i.e., large impact of the WSF. Potential implications for real-world dynamics are discussed.

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean-atmosphere model on a beta-plane. We wish to to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing. The increase of the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The convergence rate of the rate functional for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric time-scale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated to the ocean dynamics, is not fully resolved because of its associated long time scales, even at intermediate orders. This paper highlights the need to investigate the natural variability of the atmosphere-ocean coupled dynamics by associating rate of growth and decay of perturbations to the physical modes described using the formalism of the covariant Lyapunov vectors and to consider long integrations in order to disentangle the dynamical processes occurring at all time scales.

Deterministic Treatment of Model Error in Geophysical Data Assimilation

This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the evolution equations for the relevant moments of the model error statistics required in data assimilation procedures, along with an approximation suitable for application to large numerical models typical of environmental science. In this contribution we first derive the equations for the model error dynamics in the general case, and then for the particular situation of parametric error. We show how this deterministic description of the model error can be incorporated in sequential and variational data assimilation procedures. A numerical comparison with standard methods is given using low-order dynamical systems, prototypes of atmospheric circulation, and a realistic soil model. The deterministic approach proves to be very competitive with only minor additional computational cost. Most importantly, it offers a new way to address the problem of accounting for model error in data assimilation that can easily be implemented in systems of increasing complexity and in the context of modern ensemble-based procedures.

Assessment of calibration assumptions under strong climate changes

Climate model calibration relies on different working hypotheses. The simplest bias correction or delta change methods assume the invariance of bias under climate change. Recent works have questioned this hypothesis and proposed linear bias changes with respect to the forcing. However, when the system experiences larger forcings, these schemes could fail. Calibration assumptions are tested within a simplified framework in the context of an intermediate complexity model for which the reference (or “reality”) differs from the model by a single parametric model error and climate change is emulated by largely different CO2 forcings. It appears that calibration does not add value since the variation of bias under climate change is nonmonotonous for almost all variables and large compared to the climate change and the bias, except for the global temperature and sea ice area. For precipitation, calibration provides added value both globally and regionally. The calibration methods used fail to correct climate variability.

Stochastic Parameterization of Subgrid-Scale Processes: A Review of Recent Physically Based Approaches

We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the atmospheric and climate variability. We illustrate these methods on a simple stochastic triad system relevant for the atmospheric and climate dynamics, and we show in particular that the stability properties of the underlying dynamics of the subgrid processes have a considerable impact on their performances.