Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models: a case study for biogenic emissions from EURAD-IM version 5

Atmospheric chemical forecasts heavily rely on various model parameters, which are often insufficiently known, such as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties with an ensemble of forecasts is impaired by the high dimensionality of the system. This study presents a novel approach, which substitutes the problem into a low-dimensional subspace spanned by the leading uncertainties. It is based on the idea that the forecast model acts as a dynamical system inducing multivariate correlations of model uncertainties. This enables an efficient perturbation of high-dimensional model parameters according to their leading coupled uncertainties. The specific algorithm presented in this study is designed for parameters that depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen–Loéve expansion. Due to their perceived simulation challenge, the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state that highly correlated uncertainties of regional biogenic emissions can be represented by a low number of dominant components. Depending on the required level of detail, leading parameter uncertainties with dimensions of 𝒪(106) can be represented by a low number of about 10 ensemble members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

Ensemble generation of regional ocean physics and biogeochemical model uncertainties, empirical consistency and suitability for probabilistic forecasting

<div><span>The study builds upon two Copernicus marine projects, SCRUM and SCRUM2, focusing on ensemble forecasting operational capabilities to better serve coastal downscaling. Both projects provided coupled physics-biogeochemistry ensemble generation approaches, tools to strengthen CMEMS in the areas of ocean uncertainty modelling, empirical ensemble consistency and data assimilation, including methods to assess the suitability of ensembles for probabilistic forecasting. The study is conducted by performing short- to medium-range ensembles in the Bay of Biscay, a subdomain of the IBI-MFC. Ensembles were generated using ocean stochastic modelling and incorporating an atmospheric ensemble. Sentinel 3A data from CMEMS TACs and arrays were considered for empirical consistency, using innovation statistics and approaches taking into account correlated observations. Finally, several properties of ensembles were estimated as components of known probabilistic skill scores: the Brier score (BS), and the CRPS. This was done for pseudo-observations (Quasi-Reliable test-bed) and for real verifying observations in a coastal upwelling test case.</span></div>

Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models

Atmospheric chemical forecasts highly rely on various model parameters, which are often insufficiently known, as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties by an ensemble of forecasts is impaired by the high-dimensionality of the system. This study presents a novel approach to efficiently perturb atmospheric-chemical model parameters according to their leading coupled uncertainties. The algorithm is based on the idea that the forecast model acts as a dynamical system inducing multi-variational correlations of model uncertainties. The specific algorithm presented in this study is designed for parameters which depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen-Loéve expansion. Due to their perceived simulation challenge the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state high spatial- and cross-correlations of regional biogenic emissions, which are represented by a low number of dominating components. Consequently, leading uncertainties can be covered by low number of perturbations enabling ensemble sizes of the order of 10 members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

A Multivariate Balanced Initial Ensemble Generation Approach for an Atmospheric General Circulation Model

Based on the multivariate empirical orthogonal function (MEOF) method, a multivariate balanced initial ensemble generation method was applied to the ensemble data assimilation scheme. The initial ensembles were generated with a reasonable consideration of the physical relationships between different model variables. The spatial distribution derived from the MEOF analysis is combined with the 3-D random perturbation to generate a balanced initial perturbation field. The Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme was established for an atmospheric general circulation model. Ensemble data assimilation experiments using different initial ensemble generation methods, spatially random and MEOF-based balanced, are performed using realistic atmospheric observations. It is shown that the ensembles integrated from the balanced initial ensembles maintain a much more reasonable spread and a more reliable horizontal correlation compared with the historical model results than those from the randomly perturbed initial ensembles. The model predictions were also improved by adopting the MEOF-based balanced initial ensembles.