Reduced models of atmospheric low-frequency variability: Parameter estimation and comparative performance

International audienceThree distinct strategies are applied here to reduce a fairly realistic, high-dimensional, quasi-geostrophic, 3-level (QG3) atmospheric model to lower dimensions: (i) an empirical–dynamical method, which retains only a few components in the projection of the full QG3 model equations onto a specified basis, and finds the linear deterministic and the stochastic corrections empirically as in Selten (1995) [5]; (ii) a purely dynamics-based technique, employing the stochastic mode reduction strategy of Majda et al. (2001) [62]; and (iii) a purely empirical, multi-level regression procedure, which specifies the functional form of the reduced model and finds the model coefficients by multiple polynomial regression as in Kravtsov et al. (2005) [3]. The empirical–dynamical and dynamical reduced models were further improved by sequential parameter estimation and benchmarked against multi-level regression models; the extended Kalman filter was used for the parameter estimation.Overall, the reduced models perform better when more statistical information is used in the model construction. Thus, the purely empirical stochastic models with quadratic nonlinearity and additive noise reproduce very well the linear properties of the full QG3 model’s LFV, i.e. its autocorrelations and spectra, as well as the nonlinear properties, i.e. the persistent flow regimes that induce non-Gaussian features in the model’s probability density function. The empirical–dynamical models capture the basic statistical properties of the full model’s LFV, such as the variance and integral correlation time scales of the leading LFV modes, as well as some of the regime behavior features, but fail to reproduce the detailed structure of autocorrelations and distort the statistics of the regimes. Dynamical models that use data assimilation corrections do capture the linear statistics to a degree comparable with that of empirical–dynamical models, but do much less well on the full QG3 model’s nonlinear dynamics. These results are discussed in terms of their implications for a better understanding and prediction of LFV

Reconstruction of electron radiation belts using data assimilation and machine learning

We present a reconstruction of radiation belt electron fluxes using data assimilation with low-Earth-orbiting Polar Orbiting Environmental Satellites (POES) measurements mapped to near equatorial regions. Such mapping is a challenging task and the appropriate methodology should be selected. To map POES measurements, we explore two machine learning methods: multivariate linear regression (MLR) and neural network (NN). The reconstructed flux is included in data assimilation with the Versatile Electron Radiation Belts (VERB) model and compared with Van Allen Probes and GOES observations. We demonstrate that data assimilation using MLR-based mapping provides a reasonably good agreement with observations. Furthermore, the data assimilation with the flux reconstructed by NN provides better performance in comparison to the data assimilation using flux reconstructed by MLR. However, the improvement by adding data assimilation is limited when compared to the purely NN model which by itself already has a high performance of predicting electron fluxes at high altitudes. In the case an optimized machine learning model is not possible, our results suggest that data assimilation can be beneficial for reconstructing outer belt electrons by correcting errors of a machine learning based LEO-to-MEO mapping and by providing physics-based extrapolation to the parameter space portion not included in the LEO-to-MEO mapping, such as at the GEO orbit in this study

On the Use of Emulators with Extreme and Highly Nonlinear Geophysical Simulators

Gaussian process emulators are a powerful tool for understanding complex geophysical simulators, including oceanic and atmospheric general circulation models. Concern has been raised about their ability to emulate complex nonlinear systems. For the first time, using the simple Stommel model, the way in which emulators can reasonably represent the full sampling space of an extreme nonlinear, bimodal system is illustrated. This simple example also shows how an emulator can help to elucidate interactions between parameters. The ideas are further illustrated with a second, more realistic, intermediate complex climate simulator. The paper describes what is meant by an emulator, the methodology of emulators, how emulators can be assessed, and why they are useful. It is shown how simple emulators can be useful to explore the parameter space (initial conditions, process parameters, and boundary conditions) of complex computer simulators, such as ocean and climate general circulation models, even when simulator outcomes contain steps in the response