Training a convolutional neural network to conserve mass in data assimilation

Yvonne Ruckstuhl,Tijana Janjić,Stephan Rasp

doi:10.5194/npg-28-111-2021

Yvonne Ruckstuhl, Tijana Janjić + Show 1 more

Open Access

https://doi.org/10.5194/npg-28-111-2021

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Abstract

Abstract. In previous work, it was shown that the preservation of physical properties in the data assimilation framework can significantly reduce forecast errors. Proposed data assimilation methods, such as the quadratic programming ensemble (QPEns) that can impose such constraints on the calculation of the analysis, are computationally more expensive, severely limiting their application to high-dimensional prediction systems as found in Earth sciences. We, therefore, propose using a convolutional neural network (CNN) trained on the difference between the analysis produced by a standard ensemble Kalman filter (EnKF) and the QPEns to correct any violations of imposed constraints. In this paper, we focus on the conservation of mass and show that, in an idealised set-up, the hybrid of a CNN and the EnKF is capable of reducing analysis and background errors to the same level as the QPEns.

Highlights

The ensemble Kalman filter (EnKF; Evensen, 1994; Burgers et al, 1998; Evensen, 2009) and versions thereof are powerful data assimilation algorithms that can be applied to problems that need an estimate of a high-dimensional model state, as in weather forecasting
As the training data is normalised, we can conclude from the root mean squared error (RMSE) of the input data with respect to the output data that the mass constraint on h and the positivity constraints on r impact the solution of the minimisation problem for all variables with the same order of magnitude
Given our choice of loss function, it is not surprising that the relative reduction of the gap between the input and output by the convolutional neural network (CNN) is proportional to the size of the gap

Summary

Introduction

The ensemble Kalman filter (EnKF; Evensen, 1994; Burgers et al, 1998; Evensen, 2009) and versions thereof are powerful data assimilation algorithms that can be applied to problems that need an estimate of a high-dimensional model state, as in weather forecasting. Mass conservation, as guaranteed by a numerical model, is violated during data assimilation (Janjicet al., 2014). The obstacle that remains in applying the QPEns on large systems is the computational demand of solving the constrained minimisation problems that appear for each ensemble member at each assimilation cycle. We propose using an artificial neural network (NN) to correct the unconstrained solution instead of solving the constrained minimisation problems

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