scholarly journals Using machine learning to correct model error in data assimilation and forecast applications

2021 ◽  
Author(s):  
Alban Farchi ◽  
Patrick Laloyaux ◽  
Massimo Bonavita ◽  
Marc Bocquet
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Model Error ◽  
Correct Model

scholarly journals Using machine learning to correct model error in data assimilation and forecast applications

2021 ◽  
Author(s):  
Alban Farchi ◽  
Patrick Laloyaux ◽  
Massimo Bonavita ◽  
Marc Bocquet
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Data Science ◽  
Weather Prediction ◽  
Realistic Model ◽  
Model Error ◽  
Underlying Assumption ◽  
Correct Model ◽  
Recent Developments ◽  
Spatiotemporal Processes

<p>Recent developments in machine learning (ML) have demonstrated impressive skills in reproducing complex spatiotemporal processes. However, contrary to data assimilation (DA), the underlying assumption behind ML methods is that the system is fully observed and without noise, which is rarely the case in numerical weather prediction. In order to circumvent this issue, it is possible to embed the ML problem into a DA formalism characterised by a cost function similar to that of the weak-constraint 4D-Var (Bocquet et al., 2019; Bocquet et al., 2020). In practice ML and DA are combined to solve the problem: DA is used to estimate the state of the system while ML is used to estimate the full model. </p><p>In realistic systems, the model dynamics can be very complex and it may not be possible to reconstruct it from scratch. An alternative could be to learn the model error of an already existent model using the same approach combining DA and ML. In this presentation, we test the feasibility of this method using a quasi geostrophic (QG) model. After a brief description of the QG model model, we introduce a realistic model error to be learnt. We then asses the potential of ML methods to reconstruct this model error, first with perfect (full and noiseless) observation and then with sparse and noisy observations. We show in either case to what extent the trained ML models correct the mid-term forecasts. Finally, we show how the trained ML models can be used in a DA system and to what extent they correct the analysis.</p><p>Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Data assimilation as a learning tool to infer ordinary differential equation representations of dynamical models, Nonlin. Processes Geophys., 26, 143–162, 2019</p><p>Bocquet, M., Brajard, J., Carrassi, A., and Bertino, L.: Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization, Foundations of Data Science, 2 (1), 55-80, 2020</p><p>Farchi, A., Laloyaux, P., Bonavita, M., and Bocquet, M.: Using machine learning to correct model error in data assimilation and forecast applications, arxiv:2010.12605, submitted. </p>

Data-driven parametrizations in numerical models using data assimilation and machine learning.

2020 ◽  
Author(s):  
Julien Brajard ◽  
Alberto Carrassi ◽  
Marc Bocquet ◽  
Laurent Bertino
Keyword(s):  
Machine Learning ◽  
High Resolution ◽  
Data Assimilation ◽  
Physical Model ◽  
Hybrid Model ◽  
Numerical Models ◽  
Coarse Graining ◽  
Model Error ◽  
Data Driven ◽  
Model Combining

<p>Can we build a machine learning parametrization in a numerical model using sparse and noisy observations?</p><p>In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most of the cases, ML is trained by coarse-graining high-resolution simulations to provide a dense, unnoisy target state (or even the tendency of the model).</p><p>Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data. Furthermore, we intentionally place ourselves in the realistic scenario of noisy and sparse observations.</p><p>The algorithm proposed in this work derives from the algorithm presented by the same authors in https://arxiv.org/abs/2001.01520.The principle is to first apply data assimilation (DA) techniques to estimate the full state of the system from a non-parametrized model, referred hereafter as the physical model. The parametrization term to be estimated is viewed as a model error in the DA system. In a second step, ML is used to define the parametrization, e.g., a predictor of the model error given the state of the system. Finally, the ML system is incorporated within the physical model to produce a hybrid model, combining a physical core with a ML-based parametrization.</p><p>The approach is applied to dynamical systems from low to intermediate complexity. The DA component of the proposed approach relies on an ensemble Kalman filter/smoother while the parametrization is represented by a convolutional neural network.  </p><p>We show that the hybrid model yields better performance than the physical model in terms of both short-term (forecast skill) and long-term (power spectrum, Lyapunov exponents) properties. Sensitivity to the noise and density of observation is also assessed.</p>

scholarly journals Combining data assimilation and machine learning to infer unresolved scale parametrization

2021 ◽  
Vol 379 (2194) ◽  
pp. 20200086
Author(s):  
Julien Brajard ◽  
Alberto Carrassi ◽  
Marc Bocquet ◽  
Laurent Bertino
Keyword(s):  
Machine Learning ◽  
High Resolution ◽  
Data Assimilation ◽  
Hybrid Model ◽  
Numerical Models ◽  
Model Error ◽  
Climate Modelling ◽  
Combining Data ◽  
Full State ◽  
Direct Data

In recent years, machine learning (ML) has been proposed to devise data-driven parametrizations of unresolved processes in dynamical numerical models. In most cases, the ML training leverages high-resolution simulations to provide a dense, noiseless target state. Our goal is to go beyond the use of high-resolution simulations and train ML-based parametrization using direct data, in the realistic scenario of noisy and sparse observations. The algorithm proposed in this work is a two-step process. First, data assimilation (DA) techniques are applied to estimate the full state of the system from a truncated model. The unresolved part of the truncated model is viewed as a model error in the DA system. In a second step, ML is used to emulate the unresolved part, a predictor of model error given the state of the system. Finally, the ML-based parametrization model is added to the physical core truncated model to produce a hybrid model. The DA component of the proposed method relies on an ensemble Kalman filter while the ML parametrization is represented by a neural network. The approach is applied to the two-scale Lorenz model and to MAOOAM, a reduced-order coupled ocean-atmosphere model. We show that in both cases, the hybrid model yields forecasts with better skill than the truncated model. Moreover, the attractor of the system is significantly better represented by the hybrid model than by the truncated model. This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

Bayesian inference of dynamics from partial and noisy observations using data assimilation and machine learning

2020 ◽  
Author(s):  
Marc Bocquet ◽  
Julien Brajard ◽  
Alberto Carrassi ◽  
Laurent Bertino
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Data Assimilation ◽  
Loss Function ◽  
Surrogate Model ◽  
Model Error ◽  
Approximate Algorithm ◽  
Error Statistics ◽  
Long Time Series ◽  
Long Time

<p>The reconstruction from observations of the dynamics of high-dimensional chaotic models such as geophysical fluids is hampered by (i) the inevitably partial and noisy observations that can realistically be obtained, (ii) the need and difficulty to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has recently been suggested to combine data assimilation and machine learning in several ways. We first rigorously show how to unify these approaches from a Bayesian perspective, yielding a non-trivial loss function.</p><p>Existing techniques to optimize the loss function (or simplified variants thereof) are re-interpreted here as coordinate descent schemes. The expectation-maximization (EM) method is used to estimate jointly the most likely model and model error statistics. The main algorithm alternates two steps: first, a posterior ensemble is derived using a traditional data assimilation step using an ensemble Kalman smoother (EnKS); second, both the surrogate model and the model error are updated using machine learning tools, a quasi-Newton optimizer, and analytical formula. In our case, the spatially extended surrogate model is formalized as a neural network with convolutional layers leveraging on the locality of the dynamics.</p><p>This scheme has been successfully tested on two low-order chaotic models with distinct identifiability, namely the 40-variable and the two-scale Lorenz models. Additionally, an approximate algorithm is tested to mitigate the numerical cost, yielding similar performances. Using indicators that probe short-term and asymptotic properties of the surrogate model, we investigate the sensitivity of the inference to the length of the training window, to the observation error magnitude, to the density of the monitoring network, and to the lag of the EnKS. In these iterative schemes, model error statistics are automatically adjusted to the improvement of the surrogate model dynamics. The outcome of the minimization is not only a deterministic surrogate model but also its associated stochastic correction, representative of the uncertainty attached to the deterministic part and which accounts for residual model errors.</p>

Using a machine learning proxy for localization in ensemble data assimilation

2021 ◽  
Vol 25 (3) ◽  
pp. 931-944
Author(s):  
Johann M. Lacerda ◽  
Alexandre A. Emerick ◽  
Adolfo P. Pires
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

scholarly journals Parameter Estimation Using Ensemble-Based Data Assimilation in the Presence of Model Error

2015 ◽  
Vol 143 (5) ◽  
pp. 1568-1582 ◽  
Author(s):  
Juan Ruiz ◽  
Manuel Pulido
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Model Error ◽  
Forecast Skill ◽  
Moist Convection ◽  
Treatment Techniques ◽  
Correction Technique ◽  
Error Treatment ◽  
Data Assimilation System ◽  
Assimilation System

Abstract This work explores the potential of online parameter estimation as a technique for model error treatment under an imperfect model scenario, in an ensemble-based data assimilation system, using a simple atmospheric general circulation model, and an observing system simulation experiment (OSSE) approach. Model error is introduced in the imperfect model scenario by changing the value of the parameters associated with different schemes. The parameters of the moist convection scheme are the only ones to be estimated in the data assimilation system. In this work, parameter estimation is compared and combined with techniques that account for the lack of ensemble spread and for the systematic model error. The OSSEs show that when parameter estimation is combined with model error treatment techniques, multiplicative and additive inflation or a bias correction technique, parameter estimation produces a further improvement of analysis quality and medium-range forecast skill with respect to the OSSEs with model error treatment techniques without parameter estimation. The improvement produced by parameter estimation is mainly a consequence of the optimization of the parameter values. The estimated parameters do not converge to the value used to generate the observations in the imperfect model scenario; however, the analysis error is reduced and the forecast skill is improved.

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