# Combining data assimilation and machine learning to estimate parameters of a convective-scale model

arXiv: https://arxiv.org/abs/2109.02953 · HTML: https://mlsanity.com/paper/2109.02953/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 7 Sep 2021.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Deep learning to represent sub-grid processes in climate models](https://mlsanity.com/paper/1806.04731/) (2018)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [Stochastic Super-Resolution for Downscaling Time-Evolving Atmospheric Fields with a Generative Adversarial Network](https://mlsanity.com/paper/2005.10374/) (2020)
- [Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model](https://mlsanity.com/paper/1909.04711/) (2019)
- [Survey of Dropout Methods for Deep Neural Networks](https://mlsanity.com/paper/1904.13310/) (2019)
- [Physically Interpretable Neural Networks for the Geosciences: Applications to Earth System Variability](https://mlsanity.com/paper/1912.01752/) (2019)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Collapse of Deep and Narrow Neural Nets](https://mlsanity.com/paper/1808.04947/) (2018)
- [Modeling Order in Neural Word Embeddings at Scale](https://mlsanity.com/paper/1506.02338/) (2015)
- [Informative Neural Ensemble Kalman Learning](https://mlsanity.com/paper/2008.09915/) (2020)
- [Sensitivity Analysis for Predictive Uncertainty in Bayesian Neural Networks](https://mlsanity.com/paper/1712.03605/) (2017)
- [Data Assimilation by Artificial Neural Networks for an Atmospheric General Circulation Model: Conventional Observation](https://mlsanity.com/paper/1407.4360/) (2014)
- [Machine Learning for Robust Identification of Complex Nonlinear Dynamical Systems: Applications to Earth Systems Modeling](https://mlsanity.com/paper/2008.05590/) (2020)
- [Embedded methods for feature selection in neural networks](https://mlsanity.com/paper/2010.05834/) (2020)

## Built on by (most cited first, 4 of 4)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Fuxi-DA: A Generalized Deep Learning Data Assimilation Framework for Assimilating Satellite Observations](https://mlsanity.com/paper/2404.08522/) (2024)
- [Interpretable Machine Learning for Weather and Climate Prediction: A Survey](https://mlsanity.com/paper/2403.18864/) (2024)
- [Uncertainty quantification via conformal prediction in data assimilation](https://mlsanity.com/paper/2606.27001/) (2026)

## Abstract (arXiv)

Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of the numerical schemes determining the evolution of humidity and temperature, but large contributions are due to the parametrization of microphysics and the parametrization of processes in the surface and boundary layers. These schemes typically contain several tunable parameters that are either not physical or only crudely known, leading to model errors. Traditionally, the numerical values of these model parameters are chosen by manual model tuning. More objectively, they can be estimated from observations by the augmented state approach during the data assimilation. Alternatively, in this work, we look at the problem of parameter estimation through an artificial intelligence lens by training two types of artificial neural networks (ANNs) to estimate several parameters of the one-dimensional modified shallow-water model as a function of the observations or analysis of the atmospheric state. Through perfect model experiments, we show that Bayesian neural networks (BNNs) and Bayesian approximations of point estimate neural networks (NNs) are able to estimate model parameters and their relevant statistics. The estimation of parameters combined with data assimilation for the state decreases the initial state errors even when assimilating sparse and noisy observations. The sensitivity to the number of ensemble members, observation coverage, and neural network size is shown. Additionally, we use the method of layer-wise relevance propagation to gain insight into how the ANNs are learning and discover that they naturally select only a few gridpoints that are subject to strong winds and rain to make their predictions of chosen parameters.