Correction of approximation errors with Random Forests applied to modelling of cloud droplet formation

Abstract

Abstract. In atmospheric models, due to their computational time or resource limitations, physical processes have to be simulated using reduced (i.e. simplified) models. The use of a reduced model, however, induces errors to the simulation results. These errors are referred to as approximation errors. In this paper, we propose a novel approach to correct these approximation errors. We model the approximation error as an additive noise process in the simulation model and employ the Random Forest (RF) regression algorithm for constructing a computationally low cost predictor for the approximation error. In this way, the overall simulation problem is decomposed into two separate and computationally efficient simulation problems: solution of the reduced model and prediction of the approximation error realisation. The approach is tested for handling approximation errors due to a reduced coarse sectional representation of aerosol size distribution in a cloud droplet formation calculation as well as for compensating the uncertainty caused by the aerosol activation parameterization itself. The results show a significant improvement in the accuracy of the simulation compared to the conventional simulation with a reduced model. The proposed approach is rather general and extension of it to different parameterizations or reduced process models that are coupled to geoscientific models is a straightforward task. Another major benefit of this method is that it can be applied to physical processes that are dependent on a large number of variables making them difficult to be parameterized by traditional methods.

Parameterising cloud base updraft velocity of marine stratocumuli

“…The probable reason why the LFRF method performs so well, outperforming even GPE, is that it is supported with an embedded dependency, the linear model LF. This is in line with Lipponen et al (2013Lipponen et al ( , 2018 where they showed that including a dependency (= correcting a rough empirical model with random forest) improved results compared to a pure random forest learning method. LF is the least accurate method in all simulation sets, except in SALSA day where it outperforms the GPE only slightly.…”

“…The approach used in this study is similar to the approximation error correction method introduced in Lipponen et al (2013) and Lipponen et al (2018). In Lipponen et al (2018), it was shown that predicting and correcting the approximation error of the output of an approximative model often leads to more accurate results than directly predicting the model output.…”

“…The parameterisations are based on detailed LES runs. The three methods are based on 1) a Gaussian process emulator, 2) a linear parameterisation based on cloud radiative cooling (Zheng et al, 2016), and 3) machine learning to correct the approximation error of the linear fit obtained with method 2 (Lipponen et al, 2013(Lipponen et al, , 2018. We also examine which parameters are most important for predicting updraft velocities.…”

Model-enforced post-process correction of satellite aerosol retrievals

“…More specifically, we train the machine learning model for post-process correction of the approximation error in the result of the conventional retrieval algorithm. While the postprocess correction approach is new to satellite retrievals, it has been found to perform better and produce more stable and accurate results than a fully learned approach in generation of surrogate simulation models (Lipponen et al, 2013(Lipponen et al, , 2018 and in medical imaging, where many of the inverse imaging problems are mathematically highly similar to the satellite retrieval problems; see for example Hamilton et al (2019). The key advantages of the new modelenforced post-process correction approach are (1) the improved accuracy over the existing data products and existing fully learned satellite data approaches and (2) the possibility to post-process-correct existing (past) satellite data products with no need for full re-processing of the enormous satellite datasets.…”

Model Enforced Post-Process Correction of Satellite Aerosol Retrievals

“…More specifically, we train the machine learning model for post-process correction of the approximation error in the result of the conventional retrieval algorithm. While the post-process correction approach is new to satellite retrievals, it has been found to perform better and produce more stable and accurate results than a fully learned approach in generation of surrogate simulation models (Lipponen et al, 2013(Lipponen et al, , 2018 and in medical imaging, where many of the inverse imaging problems are mathematically highly similar to the satellite retrieval problems, see for example Hamilton et al (2019). The key advantages of the new model enforced post-process correction approach are 1) the improved accuracy over the existing data products and existing fully learned satellite data approaches, and 2) the possibility to post-process correct existing (past) satellite data products with no need for full re-processing of the enormous satellite datasets.…”