A Multi-Scale Deep Learning Framework for Projecting Weather Extremes Antoine Blanchard

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A Multi-Scale Deep Learning Framework for

Projecting Weather Extremes

Antoine Blanchard

Verisk Analytics

Boston, MA 02115

ablanchard@verisk.com

Nishant Parashar

Verisk Analytics

Boston, MA 02115

nparashar@verisk.com

Boyko Dodov

Verisk Analytics

Boston, MA 02115

bdodov@verisk.com

Christian Lessig

Otto-von-Guericke Universität

Magdeburg, Germany

christian.lessig@ovgu.de

Themistoklis Sapsis

Massachusetts Institute of Technology

Cambridge, MA 02139

sapsis@mit.edu

Abstract

Weather extremes are a major societal and economic hazard, claiming thousands of

lives and causing billions of dollars in damage every year. Under climate change,

their impact and intensity are expected to worsen signiﬁcantly. Unfortunately,

general circulation models (GCMs), which are currently the primary tool for climate

projections, cannot characterize weather extremes accurately. To address this, we

present a multi-resolution deep-learning framework that, ﬁrstly, corrects a GCM’s

biases by matching low-order and tail statistics of its output with observations at

coarse scales; and secondly, increases the level of detail of the debiased GCM output

by reconstructing the ﬁner scales as a function of the coarse scales. We use the

proposed framework to generate statistically realistic realizations of the climate over

Western Europe from a simple GCM corrected using observational atmospheric

reanalysis. We also discuss implications for probabilistic risk assessment of natural

disasters in a changing climate.

1 Introduction

The development of extreme weather under climate change is of growing concern for many stake-

holders across the globe, including civil society, governments, and businesses [

–

]. The assessment

of the risks associated with weather extremes is thereby highly critical. Quite often, the most unlikely

events in the tail of a hazard’s probability distribution are also the most devastating. Because of

their unlikely nature, their statistics are difﬁcult to predict, even more so on a regional scale [

]. In

addition, the effects of climate change are expected to vary across weather perils, making exploration

of catastrophic scenarios even more challenging.

Extreme weather risk is often estimated by generating ensembles of possible climate states using

global circulation models (GCMs). Unfortunately, ensemble size and resolution are insufﬁcient to

characterize tail events properly. Even at high resolution, GCMs suffer from statistical biases [

]

which can lead to the incorrect characterization of extreme-weather inducing processes (e.g., blocking

events [

]). Moreover, high-resolution GCMs require vast computing resources. Hence, to create

large ensembles that provide a better statistical sampling, simple GCMs and coarse resolutions have

to be employed. However, these simulations will be polluted with severe biases.

To remedy these issues, one strategy is to leverage the wealth of observational data available about the

Earth system and the power of machine learning [

]. This can be pursued either in a purely data-based

Tackling Climate Change with Machine Learning workshop at NeurIPS 2022.

arXiv:2210.12137v1 [cs.LG] 21 Oct 2022

Coarse-scale debiased

simulation

Wavelet transform

LSTM-based

Neural Networks

Coarse-scale biased

GCM simulation

Inverse wavelet transform

Coarse-scale biased

wavelet coefficients Coarse-scale debiased

wavelet coefficients

Coarse-scale

reanalysis Fine-scale

reanalysis

Wavelet transform

TCN-based

Neural Networks

Inverse wavelet transform

Coarse-scale

wavelet coefficients Fine-scale

wavelet coefficients

Full-scale debiased

simulation

Testing

Step 1

Step 2

Figure 1: Overview of framework. Reanalysis data is used as benchmark as it provides the most

comprehensive description of the observed climate.

fashion [

], or by augmenting the GCM dynamical equations with data-driven terms [

] or post-

processing the GCM output to make it consistent with observations [

]. The main challenges

are thereby the strongly nonlinear energy scattering across scales as well the non-deterministic nature

of the very ﬁne scales [

]. These two issues often compromise the stability of machine-learning

schemes [13, 14] and the physical consistency of the output [15, 16].

We introduce a multi-resolution deep learning framework for accelerating the simulation of weather

extremes. We combine a physics-based GCM run at coarse resolution with machine-learning models

trained on observational data to reduce the biases and enhance the resolution of the GCM simulation.

The key ingredients are a) a compact, multi-scale representation of physical processes on the sphere

which efﬁciently captures energy transfers across scales; b) novel statistical loss functions which

place emphasis on extreme values and space–time coherency; and c) a divide-and-conquer training

strategy which enables training of regional models at high spatial resolution. The full-scale debiased

simulation provides a complete view of risk at arbitrary resolution which decision makers can use to

investigate near-present scenarios and assess their vulnerability to catastrophic weather events.

2 Methods

We start from coarse-resolution runs of a simple but fast GCM polluted by strong biases. Based on

these, we proceed in two steps; see Figure 1. First, we correct the low-order and tail statistics of

the GCM output at coarse scales to match the statistics of observations. Second, we enhance the

resolution of the debiased GCM output by reconstructing the ﬁner scales as a function of the coarse

ones. In both steps, the ground truth is reanalysis data, a blend of observations and past forecasts

which provides the most realistic picture of past atmospheric states that is available.

Decomposition of spatial scales

The dynamics of the atmosphere are characterized by a wide

range of scales, from thousands of kilometers to a few meters. To delineate coarse- and ﬁne-scale

phenomena, we use a discrete spherical wavelet frame [

] which provides a mathematically robust

framework for scale separation and allows us to achieve a good balance between spatial and frequency

localization. Each physical variable is decomposed on a set of wavelet levels of increasing granularity,

with lower levels capturing large-scale spatial features (Figure 2a). At each level, the locations of

the wavelet centers are chosen as in [

] so as to guarantee the existence of a fast transform. This is

important for manipulating very large climate ensembles at high spatial resolution. This also enables

a highly efﬁcient divide-and-conquer strategy whereby a multitude of small, local neural networks

(one for each wavelet location) are trained concurrently, with communication between models being

through a custom loss function (described below). More details are available in Section A.1.

(a) (b)

Figure 2: (a) Wavelet decomposition for ERA5 reanalysis and (b) cone of inﬂuence for model input.

Step 1: Bias-correction of coarse GCM output

The wavelet coefﬁcients of the coarse, biased

GCM output are mapped into a different set of wavelet coefﬁcients whose statistics match those of

coarse-scale observations; speciﬁcally, ERA5 reanalysis [

]. The bias-correction step is formulated

as a semi-supervised learning problem whereby reanalysis data is used as target for all GCM ensemble

members. For each wavelet center, we employ an LSTM-based neural network whose input consists

of time series for that center and its nearest neighbors. To capture energy transfers across scales—a

landmark of turbulent ﬂows—the input to the network also includes wavelet centers that belong to

coarser wavelet levels. This deﬁnes a cone of inﬂuence for the center under consideration (Figure

2b). From this input, the model outputs a time series whose statistics are required to match those

of reanalysis data. Once the models have been trained, the statistically-corrected time series are

assembled and transformed back from wavelet to physical space to produce bias-corrected realizations

of coarse-scale atmospheric dynamics.

Step 2: Reconstruction of small-scale features

The ensemble obtained from Step 1 has the same

resolution as the GCM on which it is based (typically, cells of size 250–500 km). To achieve a higher

resolution and be able to describe the local effects of extreme events, small-scale structures must be

added. This is done with a second machine-learning step whose task is to reconstruct the ﬁne scales

(i.e., those below the GCM resolution) as a function of the coarse scales (i.e., those resolved by the

GCM). The algorithm is trained on ERA5 reanalysis data in a supervised setting and tested on the

debiased output from Step 1. Each wavelet center is assigned a TCN-based model that operates on a

multi-scale cone of inﬂuence. Wavelet levels can be trained in parallel, but this might lead to error

accumulation across levels at testing time. To combat this, we employ a sequential strategy akin to

imitation learning [

] whereby the input to each model is replaced with model predictions from

previous levels. This improves robustness of the predictions, especially for the coarser levels.

Statistical loss functions

In Step 1, the models are trained using statistical loss functions; this is

a key innovation of our framework. We consider two classes of statistical losses: quantile losses,

which capture heavy tails and extreme values; and spectral losses, which capture cross-correlations

between wavelet centers. The former guarantee that the frequency and amplitude of extreme weather

events in the output is consistent with reanalysis data. The latter guarantee space–time coherency of

the output with respect to wave propagation and transport phenomena. These losses are computed

over several decades of weather data to ensure convergence of the statistics with respect to sample

size (see Section A.2). Crucially, enforcing statistical consistency with reanalysis data still allows for

variability of events in the output, especially the most extreme ones. In Step 2, statistical losses are

used as regularizers, with the MSE loss (or a variant of it that emphasizes extreme values [

]) being

the main driver for the optimization.

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AMulti-ScaleDeepLearningFrameworkforProjectingWeatherExtremesAntoineBlanchardVeriskAnalyticsBoston,MA02115ablanchard@verisk.comNishantParasharVeriskAnalyticsBoston,MA02115nparashar@verisk.comBoykoDodovVeriskAnalyticsBoston,MA02115bdodov@verisk.comChristianLessigOtto-von-GuerickeUniversitätMagdeburg,...

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A Multi-Scale Deep Learning Framework for Projecting Weather Extremes Antoine Blanchard

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