# Narrowing Uncertainties of Climate Projections using Data-driven Methods: the AMOC Case Study

Pierre Tandeo, Pierre Le Bras, Florian Sévellec, Pierre Ailliot, Juan Ruiz

► To cite this version:

Pierre Tandeo, Pierre Le Bras, Florian Sévellec, Pierre Ailliot, Juan Ruiz. Narrowing Uncertainties of Climate Projections using Data-driven Methods: the AMOC Case Study. NHM 2023: 6th International Workshop on Nonhydrostatic Models, Aug 2023, Sapporo, Japan. pp.1-13. hal-04193133

HAL Id: hal-04193133

https://imt-atlantique.hal.science/hal-04193133v1

Submitted on 4 Sep 2023

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
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IMT Atlantique
Bretagne-Pays de la Loire
École Mines-Télécom

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Lab-STICC

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iuem

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INSTITUT
UNIVERSITAIRE
EUROPEEN
DE LA MER

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# Narrowing Uncertainties of Climate Projections using Data-driven Methods

## *The AMOC case study*

Pierre Tandeo<fnref n="1" />, Pierre Le Bras<fnref n="1" />,<fnref n="2" />, Florian Sévellec<fnref n="2" />, Pierre Ailliot<fnref n="3" />, and Juan Ruiz<fnref n="4" />

## The 6th International Workshop on Nonhydrostatic Models
(NHM-WS 2023)

<figure><img src="image_8.png" /></figure>

31 August - 2 September 2023

<figure><img src="image_9.png" /></figure>

Hokkaido University Conference Hall, Sapporo, Japan

<footnote n="1">¹ Lab-STICC, IMT Atlantique, FRANCE</footnote>

<footnote n="2">² Laboratoire d'Océanographie Physique et Spatiale, IUEM, FRANCE</footnote>

<footnote n="3">³ Laboratoire de Mathématiques de Bretagne Atlantique, UBO, FRANCE</footnote>

<footnote n="4">⁴ Centro de Investigaciones del Mar y la Atmosfera, Univ. Buenos Aires, ARGENTINA</footnote>
<figure><img src="image_10.png" /><figcaption>Fig.1: Schematic of AMOC
http://www.noc.soton.ac.uk/rapidmoc/</figcaption></figure>

[Source:

<figure><img src="image_11.png" /><figcaption>Fig.2: Experiences of AMOC collapse/resumption and influence on surface temperature anomalies
[Source: Pedro et al., 2018]</figcaption></figure>

AMOC

→ Circulation in the Atlantic ocean

Shallow warm water northward

Deep cold water southward

→ Influence on climate of Atlantic regions

→ Essential to monitor its evolution
<figure><img src="image_12.png" /><figcaption>Fig.1: AMOC observations from RAPID/MOCHA system</figcaption></figure>

[Source: Moat et al., 2020]

<figure><img src="image_13.png" /><figcaption>Fig.2: AMOC anomalies from different models (SSP5-8.5 in CMIP5-6)</figcaption></figure>

[Source: Lyu and Church, 2020]

**Observations:**

→ Seasonal and interannual variability

→ Hard to measure, lot of noise

**CMIP Model projections:**

→ Models predict severe decrease of the AMOC

→ **Wide spread** (model uncertainty)

**How to improve accuracy**
**and reliability of AMOC projections?**
<figure><img src="image_14.png" /></figure>

**State of the art** → Model democracy
(same weights)

→ Questionable
(e.g., Knutti et al., 2019)

**Our goal** → Weight the projections

→ <u>Using available simulations and observations</u>

→ Reduce the uncertainty
<figure><img src="image_15.png" /><figcaption>Fig.1: Scheme of the methodology</figcaption></figure>

[Source: Ruiz et al., 2022]

Step (a): Data assimilation

→ start from an accurate initial condition

→ Ensemble Kalman filter (EnKF)

Step (b): Data-driven forecast

→ make forecasts without equations

→ analog method

Step (c): Weighting procedure

→ compute observation-forecast distance

→ contextual model evidence (CME)

Ruiz, J., Ailliot, P., Chau, T. T. T., Le Bras, P., Monbet, V., Sévellec, F., & Tandeo, P. (2022). Analog data assimilation for the selection of suitable general circulation models. *Geoscientific Model Development*, *15*(18), 7203-7220.
3-variable AMOC chaotic model

(Sévellec and Fedorov, 2014)

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

$$ 
\begin{aligned}
\frac{d\omega}{dt} &= -\lambda\omega - \epsilon\beta S_{NS}, \\
\frac{dS_{BT}}{dt} &= (\Omega_0 + \omega) S_{NS} - K S_{BT} + \frac{F_0 S_0}{h}, \\
\frac{dS_{NS}}{dt} &= -(\Omega_0 + \omega) S_{NS} - K S_{NS}
\end{aligned}
$$

$\Delta_{N-S}$: Meridional salinity gradient

$\Delta_{B-T}$: Stratified salinity
$\lambda = 1e-02; \epsilon = 0.350$
$\Omega_0 = -2.50e-02; K = 1e-04$

$\lambda = 1e-02; \epsilon = 0.350$
$\Omega_0 = -1.25e-02; K = 1e-04$

$\lambda = 1e-02; \epsilon = 0.350$
$\Omega_0 = -1.25e-02; K = 2e-04$

$\lambda = 1e-02; \epsilon = 0.350$
$\Omega_0 = -5.00e-02; K = 5e-05$

<figure><img src="image_18.png" /></figure>

$\lambda = 1e-02; \epsilon = 0.175$
$\Omega_0 = -2.50e-02; K = 1e-04$

<figure><img src="image_19.png" /></figure>

$\lambda = 1e-02; \epsilon = 0.175$
$\Omega_0 = -2.50e-02; K = 2e-04$

<figure><img src="image_20.png" /></figure>

$\lambda = 1e-02; \epsilon = 0.175$
$\Omega_0 = -1.25e-02; K = 5e-05$

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

$\lambda = 1e-02; \epsilon = 0.175$
$\Omega_0 = -5.00e-02; K = 5e-05$

<figure><img src="image_23.png" /></figure>

$\lambda = 1e-02; \epsilon = 0.175$
$\Omega_0 = -5.00e-02; K = 2e-04$

<figure><img src="image_24.png" /></figure>

$\lambda = 5e-03; \epsilon = 0.350$
$\Omega_0 = -2.50e-02; K = 5e-05$

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

→ **11 perturbed-parameter versions**

→ **Leave-One-Out strategy**

→ **Mimic 10 climate simulations and 1 observation**

<figure><img src="image_29.png" /><figcaption>Schematic of the Leave-One-Out strategy</figcaption></figure>

→ **Compute 10 weights**

→ **Approximate observation distribution**
## TRAINING STAGE

<figure><img src="image_30.png" /></figure>

(with data-driven forecasts)

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

VS

<figure><img src="image_33.png" /></figure>

## TESTING STAGE

<figure><img src="image_34.png" /></figure>

Reconstructed PDFs

<figure><img src="image_35.png" /></figure>
→ Out-of-training simulations

PDFs simulations for each model

<figure><img src="image_36.png" /></figure>

Model democracy

Climatologies

AnDA+CME)

Weighting

Attributed weights to each model

<figure><img src="image_37.png" /></figure>

~ 3 selected models

Truth
<figure><img src="image_38.png" /></figure>

Out-of-training simulations

<figure><img src="image_39.png" /></figure>

Model democracy

Climatologies

AnDA+CME)

Attributed weights to each model

<figure><img src="image_40.png" /></figure>

~ 3 selected models

Truth

<figure><img src="image_41.png" /></figure>

Weighting

PDFs of weighted simulations

<figure><img src="image_42.png" /></figure>

Results: reconstruction skillness

<table><thead><tr><th>% PDFs overlap</th><th>One experiment</th></tr></thead><tbody><tr><td>Model democracy</td><td>77.6</td></tr><tr><td>Climatologies</td><td>78.3 (+0.7)</td></tr><tr><td>AnDA+CME</td><td>92.3 (+14.7)</td></tr></tbody></table>

AnDA with CME outperforms model democracy
LOO results: % PDF overlap between each weighted PDF and the true one

<figure><img src="image_43.png" /></figure>

AnDA with CME performs at least as good as model democracy
→ Weight climate simulations using noisy observations

→ Data-driven approach (no need to run climate models)

→ Combination of Data Assimilation & Machine Learning

→ Application to synthetic data of the AMOC

→ The proposed method outperforms “model democracy”

<figure><img src="image_44.png" /></figure>
<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

## Article

Articles / Volume 15, issue 18 / GMD, 15, 7203–7220, 2022

https://doi.org/10.5194/gmd-15-7203-2022

© Author(s) 2022. This work is distributed under the Creative Commons Attribution 4.0 License.

Methods for assessment of models

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Search

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Article

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Metrics

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26 Sep 2022

## Analog data assimilation for the selection of suitable general circulation models

Juan Ruiz, Pierre Ailliot, Thi Tuyet Trang Chau, Pierre Le Bras, Valérie Monbet, Florian Sévellec, and Pierre Tandeo

<figure><img src="image_51.png" /></figure>

### Abstract

Data assimilation is a relevant framework to merge a dynamical model with noisy observations. When various models are in competition, the question is to find the model that best matches the observations. This matching can be measured by using the model evidence, defined by the likelihood of the observations given the model. This study explores the performance of model selection based on model evidence computed using data-driven data assimilation, where dynamical models are emulated using machine learning methods. In this work, the methodology is tested with the three-variable Lorenz model and with an intermediate complexity atmospheric general circulation model (a.k.a. the SPEEDY model). Numerical experiments show that the data-driven implementation of the model selection algorithm performs as well as the one that uses the dynamical model. The technique is able to select the best model among a set of possible models and also to characterize the spatiotemporal variability of the model sensitivity. Moreover, the technique is able to detect differences among models in terms of local dynamics in both time and space which are not reflected in the first two moments of the climatological probability distribution. This suggests the implementation of this technique using available long-term observations and model simulations.

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### Short summary

We present a new approach to validate numerical simulations of the current climate. The method...

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ありがとうございま!
arigato gozaimasu!

Contact:
https://tandeo.wordpress.com/
pierre.tandeo@imt-atlantique.fr