Santander Meteorology Group A multidisciplinary approach for weather & climate http://www.meteo.unican.es

Spatiotemporal MVL Analysis of EPS: Application to DEMETER multi-model

Seasonal Predictions

José M. Gutiérrez manuel.gutierrez@unican.es

Miguel Angel Rodríguez Sixto Herrera

Jesús Fernández Antonio S. Cofiño

Cristina Primo

Meteorology Group Instituto de Física de Cantabria (IFCA)

ECODYC10. Max Plack Institute Physics Complex Systems. Dresden, 25-29/1/2010

Juan M. López, Diego Pazó, ... Statistical Physics Group

Instituto de Física de Cantabria (IFCA)

Spatiotemporal Chaos Research Line

Santander Meteorology Group A multidisciplinary approach for weather & climate

From theory to operations

TOY Models (Physics) Lorenz96

OPERATIONAL Models (Physics + Engineering)

€

dvdt

= −α∇p −∇φ + F − 2Ω× v

∂ρ∂t

= −∇⋅ (ρv)

pα = RT

Q = CpdTdt

−αdpdt

∂ρq∂t

= −∇⋅ (ρvq) + ρ(E −C)

Santander Meteorology Group A multidisciplinary approach for weather & climate

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  What we learned from our “theoretical” colleagues –  Spatiotemporal growth of errors

  What we jointly developed for practical applications: –  MVL diagram

  Application to DEMETER Hindcast

  Going back to theory: –  Extension to two-scale systems (Lorenz96)

Table of contents

Santander Meteorology Group A multidisciplinary approach for weather & climate

Error Growth (Primo et al. 2005, 2007)

€

δxi(t) = xip (t) − xi(t)

Control

Temporal growth

Spatial growth

Santander Meteorology Group A multidisciplinary approach for weather & climate

MVL Diagram

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The MVL diagram provides a “fingerprint” of the system dynamics

Climatological fluctuations

A: Random and spatially uncorrelated C: Assimilated perturbations (e.g. bred vec.) B: Spatially correlated and non-assimilated (e.g. lagged)

Moreover, the initial transient is related to the initial perturbations.

Santander Meteorology Group A multidisciplinary approach for weather & climate

DEMETER Seasonal Hindcast

Ocean-atmosphere global circulation models running ensemble initial condition perturbations (9 members) for seasonal forecasts.

Feb 87 May 87 Aug 87 Nov 87 Feb 88 ...

Initial conditions

9 members for 6 months = 1 forecast Production for 1980-2001 starting 4 times per year:

1st February 1st May 1st August 1st November

x 7 models

Multi-model ensemble addresses the problem of model error.

thanks to Francisco Doblas-Reyes

Santander Meteorology Group A multidisciplinary approach for weather & climate

DEMETER GCMs

Santander Meteorology Group A multidisciplinary approach for weather & climate

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GCMs building blocks

Different models share common building blocks (atmospheric and/or oceanic components), so they cannot be considered as equiprobable representations of the model error. Thus, we need some diagnostic tool to find similarities among models dynamically.

Santander Meteorology Group A multidisciplinary approach for weather & climate

MVL for T2m

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Robust to interannual variability

Santander Meteorology Group A multidisciplinary approach for weather & climate

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Santander Meteorology Group A multidisciplinary approach for weather & climate

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MVL for z500

Robust to interannual variability

Santander Meteorology Group A multidisciplinary approach for weather & climate

Model weighting

All these methods weight models according to performance.

Thus, if a “good” model is included several times in the ensemble, then the results will be biased towards this particular model.

Santander Meteorology Group A multidisciplinary approach for weather & climate

Model Comparison & weighting

Santander Meteorology Group A multidisciplinary approach for weather & climate

MVL control vs MVL reanalysis

€

δxi(t) = xip (t) − xi(t)

Control

€

δxi(t) = xip (t) − xi(t)

Reanalysis

Santander Meteorology Group A multidisciplinary approach for weather & climate

Role of slow-fast dynamics

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Santander Meteorology Group A multidisciplinary approach for weather & climate

Two-Scale Lorenz96

h=0.3

h=1

Santander Meteorology Group A multidisciplinary approach for weather & climate

h=0.3 17

h=0.6

h=1

Santander Meteorology Group A multidisciplinary approach for weather & climate

Sensitivity of the coupling param.

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Santander Meteorology Group A multidisciplinary approach for weather & climate

Fast variables vs Noise

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The fast variables play a role in the dynamics of slow variables even after saturation. They cannot be substituted by an “effective” noise.

Santander Meteorology Group A multidisciplinary approach for weather & climate Conclusions

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The MVL diagram is a powerfull diagnosis and characterization tool.

We (operational meteorology) can benefit from the advances in spatiotemporal nonlinear physics.

ALSO THE OTHER WAY AROUND.

Santander Meteorology Group A multidisciplinary approach for weather & climate More Info ...

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S. Herrera, J. Fernández, M.A. Rodríguez and J.M. Gutiérrez (2010) Spatio-temporal Error Growth in the Multi-Scale Lorenz96 Model Nonlinear Processes in Geophysics, submitted.

J. Fernández, C. Primo, A. S. Cofiño, J.M. Gutiérrez, M.A. Rodríguez (2009) MVL Spatiotemporal analysis for model comparison. Application to the DEMETER Multi-model Ensemble Climate Dynamics, 33, 233-243. DOI: 10.1007/s00382-008-0456-9

J.M. Gutiérrez, C. Primo, M.A. Rodríguez and J. Fernández (2008) Spatiotemporal Characterization of Ensemble Prediction Systems. The Mean-Variance of Logarithms (MVL) Diagram Nonlinear Processes in Geophysics, 15, 109-114.