Calibration statistique du modèle Arpège-Climat - Meteo France
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Calibration statistique
du modèle Arpège-Climat
Aurélien Ribes, Olivier Audouin, Romain Roehrig
CNRM – Météo-France and CNRS
AMA, 11 mars 2019
Motivation I Tuning of Arpège-Climat v6 (new global model, widely revisited physical parametrisations, atmosphere only), I Tuning based on 3D global climate properties (as opposed to 1D models and/or single parametrisations), I Tuning by hand is challenging – a number of physical parameters could be tuned. I Primary objective: adjust the model as well as possible to the observed (∼2000’s) climate. I Secondary objective: provide information to modellers on dependencies between parameters. I Use existing mathematical techniques and literature (UQ: Uncertainty Quantification). I First (exploratory) attempt, aside from our official CMIP version,
General algorithm
1. Inputs: Define which (input) parameters to perturb,
2. Training Data: Run the model for some combination of parameters,
3. Outputs: Define a few (output) metrics / variables to be used to evaluate the
model,
4. Emulator: Construct a statistical emulator of the climate model, to estimate
what would be the model behaviour (ie output variables) for other combinations
of parameters,
5. Calibration: Optimise model performance by minising a cost function over the
parameter space... or...
Select regions of the (input) parameter space where the model is consistent
with available observations (given the uncertainties involved; NROY space
approach).
Which (input) parameters?
I We used 21 parameters (out of... many), mainly related to cloud radiative
properties, microphysics and convection.
Paramètres perturbés
Paramètres Valeur refT2x Minimum Maximum Signification
RKDN 50.e-6 20.e-6 50.e-6 Freinage minimale pour vitesse
verticale de l'updraft convectif
RKDX 100.e-6 50.e-6 1000.e-6 Freinage maximale pour vitesse
verticale de l'updraft convectif
TENTR 5.e-6 4.e-6 20.e-6 Entrainement minimale pour
ascendance convective
TENTRX 57.e-6 40.e-6 150.e-6 Entrainement maximale pour
ascendance convective
VVX -35 -50 -20 Vitesse verticale convective de
transition entre régimes
d'entrainement/freinage
RAUTEFR 1.e-3 0,5.e-3 6.e-3 Inverse du temps caractéristique de
l'autoconversion liquide
RAUTEFS 5,2e-3 0,5.e-3 6.e-3 Inverse du temps caractéristique de
l'autoconversion solide
RQICRMIN 0,04e-6 0,01e-6 0,3e-6 Contenu spécifique en glace critique
minimum pour autoconversion
solide
RQICRMAX 0,21e-4 0,1e-4 0,5e-4 Contenu spécifique en glace critique
maximum pour autoconversion
solide
RQLCR 2.e-4 0,5e-4 10.e-4 Contenu spécifique en eau liquide
critique minimum pour
autoconversion liquide
TFVI 0,08 0 0,2 Vitesse de chute des cristaux de
glace
TFVL 0,02 0 0,2 Vitesse de chute des gouttelettes
d'eau nuageuse
RACCEF 1 0,5 1,5 Efficacité d'accrétion des
hydrométéores
RRIMEF 1,3 0,5 2 Efficacité d'aggrégation des
hydrométéores
RAGGEF 0,3 0,1 1,5 Efficacité de riming et d'aggrégation
des hydrométéores
REVASX 1.e-7 0 1.e-6 Evaporation des précipitations
grande échelle
RREVASXCS 1 0 1 Ratio entre évaporation des
précipitations convective et
évaporation des précipitations
grande échelle
RSWINHF_LIQ 0,6 0,5 1 Coefficient d'hétérogénéïté des
propriétés radiaves des nuages en
phase liquide en SW
RSWINHF_ICE 0,6 0,5 1 Coefficient d'hétérogénéïté des
propriétés radiaves des nuages en
phase glace en SW
RLWINHF_LIQ 0,8 0,5 1 Coefficient d'hétérogénéïté des
propriétés radiaves des nuages en
phase liquide en LW
RLWINHF_ICE 0,8 0,5 1 Coefficient d'hétérogénéïté des
propriétés radiaves des nuages en
phase glace en LWWhich training data / ensemble
I Sample 200 combinations of parameters, i.e. points in the predefined 21-d
hypercube,
I Only one step – no iteration,
I Sampling is done using a Latin Hypercube Sampling (LHS) technique with
minimax optimisation,
I For each combination, run a 10-yr long simulation (forced atmosphere only with
2000-2009 SSTs), i.e. 2000 years of simulation.
I 17 simulations out of 200 crashed and are not considered... probably because we
perturbed the model a bit too muchWhich (output) variables / metric to evaluate the
model?
We focus on the global radiation budget first:
I RST: net shortwave radiative flux at the top of the atmosphere,
240.48 ± 2W .m−2 ,
I RLUT: net long-wave radiative flux at the top of the atmosphere,
239.68 ± 3.5W .m−2 ,
RLUT RST
80
80
60
60
Frequency
Frequency
40
40
20
20
0
0
220 225 230 235 240 245 250 255 220 225 230 235 240 245 250 255
RLUT RSTWhich (output) variables / metric to evaluate the model? In addition to global radiation budget, we consider the RMSE of 8 variables: I Cloud cover, high and low, I Cloud radiative effect, SW and LW, I Near-surface temperature over continents, summer and winter, I Precipitation, summer and winter. These 8 metrics are aggregated into one single metric (weighted sum of RMSE).
Statistical emulator
I Input data: 183 realisations for 21 parameters,
I Statistical model: Kriging / Gaussian Process
- Need to specify a Covariance structure,
Separable with Matérn 5/2 kernel and nugget effect,
- Fit this covariance structure to the sample,
24 parameters, which are estimated by maximizing likelihood in R24
- Likelihood maximisation is difficult: iterative optimisation algo with random
starting points
We explore sensitivity to starting points.Illustration of the emulator
Radiation budget Top of the Atmosphere (TOA) as a function of 2 key parameters:
I TFVL: fall velocity of liquid droplets (x-axis)
I RSWINHF_LIQ: SW radiation heterogeneity coefficient for liquid clouds
(y -axis),
Emulated radiative budget Variance of emulator
TOA Bilan radiatif TOA Variance
8 4.5
6
4 4.0
RSWINHF_LIQ
RSWINHF_LIQ
2
3.5
0
−2
3.0
−4
−6
TFVL TFVLModélisation statistique de ARPEGE-CLIMAT
Exemple d’information apportée par une analyse de sen
Sensitivity analysis
I Fraction of variance explained by each (input) parameter: the Sobol indices.
Sobol indices for the net radiative budget TOA
Météo-France Calibration statistique d’u
I Input parameters which explain less than 1% of the total variance are removed
from the emulator.
For radiative budget TOA, we retain only 8 input parameters.
I Maximisation of the likelihood is much easier in such a reduced set of
parameters.Final calibration strategy
I We construct emulators for each of the 9 outputs considered
I Net radiation TOA and RMSE of the 8 output variables mentioned.
I Sensitivity analysis and selection of useful (input) parameters is
done in each case
I We compute the NROY space for net radiation budget
I asking the 2000’s value to be near +0.75 W.m− 1 ([0, 1.5]),
I assuming no structural error.
I The 8 emulated RMSE are added in one single metric measuring
model accuracy,
I We minimise the aggregated metric over the net radiation NROY space.Results
Calibration statistique de ARPEGE-CLIMAT – 2
Résultat de la calibration
I New parameter values, quite close from their reference values
i.e. values selected by modellers
I Tuned model close to previous version but apparently slightly better.
Bias of annual mean high cloud cover for the reference (i.e. before calibration, left), vs the
Météo-France
calibrated (right) versions of Arpège-Climat.
Calibration statistique d’un modèle de climat — 05Conclusions and outlook
I This first attempt suggests this statistical approach is of interest to calibrate the
model and describe sensitivity to input parameters.
I We explore the parameter space quite systematically,
I Our procedure could be improved in many ways
I Design of simulations (e.g. larger ensemble, with shorter runs),
I Statistical emulator,
I Aggregated metric to evaluate the model,
I Other inputs parameters to be potentially considered,
I etc
I The technique could be applied to weather forecast model (with existing scoring
rules).
I Provide better information on how some parameters should be adjusted given
another (or a few others).
I Usefulness for calibrating future versions of the model is to be determined.You can also read
