the effect of indiscriminate nudging time in regional climate modeling of the mediterranean basin...

The effect of indiscriminate nudging time in regional climate modeling of the

Mediterranean basin

Tamara Salameh, Philippe Drobinski, Thomas Dubos and Hiba Omrani

Laboratoire de Météorologie Dynamique/Ecole Polytechnique,

Tamara Salameh

General contextGlobal climate change

Global climate models agree on:

- A decrease in precipitation rate (mm/j) for scenario A1B (21st century)

- Increase in extreme cold temperature- Increase in extreme precipitation (Goubanova and Li 2006)

Need to know as precise as possible future climate conditions at regional scales (city, valley,…)

IPSL

-0,4-0,8

00,4

0,8

1,2

CNRMBy J.L. Dufresne

1/13

Tamara Salameh

General context– Important needs in water and energy– Understanding the Mediterranean regional climate has

environmental, economical and societal implications– Coupled system (ocean-atmosphere-hydrology)– Strong topographic component that induces extreme events

Strong scales interaction

2/13

Tamara Salameh

Regional dynamical modeling of the atmospheric circulation over the Mediterranean basin

Brief state of the art

• Consists on forcing a regional model (limited area model, RCM) by a GCM, generally to ameliorate the realism of the modeled fields (Mass et al., 2002)

•Sensitivity studies on initial and boundary conditions of the GCM (forcing resolution, frequency of update of boundary conditions), physical parameterization of the RCM (Bhaskaran et al., 1996; Seth et Giorgi, 1998; Noguer et al., 1998; Denis et al., 2002, 2003) impact on the RCM results

• High-cost calculation method but transferrable from region to another

• For long regional runs, periodic reinitilization gives better results (scores) than the continuous regional run (Qian et al. 2003; Lo and Yang, 2008) affect the temporel variability alternative solution: nudging the RCM fields to the GCM fields (relatively less considered in the literature): 2 nudging types: temporal (Salameh et al., en révision) and spectral (Von Storch et al., 2000), both need adjustment of constants

3/13

Tamara Salameh

xsx

qU

t

q

xqtUxqq ss0

tUxqq 0ls

xsx

qU ss

0x

qU

t

q lsls

Example: equation to resolve for a linear approach 1D (e.g. q = PV)

The GCM problem

Small-scale source (e.g. convection, relief)

Stationary answer to the large-scale forcing

General solution

1

Simplified approach, one dimension, linear

4/13

Challenge: evaluation of the impact of nudging on the physical processes at all scales and evaluation of the existence of an optimal nudging time that minimizes the total error committed on the large and small scales

Problem: relaxing the fields of the RCM to those of the GCM by adding to the conservation equations a relaxation term to the large-scale forcing variables


Tamara Salameh

xsx

qU

t

q

xqtUxqq ss0

tUxqq 0ls

xsx

qU ss

0x

qU

t

q lsls

Example: equation to resolve for a linear approach 1D (e.g. q = PV)

The GCM problem

Small-scale source (e.g. convection, relief)

Stationary answer to the large-scale forcing

General solution

1

Simplified approach, one dimension, linear

4/13

Challenge: evaluation of the impact of nudging on the physical processes at all scales and evaluation of the existence of an optimal nudging time that minimizes the total error committed on the large and small scales

Problem: relaxing the fields of the RCM to those of the GCM by adding to the conservation equations a relaxation term to the large-scale forcing variables


tUiklsss

2numr

r eq̂1

q̂UikkK1

Uikq̂t

q̂

Approached equation resolved by the RCM

In the Fourier space

2r

2

numlsrssrr

x

qKqq

1

x

qU

x

qU

t

q

Numerical diffusion induced by the discretization of conservation equations

Relaxation time to the large-scale qls

3

2

Tamara Salameh


Objective: determination of an optimal nudging time that minimizes the total error committed on the large and small scales (if it exists)

Optimal nudging time minimizing the total error

Total error

)k(q̂e)k(q̂)k(q̂ sstUik

lsr

Exact solution

Small-scale error

ssnumls

ssopt q̂

q̂

ss

ss1

ss1ssss q̂≈1kUi1

1q̂≈

ss

Large-scale error

numls2

lsnum

lsls q̂1kK1

1q̂

num The real variability of the large-scale flow

2

num

ss2num

tUiklsr

kΚ1

Uik

Uikkq̂

kK1

1ekq̂kq̂

ττ

Exact solution: and Knum 0

The regional solution:

Contribution of the large-scale Contribution of the small-scale

5/13

Tamara Salameh


=1h

=3h

=5h

=12h

=2h

=4h

=6h

=

Mean wind (MM5: Nov-Dec. 1998*)

* Year rich in Mistral events and dense water formation

MM5 simulations all indentic except of the nudging time

Real RCM’s approach

Weak impact on mean wind field at 10 m but strong impact on the wind variability

6/13

Tamara Salameh


=1h

=3h

=5h

=12h

=2h

=4h

=6h

=

Stability of wind direction

UR

U

vuS

U

2/122100=1h

=3h

=5h

=12h

=2h

=4h

=6h

=

Variability of wind speed

This variability has very strong impact

on precipitation and extreme wind

7/13

Tamara Salameh


qr=potential vorticity (PV)2/12

0

2/12)(ˆ)(ˆˆ

dkkqdkkqq

c

ls

k

rk rlsr

2/12

2/12)(ˆ)(ˆˆ

css k rk rssr dkkqdkkqq

numlslsr qq

/1

1ˆˆ

2/1

1ˆˆ

ssssssr qq

||qls|| is the variance for = 0 ;

||qss|| is the variance for =

The cutoff frequency Kc = π/Δx (resolution of ERA-40)

9/13

=1h

=3h

=5h

=12h

=2h

=4h

=6h

=

Tamara Salameh


Domination of the diffusion:Linear model ~ OK Diffusion+contribution of non

linear processes:Linear model not OK

Evolution of the variance dominated by the development of fine-scale structures : linear model ~ OK

10/13

Tamara Salameh


Domination of the diffusion:Linear model ~ OK Diffusion+contribution of non

linear processes:Linear model not OK

Evolution of the variance dominated by the development of fine-scale structures : linear model ~ OK

10/13

num = 10h ss = 1h

Robust estimation

Tamara Salameh


Conclusions:

1. Strong impact of nudging on dynamical regionalization: variability of surface wind precipitation and wind extremes

2. Simplified linear one dimension model

1. Existence of an optimal nudging time

2. Existence of two characteristic time scales : et

3. Impact of nudging on the small-scale in MM5 ~ linear model

numτ ssτ

13/13

Tamara Salameh

Application to regional climate simulations conducted with WRF

11/13

WRF forced by IPSL CM4 (LMDZ outputs) used for IPCC AR4

Wintertime periods (November to March) 1861-1871 and 1990-2000

60 km spatial resolution

Tamara Salameh

Application to regional climate simulations conducted with WRF

12/13

• The impact of nudging is not uniform over the domain• Nudging produces better results• The difference in averaged temperature between 1990-2000 and

1861-1871 is positive over all the domain

• Increase in the precipitation rate over mountains and decreases everywhere else

• WRF tends to over-estimate precipitation over the domain• Nudging produces more precipitation over the eastern basin and

less over mountains

Nud

gin

g t

ime =

6 h

Sim-obs CRU 0.5° (1990_2000)

Nudged simulation – no nudging simulation

1990_2000 -1861_1871

No n

ud

gin

g

1990-2000

Tamara Salameh

The end!!!!

Thank you for your attention!!

Tamara Salameh


=1h

=3h

=5h

=12h

=2h

=4h

=6h

=

Précipitations Extreme wind (>15 m s-1)

=1h

=3h

=5h

=12h

=2h

=4h

=6h

=

Coherent result with Lo et al. 2008 on the necessity of nudging to ameliorate precipitation

8/13

the effect of indiscriminate nudging time in regional climate modeling of the mediterranean basin...

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