Stochastic parameterization in NWP and climate models · Stochastic parameterization in NWP and climate models Judith Berner, ECMWF ... Coupled system of grid-scale and subgrid-scale

ECMWFIMAGe III: Stochastic and Statistical Parameterizations in the A/O Sciences, NCAR, Feb27-Mar03

Stochastic parameterization in Stochastic parameterization in NWP and climate modelsNWP and climate models

Judith Judith BernerBerner, ECMWF, ECMWF

Acknowledgements:Acknowledgements:

Tim Palmer, Mitch Tim Palmer, Mitch MoncrieffMoncrieff, Glenn , Glenn ShuttsShutts


Parameterization of unrepresented Parameterization of unrepresented processesprocesses

Motivation: unresolved and unrepresented processes lead to model errorUnresolved sub-gridscale processes - Example: Stochastic backscatter of dissipated energy on resolved flow (CABS)

Unrepresented super-gridscale processes - Example: Stochastic cloud clusters (SSC) as part of organized tropical convection (scales of several thousand kilometers)


Stochastic parameterization: Closing the Gap?!Stochastic parameterization: Closing the Gap?!

Sophistication of methods for stochastic parameterization

Dimensionality*

Complexitylow high

**

* **

* ***

Mathematically vigorous

“Ad hoc” ; capturing essential physically nature


Parameterization of subgridParameterization of subgrid--scale scale processesprocesses

Coupled system of grid-scale and subgrid-scale processes (Lorenz, 1996)

Equation for grid-scale process with parameterized subgrid-scale processes :

Classical bulk-parameterization: local and deterministic: each large scale state is in equilibrium with ensemble of subgrid-states

Stochastic-dynamic parameterization:nonlocal and random: particular realization of subgrid-scale state


Shortcomings of classical bulkShortcomings of classical bulk--parameterizationparameterization

There are several realizations of the subgrid-state for a given large-scale state

)|( , kij xyP

y

********

****

**

**

****

****

**

XX

ijy ,


Conventional Conventional vsvs stochasticstochastic--dynamic dynamic parameterizationparameterization

Stochastic-parameterization:

Non-local: coherent structure spanning several gridboxesStochastic or quasi-randomState-dependent, i.e., flow-dependent

Here: Cellular Automaton

Conventional parameterization in NWP:Local: determined by state in one gridboxDeterministicState-dependent, i.e., flow-dependent


Model Error of NWP modelsModel Error of NWP models

NWP: Model is under-dispersive on medium-range

2t

0t

1t

∞→t

Systematic error

Insufficient representation of subgrid-scale processes?

Missing physical processes on super-grid scale (e.g., cloud super-clusters for OC)


Additional degrees of freedomIncrease spread without degradation of the forecast error Improve skill

Noise-induced drift and transition Reduce systematic error

Potential benefits of stochasticPotential benefits of stochastic--dynamic parameterizationsdynamic parameterizations


Stochastic Parameterization for Stochastic Parameterization for Organized ConvectionOrganized Convection

Rationale: Develop a stochastic representation of cloud-clusters currently not captured by conventional parameterizations, but play an important role in organized convection in the tropics

Super-gridscale!

Is stochastic approach valid or should this be the goal for deterministic physical parameterization?


Develop of a multi-scale cellular automaton (MSCA) for organized convection that captures the subgrid-scale forcing not represented by conventional parameterizations.

Potential to reduce systematic error by better representation of MJO (connect to ENSO)

Potential of improved skill of medium- to extended-range weather forecasts by better representation of tropical variability (Ferranti et al.,1990)

SSC SSC –– Stochastic Stochastic superclusterssuperclusters


MultiMulti--scale character of organized scale character of organized convectionconvection

Nakazawa, 1988Superclusters~20000km

Organized convection ~1000km

tttt


MultiMulti--scale Cellular Automaton (MSCA)scale Cellular Automaton (MSCA)for convective organization (Palmer)for convective organization (Palmer)

Small-scale CA models convective cells advectingwestwardsLarge-scale CA models envelope of convective cells (cloud-clusters) propagating eastward


SmallSmall--scale CA for convectionscale CA for convection

ShuttsShutts and Palmer, 2003and Palmer, 2003


Rules for smallRules for small--scale CAscale CAVariant of the ‘Game of Life’Find the number of fertile cells in immediate neighbourhood: SIf cell dead and S=2 or 3 => create fertile cellIf cell alive and S=3, 4 or 5 => cell survives with same number of livesIf cell alive and S 3, 4 or 5=> cell loses one lifeOne Parameter: Number of lives N

Fertile cell (N lives)

Living cell (n lives)

System has memory System has memory (=> temporal correlation)(=> temporal correlation)

Evolution depends on immediate neighbours Evolution depends on immediate neighbours (=> Coherent structures span several (=> Coherent structures span several gridpointsgridpoints))

≠

Dead cells


MultiMulti--scalescale--Cellular AutomatonCellular AutomatonSmall-scale cells evolve according to rules and propagate to the westLarge-scale cells can be on/off (depending on CAPE) and propagate to the eastFertile cells in small-scale CA can only be born if large-scale cell is ‘on’

Intermediate Scale: 40° 4444 km

Small Scale: 1° 111 km

≈

⎭⎬⎫⎭⎬⎫

GCM Scale: 5° 560 km≈≈


MultiMulti--scalescale--CA for Convective OrganizationCA for Convective Organization


HovmöllerHovmöller diagramdiagram


Towards a MSCATowards a MSCA--representation of representation of organized convection in the ECMWF modelorganized convection in the ECMWF model

0 90 180 -90 0

-12-4412

0 90 180 270 360Longitude (degrees)

17 Jun 03

17 May 03

17 Apr 03

17 Mar 03

14 Feb 03

15 Jan 03

15 Dec 02

Tim

e (d

ays)

Control (Model)Control (Model)Analysis (“Observations”)Analysis (“Observations”)

Velocity potential (200hPa)Velocity potential (200hPa)

tt


VitartVitart and Anderson, 2004and Anderson, 2004

VitartVitart et al. 2003:et al. 2003:

MJO variance decreases MJO variance decreases during the first 10d by as during the first 10d by as much as 50%much as 50%

MJO in coupled ECMWF modelMJO in coupled ECMWF model

ERA40ERA40--ReanalysisReanalysis

Model: IFS CY28R3Model: IFS CY28R3


Stochastic Stochastic superclusterssuperclusters

smooth

scale

Parameterization of organized convection is introduced as streamfunction pertubation:

Streamfunction forcing Convective

available potential energy

Quasi-random noise from CA (smoothed, coarse-grained)

),,(*)),(( tCAPEztft

φλψ φ,λ,Ψ∝∂∂

Horizontal and vertical structure function


smooth

scale

Non-local, quasi-random, state-dependent

),,(*)),,(( tCAPEztf φλψ φλ,Ψ=Δ

Stochastic super clusters as part of organized Stochastic super clusters as part of organized convection (superconvection (super--gridscalegridscale))

30°S30°S

0° 0°

30°N30°N

160°W

160°W 130°W

130°W 100°W

100°W 70°W

70°W 40°W

40°W 10°W

10°W 20°E

20°E 50°E

50°E 80°E

80°E 110°E

110°E 140°E

140°E 170°E

170°E

Sunday 15 December 2002 12UTC ECMWF Forecast t+24 VT: Monday 16 December 2002 12UTC Model Level 30

-39.08 0 60 120 180 240 300 360 420 480 540 545.2

Cartoon


Archetype for organized convectionArchetype for organized convection

Moncrieff,2004Moncrieff,2004

Horizontal and vertical tilt!Horizontal and vertical tilt!


Streamfunction forcingStreamfunction forcing

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


-122.6

-75

-25

25

75

119.1

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E

Sunday 15 December 2002 12UTC ECMWF Forecast t+11 days VT: Thursday 26 December 2002 12UTC Model Level 45

-128.1

-100

-50

0

50

100

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E

Sunday 15 December 2002 12UTC ECMWF Forecast t+21 days VT: Sunday 5 January 2003 12UTC Model Level 45

-120.8

-75

-25

25

75

109.4

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E

Sunday 15 December 2002 12UTC ECMWF Forecast t+31 days VT: Wednesday 15 January 2003 12UTC Model Level 45

-127

-100

-50

0

50

100

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


-124.3

-75

-25

25

75

105.1

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


-133

-90

-30

30

90

143.1

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


-120.0

-75

-25

25

75

120.0

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


-12 6 .3

-1 00

-5 0

0

5 0

1 00

250hPa250hPa

750hPa750hPa

30d30d


Smoothed divergenceSmoothed divergence

SSCSSC

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


133.9

200

280

360

440

520

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


77.03

160

320

480

640

764.8

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


92.47

240

400

560

720

834.8

0° 0°

160°W 130°W 100°W 70°W 40°W 10°W 20°E 50°E 80°E 110°E 140°E 170°E


85.24

180

300

420

540

660

0 90 180 -90 0

-12-4412

qy


-12.0-10.0-8.0-6.0-4.0-2.00.02.04.06.08.010.012.0

0 90 180 -90 0

-12-4412


3

3

3

3

3

3

2

AnalysisAnalysis SSCSSCControlControl


DayDay--5 forecasts5 forecasts


CABSCABSNo CABSNo CABS

Courtesy Courtesy AntjeAntje WeisheimerWeisheimer, , PacoPaco DoblasDoblas--ReyesReyes

DemeterDemeter

ErrorError

SpreadSpread


CABS improves SST anomalies in CABS improves SST anomalies in tropical Pacifictropical Pacific

Courtesy Courtesy AntjeAntje WeisheimerWeisheimer, , PacoPaco DoblasDoblas--ReyesReyes

CABSCABSNo No stochstoch physphys


Open questionsOpen questions

smooth

scaleCan organized convection be fully represented by local parameterizations?

Should super-clusters be resolved explicitely rather than represented stochastically?

System self-organizing on the subgrid-scale or is organization coming through the large-scales?

Documents

Stochastic parameterization in NWP and climate models · Stochastic parameterization in NWP and climate models Judith Berner, ECMWF ... Coupled system of grid-scale and subgrid-scale