Experimental Ensembles with Experimental Ensembles with the LM/LMKthe LM/LMK

Past and Future WorkPast and Future Work

Susanne Theis

Past Work:Past Work:

Stochastic ParametrizationStochastic Parametrization

in the LMin the LM

Susanne Theis (PhD Thesis)

Supervisor: Prof. Andreas Hense, University of Bonn

Motivation ofMotivation of

Stochastic ParametrizationStochastic Parametrization

Problem in Ensemble ForecastingProblem in Ensemble Forecasting

uncertainty ininitial conditions

uncertainty inparametrised processes

uncertainty inNWP model output

uncertainty inlateral boundary

conditions

Ensemble represents some sources of uncertainty, but not all

Missing: uncertainty in parametrised processes(= stochastic effect of subgrid scale processes)

Conventional ParametrizationsConventional Parametrizations

resolved process

sub

grid

sca

le e

ffect

experimentaldata

mean effect

Estimating the subgrid scale effect:

…only simulate the mean effect of subgrid scale processes!

Conventional ParametrizationsConventional Parametrizations

resolved process

sub

grid

sca

le e

ffect

pro

ba

bili

ty d

en

sity

fu

nct

ion

subgrid scale effect

experimentaldata

mean effect

mean

Estimating the subgrid scale effect:

…only simulate the mean effect of subgrid scale processes!

Subgrid scale effect for a fixed value of the resolved process:

Conventional ParametrizationsConventional Parametrizations

resolved process

sub

grid

sca

le e

ffect

pro

ba

bili

ty d

en

sity

fu

nct

ion

subgrid scale effect

variability neglected!

experimentaldata

mean effect

mean

Estimating the subgrid scale effect:

…only simulate the mean effect of subgrid scale processes!

Subgrid scale effect for a fixed value of the resolved process:

Aim of Stochastic ParametrizationAim of Stochastic Parametrization

Problem: Neglect of subgrid scale variability potentially leads to insufficient ensemble spread

Aim: return some of this missing variability to the model

simulate the stochastic effect of subgrid scale processes on the resolved scales

Methodology ofMethodology of

Stochastic ParametrizationStochastic Parametrization

Subscale Processes in the ModelSubscale Processes in the Model

);;(P);(A tetet

e

„Physics“(parametrised processes)

„Dynamics“

dtt

ete

t

t

1

0 0

1)(

Model Simulation:

Separation of the prognostic model equations:

Stochastic ParametrizationStochastic Parametrization

);;(P);(A tetet

e

„Physics“(parametrised processes)

„Dynamics“

Injection of „noise“ into the deterministic bulk formulae:

noise

Stochastic ParametrizationStochastic Parametrization

);;(P);(A tetet

e

„Physics“(parametrised processes)

„Dynamics“

Injection of „noise“ into the deterministic bulk formulae:

noise

Stochastic ParametrizationStochastic Parametrization

);;(P);(A tetet

e

„Physics“(parametrised processes)

„Dynamics“

Injection of „noise“ into the deterministic bulk formulae:

noise

Stochastic ParametrizationStochastic Parametrization

);;(P);(A tetet

e

„Physics“(parametrised processes)

„Dynamics“

Injection of „noise“ into the deterministic bulk formulae:

noise

Stochastic Parametrization in LMStochastic Parametrization in LM

(1) Perturbation of the Net Effect of Diabatic Forcing

);;P();;(P' , texte tr

Stochastic Parametrization in LMStochastic Parametrization in LM

turbulence

radiation

microphysics

convection

(1) Perturbation of the Net Effect of Diabatic Forcing

);;P();;(P' , texte tr

Stochastic Parametrization in LMStochastic Parametrization in LM

turbulence

radiation

microphysics

convection

randomnumber

(1) Perturbation of the Net Effect of Diabatic Forcing

perturbation• in each time step• at each grid point

);;P();;(P' , texte tr

Perturbation PropertiesPerturbation Properties

10 x

example:

ampl

itude

temporal correlation

spatialcorrelation

uniform distribution

choice motivated by ECMWF ensemble setupfurther experiments: temporal correlation more smooth

(2) Perturbation of the Roughness Length over Land

Stochastic Parametrization in LMStochastic Parametrization in LM

• each member is assigned a specific (perturbed) field• the fields are constant with time

The roughness length is one of many parameters that need to be set experimentally. They are optimized with regard to their best performance and will not represent related uncertainty in a conventional setting.

);;(P te

Experiments withExperiments with

Stochastic ParametrizationStochastic Parametrization

Setup of Ensemble ExperimentsSetup of Ensemble Experiments

Long term goal:improvement of ensemble forecasts

First step:look at effect of stochastic parametrization in isolation

Focus:short-range precipitation forecasts

Setup of Ensemble ExperimentsSetup of Ensemble Experiments

• 16 ensemble forecasts are produced:

- Juli 09, 2002 00 UTC

- Juli 10, 2002 00 UTC

...

- Juli 24, 2002 00 UTC

• 10 ensemble members per forecast

= 9 perturbed members + 1 unperturbed

• each forecast has a lead time of 48 hours

Setup of Ensemble ExperimentsSetup of Ensemble Experiments

);;P( te );;P( te

perturbation ofinitial conditions

perturbation ofparametrised processes

perturbation oflateral boundary

conditions

net diabatic forcing

roughness length

perturbedensemble member

Example of Ensemble ExperimentExample of Ensemble Experiment

• 1h-precipitation

• 10 July, 2002 17 – 18 UTC

• lead time: 18 hours

[mm]

original LM simulation (unperturbed)

case study Berlin

Ensemble

Example of Ensemble ExperimentExample of Ensemble Experiment

[mm]

ensemble spreadoriginal LM simulation

(unperturbed)

Results of Ensemble ExperimentsResults of Ensemble Experiments

The stochastic parametrization scheme…

• has a considerable effect on precipitation amount

• shows hardly any effect on precipitation occurence

Further InvestigationsFurther Investigations

• Sensitivity studies on the configuration of random numbers

large sensitivity to amplitude and correlation

• Relevance in comparison to initial condition perturbations

low relevance of stochastic parametrisation

• Verification of the experimental ensemble forecasts (comparison to station data, 2 weeks)

only marginal improvement of forecast quality and value, when compared to the unperturbed forecast

Lessons LearnedLessons Learned

Lessons LearnedLessons Learned

Need to clarify the following questions:

• how to decide whether the stochastic representation is realistic

• how to optimize the choice of input perturbations (amplitude etc) without obtaining unphysical parameter values

• how to obtain a larger spread from stochastic parametrization

• technical issue: random number generator on parallel machine?

Implementation of a stochastic parametrization scheme is feasible

Future Work:Future Work:

Experimental EnsemblesExperimental Ensembles

with the LMK (EELMK)with the LMK (EELMK)

Volker Renner, Peter Krahe, Susanne Theis

Aim of EELMKAim of EELMK

• produce experimental ensembles with the model LMK

LMK: very short-range forecasting with explicit convection (see presentation of M.Baldauf)

• explore its benefit…

…for high-resolution weather prediction …for hydrological applications (application of hydrological models for ensemble verification)

The project is considered to be part of the development of a planned operational ensemble prediction system based on the LMK.

Methodology EnvisagedMethodology Envisaged

);;P( te

perturbation ofinitial conditions

perturbation ofparametrised processes

perturbation oflateral boundary

conditions

all sorts of tunable parameters

perturbedensemble member

• INM-Ensemble?

• COSMO-SREPS?

• LAF-Ensemble?

some simple approach?

Thank youThank you

for your Attention!for your Attention!

Backup SlidesBackup Slides

Problems in Ensemble ForecastingProblems in Ensemble Forecasting

Ensemble prediction sometimes fails in capturing

• the pdf of the atmospheric state• the risk of extreme events• variations in forecast uncertainty observation

Simulation of the Stochastic EffectSimulation of the Stochastic Effect

Approximation by noise:

time

≈

subgrid scale processesin model grid box noise

Vorhersagezeit [Stunden]

Sta

ndar

dabw

. /

Mitt

elFehlerwachstum mit der ZeitFehlerwachstum mit der Zeit

• nur Fälle mit Mittel > 0.01 mm

• Flächenmittel über das Gebiet

• gemittelt über 10. – 24.Juli 2002

SkalenbetrachtungSkalenbetrachtung

Originalvorhersage (gestört – original)

[mm] [mm]

SkalenbetrachtungSkalenbetrachtung

Originalvorhersage (gestört – original)

[mm] [mm]

die Differenzen scheinen räumlich autokorreliert

Au

toko

rre

latio

n

räumlicher Abstand [km] zeitl. Abstand [h]

• 1h-Niederschlag

• nur Fälle mit Mittel > 0.01 mm

• Vorhersagezeit: 25 – 48 Stunden

• komplettes Gebiet

• 10. – 24.Juli 2002

• 9 gestörte Simulat.

SkalenbetrachtungSkalenbetrachtung

Autokorrelation der Differenzen zwischen gestörter und ungestörter Simulation

Relevanz des Stochast. EffektesRelevanz des Stochast. Effektes

• 1h-Niederschlag

• Juli 10, 2002 17 – 18 UTC

• Vorhersagezeit: 18 Stunden

Originalvorhersage

[mm]

...im Vergleich zu Störungen der Anfangsbedingung

Relevanz des Stochast. EffektesRelevanz des Stochast. Effektes

Analysevon 01 UTC

Analysevon 00 UTC

3 Simulationen 3 Simulationen 3 Simulationen

Analysevon 23 UTC(vorher. Tag)

Zusätzlich zur stochastischen Parametrisierung:Simple Störung der Anfangsbedingung

Relevanz des Stochast. EffektesRelevanz des Stochast. Effektes

[mm][mm]

Originalvorhersage Ensemble Standardabweichung

Versatz der Maxima

(1) Rauigkeitslänge

Zufällig gestörte Felder der Rauigkeitslänge:

Vorgehensweise im LMVorgehensweise im LM

Jedes Ensemblemitglied erhält ein eigenes, zeitlich konstantes Feld

(1) Rauigkeitslänge

Zufällig gestörte Felder der Rauigkeitslänge:

Vorgehensweise im LMVorgehensweise im LM

(2) Netto-Effekt der Parametrisierungen

Zufällige Störung des diabatischen Gesamt-Antriebs injedem Integrations-Zeitschritt

Jedes Ensemblemitglied erhält ein eigenes, zeitlich konstantes Feld

Störung der RauigkeitslängeStörung der Rauigkeitslänge

[m]

LM Rauigkeitslänge

Annahme über die zufällige Variabilität der Rauigkeitslänge?

Störung der RauigkeitslängeStörung der Rauigkeitslänge

[m]

Unsere Störungen lassen großskalige Strukturen unangetastet...

LM Rauigkeitslängegestörte

Rauigkeitslänge

Störung der RauigkeitslängeStörung der Rauigkeitslänge

[m]

LM Rauigkeitslänge[Stand.Abw. zwischen Ensemble-Läufen] x 10

... und die Störungs-Amplitude hängt von der lokalen räumlichen Variabilität ab

Verteilung der ZufallszahlenVerteilung der Zufallszahlen

Vorhersagezeit t [Zeitschritt]

• Gleichverteilung

• zeitliche Autokorrelation:

nimmt mit exponentiell

ab: r (= 5min) = 1/e

• keine räumliche Autokorrelation über eine Modellgitterbox hinaus

Beispiel:

Sensitivität des Stochast. EffektesSensitivität des Stochast. Effektes

...auf Eigenschaften des Rauschens

5 x10 x

Konfiguration „schwach“ Konfiguration „stark“

Sensitivität des Stochast. EffektesSensitivität des Stochast. Effektes

[mm] [mm]

Konfiguration „schwach“ Konfiguration „stark“

Ensemble Standardabw.Ensemble Standardabw.

Fallstudie Fallstudie BerlinBerlin

• 1h-Niederschlag

• Juli 10, 2002 18 – 19 UTC

• Vorhersagezeit: 43 Stunden

[mm]

Originalvorhersage

Ensemble StandardabweichungEnsemble Standardabweichung

Ensemblemittel Ensemble Standardabw.

[mm]

• Standardabweichung nur hoch in Gegenden mit RR > 0• kein Versatz von Niederschlagsgebieten

Methodology EnvisagedMethodology Envisaged

• physics perturbation: a set of tunable parameters will be perturbed (e.g. plant cover, leaf area index, maximal turbulent length scale, roughness length, etc) physical reasoning possible

• lateral boundary conditions:

an available coarse-resolution ensemble will be applied, e.g. the INM-Ensemble, COSMO-SREPS, or a LAF-Ensemble

• initial conditions:

perhaps only a simple approach (low priority in this project)

);;P( te