Quantifying error growth during convective initiation in a mesoscale model

Quantifying error growth during Quantifying error growth during convective initiation in a convective initiation in a

mesoscale modelmesoscale model

Peter Lean1

Suzanne Gray1

Peter Clark2 1

2

J.C.M.M.J.C.M.M.

administrator

I'm going to say something along the lines of....Motivation:*Predictability*Here you see UK...a cold front...convective showers triggering in cold air over warm ocean.*Forecast models with low resolution represent these with parameterisation scheme: say -showers in this box*Increasingly models can resolve features on this scale explicitly*But just because a model produces a realistic looking field of showers doesn't mean that it is accurate*What I'm interested in is how rapidly forecasts of features at these scales lose skill and what causes the errors to grow.

Aims:

• Understand error growth mechanisms dominant in first 3hrs of a forecast

• Quantify error growth rates associated with initiation of deep convection.

• Quantify error saturation timescale (time over which forecasts lose skill relative to climatology of situation) as a function of spatial scale and initial error amplitude

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administrator25/08/2005Previous studies:-have quantified error growth at synoptic and planetary scales over 0-10 days.-little work has been done quantifying error growth over 0-3 hour.This study quantifies error growth associated with initiation of deep moist convection in a mesoscale model.Situation climatology: ie. here am looking at scattered convection. Climate of system given this environment. These situations have a climatology which is different to the climatology of a different situation (eg stable)

Idealised case study:

• Met Office UM v5.3 – non-hydrostatic– 4km horizontal resolution– no deep convective parameterisation used– fluxes of heat and moisture by boundary layer eddies

are parameterised

• Idealised oceanic cold air outbreak– homogenous destabilization imposed by tropospheric

cooling of 8K/day and fixed SST of 300K.

w [ms-1] and bulk cloud

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*Initial profile : moist neutral*destabilised -> outbreak of widespread convection

Perturbation strategy:

• Potential temperature, , perturbed at one height by a smooth random field (random numbers convolved with a Gaussian kernel).

Unperturbed run, xc(t0)

+

-

x +(t)

x –(t)

x(t)=x +(t) – x -(t)

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*Theta perturbed since dth/dz determines static stability of atmosphere*I have found that errors grow more rapidly in the boundary layer, therefore insert there*I'm interested in how the two forecasts diverge due to initial condition differences... therefore look at difference between two runs.

Mean square difference in :

error growth due to error growth due to boundary layer regime boundary layer regime differencesdifferences

error growth due to differences in error growth due to differences in deep convective cellsdeep convective cells

diffusion of diffusion of perturbations in stable perturbations in stable environmentenvironment initiation of deep initiation of deep

convectionconvection

error saturationerror saturation

Results from 0.002K perturbations added at 08:30 in boundary layer (500m)

N

iiiN

MSD1

21

administrator

Point out logarithmic scaleHighlight 2 growth mechanisms:*Error growth due to boundary layer regime differences*Error growth due to differences in explicitly represented convective plumes(BE CAREFUL NOT TO DESCRIBE THE MECHANISMS IN DETAIL... THAT COMES ON NEXT SLIDES.)-say "first error growth mechanism is associated with boundary layer regime changes -I'll ellaborate further shortly, the second is associated with...."

1) Error growth due to boundary layer regime change

• UM boundary layer parameterisation scheme diagnoses a boundary layer “type”– uses profiles of and q– determines fluxes of heat and moisture in mixed layers

• In some locations, boundary layer type is sensitive to small perturbations– leads to perturbation growth if diagnosed differently

between runs

administrator

Give examples of BL type:stablewel--mixedcumulus cappeddecoupled stratacumulus

2) Error growth in explicitly represented deep convection

• Timing/intensity differences between storms in different model runs lead to errors which grow with the storms.

• As errors become larger storms form in totally different locations between forecasts.

Initial error growth rate during initiation of convective plumes compared with that expected from linear theory:

2

22

1

N

dx

dz

administrator

*Found growth rate as function of scale by looking at the time evolution of the perturbation spectrum -gives spatial scale content of differences.GIVE DETAILS OF WHAT ASSUMPTIONS YOU HAVE MADE.ie. dz=1kmN^2 = 10^-2 s^-2

Saturation variance:

),cov(2)var()var()var( xxxxxx

)var(2)var(lim

xx

stt

administrator

As errors saturate, covarience between forecasts tends to zero.Therefore, saturation variance prortional to vairance in a single run (if var of two runs is same)Saturation error variance increases dramatically during convective initiation.(IF TIME IS GETTING SHORT THEN YOU CAN SKIP THROUGH THIS SLIDE...)

Perturbation spectral density Full field spectral

density

1.0K

0.25K

0.025K

0.0025K

-for different spatial scales and initial perturbation amplitudes

128km 85km

42km 32km

16km 8km

))(

(

administrator

Main Points:* Larger amplitude initial perturbations saturate sooner than small amplitude.* Forecasts of features at smaller spatial scales lose skill more rapidly than forecasts at large spatial scales*Numbers: =>1.0K uncertainty at ONLY ONE HEIGHT leads to skilless forecasts at all scales less than 128km in less than 1 hr=>0.0025K uncertainty will lead to skilless forecasts for features 8km (small convective storms) across within 3 hrs.ie. actual observations have large uncertainty -> rapid loss of skill in forecasts

Conclusions:

• Error growth in boundary layer rapidly saturates highly non-linear

• Error growth in convective plumes is faster at small spatial scales (as expected from linear theory)

• Error saturation variance changes significantly with time on a limited area domain during convective initiation

• Initial condition errors of only 1.0K in the boundary layer can lead to error saturation at all scales below 128km in less than 1 hour.

But, these results only apply in cases of homogenous forcing.Features such as orography, land/sea contrasts etc. may allow skilful forecasts over longer timescales.

• Two error growth mechanisms dominant in first 3hrs of forecast:1) due to boundary layer regime differences2) due to differences in explicitly represented convective plumes

Thanks for listening!

Any questions?

administrator

Anticipated questions:*Isn't 4km resolution too low to not be using a parameterisation scheme?-yes, any grid size above about 50-100m will not resolve all (statistically unpredictable) energy containing eddies therefore, some form of conv. parameterisation required... but not clear what best way to do that is. Therefore am looking at this more simple case and interpreting results in context of the model.*What is the doubling time of errors at the convective scale?-order of 10 mins : 1.001^t=2 ln(1.001^t)=ln 2t ln 1.001 =ln 2t=(ln 2)/(ln 1.001)t=693.5s(5 -> 20 mins)*How have you found growth rate as a function of scale?-looked at perturbation spectrum and how it evolves with time*If resolution is 4km surely you should ignore all scales up to about 4dx as not properly resolved...-yes, maybe should ignore the 8km data and anything up to 16km... it seems to fit in with rest of results but still maybe shouldn't read too much into it.

Quantifying error growth during convective initiation in a mesoscale model

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