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Quantifying error growth during convective initiation in a mesoscale model. Peter Lean 1 Suzanne Gray 1 Peter Clark 2. 2. J.C.M.M. 1. Aims:. Understand error growth mechanisms dominant in first 3hrs of a forecast - PowerPoint PPT Presentation
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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.
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
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
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)
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
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
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
Saturation variance:
),cov(2)var()var()var( xxxxxx
)var(2)var(lim
xx
stt
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
))(
(
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?