Quantifying error growth during convective initiation in a mesoscale model

1. Quantifying error growth during convective initiation in a mesoscale model Peter Lean1 Suzanne Gray1 Peter Clark2 2 J.C.M.M. 1

2. 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

3. w [ms-1] and bulk cloud 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.

4. x +(t) + Unperturbed run, xc(t0) - x –(t) Perturbation strategy: • Potential temperature, q, perturbed at one height by a smooth random field (random numbers convolved with a Gaussian kernel). dx(t)=x +(t) – x -(t)

5. error growth due to differences in deep convective cells error growth due to boundary layer regime differences error saturation diffusion of perturbations in stable environment initiation of deep convection Mean square difference in q: Results from 0.002K q perturbations added at 08:30 in boundary layer (500m)

6. 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

7. 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.

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

9. Saturation variance:

10. 1.0K 0.25K 0.025K 0.0025K ( ) Perturbation spectral density Full field spectral density ( ) 128km 85km -for different spatial scales and initial perturbation amplitudes 42km 32km 16km 8km

11. Conclusions: • Two error growth mechanisms dominant in first 3hrs of forecast: • 1) due to boundary layer regime differences • 2) due to differences in explicitly represented convective plumes • 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.

12. Thanks for listening! Any questions?