Using Observations and Theory to Evaluate Model Convergence at Fronts Ben Harvey Thanks to: John Methven (Reading) Chloe Eagle, Humphrey Lean (Met Office) 10/12/15: NCAS Atmospheric Physics Meeting, Reading

T-NAWDEX pilot flight 3 FAAM BAe146 24th November 2009 Trailing cold front approaching UK Aircraft performed low-level (300m) circuit around front adapted from Knippertz et al., Weather (2010) 12Z18Z

T-NAWDEX pilot flight 3 Time [hrs] Front width ≈ 600mDouble front structure on return leg Timing of circuit: Altitude: 300 m, speed: 100 m/s Circuit closed in a front-relative sense Novelty: enables an accurate calculation of vorticity and divergence simulated 300m v at 15Z B C D E F direction speed

Model Simulations L38L70 L140 Conv scheme ONConv scheme OFF 1-d BL scheme1-d BL with 2-d Smagorinsky3-d Smagorinsky 12 km2.2 km1.5 km500 m200 m Precip

Model Simulations Vorticity (300m) Precip 12 km2.2 km1.5 km500 m200 m

Model Simulations Vorticity (300m) 12 km2.2 km1.5 km500 m200 m Horizontal shear instability:

Vortex width Simple measure of frontal width: distance between thresholds of along-front wind Observations1.5 km model

Vortex width High resolution runs capture the observed filament width Only 1.5km run is close to capturing vortex width Vortices become too small at high resolution Interpretation Small value = width of vorticity filament Large value = width of vortex

Vortex spacing Narrow cold-frontal rainband is clear in radar image Vortices are located in the precipitation gaps 19Z

The vortex width and vortex spacing both collapse to too small scales in the sub-kilometre models Why? Possible hypotheses: 1.The frontal collapse is too strong (insufficient mixing?) 2.A damping of the horizontal shear instability due to a change in boundary-layer structure

Kawashima (2011) Ambient vertical shear can inhibit/enhance the horizontal shear instability If there is CAPE present then the instability can transition to a convective type Could this be happening in the sub-kilometre simulations?

Turbulent fluxes Behind front Ahead of front There is a gradual transition from parameterised to resolved fluxes behind the front Ahead of the front: – very little resolved component at any resolution – 3-d Smagorinsky scheme performs poorly

Do the simulations converge with resolution? Net shear and convergence across front – Circuit integrals are converged by 2.2 km – However, the vorticity values are inconsistent with the observations The width of the front – The <=500 m models reproduce the observed frontal width The structure of the NCFR instability – These do not converge with resolution – 1.5km is most like observations, higher resolutions have instability at too small spatial scales – What sets the spatial scale of the instability?

Area-average vorticity and divergence: Use a sample of circuits to account for the low predictability of the phase of the instability Circuit Integrals s n

Sample spread (along-front inhomogeneity) is large The vorticity sample means have converged by 2.2 km, but the sample spread has not Observed divergence is within the sample spread, but observed vorticity is not vorticity divergence Do the observations tell us anything about the true size of the spread?

Aside: Overshoots and Interpolation Semi-Lagrangian scheme requires interpolation This causes implicit numerical (hyper-)diffusion The order of the interpolation scheme determines the order of the diffusion – Linear interpolation – Cubic interpolation linear cubic Simple illustration: front in strain s

Observed turbulent fluxes Calculated from 32 Hz data as in Cook and Renfrew (2015)

Behind the front (C to D) Latent heat and wind stress: Gradual transition from fully parameterised in 12 km model to mostly resolved at 100 m; total remains roughly constant Sensible heat: Strange behaviour, with opposing resolved and parameterised components at intermediate resolution

Ahead of the front (A to B; 40 m) Resolved component very small at all resolutions Parameterised fluxes are too large at coarse resolution, improve at fine resolution

Ahead of the front 2 (E to F; 300 m) Similar resolution dependence as at 40 m, except the 100 m model has gone too far (fluxes are too small) Smagorinsky subgrid mixing scheme assumes a partially- resolved inertial cascade, but this is not the case here

Have the turbulent fluxes converged? Behind front – Gradual transition from fully parameterised in 12 km model to about 80% resolved in 100 m model Ahead of front – Very small resolved component at all resolutions – Parameterised component reduces systematically with resolution towards observation