Ben Green Group meeting, 9/13/2013 Tropical Cyclones and Large Eddy Simulations: From Idealized to Real-Data Cases Ben Green Group meeting, 9/13/2013

Background More computing power = higher resolution NWP Current mesoscale NWP has Δx ~O(1 km) Caution! Going to higher resolution is not as simple as changing a number in a namelist file Δx > 1 km: all turbulence is fully parameterized Δx < 100 m: largest turbulent eddies are explicitly resolved 100 m < Δx < 1 km: “no man’s land” for turbulent eddies Bottom line: Large Eddy Simulation (LES) is the next step in real-time mesoscale NWP

What is LES? Largest eddies contain/produce the most energy Smallest eddies dissipate nearly all of the energy Energy is transferred from largest eddies to smallest eddies (inertial subrange) LES decomposes equations into 2 parts: Resolved scales (large eddies): use Navier-Stokes equations Subgrid (unresolved) scales (smallest eddies): use closure model Caution! LES grid spacing (filter width) needs to be in inertial subrange!

What is LES? kcutoff = π/Δ log(E) Inertial subrange Dissipation range Large eddies (energy- containing) kcutoff = π/Δ log(E) Inertial subrange Dissipation range Energy cascade log(k=2π/x) kcutoff Explicitly resolved turbulence on LES grid Closure model (subgrid scale)

Tropical Cyclones (TCs) and LES Planetary boundary layer (PBL) is a crucial but unknown part of TCs – active area of research Limited observations: dangerous! Not many simulations: high wind speed = high computational cost Two ways to use LES in TC research Idealized studies: How does turbulence behave at very high winds? Real data cases: Can LES improve TC intensity forecasts? Each way has advantages + disadvantages

Real-data TC LES Cray is willing to give free computing to Fuqing to simulate Katrina (or other infamous TC) at LES-scale Amazing opportunity (especially if intensity forecasts improve) Very risky endeavor… Why is real-data TC LES so risky? High computational cost: increased by a factor of ~2000 compared to current real-time forecasts Turn off PBL scheme: necessary, but will forecast improve? Is Δx really in the inertial subrange? Probably not (for Δx = 333 m), so not all energy-containing eddies will be resolved (see Bryan and Rotunno 2009, BAMS) A 3-hour test for Katrina was run – output seems realistic. Stay tuned…

Idealized TC LES Continuation of my work at NCAR this summer Old approach (Eulerian): Simulate passage of quasi-idealized TC over a fixed location in physical space New approach (Lagrangian): Simulate PBL of idealized slow-moving TC at a fixed location relative to TC center

Idealized TC LES: Experimental setup Unchanged between experiments (all used NCAR LES): Δx = Δy = Δz = 40m; time step = 0.1 seconds 500x500x100 grid (20km x 20km x 4km) Initial θ profile: θsurface = 300 K; θ increases 4 K every 1 km up No surface heat flux (as in Nakanishi and Niino 2012, JAS) Initial gradient wind: Ugradient = 35 m s-1; Vgradient = 0 m s-1 everywhere Periodic lateral boundary conditions Changes between experiments: LAND_GEO: z0 = 0.1 m (roughness over land) No centrifugal force DONELAN_GEO: z0 follows Donelan curve (sea) LAND_CURVED: z0 = 0.1 m (roughness over land) Centrifugal force (see NN2012) DONELAN_CURVED: z0 follows Donelan curve (sea)

Results (time series) Solid = land; Dashed = Donelan (sea) Thick = curvature; Thin = no curvature Time (hours) Time (hours) Land: higher PBL top (zi) and thus higher surface temperature Curvature: faster spinup of turbulence, lower equilibrium zi(?)

Results (time series) Land: higher u* and much higher TKE Solid = land; Dashed = Donelan (sea) Thick = curvature; Thin = no curvature Time (hours) Time (hours) Land: higher u* and much higher TKE Curvature: higher u*, faster spinup, comparable TKE by 5.5 hours

Results (profiles at ~5.5 hours) Solid = land; Dashed = Donelan (sea) Thick = curvature; Thin = no curvature Curvature: supergradient jet, faster surface wind (especially azimuthal), faster spinup of turbulence, shallower inflow layer, strongest inflow closer to ground Land: Warmer/deeper thermodynamic PBL, weaker surface winds, stronger/deeper inflow layer

Summary of results Time to spin-up turbulence changes between all experiments More curvature = faster spinup (consistent w/ Nakanishi & Niino 2012) More friction = faster spinup What is the significance of this? (I don’t know) Curvature allows supergradient jet to develop at PBL top But, more curvature = weaker jet (Kepert 2001; NN2012) Question: what would happen for little curvature (say, R = 1000 km)? Side note: Magnitude of supergradient jet is still much less than “geostrophic” value corresponding to same PGF and Coriolis values More friction = stronger vertical fluxes (duh) and higher PBL top Characteristics of inflow layer sensitive to both drag and curvature

Future work Run additional tests More analysis Increase Ug and/or decrease radius Possibly add Charnock-based Cd for faster Ug experiments More analysis TKE budgets Structural analysis of rolls (power spectra) Compare with mesoscale model output