Multiple Equilibria in a Cloud Resolving Model: Using the Weak Temperature Gradient Approximation to Understand Self-Aggregation 1

Transcription

1 Multiple Equilibria in a Cloud Resolving Model: Using the Weak Temperature Gradient Approximation to Understand Self-Aggregation 1 Sharon Sessions, Satomi Sugaya, David Raymond, Adam Sobel New Mexico Tech SWAP This work is supported by the National Science Foundation Sessions (NMT) Multiple Equilibria in a CRM May / 21

2 Self-Aggregation Bretherton et al (2005) precipitation WVP = 1 g rt dp Day 1 Day 50 Sessions (NMT) Multiple Equilibria in a CRM May / 21

3 Possible insight from limited domain WTG simulations Bretherton et al (2005) Day 1 Day 50 Sessions (NMT) Multiple Equilibria in a CRM May / 21

4 Weak Temperature Gradients in the Tropics Charney 1963 scaling analysis Extratropics (small Rossby number) Tropics (Rossby number not small) δθ F r R o θ δθ F r θ Froude number: F r = U 2 /gh 10 3, measure of stratification Rossby number: R o = U/fL 10 5 /f, characterizes rotation Sessions (NMT) Multiple Equilibria in a CRM May / 21

5 Weak Temperature Gradients in the Tropics Charney 1963 scaling analysis Extratropics (small Rossby number) Tropics (Rossby number not small) δθ F r R o θ δθ F r θ Froude number: F r = U 2 /gh 10 3, measure of stratification Rossby number: R o = U/fL 10 5 /f, characterizes rotation In the tropics, gravity waves rapidly redistribute buoyancy anomalies Sessions (NMT) Multiple Equilibria in a CRM May / 21

6 Weak Temperature Gradient (WTG) Approximation Sobel & Bretherton 2000 Single column model (SCM) representing one grid cell in a global circulation model Convection is not explicitly resolved Temperature (T) and moisture (q) governed by: T t +u h T +ωs = Q T total q t +u h q +ω q p = Qq total and S = T θ θ p is the static stability Sessions (NMT) Multiple Equilibria in a CRM May / 21

7 Weak Temperature Gradient (WTG) Approximation Sobel & Bretherton 2000 Single column model (SCM) representing one grid cell in a global circulation model Convection is not explicitly resolved Temperature (T) and moisture (q) governed by: T t +u h T +ωs = Q T total q t +u h q +ω q p = Qq total Steady state WTG approximation and S = T θ θ p is the static stability Sessions (NMT) Multiple Equilibria in a CRM May / 21

8 Weak Temperature Gradient (WTG) Approximation Sobel & Bretherton 2000 Parameterize the large scale circulations ωs = Q T total Conventional parameterizations: specify ω, diagnose T WTG parameterization: specify T, diagnose ω and S = T θ θ p is the static stability Sessions (NMT) Multiple Equilibria in a CRM May / 21

9 WTG Implementation in a Cloud Resolving Model (CRM) Raymond & Zeng 2005 θ t + (ρvθ+t θ) ρ(s θ E θ ) r t t + (ρvr t +T r ) ρ(s r E r ) Sessions (NMT) Multiple Equilibria in a CRM May / 21

10 WTG Implementation in a Cloud Resolving Model (CRM) Raymond & Zeng 2005 θ t + (ρvθ+t θ) ρ(s θ E θ ) r t t + (ρvr t +T r ) ρ(s r E r ) Enforcing WTG generates w wtg [ θ θ E θ = w wtg z = sin(πz/h) θ0 (z) ] t θ Sessions (NMT) Multiple Equilibria in a CRM May / 21

11 Specifying Convective Environment Reference profiles of potential temperature, θ 0, and moisture, r 0, are generated by running model to radiative-convective equilibrium (RCE) WTG: vertical θ profile approximately horizontally homogeneous Average moisture in immediate convective vicinity height (m) θ (K) r t (g/g) Moisture advected from environment via mass continuity Sessions (NMT) Multiple Equilibria in a CRM May / 21

12 WTG Implementation in our CRM Raymond & Zeng 2005 θ t + (ρvθ+t θ) ρ(s θ E θ ) r t t + (ρvr t +T r ) ρ(s r E r ) w wtg vertically advects moisture and brings in environmental moisture via mass continuity: E r = (r t r x (z)) (ρw wtg ) r t +w wtg ρ z z Sessions (NMT) Multiple Equilibria in a CRM May / 21

13 Environmental moisture in WTG simulations E r = (r t r x ) (ρw WTG ) r t +w WTG ρ z z height r x = { r0 (ρw wtg )/ z > 0 r t (ρw wtg )/ z < 0 mass flux ( ρw ) wtg Sessions (NMT) Multiple Equilibria in a CRM May / 21

14 Precipitation in WTG simulations E θ = w wtg θ z = sin(πz/h) [θ θ 0(z)] t θ θ 0 (z) is RCE profile for v y = 5 m/s on 2D 200 km domain t θ is a measure of the enforcement of WTG rain rate (mm/day) t θ =30 sec (strict WTG) t θ =31 min t θ =1.85 hours t θ = (RCE) horizontal windspeed (m/s) Sessions (NMT) Multiple Equilibria in a CRM May / 21

15 Multiple Equilibria in Precipitation Sobel, Bellon & Bacmeister (2007) Single column model (SCM) with WTG approximation Parallel experiments: identical forcing initially moist troposphere initially dry troposphere Observe convective response with different SSTs Sessions (NMT) Multiple Equilibria in a CRM May / 21

16 Multiple Equilibria in Precipitation Sobel, Bellon & Bacmeister (2007) initially moist initially dry Reference profile is RCE with SST of 301 K Sessions (NMT) Multiple Equilibria in a CRM May / 21

17 Multiple Equilibria in a CRM Sessions, Sugaya, Raymond & Sobel (2010) 2-D Cloud Resolving Model (CRM) with WTG approximation periodic boundary conditions horizontal domains vary from km (0.5-1 km resolution) vertical dimension of 20 km (250 m resolution) Parallel experiments: Initial moisture profile of tropics same as surrounding environment completely dry Observe convective response with different surface wind speeds (surface wind speed and SST both control surface fluxes) 4 month simulations, averaged over last month of simulation Sessions (NMT) Multiple Equilibria in a CRM May / 21

18 Multiple Equilibria in a CRM Sessions, Sugaya, Raymond & Sobel (2010) rain rate (mm/day) km domain, t θ =1.85 hours RCE input dry initial Reference profile is RCE with v y = 5 m/s horizontal windspeed (m/s) Sessions (NMT) Multiple Equilibria in a CRM May / 21

19 Normalized Gross Moist Stability (NGMS) Define NGMS to characterize the convective environment NGMS = T R 1 g (sv)dp = (rv)dp L 1 g moist entropy export moisture import GMS based on moist static energy budget (Neelin & Held 1987) Thorough discussion of NGMS (Raymond et al. 2009) Sessions (NMT) Multiple Equilibria in a CRM May / 21

20 NGMS in the Steady State Sessions, Sugaya, Raymond, Sobel (2010) rain rate (mm/day) km domain, t θ =1.85 hours RCE input dry initial In the steady state, Net precipitation = net entropy forcing NGMS NGMS horizontal windspeed (m/s) Sessions (NMT) Multiple Equilibria in a CRM May / 21

21 NGMS as a diagnostic Sign of NGMS moist entropy import moist entropy export moisture import + moisture export + NGMS = T R 1 g (sv)dp = (rv)dp L 1 g moist entropy export moisture import Sessions (NMT) Multiple Equilibria in a CRM May / 21

22 Steady state precipitation and NGMS 50 rain rate (mm/day) m/s 10 m/s 15 m/s 20 m/s NGMS = Dry equilibrium NGMS + or - Rain rate = moist entropy export moisture import net entropy forcing NGMS NGMS=0.3 divides equilibria NGMS Sessions (NMT) Multiple Equilibria in a CRM May / 21

23 Multiple Equilibria & Self-Aggregation NGMS Day 50 Bretherton et al (2005) + GMS in precipitating region GMS in dry region Sessions et al (2010) + NGMS in precipitating equilibria small or NGMS in dry equilibria Sessions (NMT) Multiple Equilibria in a CRM May / 21

24 Summary WTG approximation parameterizes the large scale circulations Multiple equilibria in CRM determined by surface fluxes initial moisture determines which state is realized NGMS characterizes the steady state atmosphere larger values for precipitating equilibrium smaller or negative values for dry equilibrium Investigating multiple equilibria in limited domain WTG simulations may be a computationally economic approach to understanding self-aggregation Sessions (NMT) Multiple Equilibria in a CRM May / 21