Improving Representation of Turbulence and Clouds In Coarse-Grid CRMs

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1 Improving Representation of Turbulence and Clouds In CoarseGrid CRMs Peter A. Bogenschutz and Steven K. Krueger University of Utah, Salt Lake City, UT

2 Motivation Embedded CRMs in MMF typically have horizontal grid sizes ~ 4 km Can we improve the representation of the unresolved processes in a computationally efficient manner?

3 Our Approach CRM embedded into MMF is System for Atmospheric Modeling (SAM) Improving turbulence and cloud representation within SAM: 1. Assumed PDF to diagnose cloud fraction, nonprecipitating cloud condensate, liquid water flux (buoyancy flux) 2. Improved formulation for the SGS turbulent length scale Can this be done without compromising computational expense too much?

4 Talk Outline LES Benchmarks Closure description a priori PDF testing Improved formulation of turbulent length scale (poster) Implementation of PDF into SAM Modeling results within 2D SAM Summary & Future work

5 LES Benchmarks The following LES cases have been used to help aide in the closure testing process. Clear Convective Boundary Layer (Wangara) Tradewind cumulus (BOMEX) Continental cumulus (ARM) Stratocumulus to cumulus transition (OWN) Deep convection (GATE) GigaLES

6 Testing Assumed PDFs with LES Data Families of PDF tested a priori on LES Data (continuation of Larson et al. 22) Families are triple joint PDF P (w, θl, qt ) Low Complexity: Single Delta Function ( all or nothing ) Double Delta Function Single Gaussian Higher Complexity: Analytic Double Gaussian 1 Analytic Double Gaussian II LewellenYoh PDFs tested for.8 km to 24.8 km grid sizes

7 Testing Assumed PDFs with LES Data 5 Cloud Fraction hr (3.2 km grid) GATE (GigaLES) 3.5 height (km) Lowest 5 km 1 Cloud Fraction Correlation Coefficient Horizontal grid size (km)

8 Testing Assumed PDFs with LES Data (Summary) Low complexity PDFs fail when cloud properties are highlyskewed High complexity PDFs provide more consistent results ADG 1 PDF least sensitive to errors in input moments Higher complexity PDFs close higher order moments accurately We select ADG 1 for implementation into SAM Details of testing assumed PDFs a priori found in Bogenschutz et al. (21, submitted)

9 Assumed PDF: Implementation into SAM Requires computation of several second order moments and one third order moment: θ 2 l, q 2 t, w 2, w θ l, w q t, q tθ l, w 3 The single column model of Golaz et al. (22) used a predictive approach to find these moments To avoid substantial computational expense, can we avoid second/third order predictive closure? Can a diagnostic approach provide realistic results?

10 Turbulent Length Scale Cheng et al. (21) suggests that eddy diffusivity schemes (Ktheory) appear to function well given the correct amount of SGS TKE can be predicted. Currently SAM sets L z For CRMs, length scale should NOT depend on grid size or grid mesh We have formulated a new dissipation length scale that appears to partition SGS/Resolved TKE accurately (see poster) = e3/2 L K H =.1Le 1/2

11 Turbulent Length Scale (BOMEX example) 3 Liquid Water Potential Temperature Flux 2.5 w θ l SGS Flux 2 height (km) (W/m 2 )

12 Diagnostic Approach to Determining Input Moments Vertical fluxes of heat and moisture: Downgradient + plus countergradient terms (related to transport and buoyancy) Variances & Covariance: Following Redelsperger (1986) Third moment of vertical velocity Algebraic equation following Canuto et al. (24)

13 Input Moments Vertical Fluxes of Heat and Moisture φ w φ =.1L e +τ z Vertical Velocity Variance 2 8 L 1/2 w 2 w = e e 3 15 Cm z 2 g w φ C1 θv φ C2 θ z Scalar Variances and Covariance φ ψ φ ψ = C1 L xi xi 2

14 Assumed PDF: Output Output: Cloud fraction, nonprecipitating condensate, liquid water flux Higher order moments / buoyancy terms Standard SAM computes the local moist BruntVaisalla frequency. Here we compute the buoyancy flux as: Lv 1 o w θv = w θl + θo w qt + o cp po p Rd /cp 1 θo w ql o

15 Standard SAM vs. PDFSAM Standard SAM 1.5 TKE closure Length scale specified as dz (except in stable grid boxes) allornothing condensation PDFSAM 1.5 TKE closure Length scale diagnosed SGS condensation No additional prognostic equations added to SAM code

16 Selected Results Liquid Water Potential Temperature Results from idealized cases CRM Results presented for SAM run in 2D and for dx=3.2 km. Results compared to predictive SCM of Golaz et al m 32 m 32 m Eddy PDF

17 Clear Convection Wangara, day 33 Clear convective boundary layer with weak largescale forcing LES: CRMs: dx = dy = 1 m, dz = 4 m dx = 32 m, dz = 4 m dz tested for 4 m up to 2 m Results shown from 13 to 14 LST

18 Clear Convection (Wangara) 2 Liquid Water Potential Temperature m 1 32 m 8 32 m Eddy PDF (K) 6 Total Water Mixing Ratio (g/kg)

19 4 Liquid Water Potential Temperature Clear Convection 35 3 (Wangara) FLUX of QT (resolved+sgs) w q t 1 m 32 m 32 m Eddy PDF (W/m 2 ) (K) Buoyancy Flux w θ v (W/m 2 )

20 Trade Cumulus BOMEX (Barbados Oceangraphic and Meteorological Experiment) Nonprecipitating tradewind cumulus LES: dx = dy = 1 m, dz = 4 m 2D CRMs: dx = 32 m, dz = 4 m dz tested for 4 m up to 2 m Results shown averaged from last three hours of simulation

21 Shallow Convection (BOMEX) 3 Liquid Water Potential Temperature 25 Golaz et al m 32 m 32 m Eddy PDF (K)

22 Shallow Convection (BOMEX) 3 Cloud Fraction m 32 m 32 m Eddy PDF ( ) Golaz et al. 22

23 Liquid Water Potential Temperature Shallow Convection (BOMEX) Non precipitating Cloud Condensate 1 m 32 m 32 m Eddy PDF (K) (g/kg) Golaz et al. 22

24 Liquid Water Potential Temperature Shallow Convection (BOMEX) 3 25 Buoyancy Flux 1 m 32 m 32 m Eddy PDF (K) (W/m 2 ) Golaz et al. 22

25 Shallow Convection (BOMEX) 3 Liquid Water Flux 25 w q l 2 15 iquid Water Potential Temperature Flux of Vertical Velocity Variance w (W/m 2 ) 1 1 m 32 m 32 m Eddy PDF (m 3 /s 3 )

26 Shallow Convection (BOMEX) 3 Variance of Theta l (resolved+sgs) Liquid Water Potential Temperature θ 2 l 3 25 Covariance of theta l and total water θ l q t (K) m 32 m 32 m Eddy PDF (g/kg K)

27 Stratocumulus OWN (Ocean Weathership North) 7 day transition case from stratocumulus to trade cumulus LES: dx = dy = 5 m, dz = 25 m in Sc boundary layer 2D CRMs: dx = 32 m, dz = 25 m dz tested for 25 m up to 2 m Results shown averaged from the first simulated day

28 Stratocumulus 1 Liquid Water Potential Temperature m 1 32 m m Eddy PDF (K) Total Water Mixing Ratio (g/kg)

29 Stratocumulus 1 Cloud Fraction Non precipitating Cloud Condensate m 32 m 32 m Eddy PDF ( ) (g/kg)

30 4 Liquid Water Potential Temperature 35 3 Stratocumulus Heat Flux (resolved+sgs) m 32 m 32 m Eddy PDF Buoyancy Flux 2 1 w θ l (W/m 2 ) (K) w θ v (W/m 2 )

31 Stratocumulus 1 Total Water (resolved+sgs) w q t (W/m 2 ) Golaz et al. 22

32 Deep Convection GATE Idealized deep convection over ocean LES ( GigaLES ; Khairoutdinov et al. 29): dx = dy = 1m, dz = 5 m near surface vertical levels 2D CRMs: dx = 32 m, dz = 2 m near surface, 33 vertical levels dz tested with 256, 128, 64, and 33 vertical levels Results shown averaged from last simulated 12 hours

33 Deep Convection Using SGS condensation scheme so we modify the precipitation code to reflect this: Does not assume entire coarsegrid box is precipitating Compute autoconversion eligible condensate amount from PDF Using cloud fraction values, compute cloud overlap assumption to determine area of grid box with precipitation (Jakob and Klein 2)

34 Deep Convection 3 x 14 Cloud Fraction m 32 m 32 m Eddy PDF x 14 Non precipitating Cloud Condensate ( ) (g/kg)

35 Deep Convection x Precip Rate m 32 m 32 m Eddy PDF Liquid Water Flux x w q l (mm/day) (K) (W/m 2 )

36 Deep Convection Liquid Water Potential Temperature 25Flux (resolved+sgs) 3 x 14 w θ l (W/m 2 ) 1 1 m 32 m 32 m Eddy PDF 3 x Flux of QT (resolved+sgs) (K) w q t (W/m 2 )

37 Summary It appears the diagnostic SAMPDF closure can improve upon SAM. SAMPDF comparable results with Golaz et al. 22. PDF leads to improved representation of clouds & buoyancy flux. Computational cost is kept comparable to standard SAM New length scale formulation is essential for partitioning of SGS/resolved energy. The real test: How does this scheme perform in the MMF (forthcoming)???

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