A data-driven stochastic parameterization of deep convection

Transcription

1 parameterization of 1 joint work with: Daan Crommelin 1, Pier Siebesma 2,3, Harm Jonker 3, Frank Selten 2, Christian Jakob 4 1 CWI, Amsterdam, The Netherlands 2 KNMI, De Bilt, The Netherlands 3 Delft University of Technology, Delft, The Netherlands 4 ARC Centre of Excellence for Climate System Science, Monash University, Melbourne, Australia Montreal, 21 August 214

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3 Variability of rainfall is missing in climate s; GCMs are heading toward the grey zone; Parameterizations of and clouds have to be improved/adapted; We present a multicloud, inferred from, that can be used to ally parameterize.

4 Our consists of N Markov, denoted by Y n (t), positioned on a microgrid; Markov with 5 states: clear sky, moderate and strong congestus, deep convective and stratiform; They form cloud type area fractions σ m : σ m = 1 N N 1[Y n (t) = m] n=1 Cloud type area fractions can be used in the convection and cloud schemes of the GCM, for example as mass flux at cloud base closure: M b = ρw cb σ 4

5 The transition probabilities of the Markov are inferred from high-resolution ( km 2 ) ; The Markov are made dependent on the large-scale (15 15 km 2 ) by conditioning on the large-scale state;

6 Data from a scanning rain radar in Darwin in Australia Integer valued cloud top height and rain rate observations at 1 minute time steps Two periods: the training data set 5 months in Nov 25- Apr 26 and the test data set 3 months in Jan-Apr 27. Horizontal length [km] (a) Cloud Top Height [km] Horizontal length [km]

7 Table : Cloud type classification using thresholds for the cloud top height and the rain rate. CTH [km] rain rate [mm h 1 ] 12 > stratiform (m = 5) deep convective (m = 4) 3 > 3 [1.5, 6.5) moderate congestus (m = 2) strong congestus (m = 3) < 1.5 clear (m = 1) Horizontal length [km] 15 deep stratiform strong congestus moderate congestus clear sky Horizontal length [km]

8 Large-scale (15 15 km 2 ) defines the large-scale dynamical and thermodynamical state of the atmosphere around Darwin; Available every 6 hours, but we perform linear interpolation to have the values every 1 minutes; Improved NWP analysis large-scale variable estimates, prepared by Davies et al. 213.

9 Well-known indicators of convection: CAPE RH ω := 1 p p p p ω(p)dp Cross-correlation analysis: CCF (τ) = CCF X (t + τ) σ 4 (t)dt <ω> CAPE RH time lag τ [day]

10 ω -intervals ω displays the highest correlation at τ =, so we choose ω to condition the Markov. We choose 25 intervals, which results in 25 different transition matrices. No. of ω values in each interval mean vertical velocity 5 interval 24 interval ω [hpa h 1 ]

11 Deep convective area fractions as a function of ω -intervals (a) 7 Area fraction [%] Observational mean + standard deviation obs. Expected values CMC + standard deviation CMC deep convective Discretized ω [interval number]

12 (a) Deep convective area fraction [%] (c) Deep convective area fraction [%] Results: comparing fractions with Darwin observations Darwin observations 27 1 Feb 27 1 Mar 27 1 Apr x1 CMCs 25 clusters ω 1 Feb 27 1 Mar 27 1 Apr 27 (b) Deep convective area fraction [%] (d) x1 CMCs 25 clusters ω 1 Feb 27 1 Mar 27 1 Apr Darwin observations 27 1x1 CMCs 25 clusters ω Deep convective area fraction [%]

13 Area fraction [%] Area fraction [%] (a) Results: comparing fractions with Darwin observations Observations 1x1 CMCs 25 clusters ω Expected values of CMC deep convective Time [days] (c) stratiform Time [days] Area fraction [%] (b) 4 Area fraction [%] strong congestus Time [days] (d) moderate congestus Time [days]

14 Results: Auto-correlation functions ACF (a) Darwin observations 27 1x1 CMCs 25 clusters CAPE 1x1 CMCs 25 clusters ω 69x69 CMCs 25 clusters ω ω deep convective time [day]

15 Test implementation in simple climate with prescribed SSTs; SPEEDY from Simplified Parameterizations, primitive-equations DYnamics developed by Franco Molteni; Deep convection mass flux scheme

16 Keep trigger function: conditional instability and relative humidity thresholds; Keep mass flux vertical profiles; Only use Multicloud fractions as a closure of the mass flux at cloud base: M b = ρw 4 σ 4 + ρw 3 σ 3

17 Precipitation time series Rain rate [mm/day] Control deterministic relaxation scheme (left) and Stochastic scheme (right) Time [4 min] Rain rate [mm/day] Time [4 min]

18 Hovmoller global total precipitation Control (left) and scheme (right)

19 Average total precipitation Deterministic control: Stochastic scheme:

20 Zonal wavenumber-frequency diagrams

21 Conclusions ω shows highest correlation with deep convective area fractions; Conditioned on ω the Markov multicloud adequately reproduces deep convective area fractions; Stochastics are essential to reproduce high peak values; Implemented in simple GCM, the scheme works; MJO improved, Kelvin waves gone;

22 References

23 Extra: relationship convergence and convection