A Stochastic Parameterization for Deep Convection

Transcription

1 A Stochastic Parameterization for Deep Convection EGU Assembly 7th April 2006 Bob Plant 1, George Craig 2 and Christian Keil 2 1: Department of Meteorology, University of Reading, UK 2: DLR-Institut fuer Physik der Atmosphaere, Germany

2 Why Stochastic? In Theory A deterministic parameterization gives unique increments due to convection for a given (local) model state 1. This assumes an equilibrium, with the forcing scales being large compared to the intrinsic scales of the convection 2. It also assumes the model grid scale to be large compared to the intrinsic scales Stochastic Parameterization for Deep Convection p.1/12

3 Why Stochastic? In Theory If equilibrium breaks down... see poster! If equilibrium holds but the number of cumulus clouds in a grid box is not large then convection on the grid scale is unpredictable... but drawn from an equilibrium distribution... so a stochastic parameterization is required Fluctuating component of sub-grid motions may have important interactions with large-scale Stochastic Parameterization for Deep Convection p.2/12

4 Range of Sub-Grid States The typical number of clouds in a GCM grid box is not enough to give a steady response to a steady forcing Temperature tendencies for 120km boxes from CRM simulations of tropical convection. Each plot is for a given range of dt /dt according to Bechtold et al. (2001) parameterization. (From Shutts and Palmer, J. Clim, submitted) Stochastic Parameterization for Deep Convection p.3/12

5 Possible Benefits Buizza et al (2005) Stochastic parameterizations may solve known problems with current approaches: NWP models have insufficient ensemble spread GCMs have insufficient variability in tropics Stochastic Parameterization for Deep Convection p.4/12

6 Characteristics of Stochastic Scheme Character and strength of the noise should have a physical basis supported/inspired by CRM studies The physically-based noise >> numerical noise from scheme The noise 0 if there are very many clouds in this limit, the scheme should be competitive with current deterministic schemes Stochastic Parameterization for Deep Convection p.5/12

7 Structure Mass-flux formalism... No trigger function. Presence of convection dictated by random subgrid variability Plumes chosen from known exponential distribution of mass fluxes Behaviour of each plume based on modified Kain-Fritsch plume model Plumes persist for finite lifetime timestep CAPE closure, with timescale that depends on forcing. Based on full spectrum using an averaged (non-local, large-scale) sounding. Stochastic Parameterization for Deep Convection p.6/12

8 Exponential Mass Flux Distributions From statistical mechanics, and found in CRM with different forcings and at different levels (Cohen and Craig 2006) Distribution at 3.1km 8K/d forcing Distribution at 1.3km 16K/d forcing Number of clouds Number of clouds Mass flux (x 10^7 kgm^2s^ 1) Mass flux (x 10^7 kgm^2s^ 1) Stochastic Parameterization for Deep Convection p.7/12

9 Single Column Tests Met Office Unified Model single column version parameterizations for boundary layer transport, stratiform cloud forced as in CRM simulations (fixed tropospheric cooling) aim is to replicate mean state and fluctuations of companion CRM simulation Stochastic Parameterization for Deep Convection p.8/12

10 Physical not Numerical Noise Does a steady forcing give a steady response (in the limit of a large grid box)? km box Flux/mean flux 1.5 Flux/mean flux km box Timestep number Timestep number 5 clouds 200 clouds Stochastic Parameterization for Deep Convection p.9/12

11 Pdf of Total Mass Flux Is the desired distribution of total mass flux reproduced for different-sized areas? samples 44 samples samples Theory samples Theory Probability (scaled) km box Probability (scaled) 20 96km box Total mass flux (kg/s) Total mass flux (kg/s) Imposed variability does not feedback onto the closure. Stochastic Parameterization for Deep Convection p.10/12

12 Plume Properties Are properties of the individual plumes consistent with CRM results? Stochastic scheme Distribution at 5.75km 1000 Number of clouds Mass flux (x 10^7 kgm^2s^ 1) Exponential distribution achieved well above cloud base. Stochastic Parameterization for Deep Convection p.11/12

13 Current / Near-Future Steps Test in different configurations: Implemented in DWD Lokal Modell for case-study tests in COSMO-LEPS regional ensemble system Statistical tests in Met Office short-range ensemble (MOGREPS) Test in aqua-planet GCM Main issues: How often, and in what circumstances, does stochastic variability matter? On what spatial and temporal scales should the variability be correlated? Stochastic Parameterization for Deep Convection p.12/12