3D experiments with a stochastic convective parameterisation scheme

Transcription

1 3D experiments with a stochastic convective parameterisation scheme R. J. Keane and R. S. Plant 3D experiments with a stochastic convective parameterisation scheme p.1/17

2 Outline Introduction to the Plant-Craig stochastic convection parameterisation scheme. Experiments in an idealised UM setup. A simple ensemble case study. 3D experiments with a stochastic convective parameterisation scheme p.2/17

3 Plant-Craig scheme: methodology Obtain the large-scale state by averaging resolved flow variables over both space and time. Obtain M from CAPE closure and define the equilibrium distribution of m (Cohen-Craig theory). Draw randomly from this distribution to obtain cumulus properties in each grid box. Compute tendencies of grid-scale variables from the cumulus properties. 3D experiments with a stochastic convective parameterisation scheme p.3/17

4 PC scheme: probability distribution Assuming a statistical equilibrium leads to an exponential distribution of mass fluxes per cloud: p(m)dm = 1 ( ) m m exp dm. m So if m r 2 then the probability of initiating a plume of radius r in a timestep dt is ( ) M 2r r 2 m r 2 exp dr dt r 2 T. 3D experiments with a stochastic convective parameterisation scheme p.4/17

5 PDF of total mass flux Assuming that clouds are non-interacting, this can be combined with a Poisson distribution for cloud number, p(n) = N N e N N! leading to the following distribution for total mass flux: ( ) ( ) 1/2 N p(m) = e ( N +M/ m ) M 1/2 N I 1 2 m m M., 3D experiments with a stochastic convective parameterisation scheme p./17

6 PDFs of mass flux in an SCM Plant & Craig, JAS, 28 3D experiments with a stochastic convective parameterisation scheme p.6/17

7 3D Idealised UM setup Radiation is represented by a uniform cooling. Convection, large scale precipitation and the boundary layer are parameterised. The domain is square, with bicyclic boundary conditions. The surface is flat and entirely ocean, with a constant surface temperature imposed. Horizontal diffusion, vertical diffusion of θ and targeted diffusion of moisture are applied. 3D experiments with a stochastic convective parameterisation scheme p.7/17

8 Energy and moisture balance Energy budget Moisture budget surface latent heat flux L H2O convective rain rate L H2O large scale rain rate energy (W m 2 ) energy (W m 2 ) time (days/3) 2 x 4 Potential temperature time (days/3) 2 x 4 Specific humidity height (m) 1 height (m) θ (K) q (kg kg 1 ) x 3 Held et. al., JAS, 27. 3D experiments with a stochastic convective parameterisation scheme p.8/17

9 PDFs of mass fluxes 2. x 9 2 ln ( p(m) (kg 1 s) ) p(m) (kg 1 s) m (kg s 1 ) x M (kg s 1 ) x 8 3D experiments with a stochastic convective parameterisation scheme p.9/17

10 PDF of number of clouds This seems to follow p(n) = exp( N/ N )/ N.6..4 p(n) N 3D experiments with a stochastic convective parameterisation scheme p./17

11 Organisation in rainfall pattern? animation 3D experiments with a stochastic convective parameterisation scheme p.11/17

12 Organisation in rainfall pattern? GR animation 3D experiments with a stochastic convective parameterisation scheme p.12/17

13 Case study: CSIP IOP18 Starts at 2th August 2, 7:. 12 km grid with grid points. Diffusion as in idealised experiments x D experiments with a stochastic convective parameterisation scheme p.13/17

14 Ensemble of 6 runs using PC scheme D experiments with a stochastic convective parameterisation scheme p.14/17

15 RMS deviation from ensemble mean The RMS deviation of total rain is accounted for mostly by the convective rain, even though the mean value of total rainfall is accounted for mostly by the large-scale rain. rainfall rate (kg m 2 s 1 ) 1 x conv rms ls rms tot rms conv mean ls mean tot mean time (hours) 3D experiments with a stochastic convective parameterisation scheme p./17

16 Comparison with Gregory-Rowntree The PC scheme produces 19% of its rain as convective rain, whereas the figure for the GR scheme is 67%. The difference in rainfall reduces as the models spin up. The difference between the PC ensemble runs is smaller than the difference between the two schemes. 3D experiments with a stochastic convective parameterisation scheme p.16/17

17 Conclusions The scheme yields the correct distribution of individual cloud mass flux. The distribution of total mass flux is not as according to non-interacting theory, suggesting that there is some organisation of cloud structure in the scheme; however, this is less the case than in the GR scheme. The scheme yields considerable convective variability in the simple ensemble case study. This seems to be due to variation in the locations of storms, rather than variation in their intensities. The scheme produces less convective rain than the GR scheme, although the convective rainfall behaviour is sensible. 3D experiments with a stochastic convective parameterisation scheme p.17/17