“High resolution ensemble analysis: linking correlations and spread to physical processes ” S. Dey, R. Plant, N. Roberts and S. Migliorini Mesoscale group 29/10/2013

Overview Linking ensemble evolution with physical processes Understanding of convective events Evaluating on believable scales Objective : Investigate methods of evaluating high resolution ensembles Background Method and case Results (4) (5) (7)

Background 1: spatial predictability hrs Predictability limits “certain turbulent systems, possibly including the earth’s atmosphere, possess for practical purposes a finite range of predictability” (Lorentz 1969) Scale dependence – Faster error growth at smaller scales Hohenegger and Schär 2007, BAMS – Need ensembles at convective scale Ensembles indicate predictability 2.2 km LM Correlation coefficient between twin +ve/-ve pairs Rand 80 km ECMW F Lin Rand hrs

Background 2: spatial verification Skilful scale not grid length Neighbourhood methods – Avoid double penalty problem – Fractions Skill Score (FSS) (Roberts and Lean 2008, MWR) Should be evaluating on scales that are believable Can we learn more from our ensembles? Roberts 2008, Met Apps Random Useful

Background 3: correlations Bannister 2008, QJRMS Auto-correlations Autocross- correlations (x…,y…,z…) Data Assimilation: Background error covariance matrix (B) Sampling uncertainties Localization Present method of analysing the ensemble using correlations. Present one case study to show utility of techniques: future work to test on more cases

Bannister et. al. (2011) Pressure increments Geostrophic balance Wind increments Background 4: correlations and physics

Method 1: case study MOGREPS-UK domain, UK Met Office UM members + control 8 th July km grid spacing Radar 1hr accumulation

Method 2: case study Member rain rates Realistic but with spatial displacements Coastal convergence

Method 3: Analysis

Method 4: Spatial scales

Method 5: Spatial scale thresholds BL top 1-2 km

Results 1: Gaussian width examples Rain rate spatial scales Horizontal divergence spatial scales Grid points 15:00 on 8 th July Grid points

Results 2: rain rate-div correlations 09:00 12:00 15:00 18:00 Single point sampling error Convective layer

Results 3: rain rate-div correlations Convective layer 09:00 12:00 15:00 18:00 Single point sampling error

Results 4: T auto-correlations 12:00 on 8 th July 2013 Temperature Smooth field Little effect from augmenting Single column Spatially augmented ensemble Height [km]

Results 5: div auto-correlations 12:00 on 8 th July 2013 Horizontal divergence Single column Spatially augmented ensemble Height [km]

Relating auto- and autocross- correlations -ve +ve Auto-correlations Autocross- correlations +ve -ve

Results 6: Cloud-div autocross-correlations Convergence Divergence -ve correlation +ve correlation Single column Height [km] Spatially augmented ensemble Height [km] Cloud Fraction Horizontal divergence

Results 7: T-cloud autocross correlations Cloud Fraction Temperature Members with More convective cloud have More latent heat release and Warmer temperatures

Conclusions from Edinburgh case 1.Extra information from convective scale ensemble using correlations. 2.Neighbourhood sampling for analysis on meaningful scales. 3.Reduce sampling error and increase confidence. 4.Application to one case: future work to look at multiple cases.

Next steps More cases Other cases from period of COPE field campaign Other correlations Temporal correlations (rain rates) Horizontal correlations Time lagged ensemble 17 th July-Organized thunderstorms 23 rd JulyBands of thunderstorms 27 th JulyMCS (IOP 6) 29 th JulyConvective showers (IOP 8) 2 nd AugustConvection along SW peninsula (IOP 9) 3 rd AugustConvection along SW peninsula (IOP 10)

Thanks for listening. Questions? Bannister, R. N., 2008: A review of forecast error covariance statistics in atmospheric variational data assimilation. i: Characteristics and measurements of forecast error covariances. Quart. J. Roy. Meteor. Soc., 134, 1951–1970 Bannister, R. N., et al. 2011: Ensemble prediction for nowcasting with a convection- permitting model- II: forecast error statistics. Tellus A, 63A, Hohenegger, C. and C. Schär, 2007: Atmospheric predictability at synoptic versus cloud- resolving scales. Bull. Amer. Meteor. Soc., 88 (7), 1783–1793. Lorenz, E. N., 1969: The predictability of a flow which possesses many scales of motion. Tellus, 21 (3), 289–307. Roberts, N., 2008: Assessing the spatial and temporal variation in the skill of precipitation forecasts from an NWP model. Meteorol. Appl., 15 (1), 163–169. Roberts, N. M. and H. W. Lean, 2008: Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Wea. Rev., 136 (1), 78– 97.