1. “High resolution ensemble analysis: linking correlations and spread to physical processes ” S. Dey, R. Plant, N. Roberts and S. Migliorini NWP 4: Probabilistic and ensemble forecasting at short and medium-range 13/09/2013

2. Overview Linking ensemble evolution with physical processes Understanding of convective events Evaluating on believable scales Objective : Investigate methods of evaluating high resolution ensembles Background Case study Results

3. Background 1: spatial predictability 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 Upscale error growth: A forecast can be unpredictable at grid scale but predictable at larger scales. – Should be evaluating on scales that are believable

4. Background 2: 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

5. Method 1: case study MOGREPS-UK domain, UK Met Office UM 7.7 11 members + control 8 th July 2011 2.2km grid spacing >2mm >10mm 13:00- 14:00

6. Method 2: Analysis

7. Results 1: Gaussian width Rain rate spatial scales Horizontal divergence spatial scales 0 4 8 12 16 Grid points 15:00 on 8 th July 2013 0 4 8 12 16 Grid points

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

9. Results 3: auto-correlations 12:00 on 8 th July 2013 Horizontal divergence Single column Spatially augmented ensemble Height [km]

10. Results 4: autocross-correlations Convergence Divergence -ve correlation +ve correlation Single column Height [km] Spatially augmented ensemble Height [km] Cloud Fraction Horizontal divergence

11. Conclusions 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.

12. 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 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. s.dey@pgr.reading.ac.uk