NWP 4: Probabilistic and ensemble forecasting at short and medium-range 13/09/2013

“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

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

Background 1: spatial predictabilityPredictability 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

Background 2: correlations

Bannister 2008, QJRMS

Auto-correlations

Autocross- correlations

(x…

,y…

,z…

)

(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

Method 1: case study

• MOGREPS-UK domain, UK Met Office UM 7.7 • 11 members + control• 8th July 2011• 2.2km grid spacing

>2mm

>10mm

13:00- 14:00

Method 2: Analysis

2σ

1. Vertical auto- and autocross-correlations

2. Neighbourhood approach

Gaussian weighting of perturbationsWidth set by FSS scale

• Believable scale• Variable dependant• Spatially varying

Results 1: Gaussian width

Rain rate spatial scales Horizontal divergence spatial scales

0 4 8 12 16 Grid points

15:00 on 8th July 2013

0 4 8 12 16 Grid points

Results 2: rain rate correlations

Convective layer

09:00 12:00 15:00

18:00 Single point sampling

error

Results 3: auto-correlations• 12:00 on 8th July 2013• Horizontal divergence

Single column

Spatially augmented ensemble

Heig

ht [k

m]

Heig

ht [k

m]

Height [km]

Height [km]

Results 4: autocross-correlations

Convergence

Divergence

-ve correlatio

n

+ve correlatio

n

Single columnHe

ight

[km

]

Height [km]

Spatially augmented ensemble

Heig

ht [k

m]

Height [km]

Clou

d Fr

actio

n

Horizontal divergence

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.

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.

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