“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

0 12 24 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 scalesHohenegger 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

ECMWF

Lin

Lin

Rand

24 96 192 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…

)

(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 7.7 • 11 members + control• 8th July 2011• 2.2km grid spacing

Radar 1hr accumulation

Method 2: case study

Member rain ratesRealistic but with spatial displacements

Coastal convergence

Method 3: 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

1. Compare fields at different scales (n)min=0

max=1

2. At what scale are we skilful?

• FSS values of 0.5 when neighbourhood twice separation distance• Weighting based on neighbourhood size Smaller neighbourhood: more stringent criteria

: criteria always met

Method 4: Spatial scales

1. Rain ratesthreshold =0.01 mm/hr

2. Horizontal divergencethreshold=

Method 5: Spatial scale thresholds

𝝎=𝟎 .𝟏−𝟎 .𝟐𝒎𝒔−𝟏BL top 1-2 km

Results 1: Gaussian width examples

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-div correlations

09:00 12:00 15:00

18:00 Single point sampling

errorConvective 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 8th July 2013• Temperature• Smooth field• Little effect from

augmenting

Single column

Spatially augmented ensemble

Hei

ght [

km]

Hei

ght [

km]

Height [km]

Height [km]

Results 5: div auto-correlations

• 12:00 on 8th July 2013• Horizontal divergence

Single column

Spatially augmented ensemble

Hei

ght [

km]

Hei

ght [

km]

Height [km]

Height [km]

Relating auto- and autocross- correlations

-ve

+ve

+ve

Auto-correlations

Autocross-correlations

+ve

-ve

Results 6: Cloud-div autocross-correlations

Convergence

Divergence

-ve correlatio

n

+ve correlatio

n

Single columnH

eigh

t [km

]

Height [km]

Spatially augmented ensemble

Hei

ght [

km]

Height [km]

Clou

d Fr

actio

n

Horizontal divergence

Results 7: T-cloud autocross correlationsCl

oud

Frac

tion

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

17th July- Organized thunderstorms

23rd July Bands of thunderstorms

27th July MCS (IOP 6)

29th July Convective showers (IOP 8)

2nd August Convection along SW peninsula (IOP 9)

3rd August Convection 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, 1951–1970Bannister, R. N., et al. 2011: Ensemble prediction for nowcasting with a convection- permitting model- II: forecast error statistics. Tellus A, 63A, 497-512Hohenegger, 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.