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“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.