mean systematic error of 500 hpa geopotential height fields lowres highres

How random numbers improve weather and climate predictions Expected and unexpected effects of stochastic

parameterizations

NCAR day of networking and discovery, April, 17, 2015

Judith Berner

With contributions from:

Dani Coleman, Hannah Christensen, Kate Fossell,

Soyoung Ha, Josh Hacker, Glen Romine, Craig

Schwartz, Chris Snyder Felipe Tagle

Mean systematic error of 500 hPa geopotential height fields

LOWRES HIGHRES

Mean systematic error of 500 hPa geopotential height fields

SKEBSLOWRES

• Reduction of z500 bias in all simulations with model-refinement

Berner et al., 2012

HIGHRES

Potential of stochastic parameterizations to reduce model error

Weak noise

Multi-modalUnimodal

Ball in double-potential well

PDF

Strong noise


Weak noise

Multi-modalUnimodal

Potential

PDF

Strong noise


Weak noise

Multi-modalUnimodal

Potential

PDF

Strong noise Stochastic parameterizations can change the mean and variance of a PDF Impacts variability Impacts mean bias

Key message

Random numbers can improve weather and climate predictions

Outline

The stochastic parameterization schemes

Climate application: Impact in coupled and uncoupled simulations with the Earth System Model CESM

Weather application: Improving reliability and reducing analysis error in cycled and uncycled forecasts with the weather model WRF

Local tendency for variable X

Dynamical tendencies => Resolved scales

Physical tendencies => Unresolved scales

Rationale: Especially as resolution increases, the equilibrium assumption is no longer valid and fluctuations of the subgrid-scale state should be sampled (Buizza et al. 1999, Palmer et al. 2009, Berner et al. 2014)

Stochastically perturbed tendency scheme (SPPT)

Perturbs accumulated U,V,T,Q tendencies from physical parameterizations packages

Same pattern for all tendencies to minimize introduction of imbalances

Rationale: A fraction of the subgrid-scale energy is scattered upscale and acts as random streamfunction and temperature forcing for the resolved-scale flow (Shutts 2005, Berner et. al 08,09). Here simplified version with constant dissipation rate: can be considered as additive noise with spatial and temporal correlations.

Stochastic-kinetic energy backscatter scheme (SKEBS)

Stochastic Forcing Pattern

Local tendency for variable X =U,V,T

Dynamical tendencies => Resolved scales

Physical tendencies => Unresolved scales

Additive stochastic perturbation tendencies => Unresolved scales

Outline




NCEP

SKEBS

CNTL

SPPT

21% 50%

35% 37%

Northern Annular Mode (MAM)1st EOF of sea level pressure over Northern Hemispheric Extratropics

CAM4 AMIP simulations (prescribed SSTs), 1900-2004

Stochastic parameterization improves pattern and reduces explained variance

Degenerate response: SKEBS and SPPT have same effect

Sketch: CAM4 behavior

Potential with stochastic perturbations

Potential without stochastic perturbations

Including a stochastic parameterization does not lead to large changes in the pattern of modes of variability, but to decreased explained variances

This is consistent with a flattening of a potential well

Stochastic parameterizations can also lead to a depending of a potential well.

Sketch: CAM4 behavior



Including a stochastic parameterization does not lead to large changes in the pattern of modes of variability, but to decreased explained variances

This is consistent with a shallowing of a potential well

Stochastic parameterizations can also lead to a depending of a potential well.

First EOF of 500hPa-field over Atlantic sector

NCEP

SPPT

CNTL

SKEBS

49% 44%

46% 53%

Impact of SPPT on sea surface temperature (SST) variability

Coupled simulations with CAM4, 1880-2004

Too much variability in SSTs in Tropical Pacific

SPPT reduces bias in SST variability in Tropical Pacific

How can a stochastic parameterization reduce variability?

Impact of SPPT on sea surface temperature (SST) variability

How can perturbations to the atmosphere improve the ocean?

SPPT reduces variability in u850 variability over the Western Pacific

Impact of SPPT on El Niño Southern Oscillation

Probability density function of daily temperatures over North America (JJA)

AMIP simulations with CAM4

Too much variability in daily temperatures in summer compared to reanalysis

General extreme value distributions fitted to annual monthly temperature maxima and minima

CAM4 has to high return values for both, TMAX and TMIN

Overestimation of extreme temperatures

SKEBS and deteriorates 20yr return values for TMAX, but slightly improves values for TMIN

Tagle et al. 2015

Impact of SKEBS on precipitation bias

Coupled control run shows significant bias due to split inter-tropical convergence zone

SKEBS reduced bias in precipitation

Outline




Representing initial uncertainty by an ensemble of states

Forecast uncertainty in weather models: Initial condition uncertainty Model uncertainty Boundary condition uncertainty

Represent initial forecast uncertainty by ensemble of states

Reliable forecast system: Spread should grow like ensemble mean error Predictable states with small error

should have small spread Unpredictable states with large error

should have large spread

\

analysis

spread

RMS error

ensemble mean

Spread and error near the surface

Ensemble is underdispersive (= not enough spread) Unreliable and over-confident Depending on cost-loss ratio potentially large

socio-economic impact (e.g. should roads be salted)

Solid lines: rms error of ensemble mean

Dashed: spread

Brier skill score near the surface

Brier skill measures probabilistic skill in regard to a reference (here CNTL). Verified event: μ<x<μ+σ

Berner et al., et al 2015

Reliability diagram for rain-thresholds, averaged over

forecast hours 18–36 using a 50-km neighborhood

Romine et al., 2014

V-10m T-2m

Including a model-error representation reduces the RMS error of the surface analysis (also prior) in 10m wind and Temperature at 2m

WRF-DART: Verification of surface analysis against independent

observations

CNTLSKEBSPHYS

Ha et al. 2015

Sketch: WRF behavior



Verifying observation

Including a stochastic parameterization increased ensemble spread

In cycled forecasts is reduces the mean analysis error

Debate in the field: A priori vs a posteriori

Model

Model uncertainty added a posteriori:

Process uncertainty added a priori during model development:

Forecast uncertainty

Stochasticity

Conclusions

Random numbers can improve weather and climate predictions by impacting variability and mean in expected (increase variability) and

unexpected (decrease variability) ways

Thank you!

Berner, J, K. Fossell, S.-Y. Ha, J. P. Hacker, C. Snyder 2015: “Increasing the skill of probabilistic forecasts: Understanding performance improvements from model-error representations, Mon. Wea. Rev., 143, 1295-1320

Berner, J., S.-Y. Ha, J. P. Hacker, A. Fournier, C. Snyder, 2011: “Model uncertainty in a mesoscale ensemble prediction system: Stochastic versus multi-physics representations” , Mon. Wea. Rev, 139, 1972-1995

Romine, G. S., C. S. Schwartz, J. Berner, K. R. Smith, C. Snyder, J. L. Anderson, and M. L. Weisman, 2014: “Representing forecast error in a convection-permitting ensemble system”, Mon. Wea. Rev, 142, 12, 4519–4541

Ha, S.-Y., J. Berner, C. Snyder, 2015: “Model-error representation in mesoscale WRF-DART cycling”, under review at Mon. Wea. Rev.

mean systematic error of 500 hpa geopotential height fields lowres highres

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