Motivation for stochastic parameterizations
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- Derrick Christopher Houston
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3 Motivation for stochastic parameterizations Unreliable and over- confident ensemble forecasts Breakdown of quasi- equilibrium assump:on at small scales Persistent systema:c errors (e.g. blocking) Scale- aware parameteriza:on
4 Representing initial uncertainty by an ensemble of states Represent ini:al uncertainty by ensemble of states Flow- dependence: Predictable states should have small ensemble spread Unpredictable states should have large ensemble spread t 0 RMS error Ensemble spread should grow like RMS error True atmospheric state should be indis:nguishable from ensemble system ensemble mean t1 analysis t
5 Spread and error, T850 over NH, for winter (90 cases) TIGGE Curtousy Buizza
6 Mean systematic error of 500 hpa geopotential height fields z500 bias in IFS CY31R1, T d) Z500 Difference f8o8-er40 ( ) 14 1
7 Mean systematic error of 500 hpa geopotential height fields z500 bias in IFS CY31R1, T Blocking Frequency (%) Analysis LOWRES STOCH HIGHRES PHYS Longitude d) Z500 Difference f8o8-er40 ( ) 14 1
8 Potential to reduce model error Stochas:c parameteriza:ons can change the mean and variance of a PDF Potential Impacts variability of model (e.g. internal variability of the atmosphere) Impacts systema:c error (e.g. blocking precipita:on error) PDF Weak noise Strong noise Unimodal Multi-modal
9 Stochastic parameterization schemes Stochas:c kine:c- energy backscauer scheme (SKEBS) Ra:onale: A frac:on of the dissipated kine:c- energy is scauered upscale and acts as forcing for the resolved flow (ShuUs, 005,Berner et al. 009,11,1,14) Stochas:cally perturbed parameteriza:on scheme (SPPT) Ra:onale: Especially as resolu:on increases, the equilibrium assump:on is no longer valid and fluctua:ons of the subgrid- scale state should be sampled (Buizza et al. 1999, Palmer et al. 009, Berner et al. 014)
10 Stochastic parameterization schemes Stochas:c kine:c- energy backscauer scheme (SKEBS) Ra:onale: A frac:on of the dissipated kine:c- energy is scauered upscale and acts as forcing for the resolved flow (ShuUs, 005,Berner et al. 009,11,1,14) Opera:onal at ECMWF, UK Metoffice, Tested in WRF, CMC Stochas:cally perturbed parameteriza:on scheme (SPPT) Ra:onale: Especially as resolu:on increases, the equilibrium assump:on is no longer valid and fluctua:ons of the subgrid- scale state should be sampled (Buizza et al. 1999, Palmer et al. 009, Berner et al. 014) Opera:onal at ECMWF, UK Metoffice Tested at DWD, Swiss Met service, Spanish Metservice
11 Perturbations added a posteriori Model Forecast Uncertain:es
12 Stochastic parameterizations increase skill a) Zonal Wind U at 700hPa b) Temperature T at 700hPa Spread;Error c) 0.1 d) 0.06 Brier Score CNTL SPPT SKEBS PHYS10 PHYS10_SKEBS PHYS3_SKEBS f) x Berner et al., 015
13 Mean systematic error of 500 hpa geopotential height fields LOWRES -10 6b) SKEBS HIGHRES Reduc:on of z500 bias in all simula:ons with model- refinement Degenera:ve response d) Z500 Difference f8o8-er40 ( ) Berner et al., PHYS
14 a) Obs c) d) LOWRES e) f) SKEBS g) Power spectra of tropical velocity potential anomalies at 00 hpa i) j) HIGHRES PHYS
15 Verification of surface analysis against independent observations V- 10m T- m CNTL SKEBS PHYS Ø Including a model- error representa:on reduces the RMS error of the surface analysis Ø SKEBS has smallest error for 10m- wind; PHYS for m temperature Ha et al 014, submiued
16 Chris Bretherton Computa:onal efficiency is not an aderthought Uncertainty assessment is not an aderthought
17 A priori vs a posteriori Model Forecast Uncertain:es Process Uncertain:es Model
18 A priori vs a posteriori If you develop a parameteriza:on, I urge you to develop an uncertainty scheme alongside OTHERWISE I WILL
19 and you don t want that!
20 and you don t want that!
21 WRF3.7:Random Fields Random pauern can be used to perturb user specific fields, e.g., lower boundary condi:ons or parameters SKEBS or SPPT pauern can now also be used to perturb the lateral boundaries Either in conjunc:on with interior SKEBS perturba:ons or just as lateral boundary perturba:on
22 Calibra 10 0 Brier Skill Score Reliability Resolution Brier Skill Score Debiased Raw CNTL PARAM SKEBS PHYS10 PHYS10_SKEBS PHYS3_SKEBS_PARAM Calibrated & Debiased Calibrated Importance of Bias Change of Model Debiased Version U700 T700 U10 T Berner et al., 015 U700 T700 U10 T U700
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24 Verification of surface analysis against independent observations V- 10m T- m CNTL SKEBS PHYS Ø Including a model- error representa:on reduces the RMS error of the surface analysis Ø SKEBS has smallest error for 10m- wind; PHYS for m temperature Ha, Berner, Snyder, 014
25 Stochas:c Forcing PaUern Stochas:c- kine:c energy backscauer scheme (SKEBS) Ra:onale: A frac:on of the subgrid- scale energy is scauered upscale and acts as random streamfunc:on and temperature forcing for the resolved- scale flow. Here: simply considered as addi:ve noise with spa:al and temporal correla:ons Similar to ECMWF global ensemble system (ShuUs 005, Berner et. al 08,09) but with constant dissipa:on rate and poten:al temperature perturba:ons (Berner et al. 011). a)
26 Stochastic kinetic- energy backscatter a) scheme Rationale: A fraction of the dissipated energy is scattered upscale and acts as streamfunction forcing for the resolved-scale flow Δψ * Dψ ψ Total Dissipation rate from numerical dissipation, convection, gravity/mountain wave drag. Spectral Markov chain: temporal and spatial correlations prescribed
27 Stochastically perturbed tendency scheme (SPPT) Ra:onale: Especially as resolu:on increases, the equilibrium assump:on is no longer valid and fluctua:ons of the subgrid- scale state should be sampled (Buizza et al. 1999, Palmer et al. 009, Berner et al. 014) X t = DX + (r+1)px Local tendency for variable X Dynamical tendencies => Resolved scales Physical tendencies => Unresolved scales
28 Other mathematical relevant areas to the parameterization problem MMF/Superparameteriza:on Emulators Stochas:c mode reduc:on (MTV) Concept from Sta:s:cal Mechanics Concepts from Enthropy
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