The Monte Carlo Independent Column Approximation and Noise/Uncertainty in GCMs. H. W. Barker
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1 The Monte Carlo Independent Column Approximation and Noise/Uncertainty in GCMs H. W. Barker Meteorological Service of Canada J.-J. Morcrette (ECMWF), R. Pincus (NOAA), P. Räisänen (MSC), and G. Stephens (CSU) the current paradigm for modelling radiative transfer in GCMs is restrictive and inevitably leads to codes that are biased... McICA method for radiative transfer + stochastic subgrid-scale cloud generator noise/uncertainty in GCMs Cloud Physics Research Division, Environment Canada
2 A stochastic view of subgrid-scale clouds and radiation 50 km km wide columns - 1D profiles of imperfect estimates of mean values - pa ( c), p( LWC), p( re), etc not to mention p( LWC,re LWC, re) infinitely many underlying, satisfying 3D fields
3 Example: overlap of layered clouds - CRM field (Grabowski et al. 1999) - mix of maximum and random uncertainties with input data + time integration distributions of profiles of radiative fluxes
4 Conjecture 1: To advance knowledge of cloud-radiation interactions and feedbacks, RT algorithms must be free of biases and respond properly to subtle changes. existing models Conjecture 2: If manageable random errors arise while eliminating bias errors... no problem. - input errors - natural, conditional stochastic uncertainty ever to be acknowledged explicitly?
5 The cica Method Monte Carlo Independent Column Approximation for CKD method: - can show (theoretically and computationally) that expectation value is the ICA... - unbiased wrt ALL assumptions about unresolved clouds etc. - simplest RT solver + Nk () = 1 ) requires LESS CPU than current codes - for single-layer homogeneous clouds, conventional solution is recovered - combinations of all hydrometeors / aerosol / vapour / surface... produces conditional random noise
6 Injection of Radiative Noise into the ECMWF Global Model - at the time, we lacked an adequate statistical cloud generator - global application of excessive radiative noise (tropical squall line) - can the model consume this which is far beyond methodological noise? Model Assessment - 30 member ensembles (10 day forecast + JJA): a. control b. random radiative heating rates c. systematic re: +1 m (liquid); +10 m (ice) d. (b) + (c)
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13 Noise/Uncertainty in GCMs (nonlinear systems) 1. artificial, methodological (e.g., McICA... directly to diabatic term) ***** 2. errors with input variables (e.g., cloud fraction, LWC) 3. additional assumptions (e.g., cloud overlap) 4. natural, conditional uncertainty (limited information - infinitely many 3D fields)
14 - unbiased noise applied to nonlinear systems - obvious catastrophe: - according to ECMWF, unbiased radiative noise goes nowhere pa ( c) - compound errors: pcdd ( ) ) pr ( e) ) p( ), p( 0), pg ( ) ) p( N) ) ) - noise onto radiative heating comes late...
15 How a celebrated, simple nonlinear system reacts to noise Lorenz s (1984) Hadley circulation model (Aires and Rossow 2002): x: intensity of westerly wind and poleward temperature gradient y: cosine phase of superimposed large-scale eddies that transport heat poleward z: sine phase of superimposed large-scale eddies that transport heat poleward F: zonally symmetric thermal forcing on x F : zonally symmetric thermal forcing on y
16 noise applied to F1and F2 (zonally-symmetric thermal forcings)
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18 (100 timesteps)
19 3 min 30 min 5hr 50hrs ECMWF + Lorenz model: (almost) immune to minor, high frequency noise - if not the case, we (GCMs) are in trouble! ideally, apply McICA at high frequency run with perturbations too long. V don t allow the rest of the model to
20 Current status: two fast stochastic cloud generators... tested using CSU super-param data - additional conditional noise beyond McICA have SW and LW codes set-up + optimal CKD? single-column model + GCM - SCM V amplify or suppress noise? - Jason: super-scm... - drive a CRM using domain-average fluxes (ICA vs. McICA) representation of process-conditional stochastic noise/uncertainty in GCMs
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23 Current status: two fast stochastic cloud generators... tested using CSU super-param data - additional conditional noise beyond McICA have SW and LW codes set-up + optimal CKD? single-column model + GCM - SCM V amplify or suppress noise? - Jason: super-scm... - drive a CRM using domain-average fluxes (ICA vs. McICA) representation of process-conditional stochastic noise/uncertainty in GCMs
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