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How to represent subgrid atmospheric processes in Climate |Models Multiscale Physics Regional Climate Division A. Pier Siebesma siebesma@knmi.nl Faculty for Applied Sciences Climate Research

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The Climate System: A Multiscale Challenge: Landsat 65kmLES 10km ~mm~1m ~1 m-100 m Earth 10 7 m Courtesy: Harm Jonker, TU Delft

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3 10 m100 m1 km10 km100 km1000 km10000 km turbulence Cumulus clouds Cumulonimbus clouds Mesoscale Convective systems Extratropical Cyclones Planetary waves Large Eddy Simulation (LES) Model Cloud System Resolving Model (CSRM) Numerical Weather Prediction (NWP) Model Global Climate Model No single model can encompass all relevant processes DNS mm Cloud microphysics

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Architecture of a Global Climate Model

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Unresolved (subgrid) Processes in Climate Models Source: ECMWF Model documentation

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Climate Model Sensistivity estimates of GCM’s participating in IPCC AR4 Source: IPCC Chapter 8 2007 Spread in climate sensitivity: concern for many aspects of climate change research, assesment of climate extremes, design of mitigation scenarios. What is the origin of this spread? Radiative Forcing, Climate feedbacks,

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Relative Contributions to the uncertainty in climate feedbacks Source: Dufresne & Bony, Journal of Climate 2008 Radiative effects only Water vapor feedback Surface albedo feedback Cloud feedback Uncertainty in climate sensitivity mainly due to (low) cloud feedbacks

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8 Governing Equations for incompressible flows in the atmosphere Continuity Equation (incompressible) NS Equations Heat equation Moisture equation Gas law with gravity term coriolis term Condensed water eq.

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9 Large scale advection subsidence Vertical turbulent/ convective transport Net Condensation Rate Filtered Equations for the Thermodynamic Variables Radiative heating Precipitation resolved subgrid

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Resolved Scales turbulence ~ 250 km convection clouds radiation Small scalesLarge scales Schematic View of how scales are connected in traditional GCM’s Depiction of the interaction between resolved and parameterized unresolved cloud-related processes (convection, turbulence, clouds and radiation) in present-day climate models. (from Siebesma et al, Perturbed Clouds in our climate system MIT) Which are the problems, errors and uncertainties that we have to face with this approach?

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1. Inherent lack of understanding of certain physical processes < 100 m [100,600 m] >800 m Source : Andrew Heymsfield Uncertainties in ice and mixed phase microphysics: Supersaturation Liquid vs ice Habits Size distribution Sedimentation Interaction with radiation No fundamental equations available describing these properties and processes.

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2. Non-linear character of many cloud related processes With: q l : cloud liquid water q l : critical threshold H : Heaviside function A : Autoconversion rate : Kessler Autoconversion Rate (Kessler 1969) Example 1: Autoconversion of cloud water to precipitation in warm clouds Autoconversion rate is a convex function: Larson et al. JAS 2001

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Example 2: Cloud fraction and Cloud liquid water (Thijs Heus TU Delft/KNMI) LES q sat qtqt T q sat(T) qtqt. (T,q t ) Cloud fraction: Cloud liquid water:

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Plane parallel cloud Scu Cloud albedo Liquid water path (LWP) x x a a(LWP) < a(LWP) Neglecting Cloud inhomogeneity causes a positive bias in the cloud albedo. Example 3: Cloud Albedo Bias

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These biased errors slowly go away when increasing model resolution: Typically allowed if x < 100m, i,e, at the LES model scale So for all models operating at a coarser resolution additional information about the underlying Probability Density Function (pdf) is required of temperature, humidity (and vertical velocity). For Example: So if only….. we would know the pdf.

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Resolved Scales turbulence ~ 250 km convection clouds radiation Small scalesLarge scales 3. Interactions between the various subgrid processes Subgrid processes strongly interact with each other while in (most) GCM’s they only interact indirectly through the mean state leading to inconsistencies and biases.

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17 4. Statistical versus Stochastic Convection ~500km Traditionally (convection) parameterizations are deterministic: Instantaneous grid-scale flow and mean state is taken as input and convective response is deterministic One to one correspondency between sub-grid state and resolved state assumed. Conceptually assumes that spatial average is a good proxy for the ensemble mean.

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18 4. Statistical versus Stochastic Convection resolution 100m 1km1000km100km Convection Explicitly resolved Statistical ensemble mean Deterministic convection parameterization Stochastic Convection That takes into account fluctuations so that the ensemble mean is not satisfied each timestep but more in a canonical sense Microcanonical limit

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19 New Pathways

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20 Resolved Scales 3.5 km turbulence convection clouds radiation Pathway 1: Global Cloud Resolving Modelling (Brute Force) NICAM simulation: MJO DEC2006 Experiment MTSAT-1R NICAM 3.5km Miura et al. (2007, Science) 3.5km run: 7 days from 25 Dec 2006 Short timeslices Testbed for interactions: deep convection and the large scale Boundary clouds, turbulence, radiation still unresolved

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21 Pathway 2: Superparameterization 2D CRM turbulence (b) convection clouds radiation 5 km 250 km Resolved Scales

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22 Pathway 2: Superparameterization What do we get? Explicit deep convection Explicit fractional cloudiness Explicit cloud overlap and possible 3d cloud effects Convectively generated gravity waves But….. A GCM using a super-parameterization is three orders of magnitude more expensive than a GCM that uses conventional parameterizations. On the other hand super-parameterizations provide a way to utilize more processors for a given GCM resolution Boundary Layer Clouds, Microphysics and Turbulence still needs to be parameterized

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23 Remarks: Resolved Scales turbulence convection clouds radiation ~100 km Large scales Unresolved scales Resolved Scales Pathway 3: Consistent pdf based parameterizations Increase consistency between the parameterizations! How? Let’s have a closer look at the subgrid variability and the way this is treated in tradiational parameterizations

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24 T q sat(T) qtqt. (T,q t ) Statistical Cloud Schemes (1): Estimate a c and q l using the subgrid variability:

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25 Statistical Cloud Schemes (2): Convenient to introduce: “The distance to the saturation curve” Normalise s by its variance: So that a c and q l can be written in a single variable PDF: What to choose for G(t) ???

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26 Statistical Cloud Schemes (3): Gaussian Case: Cloud cover and liquid water function of only one variable!!!! Sommeria and Deardorf (JAS,1976)

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27 Verification (with LES) Cloud cover Bechtold and Cuijpers JAS 1995 Bechtold and Siebesma JAS 1999

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28 Verification (with Observations) Wood and Field (unpublished)

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29 Remarks: Correct limit: if and the scheme converges to the all-or-nothing limit Parameterization problem reduced to finding the subgrid variability, i.e. finding.

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30 Convective transport in Shallow Cumulus: Characteristics Courtesy Bjorn Stevens LES Heus TU Delft

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31 Typical Mean Profiles Horizontal Variability Upward transport by moist buoyant cumulus cores

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32 less distinct updrafts in subcloud layer

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a wcwc a a Strong bimodal character of joint pdf has inspired the design of mass flux parameterizations of turbulent flux in Large scale models (Betts 1973, Arakawa& Schubert 1974, Tiedtke 1988)

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34 M The old working horse: Entraining plume model: Plus boundary conditions at cloud base. How to estimate updraft fields and mass flux? Betts 1974 JAS Arakawa&Schubert 1974 JAS Tiedtke 1988 MWR Gregory & Rowntree1990 MWR Kain & Fritsch1990 JAS And many more……..

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35 Double counting of processes Inconsistencies Problems with transitions between different regimes: dry pbl shallow cu scu shallow cu shallow cu deep cu This unwanted situation can lead to: Standard transport parameterization approach:

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36 Remarks: Resolved Scales turbulence convection clouds radiation ~100 km Large scales Unresolved scales Resolved Scales Intermezzo (2) Increase consistency between the parameterizations! How?

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37 z inv Nonlocal (Skewed) transport through strong updrafts in clear and cloudy boundary layer by advective Mass Flux (MF) approach. Remaining (Gaussian) transport done by an Eddy Diffusivity (ED) approach. Advantages : One updraft model for : dry convective BL, subcloud layer, cloud layer. No trigger function for moist convection needed No switching required between moist and dry convection needed Eddy-Diffusivity/Mass Flux approach : a way out?

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38 Cumulus clouds are the condensed, visible parts of updrafts that are deeply rooted in the subcloud mixed layer (ML) LeMone & Pennell (1976, MWR)

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39 z inv The (simplest) Mathematical Framework :

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40 Figure courtesy of Martin Koehler Cumulus Topped Boundary Layer Neggers, Kohler & Beljaars accepted for JAS 2009 alternatives: Lappen and Randall JAS 2001 Rio and Hourdin JAS 2008 Dry updraft Moist updraft K diffusion Top 10 % of updrafts that is explicitly modelled Flexible moist area fraction

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Assume a Gaussian joint PDF( l,qt,w) shape for the cloudy updraft. Mean and width determined by the multiple updrafts Determine everything consistently from this joint PDF Remarks: No closure at cloud base No detrainment parameterization Pdf can be used for cloud scheme and radiation An reconstruct the flux:

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42 Convection and turbulence parameterization give estimate of s Cloud scheme : radiation scheme : Subgrid variability (at least the 2 nd moment) for the thermodynamic variables needs to be taken into acount in any GCM for parameterizations of convection, clouds and radiation in a consistent way. At present this has not be accomplished in any GCM.

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43 But… Many open problems remain Convective Momentum Transport Influence of Aerosols/Precipitation on the (thermo)dynamics of Scu and Cu Mesoscale structures in Scu and Shallow Cu Transition from shallow to deep convection (deep convective diurnal cycle in tropics) Conceptually on process basis Parameterization Vertical velocity in convective clouds Convection on the 1km~10km scale. (stochastic convection) Microphysicis (precip) Transition regimes. Climate Determine and understand the processes that are responsable for the uncertainty in cloud-climate feedback.

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44 A slow, but rewarding Working Strategy Large Eddy Simulation (LES) Models Cloud Resolving Models (CRM) Single Column Model Versions of Climate Models 3d-Climate Models NWP’s Observations from Field Campaigns Global observational Data sets DevelopmentTestingEvaluation See http://www.gewex.org/gcss.html

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ll qtqt q sat Cloud fraction Condensate SCM LES Tested for a large number of GCSS Cases………………..

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46 A slow, but rewarding Working Strategy Large Eddy Simulation (LES) Models Cloud Resolving Models (CRM) Single Column Model Versions of Climate Models 3d-Climate Models NWP’s Observations from Field Campaigns Global observational Data sets DevelopmentTestingEvaluation See http://www.gewex.org/gcss.html

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