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Cloud Parametrization 2: Cloud Cover tompkins@ictp.it Cloud Cover: The problem Most schemes presume GCM Grid cell: 40-400km cloud fills GCM box in vertical Still need to represent horizontal cloud cover, a a GCM Grid First: Some assumptions! qv = water vapour mixing ratio qc = cloud water (liquid/ice) mixing ratio qs = saturation mixing ratio = F(T,p) qt = total water (vapour+cloud) mixing ratio RH = relative humidity = qv/qs (#1) Local criterion for formation of cloud: qt > qs This assumes that no supersaturation can exist (#2) Condensation process is fast (cf. GCM timestep) qv = q s , q c = q t – q s !!Both of these assumptions are suspect in ice clouds!! Partial cloud cover Homogeneous Distribution of water vapour and temperature: q Note in the qs ,1 second case the q relative humidity=1 qs ,2 from our assumptions x One Grid-cell Partial coverage of a grid-box with clouds is only possible if there is a inhomogeneous distribution of temperature and/or humidity. Heterogeneous distribution of T and q cloudy= q q qs RH=1 RH<1 x Another implication of the above is that clouds must exist before the grid-mean relative humidity reaches 1. The interpretation does not change much if we only consider humidity variability cloudy qt qs qt RH=1 RH<1 x Throughout this talk I will neglect temperature variability In fact : Analysis of observations and model data indicates humidity fluctuations are more important Simple diagnostic schemes: RH-based schemes qt RH=60% qs qt x Take a grid cell with a certain (fixed) 1 distribution of total water. C At low mean RH, the cloud cover is zero, since even the moistest part of 0 RH the grid cell is subsaturated 60 80 100 Simple diagnostic schemes: RH-based schemes qt RH=80% qs qt x 1 Add water vapour to the gridcell, the moistest part of the cell C become saturated and cloud forms. The cloud cover is low. 0 RH 60 80 100 Simple diagnostic schemes: RH-based schemes qt RH=90% qs qt x 1 Further increases in RH C increase the cloud cover 0 RH 60 80 100 Simple diagnostic schemes: RH-based schemes RH=100% qt qt qs x 1 The grid cell becomes C overcast when RH=100%, due to lack of supersaturation 0 RH 60 80 100 Simple Diagnostic Schemes: Relative Humidity Schemes • Many schemes, from the 1 1970s onwards, based cloud C cover on the relative humidity (RH) 0 60 80 100 RH • e.g. Sundqvist et al. MWR 1989: C=1− 1− RH 1− RH crit RHcrit = critical relative humidity at which cloud assumed to form (function of height, typical value is 60-80%) Diagnostic Relative Humidity Schemes • Since these schemes form cloud when RH<100%, they implicitly assume subgrid- scale variability for total water, qt, (and/or temperature, T) exists • However, the actual PDF (the shape) for these quantities and their variance (width) are often not known • “Given a RH of X% in nature, the mean distribution of qt is such that, on average, we expect a cloud cover of Y%” Diagnostic Relative Humidity Schemes • Advantages: – Better than homogeneous assumption, since clouds can form before grids reach saturation • Disadvantages: – Cloud cover not well coupled to other processes – In reality, different cloud types with different coverage can exist with same relative humidity. This can not be represented • Can we do better? Diagnostic Relative Humidity Schemes • Could add further predictors • E.g: Xu and Randall (1996) sampled cloud scenes from a 2D cloud resolving model to derive an empirical relationship with two predictors: C=F RH ,q c • More predictors, more degrees of freedom=flexible • But still do not know the form of the PDF. (is model valid?) • Can we do better? Diagnostic Relative Humidity Schemes • Another example is the scheme of Slingo, operational at ECMWF until 1995. • This scheme also adds dependence on vertical velocities • use different empirical relations for different cloud types, e.g., middle level clouds: { 0 ω≥0 2 C m = C m ω /ω crit ¿ C ¿ m ω crit ≤ω 0 ωω crit C = max m ¿ [ RH −RH crit 1−RH crit ,0 ] Relationships seem Ad-hoc? Can we do better? Statistical Schemes • These explicitly specify qt the probability density function (PDF) for the q total water qt (and qs sometimes also x temperature) Cloud cover is PDF(qt) ∞ integral under C=∫ PDF q t dq t supersaturated q ∞s part of PDF q c =∫ q t −q s PDF q t dqt qt qs qs Statistical Schemes • Others form variable ‘s’ that also takes temperature variability into account, which affects qs L T L =T − q L ' ' Cp s=a L q t −α T L LIQUID WATER TEMPERATURE conserved during changes of state −1 Cloud mass if T variation is neglected qs ∂ qs α L= T L ∂T [ L aL = 1 α L Cp ] S ∞ qt C=∫ G s ds T ss TL S is simply the ‘distance’ from the linearized INCREASES COMPLEXITY saturation vapour pressure curve OF IMPLEMENTATION Statistical Schemes • Knowing the PDF has PDF(qt) advantages: – More accurate calculation of radiative qs qt fluxes C – Unbiased calculation of microphysical processes y • However, location of clouds within gridcell x unknown e.g. microphysics bias Statistical schemes • Two tasks: Specification of the: (1) PDF shape (2) PDF moments • Shape: Unimodal? bimodal? How many parameters? • Moments: How do we set those parameters? TASK 1: Specification of the PDF • Lack of observations to determine qt PDF – Aircraft data • limited coverage modis image from NASA website – Tethered balloon • boundary layer – Satellite • difficulties resolving in vertical • no qt observations • poor horizontal resolution – Raman Lidar • only PDF of water vapour • Cloud Resolving models have also been used • realism of microphysical parameterisation? Wood and field JAS 2000 Aircraft observations low clouds < 2km Aircraft Observe d PDFs Height Heymsfield and PDF(qt) McFarquhar JAS 96 qt Aircraft IWC obs during CEPEX PDF Data More examples from Larson et al. JAS 01/02 Note significant error that can occur if PDF is unimodal Conclusion: PDFs are mostly approximated by uni or bi- modal distributions, describable by a few parameters TASK 1: Specification of PDF Many function forms have been used symmetrical distributions: PDF( qt) qt qt Uniform: Triangular: Letreut and Li (91) Smith QJRMS (90) qt qt Gaussian: s4 polynomial: Mellor JAS (77) Lohmann et al. J. Clim (99) TASK 1: Specification of PDF skewed distributions: PDF( qt) qt qt qt Exponential: Lognormal: Gamma: Sommeria and Deardorff Bony & Emanuel Barker et al. JAS (96) JAS (77) JAS (01) qt qt Beta: Double Normal/Gaussian: Tompkins JAS (02) Lewellen and Yoh JAS (93), Golaz et al. JAS 2002 TASK 2: Specification of PDF moments Need also to determine the moments of the saturation distribution: PDF(qt) – Variance (Symmetrical cloud forms? PDFs) – Skewness (Higher qt order PDFs) e.g. HOW WIDE? – Kurtosis (4-parameter PDFs) Skewness Kurtosis Moment 1=MEAN positive e negative itive tiv Moment 2=VARIANCE ga Moment 3=SKEWNESS po s ne Moment 4=KURTOSIS TASK 2: Specification of PDF moments (1-RHcrit)qs • Some schemes fix the G(qt) moments (e.g. Smith 1-C C 1990) based on critical RH at which clouds qt assumed to form q q q s • If moments (variance, e t skewness) are fixed, q v =Cq s 1−C qe then statistical schemes are identically where q e =q s 1− 1− RH crit 1−C equivalent to a RH qv 2 formulation RH= =1− 1− RH crit 1−C qs • e.g. uniform qt distribution = Sundqvist form ∴ C =1− Sundqvist formulation!!! 1− RH 1 −RH crit Clouds in GCMs Processes that can affect distribution moments convection microphysics turbulence dynamics Example: Turbulence In presence of vertical gradient of total water, turbulent mixing can increase horizontal variability dry air moist air ' dq2 d qt t ' ' =−2 w q t dt dz Example: Turbulence In presence of vertical gradient of total water, turbulent mixing can increase horizontal variability dry air moist air while mixing in the horizontal dq2 ' ' q2 plane naturally reduces the t =− t horizontal variability dt τ Specification of PDF moments If a process is fast turbulence compared to a GCM timestep, an equilibrium can be assumed, e.g. Turbulence dq2 ' d q t qt 2 ' local ' d qt ' ' t ' ' =−2 w q t − equilibrium q 2=−τ2 w q t dt dz τ t dz Source dissipation Example: Ricard and Royer, Ann Geophy, (93), Lohmann et al. J. Clim (99) • Disadvantage: – Can give good estimate in boundary layer, but above, other processes will determine variability, that evolve on slower timescales Prognostic Statistical Scheme • I previously introduced a prognostic statistical scheme into ECHAM5 climate GCM • Prognostic equations are introduced for the convective detrainment variance and skewness of the total water PDF precipitation • Some of the sources and generation sinks are rather ad-hoc in their derivation! mixing qs Scheme in action Minimum Maximum qsat Scheme in action Turbulence breaks up cloud Minimum Maximum qsat Scheme in action Turbulence breaks up cloud Turbulence creates cloud Minimum Maximum qsat Production of variance Courtesy of Steve Klein: Change due to difference in means Transport Change due to difference in variance Also equivalent terms due to entrainment Microphysics • Change in variance ' ' Where P is the P=Kq n P qt precipitation l − ql generation rate, e.g: qlcrit P=Kq l 1−e • However, the tractability depends on the PDF form for the subgrid fluctuations of q, given by G: !! G s ty ! n d q t _max na r P a ty p ret m fo ∫ ' ' P qt G qt dq t et for n g on Ca ing en d qt =qsat D ep But quickly can get untractable • E.g: Semi-Lagrangian ice sedimentation • Source of variance is far from simple, also depends on overlap assumptions • In reality of course wish also to retain the sub-flux variability too Summary of statistical schemes • Advantages – Information concerning subgrid fluctuations of humidity and cloud water is available – It is possible to link the sources and sinks explicitly to physical processes – Use of underlying PDF means cloud variables are always self-consistent • Disadvantages – Deriving these sources and sinks rigorously is hard, especially for higher order moments needed for more complex PDFs! – If variance and skewness are used instead of cloud water and humidity, conservation of the latter is not ensured Issues for GCMs If we assume a 2-parameter PDF for total water, and we prognose the mean and variance such that the distribution is well specified (and the cloud water and liquid can be separately derived assuming no supersaturation) what is the potential difficulty? Which prognostic equations? Take a 2 parameter distribution & Partially cloudy conditions Can specify distribution with Can specify distribution with (b) Mean (b) Water vapour (c) Variance (c) Cloud water of total water mass mixing ratio qt qsat qsat Cloud Cloud qv ql+i Variance Which prognostic equations? qsat • Cloud water budget conserved (a) Water vapour • Avoids Detrainment term (b) Cloud water • Avoids Microphysics terms (almost) mass mixing ratio qv ql+i But problems arise in Overcast conditions qsat (…convection + microphysics) Clear sky (al la Tiedtke) conditions (turbulence) qv qv+ql+i Which prognostic equations? Take a 2 parameter distribution & Partially cloudy conditions qsat (a) Mean (b) Variance of total water • “Cleaner solution” • But conservation of liquid water compromised due to PDF • Need to parametrize those tricky microphysics terms! qcloud qs qcrit If supersaturation allowed, equation for cloud-ice no longer holds PDF(qt) ∞ q i ≠∫ q t −q s PDF q t dqt qs qs qcrit qt If assume fast adjustment, PDF(qt) derivation is straightforward ∞ q i = ∫ q t −q s PDF q t dq t q cloud qs qcrit qt Much more difficult if want to PDF(qt) integrate nucleation equation explicitly throughout cloud qt qi = ??? Issues for GCMs What is the advantage of knowing the total water distribution (PDF)? You might be tempted to say… Hurrah! We now have cloud variability in our models, where before there was none! WRONG! Nearly all components of GCMs contain implicit/explicit assumptions concerning subgrid fluctuations e.g: RH-based cloud cover, thresholds for precipitation evaporation, convective triggering, plane parallel bias corrections for radiative transfer… etc. Variability in Clouds Is this desirable to have so many independent tunable parameters? ‘N’ Metrics ‘M’ tuning e.g. Z500 scores, parameters TOA radiation fluxes With large M, task of reducing error in N metrics Becomes easier, but not necessarily for the right reasons Solution: Increase N, or reduce M Advantage of Statistical Scheme Microphysics Convection Scheme Can use information in Other schemes Statistical Cloud Scheme Thus ‘complexity’ is not synonymous with ‘M’: the Radiation tunable parameter space Use in other Schemes (II) IPA Biases Knowing the PDF allows the IPA bias to be tacked Use variance to calculate Effective thickness Approximation G(qt) ETA adjustment Effective Liquid = K x Liquid Cahalan et al 1994 Total qsat Water Use Moments to find best-fit Gamma Function Gamma Distribution PDF and G(qt) apply Gamma weighted TSA Total Barker (1996) qsat Water Thick Cloud etc. G(qt) Split PDF and perform N radiation calculations Total qsat Water Cloud Inhomogeneity and microphysics biases qs qs q L Most current microphysical G(qt) schemes use the grid-mean cloud mass (I.e: neglect qt variability) cloud cloud range Result is not equal in the two cases since precip mean microphysical processes are non-linear generation Example on right: Autoconversion based on Kessler Grid mean cloud less than threshold and gives zero precipitation formation qL0 qL

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posted: | 1/3/2010 |

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