Cloud cover and overlap parameterizations Adrian Tompkins, ICTP tompkins@ictp.it 1 1 Cloud cover and Overlap
Clouds in General Circulation models=GCMs GCMs describe the equations of motion on a discrete grid E.g. ECMWF global forecast model with T1280 spectral resolution (~9km equivalent) with 137 vertical levels T,q,U,V,W … Many processes occur on scales smaller than this 2 2 Cloud cover and Overlap
Clouds in GCMs - What are the problems ? Clouds are subgrid-scale (both horizontally and vertically) GCM Grid cell 10-400km 3 3 Cloud cover and Overlap
Clouds in GCMs: The aim Cloud/no cloud? Ice/liquid, amount, crystal size/shape…? Depends on use! To represent the “ important” characteristics of clouds with the smallest number of parameters possible ( = parametrization task) 4 4 Cloud cover and Overlap
How can we describe clouds? Which characteristics? VERTICAL COVERAGE Most models assume that this is 1 This can be a poor assumption with coarse vertical grids. Many climate models still use fewer than 30 vertical levels currently, some recent examples still use only 9 levels z ~1km ~100km x 5 5 Cloud cover and Overlap
How can we describe clouds? Which characteristics? HORIZONTAL COVERAGE, C Spatial arrangement? z ~500m C ~100km x 6 6 Cloud cover and Overlap
How can we describe clouds? Which characteristics? VERTICAL OVERLAP OF CLOUD Important for Radiation and Microphysics Interaction z ~500m x ~100km 7 7 Cloud cover and Overlap
Overlap approaches Solar Zenith Effects A. M. Tompkins and F. Di Giuseppe. Generalizing cloud overlap treatment to include solar zenith angle effects on cloud geometry. J. Atmos. Sci., 64:2116-2125, 2007 A. M. Tompkins and F. Di Giuseppe. An interpretation of cloud overlap statistics. J. Atmos. Sci., 72:2877- 2889, 2015 F. Di Giuseppe and A. M. Tompkins. Generalizing cloud overlap treatment to include the effect of wind shear. J. Atmos. Sci., 72:2865-2876, 2015 8 8 Cloud cover and Overlap
How can we describe clouds? Which characteristics? IN-CLOUD INHOMOGENEITY in terms of cloud particle size and number z ~500m x ~100km 9 9 Cloud cover and Overlap
Macroscale Issues of Parameterization Just these issues can become a little complex!!! z ~500m x ~100km 10 10 Cloud cover and Overlap
This talk will concentrate on how GCMs represent horizontal cloud cover, C C Talk Outline: 1. Simple diagnostic schemes 2. Statistical schemes 3. The current ECMWF scheme 4. Complications with ice 11 11 Cloud cover and Overlap
First! Some assumptions: q v = water vapour mixing ratio q c = cloud water (liquid/ice) mixing ratio q s = saturation mixing ratio = F(T,p) q t = total water (vapour+cloud) mixing ratio RH = relative humidity = q v /q s (#1) Local criterion for formation of cloud: q t > q s This assumes that no supersaturation can exist (#2) Condensation process is fast (cf. GCM timestep) q v = q s , q c = q t – q s !!Both of these assumptions are suspect in ice clouds!! 12 12 Cloud cover and Overlap
Partial coverage of a grid-box with clouds is only possible if there is a inhomogeneous distribution of temperature and/or humidity. Homogeneous Distribution of water vapour and temperature: q q s, 1 Note in the second q case the relative q s, 2 humidity=1 from our assumptions x One Grid-cell 13 13 Cloud cover and Overlap
Heterogeneous distribution of T and q cloudy= q q q s RH=1 RH<1 x Another implication of the above is that clouds must exist before the grid-mean relative humidity reaches 1. 14 14 Cloud cover and Overlap
The interpretation does not change much if we only consider humidity variability cloudy q t q s q t 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 15 15 Cloud cover and Overlap
#1 Simple Diagnostic Schemes 16 16 Cloud cover and Overlap
#1 Simple diagnostic schemes: RH-based schemes q t RH=60% q s q t 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 17 17 Cloud cover and Overlap
#1 Simple diagnostic schemes: RH-based schemes q t RH=80% q s q t 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 18 18 Cloud cover and Overlap
#1 Simple diagnostic schemes: RH-based schemes q t RH=90% q s q t x 1 Further increases in RH C increase the cloud cover 0 RH 60 80 100 19 19 Cloud cover and Overlap
#1 Simple diagnostic schemes: RH-based schemes RH=100% q t q t q s x 1 The grid cell becomes C overcast when RH=100%, due to lack of supersaturation 0 RH 60 80 100 20 20 Cloud cover and Overlap
#1 Simple Diagnostic Schemes: Relative Humidity Schemes Many schemes, from the 1 1970s onwards, based C cloud cover on the relative 0 RH 60 80 100 humidity (RH) e.g. Sundqvist et al. MWR 1989: C = 1 − √ 1 − RH 1 − RH crit RH crit = critical relative humidity at which cloud assumed to form (function of height, typical value is 60-80%) 21 21 Cloud cover and Overlap
Diagnostic Relative Humidity Schemes Since these schemes form cloud when RH<100%, they implicitly assume subgrid- scale variability for total water, q t , (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 q t is such that, on average, we expect a cloud cover of Y%” 22 22 Cloud cover and Overlap
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? 23 23 Cloud cover and Overlap
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? 24 24 Cloud cover and Overlap
#2 Statistical Schemes 25 25 Cloud cover and Overlap
#2: Statistical Schemes These explicitly q t specify the probability density function (PDF) q q s for the total water q t (and sometimes also x temperature) ∞ C = ∫ Cloud cover is PDF(q t PDF ( q t ) dq t integral under supersaturated q s ∞ part of PDF ) q c = ∫ ( q t − q s ) PDF ( q t ) dq t q t q s q s 26 26 Cloud cover and Overlap
#2: Statistical Schemes Knowing the PDF has advantages: PDF(q t More accurate calculation of ) q t q s radiative fluxes C Unbiased calculation of microphysical processes y However, location of clouds within gridcell unknown x e.g. microphysics bias 27 27 Cloud cover and Overlap
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? 28 28 Cloud cover and Overlap
TASK 1: Specification of the PDF Lack of observations to determine q t PDF Aircraft data limited coverage Tethered balloon modis image from NASA website boundary layer Satellite difficulties resolving in vertical no q t observations poor horizontal resolution Raman Lidar only PDF of water vapour Cloud Resolving models have also been used realism of microphysical parameterisation? 29 29 Cloud cover and Overlap
Wood and field JAS 2000 Aircraft observations low clouds < 2km Aircraft Observed PDFs Height Heymsfield and PDF(q t ) McFarquhar JAS 96 Aircraft IWC obs q t during CEPEX 30 30 Cloud cover and Overlap
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 31 31 Cloud cover and Overlap
TASK 1: Specification of PDF Many function forms have been used symmetrical distributions: PDF( q t ) q t q t Uniform: Triangular: Letreut and Li (91) Smith QJRMS (90) q t q t Gaussian: s 4 polynomial: Mellor JAS (77) Lohmann et al. J. Clim (99) 32 32 Cloud cover and Overlap
TASK 1: Specification of PDF skewed distributions: PDF( q t ) q t q t q t Lognormal : Gamma: Exponential: Bony & Emanuel Barker et al. JAS (96) Sommeria and Deardorff JAS (01) JAS (77) q t q t Beta: Double Normal/Gaussian: Tompkins JAS (02) Lewellen and Yoh JAS (93), Golaz et al. JAS 2002 33 33 Cloud cover and Overlap
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