Can we use a statistical cloud scheme coupled to convection and moist turbulence parameterisations to simulate all cloud types? Colin Jones CRCM/UQAM

1-D TKE equation used in HIRLAM ABCD A is buoyant production B is shear production C is transport (vertical diffusion of TKE) and pressure force term. TKE evolution is dependent on subgrid scale vertical fluxes which in turn are dependent on TKE D is dissipation of TKE ( l  is a typical length scale for eddies responsible for TKE loss) Turbulence (and subgrid scale vertical transport) is often larger inside clouds than in the surrounding atmosphere. This is due to latent heat release and cloud top radiative cooling and/or entrainment which are strong sources of turbulence inside clouds through the buoyant production term A. It is important this term is modelled correctly for an accurate description of subgrid scale vertical transport by boundary layer clouds. l h,m follows ideas of Bougeault and Lacarrare with wind shear included Via Richardson number.

Moist conservative turbulence and statistical cloud representation Turbulence phrased in moist conservative variables (  l and r t ) naturally incorporates phase change effects in buoyancy production term. Cloud fraction can be calculated by the present cloud scheme (external to Turbulence scheme) but due to the fast nature of incloud turbulent mixing this risks ”mis-matches” in time and/or space between moist turbulence and cloud fields leading to potential numerical instability. Better to use a cloud fraction embedded within the turbulence scheme and directly influenced by the degree of turbulent mixing, using the same stability measures as used for calculating the turbulent length scales and vertical fluxes. (e.g. Statistical Clouds) In the HIRLAM moist TKE scheme atmospheric static stability plays a key role in determining the Mixing length scales used in determining the vertical fluxes of the conserved variables. Atmospheric stability is calculated relative to clear and cloudy portions of the model grid box. C f is cloud fraction and appears in the vertical stability and thus vertical eddy flux term through both the resolved gradient and in determining the mixing length

The buoyancy flux term is the main generator of TKE in boundary layer clouds and therefore is crucial to model accurately. Following Cuijpers & Bechtold (1995) the buoyancy flux in a (partly) cloud layer can be schematically represented by: N is cloud fraction and the 3rd term on the RHS plays an important role in the buoyancy flux in cloudy boundary layers with small cloud fractions (N<0.4) where the buoyancy flux is increasingly skewed (towards values dominated by the incloud portion). In these types of cloudy boundary Layers (say with N<0.1) the 2nd (clear sky) and 3rd (non-Gaussian) terms dominate the buoyancy flux and by implication TKE evolution and turbulent mixing lengths. f NG expresses the contribution of the non-Gaussian (skewed) fluxes of  l and q t to the total buoyancy flux. f NG increases rapidly with decreasing N (increasing skewness) and like N and q l can be parameterised in terms of the normalised saturation deficit Q 1. Introducing a variable s describing the effect of changes in r t and T l on the saturation state of the grid box leads to a formualtion of Q 1

CRM and LES models can be used to explicitly simulated cloud scale turbulence in a variety Of cloud situations. These results can be used to estimate  s and develop expressions for N, q l and f NG as a function of Q 1 In these expressions  s is the term linking the subgrid scale variability in the saturation state of the model grid box to the mean (sub) saturation conditions. It plays the role of rh crit in relative humdity fractional cloud schemes and allows clouds to form when the grid box mean is subsaturated (Q 1 <0)

 s can parameterised in a manner analagous to other subgrid scale correlation terms (i.e. as a vertical diffusion flux) l tke is a length scale from the turbulence scheme and links the cloud terms to the turbulence.  s is a measure of the subgrid scale variability of saturation characteristics in a grid box due to fluctuations not resolved by the model. In HIRLAM  sturb as defined is from (classical small scale) PBL turbulence only. In models at resolutions ~2km this may be the only unresolved variance. But for models at ~>10km we must also include variance due to convective scale and mesoscale circulations.  SFIX uses equation A above with l tke fixed to a free tropospheric value of 250m Lenderink & Siebsma 2000

Cloud Fraction and normalised cloud water as a function of the normalised grid box mean saturation deficit Q 1 If  s is relatively small Cloud Fraction will be skewed Towards fraction 1 (Q 1 >0) or Fraction zero (Q 1 <0). This scenario is okay for very high resolution models (e.g. dx~2km) where only typical boundary layer turbulence is not resolved. At lower resolutions we need to develop parameterisations of mesoscale and convective scale variance (in r and T). We need to include all factors contributing to subgrid scale variance in the term s

Standard cloud schemes (RH based and RH/q l based) exhibit large instability at high vertical resolution, when coupled to a moist TKE mixing scheme. This motivated us to build a statistical cloud scheme within the moist turbulence parameterisation. Cloud amounts and cloud buoyancy contribution to TKE generation are then in phase and resulting simulation is far more stable. Cloud and turbulence simulations Improve at high vertical resolution. But turbulence is a fast process this can lead to Numerical stability problems FIRE-EUROCS 2 day Stratocumulus simulation Using 25m vertical resolution

With high vertical resolution moist CBR plus statistical cloud scheme produces An accurate and stable simulation of cloud water, cloud fraction and drizzle For the FIRE-EUROCS stratocumulusc case

Cloud Fraction Cloud Water (g/kg) TKE Relative Humidity Vertical cross-section of EUROCS Stratocumulus with moist CBR + statistical clouds

Can we use the same statistical cloud scheme to diagnose cloud fraction and Cloud water in ARM-EUROCS shallow cumulus case? Initial results using a seperate treatment for shallow convective cloud fraction and cloud water and ”large scale” clouds. Problem with this approach is deciding which cloud fraction and cloud water to use convective or large scale, it would be easier with a single common estimate of both terms

KNMI LES and HIRLAM 1D cloud water evolution for ARM shallow cumulus case. Kain-Fritsch convection provides tendencies of heat and water vapour. In regions of active convection d/dt CBR are set to zero. Contributions to  s from convection, turbulence and above 2xpblh, turbulence using fixed l tke =250m cloud fraction from statistical cloud scheme, dCW/dt=q l(new) -q l(old) diagnosed from statistical cloud scheme, with RK large scale precipitation active. KNMI LES HIRLAM 1D

HIRLAM and KNMI LES Relative Humidity for ARM shallow cumulus case. Magnitude of RH mixing slightly underestimated leading to slightly less deep cloud in HIRLAM HIRLAM KNMI LES

RH  scu  sturb Variance in s dominated by contribution from Convection scheme.

In the original ARM shallow Cumulus integrations KF convection accounted for mixing of heat and water vapour where cumulus convection was diagnosed. At these points vertical fluxes due to CBR were set to zero. But statistical cloud scheme (within CBR) using the variance terms from both CBR and convection was used to diagnose cloud fraction and cloud water. New integrations here reset all KF convection thermodynamic tendencies to zero. All vertical mixing done only by moist CBR. Using convective & turbulent variance terms for statistical cloud fraction calculation and q l in calculating the non-Gaussian contribution to the buoyancy flux. Relative Humidity KNMI LES Relative Humidity CBR only dz=25m Relative Humidity CBR only dz=12m

Presently cloud scheme very sensitive to small combined errors in over-estimation of vertical flux and saturation state, plus (possible) underestimate of variance near cloud top. But depth and overall character of mixing by moist CBR including skewness term in buoyancy production term not completely wrong!! Cloud Water Moist CBR only 25m Cloud water CBR and KF convection KNMI LES Cloud Water

Without inclusion of KF convection generated variance of s (saturation measure of the grid box), the variance term appears underestimated and the model simulation goes between 0 and 1 too much, with strong evaporation of diagnosed cloud water. More work is needed to understand how to parameterise the variance of water within the moist CBR using the skewness term. RH Moist CBR only and no convective variance of S RH KNMI LES Cloud Fraction CBR only

4 day GCSS period of deep convection and associated cloud fields. Can statistical cloud scheme simulate all cloud types? Cloud Fraction Upper level cloud as observed Convective events

Areas moistened by convective detrainment 4 day simulation with of GCSS deep convection case using KF convection and statistical cloud diagnosis of cloud Fraction and cloud liquid/ice water. Shown is q tot /q sat (T liq ) This area of upper level clouds occurs after convection has ceased and is in a region of subsaturation

Where  s uses the vertical flux Formulation and a fixed l tke =250m Cloud fraction VERY sensitive in free troposphere to magnitude of  s term Which sets Q 1 tern for a given q t -q s (T liq )

 s x10 -4 the 4-day GCSS deep convection case. Cloud fraction and cloud water amounts are very sensitive to free tropospheric variance of s term  SFIX included  SFIX NOT included

Summary Statistical cloud scheme within moist turbulence parameterisation seems a promising way to simulate all cloud types (both fraction and water/ice content) Moreover the simulated clouds are well balanced with the prognosed turbulence and thus allow for stble integrations at high vertical resolution. But the simulated clouds are critically sensitive to the accurate representation of the variance of water variable s around the grid box mean value. While using solely moist turbulent mixing and statistical cloud scheme for all aspects of shallow cumulus mixing and cloud formation is not yet successful, results seem encouraging enough to pursue the idea further. More work is needed to carefully evaluate the skewness contribution to the buoyancy production term in the TKE equation. This will lead to a better understanding/simulation of the mixing length in partially cloudy boundary layers and by impliciation the variance of water term. It may be necessary to calculate mixing lengths and vertical diffusion seperately for clear and cloudy fractions before averaging.