Convective Parameterization Jack Kain and Mike Baldwin OAR/NSSL/CIMMS

What is Convective Parameterization? A technique used in NWP to predict the collective effects of (many) convective clouds that may exist within a single grid element…As a function of larger-scale processes and/or conditions

Eta Grid Points

Why do NWP models need to worry about it? Direct concern To predict convective precipitation Feedback to larger scales Deep convection “overturns” the atmosphere, strongly affecting mesoscale and larger scale dynamics Changes vertical stability Redistributes and generates heat Redistributes and removes moisture Makes clouds, strongly affecting surface heating and atmospheric radiation

How Does the Feedback Occur in a Model? At every grid point, predictive variables change at each time step as a function of a number of processes, including convection…

…when activated, a convective parameterization computes the changes in temperature and moisture (and possibly cloud water, momentum, etc.) that would occur at each vertical level if convection developed in the given grid-point environment for example where tc is a convective timescale, typically 30min to 1hr

How to Parameterize... Relate unresolved effects (convection) to grid-scale properties using statistical or empirical techniques What properties of convection do we need to predict? convective triggering (yes/no) convective intensity (how much rain?) vertical distribution of heating vertical distribution of drying

When, where, and how much... Triggering (always requires positive area on a thermodynamic [e.g., Skew-T Log-P] diagram) - Different approaches 1.) mass or moisture convergence exceeding a certain threshold at a grid point, or 2.) positive destabilization rate, or 3.) perturbed parcels can reach their level of free convection, or 4.) sufficient cloud layer moisture

When, where, and how much... Convective intensity (net heating) proportional to mass or moisture convergence sufficient to offset large-scale destabilization rate sufficient to eliminate CAPE (constrained by available moisture)

When, where, and how much... Vertical distribution of heating and drying determined by nudging to empirical reference profiles estimated using a simple 1-D cloud model to satisfy the constraints on intensity

Quasi-equilibrium schemes Arakawa-Schubert for example Large-scale destabilization rate ~ convective stabilization rate Convective stabilization is achieved by an ensemble of cloud types

Convergence schemes Kuo-type schemes If: Then: atmosphere is conditionally unstable horizontal moisture (or maybe mass) convergence is positive Then: converged moisture is assumed to go up in deep convective clouds (rather than broadscale ascent) convective heating is distributed vertically according to the distribution of T’-T where T’ is the moist adiabatic profile of most unstable air moisture is all condensed out (or a specified fraction is condensed out)

Current EMC models use different approaches RUC II: Grell scheme Eta: Betts-Miller-Janjic (Kain-Fritsch used experimentally) MRF/AVN: Grell-Pan scheme Grell, Grell-Pan, and Kain-Fritsch schemes are Mass-Flux schemes*, meaning they use simple cloud models to simulate rearrangements of mass in a vertical column Betts-Miller-Janjic adjusts to “mean post-convective profiles” based on observational studies

Grell and Grell-Pan Schemes Initiation (on/off) 1.) Find highest qe air in column below ~400mb level…does CAPE exist? 2.) Evaluate CAP strength: Does lifted parcel reach LFC (level of free convection) within 150 mb of its source level? 3.) Is large-scale destabilization rate > 0? (i.e. is d(CAPE)/dt > 0?) If yes to all 3, initiate convection...

Grell and Grell-Pan Schemes Characteristics of convection use simple models of an updraft and downdraft to simulate mass rearrangements by convection make updraft and downdraft mass fluxes strong enough that their stabilizing effect approximately balances rate of large-scale destabilization:

Grell and Grell-Pan Schemes Feeding back the effects of convection Introduce tendency terms in the prognostic equations for temperature and moisture: where a represents T or qv

Kain-Fritsch Scheme Basic operating procedures are similar to Grell-type schemes except… Convective inhibition evaluated in terms of negative area, not pressure depth Large-scale destabilization not required, only CAPE Updraft and downdraft formulations more sophisticated Convective intensity based on instantaneous CAPE value rather than d(CAPE)/dt

Betts-Miller-Janjic Scheme Checks for CAPE, cloud depth, using highest qe air in lowest 130mb above surface makes a “first-guess” at a reference temperature profile based on a moist adiabat makes a corresponding first guess reference profile for moisture based on an imposed sub-saturation (~relative humidity) imposes enthalpy conservation

Enthalpy conservation This usually requires an adjustment to the “first-guess” profiles (“sliding over” on a skew-T) of both T and q Implications of this adjustment: BMJ convection will be weak (or non-existent) when cloud column RH is low even if CAPE exists, increase with intensity as column moistens Nudges grid-scale T, q to convectively adjusted profiles over a ~1h time scale

Kain-Fritsch convective initiation check Beginning at the surface, mix in model layers overhead until a mixture 50-100mb deep is found. This compromises a potential updraft source layer. Find mean q, qv of this layer. Lift a parcel with these characteristics to its LCL. At the LCL, compute a temperature perturbation, DTp based on grid point vertical velocity: DTp = (wg - wc)1/3 + DTp(RH) where wg is the grid point vertical velocity (cm/s), wc is a correction factor wc=2*Z(LCL)/2km

Kain-Fritsch convective initiation check For example: wg - wc=1 cm/s -> DTp=1.0 K wg - wc=10 cm/s -> DTp=2.5 K In the Eta Model, an additional perturbation, DTp (RH) (magnitude ~0.5K) is given to account for low RH So…In a typical convective environment with some larger-scale forcing, DTp ~ 1 - 2 K

Kain-Fritsch convective initiation check Is (DTp(LCL) + DTp) > Tg???? If no, move up one model level and repeat process above If yes, compute a vertical velocity perturbation, Wp, based on magnitude of DTp. For DTp=1.5K, Wp ~ 4-5 m/s

Kain-Fritsch convective initiation check Release a parcel at the LCL with T given by Tp(LCL) and vertical velocity Wp, begin solving “parcel buoyancy equation” at model levels overhead Determine cloud top as highest model level where Wp > 0

Kain-Fritsch convective initiation check Is Z(top) - Z(LCL) > 3km? If yes, initiate deep convection from this source layer If no, remember this layer as a possible source for shallow convection, move up to next potential source layer and repeat all above steps If no potential source layer in the lowest 300mb can generate a convective cloud, move on to next grid point

Stabilizing mechanisms of Kain-Fritsch Convective Updraft removes high qe air from lower troposphere, transports it aloft generates condensation

Stabilizing mechanisms of Kain-Fritsch Convective Downdraft draws mass from layer beginning at cloud base and extending up 150-200mb deposits low qe air in sub-cloud layers assumed to be saturated above cloud base, RH decreasing at ~10%/km below continues until it either 1) reaches the surfaces or 2) becomes warmer than the environment mass flux = updraft mass flux at cloud base

Stabilizing mechanisms of Kain-Fritsch Return flow, i.e., “compensating subsidence” compensates for any mass surplus or deficit created by updraft and downdraft typically the updraft creates a mass surplus aloft and deficit below so that return flow is downward

Kain-Fritsch precipitation amounts It depends… Updraft generates condensation Updraft dumps condensate into environment Downdraft evaporates condensate at a rate that depends on RH of downdraft source air depth of downdraft Any leftover condensate accumulates at the ground as precipitation

Consider some typical convective environments

Negative Precipitation

Shallow convection allowed

BMJ Heating/Drying profiles heating K/hr drying %RH/hr

Increase cloud layer RH by 20%

Deep convection allowed

Heating/Drying profiles

Kain-Fritsch Trigger Increase source layer Td by 1 K some parcels break cap, initiate deep convection updraft path updraft source layer downdraft path

Kain-Fritsch adjusted profile

Heating/Drying profiles

BMJ 1st guess profiles

After enthalply adjustment Deep convection allowed Strong cooling from 850-600mb rainfall = 0.032 cm/h

Heating/drying profiles

Increase cloud-layer RH by 5% Rainfall = 0.211 cm/h

Increase cloud-layer RH by 10% Rainfall = 0.388 cm/h

RH increased 10%

Convective Rainfall vs. Change in cloud-layer RH Precip Amount Change in cloud-layer RH

BMJ Oklahoma Tornadoes Too dry for deep convection can see shallow convection grow with time

BMJ Oklahoma Tornadoes Still too dry 24h fcst valid 5 Oct 98

BMJ Oklahoma Tornadoes Shallow convection cloud top now up to ~650mb

Shallow convection profile Transports moisture upward