2Thematic Outline of Basic Concepts What is a convective parameterization?What are the key tenets of convective parameterization?How are these tenets manifest within selected popular convective parameterizations?What impact(s) do differences between convective parameterizations have upon model forecasts?What is a cloud-cover parameterization?
3“An Overview of Convective Parameterization” – David Stensrud Additional Reference“An Overview of Convective Parameterization” – David Stensrud
4What is Convective Parameterization? A technique used to predict the effects of sub-grid scale convective clouds upon the model atmosphere in terms of known model variables.Objective: to define moist convection…In the right place……at the right time……with the correct evolution and intensity……and with the correct impact upon its environment!
5General FormulationDetermine whether the model atmosphere at a given grid point supports moist convection.If so, generate moist convection.Note that this can occur even if sub-saturated on the grid scale; saturation may be seen between grid points.Subsequently, mimic the impacts of the moist convection upon its environment.
6Importance of Moist Convection Vertical redistribution of heat and moisture.Produces precipitation, beneficial or devastating in nature.Associated cloud cover impacts the radiation budget.Spatial gradients in convective heating impact the Hadley and Walker circulations, monsoons, and ENSO.Organized convective systems are often associated with high-impact weather and can substantially impact larger-scales.
7Simplified Perspective Control on moist convection; feedback to large scale.In reality, however, smaller-scale processes are also important in triggering moist convection!
8Types of Moist Convection Deep, moist convectionExamples: thunderstorms, stratiform precipitationLarge vertical extentAssociated with large-scale low-level convergence and deep conditional instabilityPrecipitation dries the environment through the removal of water vaporPrecipitation warms the environment through compensating subsidence warming(Stensrud)
9Types of Moist Convection 2. Shallow convectionExamples: cumulus cloudsShallow vertical extent (< 2-4 km)Non-precipitating in natureTurbulent mixing within clouds cools and moistens the top of the cloud while warming and drying its bottomCloud shading impacts the radiation budget (notably within the planetary boundary layer)(Stensrud)
10Why Convective Parameterization? Think to the typical scales of moist convective activityParameterizations typically employed for ∆x ≥ 5 kmConvection crudely resolved for 1 km ≤ ∆x ≤ 5 kmLikely need ∆x ≈ 100 m to truly be able to explicitly resolve moist convection (G. Bryan)
11Model NomenclatureA mesoscale model simulation that explicitly resolves moist convection is said to be convection-permitting.A model simulation that utilizes a convective parameterization is said to be convection-parameterizing.
12Convective Parameterization Tenets Activation: what determines the triggering of convection?Intensity: how strong is the triggered convection?Vertical Distribution: how are the vertical profiles of temperature, moisture, and momentum modified in response to the convective activity?
13Overarching Principle: Energy CAPE: convective available potential energyMaximum energy available to an ascending parcel as determined via parcel theory (i.e., no explicit consideration of entrainment or detrainment).CIN: convective inhibitionEnergy necessary to lift a parcel pseudoadiabatically from its starting level (SL) to its level of free convection (LFC)LFC: level above which parcel is positively buoyant
16Convective Parameterization Approaches Deep layer control: ties convective development to the creation of CAPE by large-scale processesLow level control: ties convective development to the removal of CINMany convective parameterizations have properties of both approaches
17Trigger FunctionsThe criteria that determine when and where convection is activated within the model.Based upon what the parameterization developers though was important for convective development.Differ substantially between individual convective parameterizations!
18Trigger Functionsdeep layerlow levelSlide 88 of Stensrud
19Selected Considerations Deep versus shallow convection parameterizationSome schemes parameterize both.Others, however, only parameterize one or the other.Why consider them differently? They impact the environment in unique ways! (see again slides 8-9)What environmental fields are impacted?Most parameterizations modify heat and moisture fields.Selected parameterizations also modify momentum fields.
20Selected Considerations How are the convective fields modified?Budget-based studies using field program data give us insight into how convection modifies its environment.Static schemes: use these data to define reference post-convective profiles, one or more of which the model atmosphere can be modified toward over a period of time.Dynamic schemes: use these data to define analytical expressions for how convection modifies its environment.
21Budget-Based InsightFor more details on the apparent heat source and moisture sink, see alsoSlide 32 of Stensrud
22Budget-Based InsightDeep moist convection (blue): warms and dries at all levels, particularly between hPa.Slide 34 of Stensrud
23Budget-Based InsightStratiform precipitation (yellow): cools and moistens low levels while warming and drying upper levels.Slide 35 of Stensrud
24Selected Considerations Scale-related considerations…Convection triggered by large-scale, well-resolved phenomena is relatively easy to parameterize.Convection triggered by smaller-scale phenomena, namely unresolved phenomena, is difficult to parameterize.Related idea: geostrophic adjustment between the mass and latent heating fields (see class text for more).Convection initiation depends upon all scales – thus, parameterizations must be flexible in their design.
25Convective vs. Microphysical Parameterization Models with ∆x ≥ 5 km generally employ both.Both types of parameterizations can produce precipitation…Convective: does not require grid scale saturationMicrophysical: does require grid scale saturationAs a result, a model often carries two precipitation fields…Parameterized / convective“Resolved” / non-convective
26Convective vs. Microphysical Parameterization Which type of precipitation dominates is a function of the meteorological phenomenon being studied…Mesoscale convective system: generally convective along leading edge, non-convective behindMid-latitude cyclone: generally convective in warm sector, non-convective elsewhereIt also depends upon the specific formulation of the parameterizations being used by the model.
27Convective vs. Microphysical Parameterization mesoscale convective systemwintertime mid-latitude cycloneConvective % of rainNote the widely disparate solutions as a function of time, convective parameterization, and meteorological event!
28Convective vs. Microphysical Parameterization Most convective and microphysical schemes do not directly interact with one another.Both act on and modify the same atmospheric state and thus interact indirectly over time.However, at a given time, they generally do not directly impact each other.
29Practical ExamplesFirst example: large-scale differences manifest by the choice of convective parameterizationEvolution of a Mei-Yu monsoon-related coastal front between China and Taiwan during 2003Shaded: 2-m temperature (warmer colors = warmer)Barbs: 10-m winds (half: 5 kt, full: 10 kt)Contour: sea-level pressure (hPa; every 2 hPa)
34Practical ExamplesSecond example: differences in precipitation forecast amounts and skill as a function of parameterization12 km simulations of a springtime convective systemOBS = observationsEX = explicitBM = Betts-MillerKF = Kain-FritschGR = GrellAK = Anthes-KuoNote the differences both as a function of time and as a function of the parameterization!
35Practical Examples36 km simulations of three warm-season convective systems, now looking at bias scores…EX = explicitBM = Betts-MillerKF = Kain-FritschGR = GrellAK = Anthes-KuoAgain, note the differences both as a function of time and as a function of the parameterization!
36Practical Examples These examples are of warm-season convection. The results presented in these examples are sensitive to the type of event considered as well as the model configuration used within the study.Therefore, care must be taken when generalizing the results of these (or your own!) studies.
37Parameterization Construction We now describe the characteristics of three popular convective parameterization schemes.There exist many more; please refer to the class text or other resources for references to such schemes.For these three schemes, we focus upon describing their trigger functions, how they modify the environment, and how they compute precipitation.These general themes apply generally to other schemes!
38Anthes-Kuo SchemeTrigger: column-integrated moisture convergence in the presence of conditional instabilityImpact: relaxes the temperature profile toward a moist adiabat chosen to provide necessary heatingSlide 38 of Stensrud
39Anthes-Kuo SchemePrecipitation: fraction of moisture convergence that is precipitated and used to heat the atmosphereProblem: moisture convergence does not necessarily result in convective activity!Thus, this scheme is presently used only to illustrate the basics of convective parameterization.
40Betts-Miller(-Janjic) Scheme A large-scale quasi-equilibrium schemeDeep, moist convection consumes CAPE as quickly as large-scale processes create CAPE.In this regard, is a deep layer control scheme.Trigger: CAPE > 0Includes quantification of cloud depth to determine whether shallow or deep convection is possibleSubsequently determines convective initiation and impacts based upon reference profiles
41Betts-Miller(-Janjic) Scheme Reference profiles are based upon similar soundings structures obtained from tropical convection.Structure: temperature and moistureJointly modify profiles in order to conserve total enthalpy.Is the modified reference moisture profile drier than the observed profile?If yes, precipitation occurs! Activate convection and nudge the temperature and moisture profiles to the reference profile over a typical convective time scale (~1 h).If no, rainfall does not occur!
42Betts-Miller(-Janjic) Scheme Slide 51 of Stensrud
43Betts-Miller(-Janjic) Scheme If precipitation does not occur and/or the cloud depth is sufficiently shallow (< 200 hPa), activate the shallow convection parameterization.This also acts to relax the temperature and moisture profiles to enthalpy-conserving reference profiles.As expected, warms and dries the lower half of the cloud while cooling and moistening the upper half.
44Betts-Miller(-Janjic) Scheme (Note: reference profiles are again the darker black lines.)Slide 53 of Stensrud
45Betts-Miller(-Janjic) Scheme Precipitation: vertically-integrated measure of moisture excess (compared to environment)As a consequence, very sensitive to moisture content!Mathematical formulation:pt is the pressure at the top of the cloudpb is the pressure at the bottom of the cloudqr is the reference profile specific humidityq is the grid point specific humidityτ is the time scale of convective adjustment
46Kain-Fritsch Scheme Trigger: both low-level and deep layer aspects… Low-level: CIN, sub-cloud mass convergence (equivalent to the vertical mass flux)Deep layer: presence of CAPEIs a dynamic scheme, where the impact of convection upon atmospheric fields is handled using mathematical equations (and not reference profiles).Works in conjunction with microphysical schemes, unlike many other convective parameterizations.
47Kain-Fritsch Scheme Consider both updrafts and convective downdrafts. Both phenomena interact with the environment via entrainment and detrainment.Convection is activated if the parcel is deemed to overcome its CIN and thus be able to reach its LFC.
49Kain-Fritsch SchemeActivated convection has a given updraft mass flux.For this updraft mass flux, determine the downdraft mass flux that can be produced via evaporation.Subsequently, increase the value of the updraft mass flux (controlling convective intensity) until it is able to achieve the desired impact upon the environment.For this scheme, this is a 90% reduction in CAPE.Other atmospheric fields are modified to bring this about.
50Kain-Fritsch SchemeNote: time scale is a function of the horizontal grid spacing and velocity in the cloud layer. Thus, the Kain-Fritsch scheme is influenced by the horizontal grid spacing it is used with in the model!Slide 70 of Stensrud
51Kain-Fritsch SchemeConvection is said to be shallow only if the cloud depth is sufficiently small (< m, temperature-dependent).Precipitation: P = ESE = precipitation efficiency, or the ratio of precipitation to the amount of water that can be precipitatedS = sum of vertical vapor and liquid fluxes 150 hPa above the LCL
59Open Questions Aerosol effects upon convection (seeding, etc.) Horizontal grid spacingParameterizations are often tuned for grid spacings ≥ 20 km but are needed down to ∆x = 5 km.Interactivity with other parameterizationsHow to best represent the trigger function?
60Open Questions Issues with convective system propagation Not always handled well by parameterizations.Impacts synoptic-scale to climate-scale simulations.Issues with representing the Madden-Julian Oscillation, a convectively-driven phenomenonModification of momentum profiles in addition to temperature and moisture profiles
61Open Questions Issues with precipitation amounts Better representation of maximum precipitation amountsOverprediction of light precipitation amountsEven as the field moves toward convection-permitting simulations for mesoscale applications, we are a long way away from being able to do so for synoptic- to climate-scale applications!Thus, we cannot neglect this aspect of the model system moving forward, much as we may want to do so!
62Cloud-Cover Parameterization With high-resolution, cloud-resolving models, it is possible to reasonably assume that an entire grid box is either cloudy or cloud-free.For larger-scale weather and climate models, however, this assumption is not reasonable.Thus, the cloud geometry within each grid box must be parameterized to aid in properly computing the radiation and surface energy budgets.
63Cloud-Cover Parameterization Geometric cloud properties to consider include...How much of the three-dimensional grid box is covered by cloud, both in the horizontal and in the vertical?How do clouds overlap in the vertical?A cloud-cover parameterization operates under the assumption that clouds may exist on the sub-grid scale even if the grid-scale is subsaturated.Most cloud-cover parameterizations only consider the horizontal cloud fraction.
64Cloud-Cover Parameterization Over the grid increment, q < qs.On the sub-grid scale, however, q ≥ qs at certain locations.How to properly assess cloud cover and its impacts in such a scenario?
65Cloud-Cover Parameterization There exist multiple methods for parameterizing cloud-cover.Method 1: diagnostic relationships between relative humidity and sub-grid cloud coverEx: Sundqvist et al. (1989)…where C = cloud fraction and RHcrit = a specified RH above which cloud is assumed to form0 ≤ C ≤ 1 for RHcrit ≤ RH ≤ 100%
66Cloud-Cover Parameterization There exist many permutations of this method…Slingo (1980, 1987): cloud type and altitude variabilityXu and Randall (1996): inclusion of non-RH predictorsMethod 2: specify the sub-grid PDF for RHDistribution can be symmetric or non-symmetricCan also include temperature influence upon saturationSolution is only as good as the specified distribution!