© crown copyright met office parametrization of “physical processes” in the metum – overview...

© Crown copyright Met Office

Parametrization of “physical processes” in the MetUM – overview for Exoplanets Workshop

Steve Derbyshire

Met Office, Atmospheric Processes and Parametrizations


Contents

This presentation covers the following areas at an “overview” level

• Introduction

• Flow over/round orography

• Basic ideas of cloud schemes

• Large-scale precipitation

• Convection in a mass-flux scheme

• *Radiation

• Boundary Layer


Needs for “physics”: (1) diagnostic

• Some physical processes need representation in order to forecast elements of the weather itself: Clouds, precipitation, screen-level temperatures, near surface winds. Effectively a diagnostic requirement.


Needs for physics: (2) prognostic• A physical processes can alter the way in which the dynamics

behaves. For example, heating rates affect temperature and hence the dynamics

• Physical processes balance the dynamical processes that ‘move’ the atmosphere around.

• They are an integral part of the prognostic atmospheric system, moving heat, moisture and momentum. Illustration from a cloud scheme change (impact on BL stability and 1000-500hPa thickness):


Subgrid and other physics

• Some of these processes are represented in the model because they act (nonlinearly) on scales smaller than the grid resolution (convection, boundary layer turbulence, orographic drag).

• Other processes (microphysics, radiation) would need to be represented regardless of model resolution

The net effect of the convection on the larger-scales need not be represented when convection can be explicitly resolved.

But precipitation generation and radiative impact still needs to be represented


1. Flow over (or around) orography


How does the UM “see” the real orography?(1) explicitly via the mean orography

• Mean = model grid-box average of a real orography source dataset

• In the example below the model resolution is 80km

• this was at the time our global operational forecast resolution (at 30N)

• the grid-box mean is thus the average of 4 source orography heights

Dotted = source dataset

Solid = UM mean orography

GLOBE = dataset used since 2002

US Navy = dataset used up to 2002

Section along 29N

Himalayas


How does the UM “see” the real orography?(2) via the sub-grid orographic parametrizations

• Turbulent form drag scheme

• deals with scales up to ~5km

• Flow-blocking & gravity-wave drag scheme

• deals with scales from ~5km up to the model grid-scale

• need to represent the drag associated with the sub-grid mountains that “stick up” into the model domain above the resolved orography.

GLOBE at 29N


The turbulent form drag scheme

• Represents the extra drag exerted on the flow within the boundary layer due to small-scale hills

• The effect of the sub-grid hills is represented via either:

1. An effective roughness length, which is bigger than the usual vegetative value (Grant and Mason, QJRMS 1990)

2. An additional explicit turbulent stress term within the boundary layer (new for UM vn 6.2)

• The drag exerted on the flow with these two approaches is the same

• Currently the effective roughness length parametrization is used operationally


• Sub-grid mountain height, h= 2

= standard deviation of sub-grid orography

, U and N are averaged over z=0 to z=h

(total) = UNh2

• U= wind perpendicular to major axis of the orography

=(tuneable) wavenumber

The flow-blocking & gravity-wave drag scheme

dh

(total)

(GWD)

z=0

t


dh

(total)

(GWD)

• Calculate blocked layer depth t= U/(NFc)

• Fc is Froude number (=U/Nh) at which flow-blocking is first diagnosed

(GWD)= (total) x (t/h)2

• GWD = gravity wave drag

• Drag to due layer of air flowing over the mountain

• Drag deposited where wave breaking diagnosed

• Typically the lower stratosphere

(blocked flow) = (total) - (GWD)

• Remaining drag (~80% of total) attributed to flow around the mountain

• drag deposited uniformly from z=0 to z=h

z=0

t


2. Cloud schemes and subgrid variation“Clouds are proverbially lawless” – K.Clark, Civilisation


Old large-scale cloud scheme (Smith 1990)

• Represents the condensation/evaporation process as a diagnostic parametrization (essentially pdf of a measure of total water excess over saturation)

aL [qT – qsat(TL)]

Latent heat adjustment

0

G

Cloudy

Clearl dl

aL [1-RHc] qsat(TL)


New cloud scheme (PC2)

• Now adopted for NWP and climate

• PC2= Prognostic cloud and prognostic condensate (i.e. carry forward in time both cloud amount and liquid water etc. as model prognostic variables)

• Better handling of precipitation processes etc.

• Does not require prior assumption of distribution (such as Smith’s triangular pdf)

• E.g. precipitation terms narrowing the distribution by removing the “high end”


3. Large-scale precipitation(“explicit microphysics”)


Large-scale precipitation

• The task of the large-scale precipitation scheme is:

• To model precipitation processes by the removal of water on the grid-scale and the effect of latent heat

• To update ice contents by microphysical processes

• Developed by modelling transfer processes between water phases.

• Representation of transfers comes from both cloud physics theory and observations.


How does the large-scale precipitation scheme work?

• The scheme acts on model columns.

• Within each box, vapour, liquid and ice contents are updated due to microphysical processes.

• Rain and Snow are passed out of a box to the next one down.

• Which processes do we represent?

T

l

q

i

Rain, Snow

T

l

q

i

Surface Rain or Snow


Microphysical conversions

Example: DepositionH H

O

H HO

H HO Ice crystals grow by diffusion of

supersaturated vapour onto their surface.If we represent an ice particle as stationary and spheroidal we can precisely solve the diffusion equation for its growth.

If we assume a particle size distribution, mass-size relationships, fallspeed-size and ventilation relationships then we can estimate the bulk transfer of vapour to ice.


4. Convection


The key function of the convection scheme is the subgrid-scale vertical transport of

• Heat (helping to regulate T-profile)

• Moisture (including precipitation)

• Momentum

• Also provides a convective cloud amount

• Strong interaction with the boundary layer.

• Results from cloud resolving models are increasingly used to support development of the convection scheme


Simple updraught plume carrying a simple scalar

[Notional bulkupdraught plume]

Environmental tendency: (d/dt)conv= M(p –) – Md/dz(detrainment) + (subsidence)

M-profile:dM/dz=(-)M

Plume values: dp/dz=(-p)

Entrainment

Detrainment

Mass flux M

Scalarp

subsidence


Mass flux formalism: (basis of current Met Office convection scheme)

• Bulk saturated updraught Mu and downdraught Md “plumes” (+ mass-compensating subsidence in “environment” - outside clouds)

• Assumes vertical transports can be attributed to the mass fluxes in each category (with associated “parcel properties” of , q etc.) Updraughts (and downdraughts) entrain mass from environment (with environmental scalar values)…

• … and detrain to environment at plume values


Moist stability

• Convection terminates when updraft “parcel” no longer buoyant (less dense than environment)

• Condensation latent heating the key driver in maintaining parcel buoyancy against dry static stability

• Parcel calculation influenced by precipitation, entrainment and other physical assumptions

• Generically Convective Available Potential Energy CAPE is a height-integrated measure of parcel buoyancy relative to environment

Environmentalbuoyancy

Parcelbuoyancy

CAPE (schematic)


Mass flux profiles in a range of humidities – idealized modelling

CRM SCM (UM4.5)

Derbyshire et al., QJRMS (2004) – EUROCS Special Issue

25%

RH=90%

25%

90%


Single-step example of “adaptive” convection

mass flux (control) mass flux (adaptive)

Model level

Adaptive detrainment is a simple statistical model for partial detrainment of a cloud ensemble as it loses buoyancy (Derbyshire et al. QJRMS 2011)

Detrainment linked to fractional decline in buoyancy excess v

ex


First climate tests of adaptive detrainment – J.Rodriguez

1-year annual mean precipitation

Adaptive mod improved Tropical W. Pacific with benefits to Pacific wind-stress

Results essentially borne out by more systematic climate- and NWP-validation

Observations

HadGAM1 control

HadGAM1 with adaptive detrainment


5. Radiative transfer


• Our (Edwards-Slingo) radiation scheme represents the effect of solar and thermal radiation on the temperature structure of the atmosphere and surface.

Sun T ~ 6000K, peak wavelength in visible ~0.5m

Earth T ~ 300K, emissions peaking in IR ~ 10m

Hence two essentially separate bands: “short” and “long” waves

• Radiation parametrization strongly grounded in well-understood physics of radiative transfer. So what are the big challenges?

• Efficient and accurate representation of the process with limited computing resources

• getting the correct inputs (primarily in terms of cloud amounts and structure).


Radiative ProcessesReflection

Scattering

Absorption/Emission

TransmissionEnergy in incoming radiation = Energy in scattered radiation.

Only direction haschanged.

If energy is absorbeda transformation ofenergy occurs.

Transmitted = Incoming –Absorbed – Scattered back.

Emitted radiation is at wavelengths determined by the temperature.


Gaseous Absorption

• Radiative quantities depend on frequency and direction.

1. Slow variations: Rayleigh Scattering, Planck function

2. Fast variations: Gaseous Absorption

• We cannot afford to model this frequency dependence accurately in a GCM.

• Hence parametrize in terms of bands Frequency

band


k-terms

Within a band there is a distribution of absorbances. We can model this by using a discretised frequency distribution of these absorbances.

Wavelength

Abs

orpt

ion

Abs

orpt

ion,

ki

Frequency of occurrence, fi

+

τi = fi ki r z

i=n

i=1

Optical depth Path length

Mixing ratio of absorber


6. Boundary Layer Turbulence

θ

Thermal Instability

Shear: <v>2 < <v2> Can drive turbulence.

SW heating

LW cooling

Turbulent transport:Heat flux; moisture flux; drag.


Role of the boundary layer

• Accurate representation of the BL in NWP is:

• Crucial for forecasting near-surface weather parameters (temperature, wind, visibility)

• Boundary layer drag important for evolution of synoptic scale features (lows, fronts, etc)

• Vertical structure of the BL important for formation and persistence of low cloud and fog

• The BL is the interface between the surface and the atmosphere

• Impact on global budgets by moderating the surface fluxes of heat and moisture


Physical Basis of BL Scheme

• Some BL parametrization needed to represent unresolved vertical turbulent fluxes of heat, moisture and momentum

• Fluxes can often be represented as diffusion down a gradient

• Strategy is to use Large Eddy Simulation (validated against limited observations) to diagnose appropriate diffusivities and their dependence on quantities known in the GCM (mean fields)


Boundary layer type

• Diagnose type of boundary layer

• 7 types

• Split between stable and unstable

• Cumulus capping?

• Extent of mixing driven from surface or within clouds


Boundary layer types in the UM


Boundary layer parametrization first order turbulence closure, mixing adiabatically conserved variables

Unstable boundary layers

• Strong transport by eddies on the scale of the layer depth motivates a non-local formulation

• Existence and depth of unstable layers diagnosed initially by moist adiabatic parcels (ascent and descent)

• Diffusion coefficients, ‘K-profiles’, are specified functions of height within the boundary layer, related to the strength of the turbulence forcing (formulation developed from large-eddy simulation data).

• Two separate K-profiles are used: one for surface sources of turbulence, one for cloud-top sources.

• Vertical extent of the K-profiles is adjusted to limit the buoyancy consumption of turbulence energy in cloud-capped BLs is

• Mixing across the top of the boundary layer is through an explicit entrainment parametrization. This is coupled to the radiative fluxes and the dynamics through a sub-grid inversion diagnosis.

• There is an additional non-local flux of heat.


Boundary layer parametrization

Stable boundary layers

• Stability limits the vertical transport of energy, motivating use of a closure based on local gradients

• HADGEM uses SHARPEST functions for the stability dependence which give less mixing at a given stability than before

Explicit coupling from BL to the convection scheme

• Diagnose cumulus convection using the mean humidity profile

• If cumulus diagnosed then:

• Cap the boundary layer scheme at convective cloud base

• Trigger the convection scheme in order to parametrize transports from cloud base upwards


Unstable Boundary Layers

• Transports are dominated by large eddies (plumes/thermals)

• Use specified vertical profiles of diffusivity (large eddies are insensitive to local gradients) driven from surface or cloud-top.

• Fluxes in convective BLs can be against the mean gradient

• special non-gradient term (currently used for heat but a generalised form is being developed)


Stable Boundary Layer

• Turbulent flux is entirely down gradient.

• Key factor is ratio of stabilizing buoyancy relative to destabilizing wind shear – represented by Richardson number (Ri).

• In existing scheme diffusivity is function of Ri.

• Alternative schemes are being explored with an explicit dependence on, eg, boundary layer depth and surface heterogeneity.


There are both diagnostic and prognostic requirements for “physics”. UM parametrizations cater for:

1. Sub-grid scale nonlinear effects of small-scale dynamical processes

• Orography

• Convection*

• Boundary layer

2. Physical processes distinct from the dynamics

• Cloud microphysics

• Convection*

• Radiation

Summary


Drivers and barriers in UM “physics” development

• Drivers for UM physics development:

• intrinsic physical accuracy (traditionally important for climate)

• performance accuracy against observations (correct forecasts and climatologies) – including those of our collaboration partners!

• Barriers (or at least complications!)

• interactions with other model components

• “appropriate complexity” requirement given: computer speed and storage, available real-time info about the atmospheric state and the requirement to be robust in all situations.

• We evaluate against: a wide range of observations, research models, and forecast or climate tests.


Supplementary slides..

© crown copyright met office parametrization of “physical processes” in the metum – overview...

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