Physical parameterisations for a high resolution operational Numerical Weather

Physical parameterisations for a high resolution operational Numerical Weather

Prediction model

Luc GERARD

Institut Royal M´ et´ eorologique de Belgique

Th` ese pr´ esent´ ee pour l’obtention du titre de Docteur en Sciences Appliqu´ ees Ann´ ee Acad´ emique 2000-2001

Universit´ e Libre de Bruxelles

Facult´ e des Sciences Appliqu´ ees

Acknowledgements

Merci ` a

M. Jean-Fran¸ cois Geleyn, chef du Groupe de Mod´ elisation et Assimilation pour la Pr´ evision au Centre National de Recherches M´ et´ eorologiqes ` a Toulouse, qui a supervis´ e ce travail et m’a fait b´ en´ eficier de son expertise,

M. Alfred Quinet, chef du D´ epartement de la Recherche ` a l’Institut Royal M´ et´ eorlogique de Belgique, qui a accept´ e d’ˆ etre mon promoteur et m’a permis de trouver un cadre propice ` a ma recherche,

M. Robert Beauwens, chef du Service de M´ etrologie Nucl´ eaire ` a la Facult´ e des Sciences Appliqu´ ees de l’ULB, qui a accept´ e le rˆ ole de co-promoteur et m’a accueilli dans son service, mes coll` egues scientifiques de l’´ equipe ALADIN, en particulier

Doina Banciu de l’Institut M´ et´ eorologique Roumain, Jean-Marcel Piriou de M´ et´ eo-France,

et aux nombreuses autres personnes qui m’ont apport´ e leur aide ` a certains moments.

Plan

• Essential notations

• Introduction

• Part I: General context: Meteorological Modelling and the Arp` ege-Aladin model.

– Chapter 1: Generalities about atmospheric modelling – Chapter 2: The Arp` ege-Aladin local area model – Bibliography for part I

• Part II: Physical parameterisations in operational model Arp` ege-Aladin (excepting convection, treated in part III)

– Chapter 3: Introduction

– Chapter 4: Physics-Dynamics interface – Chapter 5: Initialisations and auxiliary tools

– Chapter 6: Turbulent fluxes and PBL (Planetary Boundary Layer) processes – Chapter 7: Subgrid Dynamic Processes

– Chapter 8: Soil Processes

– Chapter 9: Cloudiness and Large scale precipitation – Chapter 10: Radiation and chemicals

– Bibliography for part II

• Part III: Enhancements to the deep convection parameterization scheme – Chapter 11: Introduction

– Chapter 12: Arp` ege-Aladin deep convection scheme

– Chapter 13: Horizontal momentum entrainment and accounting for cloud-environment pressure gradients

– Chapter 14: Discussion of present scheme

– Chapter 15: Prognostic scheme for convective activity – Chapter 16: Significant Convective Mesh Fraction

– Chapter 17: New scheme tuning and validation in Single column 1D model and in 3D operational model

– Bibliography for part III

• Part IV: General Conclusions

• Appendix A: Arp` ege-Aladin convection scheme implementation details

PLAN

Essential Notations

A advection part of the model

A(η) implicit vertical coordinate definition array A g , A n ground albedo, snow albedo

a earth radius

[] a dry air

[] ad non entraining moist adiabatic ascent

arg soil clay fraction

B(η) implicit vertical coordinate definition array B ν (η) black body Planck function

[] b layer bottom

C condensation

C 1 , C 2 , C 3 surface hydrous coefficients

C M , C H , C nM , C nH surface exchange coefficients for momentum and heat, general and neutral case C T , C G , C V , C N thermal coefficient, for ground, vegetation, snow

C w hydraulic capacity [m]

c sound speed; light speed

c g ground heat capacity

c p , c pa , c pv isobar specific heat, for dry air and vapour c w , c i specific heat of liquid water and of ice CAPE Convection Available Potential Energy

CIN Convection Inhibition Energy

CVGQ horizontal large scale moisture convergence D u , D d detrainment from updraught and downdraught

D

Dt material derivative implying the advection by the mean (large scale) velocity d 1 , d 2 capacities of surface and deep reservoirs

[] d downdraught

E precipitation evaporation flux

E surface evaporation

E kin , E pot kinetic energy, potential energy

E u , E d entrainment in updraught and downdraught e, e sat water vapour partial pressure and saturation value

F evolution vertical fluxes

F _b buoyancy force

F cond , F cond i , F cond l total condensation flux, solid and liquid part of it (under LCONDWT)

F dew dew flux

F evg bare ground evaporation flux

F evi evaporation flux from surface ice reservoir F evl total liquid water evaporation flux

F evn total solid water evaporation flux

F evr evaporation flux from interception reservoir F evv evapo-transpiration flux

F m vertical mass flux

F n snow melting flux

F P vertical mass flux associated to the precipitation flux F pi deep soil freezing/melting flux

F _q ^cdif , F _q ^udif , F _q ^ddif convective diffusion flux of moisture, updraught and downdraught contributions F _q ^detr moisture detrainment flux

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NOTATIONS

F ror , F ros , F rop runoffs from interception, surface, deep reservoirs

F _s ^cdif , F _s ^udif , F _s ^ddif convective diffusion flux of dry static energy, updraught and downdraught contributions F si surface freezing/melting flux

F sP vertical dry static energy flux associated to the precipitation flux F _sp ^k heat flux at underground level k

Fs p saturation fraction of the total reservoir

F tr transpiration flux

F ^V , F V ^u , F V ^d convective diffusion flux of horizontal momentum, updraught and downdraught contri- butions

F _ν ^↓ , F _ν ^↑ descending and ascending radiation fluxes at frequency ν

F _ψ ^ps , F _ψ ^pa vertical flux of variable ψ associated to the pseudo subsidence and the pseudo ascent in the convection scheme.

F † , F thermal and solar radiation fluxes

F ↓ , F ↑ solar diffuse descending and ascending flux F †↓ , F †↑ thermal diffuse descending and ascending flux

F _↓ ^∗ , F _↑ ^∗ difference between black body radiation and thermal diffuse descending and ascending flux

f Coriolis parameter

f V , f H Monin-Obukhov functions G u , G d Gregory-Kershaw coefficients

g acceleration of gravity

[] G grid point location (semi-Lagrangian)

H normalized mountain height

H effective obstacle height

H 0 diurnal wave e-folding depth

HU, HQ Weighting coefficients respectively for saturating and air moisture in surface moisture computation

¯

h (pseudo) enthalpy

h Planck constant

h = s + Lq moist static energy

h s standard deviation of unresolved orography

[] h top of the layer

I b Vertically integrated buoyancy based on a non entraining saturated adiabatic ascent from the lowest buoyant layer

I ν monochromatic radiation intensity

[] i ice

J vertical turbulent diffusion flux J a dry air vertical turbulent diffusion flux

J h moist static energy flux from the turbulent diffusion scheme J _h ^meso enthalpy flux from the mesosphere

J _q ^conv , J _s ^conv water vapour and dry static energy fluxes from the convective scheme J q or J _q ^turb ,

J s or J _s ^turb , J ^V or J V ^turb

water vapour, dry static energy and horizontal momentum fluxes from the turbulent diffusion scheme

J v water vapour vertical diffusion flux

K _du , K _dd drag coefficients for prognostic updraught and downdraught

K hydraulic conductivity

K m , K h , K ψ eddy exchange coefficients (momentum, heat, or any K u , K d detrainment rates

k = 1 _z unit vector in upward direction

k Boltzmann constant

k 4ν absorption / diffusion optical depths k νabs , k νdiff ,

k νemis , k νext

monochromatic radiation absorption, diffusion, emission, extinction coefficients [] k iteration index; underground layer index

L Linear part of the model

L Monin Obukhov length; latent heat; lift volumetric force

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NOTATIONS

L, L, [] L , [] _L Lowest full model level and its lower interface L, L v , L v−w ,L v−i ,

L w−i

latent heats, condensation (generic), vaporisation, sublimation, melting l, l, [] l , [] _l full model level, lower interface of model level

l m , l h mixing lengths, for momentum and heat

` condensed water specific contents

d` radiation path segment

lai leaf area index

M Model

M detr total detrained moisture over the vertical

M u , M d updraught and downdraught absolute mass fluxes [] M medium point of semi-Lagrangian trajectory m = ^∂π _∂η vertical pressure divergence in η coordinate

N Non linear part of the model

N e , N w Brunt-V¨ ais¨ al¨ a frequency, based on θ e and θ w

N s surface Brunt-V¨ ais¨ al¨ a frequency

n, n s , n c total, large scale (“stratiform”) and subgrid (“convective”) cloudiness [] O origin point of semi-Lagrangian trajectory

P , P s , P con , P LS precipitation flux, surface value, convective (subgrid) and large scale scheme parts P i , P w solid (snow) and liquid precipitation fluxes

P ˆ non hydrostatic pressure departure

P ie fraction of the surface evaporating in ice phase

P n , P nc fraction of the ground covered by snow, and value to use in thermal calculations P ng cfr P n , but possibly taking into account accumulation on the slopes

P nv snow fraction covering vegetation P wsi ice fraction in the surface reservoir

p true pressure (p = π in hydrostatic model) p t , p b top and base pressure levels of an active cloud [] p deep soil value; air parcel

[] ps , [] pa pseudo subsidence and pseudo ascent (so-called compensative subsidence and ascent)

Q heat (flux)

Q 1 , Q 2 , Q 3 convective tendencies: sensible heating, latent heating, momentum tendency Q lat = Q wlat + Q ilat surface latent heat flux (liquid water and ice)

Q R net radiative heating

Q sens surface sensible heat flux

q specific moisture due to water vapour contents

q a dry air specific contents

q c = q cs + q cc total condensed water contents sum of large scale (“stratiform”) and subgrid (“convec- tive”) contributions

q cl , q ci liquid and solid condensed phases q c max maximum sustainable water contents 4q exc potential water vapour excess q w , q i liquid water and ice specific contents

R moisture convergence modulation factor accounting for mesh size

R i Richardson number

R, R a , R v perfect gas constant, for moist air, dry air and water vapour R s , R smin , R s max surface resistance to water transfers

r snow to water ratio; water vapour mixing ratio

RH relative humidity

S n snow reservoir

S _ν ⁰ direct parallel radiation at frequency ν S ψ source term in budget equation for ψ s = c p T + φ dry static energy

[] s surface value

[] sat saturation value

sab soil sand fraction

T temperature

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NOTATIONS

T d , T w , T v dew point temperature, wet bulb temperature, virtual temperature T s , T p surface temperature, deep soil temperature

T t water triple point temperature

t, 4t time, time step

U projection of the altitude wind on the effective surface wind

u wind zonal velocity

u ∗ scaling velocity

u f s zonal component of effective surface wind

u s see v _s

[] u updraught

V = (u, v) horizontal wind

v _{f s} , v _s effective surface wind – v _s in case of isotropic subgrid orography

[] v water vapour

veg, veg _a vegetation fraction, part of it not covered by snow veg _e efficient vegetation fraction for convective precipitation W work; reservoir contents (kg/m ² )

W p , W p max (deep and) total reservoir contents and capacity

W pi total ice reservoir

W r , W r max interception reservoir contents and capacity

W s , W s max , W seq surface reservoir contents, capacity, equilibrium contents

W si surface ice reservoir

w = ˙ z vertical velocity in z coordinate

w reservoir volumetric specific contents (m ³ /m ³ ) w fc deep reservoir volumetric contents at field capacity

[] w liquid water

x zonal coordinate; reduced coordinate x = z/H for soil depth

4x horizontal mesh size

4x _k underground layers thicknesses

y meridian coordinate

Z scale height for the decrease of the mixing length l m

z upwards metric (geopotential height) coordinate z 0 , z oH roughness length, heat roughness length

z ^V , z T PBL standard height for wind observation (10m) and temperature (2m).

α snow snow rate for convective precipitation partition

β semi-implicit coefficient; diffusivity factor (radiation); GCVBETA

Γ l ratio of the turbulent vertical flux of horizontal momentum at level l to the flux at the surface (orographic drag).

γ auxiliary variable, c pv − c w|i , or R a /cpa, see context

γ ⁰ pseudo-mass coefficient

δ land land-sea mask (=1 on land) δ m NDPSFI mass conservation option δ stab stability indicator in PBL scheme

δ stab , δ _stab ^↓ convective activity indicator, for updraught and downdraught

δ ν optical depth

δ ^↓ , δ ^↑ optical thicknesses for the parallel descending and ascending (reflected) radiation fluxes δ ^†↓ , δ ^†↑ optical thicknesses for the thermal descending and ascending radiation fluxes

emissivity; ratio R a /R v

n , g , f emissivities of snow, bare ground and ground free of snow

η hybrid vertical coordinate

θ phase angle; zenithal angle

θ, θ e , θ w potential temperature, equivalent potential temperature, wet bulb potential temperature

κ von Karmann constant

λ wave length; thermal conductivity

λ m , λ h asymptotic mixing length, for momentum and heat λ u , λ d entrainment rates for updraught and downdraught

µ ^R

_R ^−R

a

; cinematic viscosity

µ = cos θ cosine of direct radiation zenithal angle

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NOTATIONS

ν wave frequency ; dynamic viscosity

ξ (auxiliary variable)

π hydrostatic pressure; π number

π s surface pressure

ρ, ρ a , ρ v density, for dry air, for vapour

ρ n density of the snow

σ Stefan Boltzmann constant

σ c , σ u , σ d , σ e convective mesh fraction, updraught, downdraught, environment

τ transmissivity coefficient

τ = 86400s diurnal period

τ, τ s turbulent vertical flux of horizontal momentum, surface value Φ(ψ), [] Φ Physical part of the model

φ geopotential; azimuthal angle

ϕ latitude

ψ relevant model variable

ω = ˙ π vertical velocity in hydrostatic pressure coordinate ω 0 = 2π/τ diurnal pulsation

ω _c ^∗ = ω c − ω e draught relative vertical velocity ;

ω u , ω d , ω e (pressure) absolute vertical velocity for updraught, downdraught, environment ω

∧

∗ = σ u ω _u ^∗ , ω

∨

∗ = σ d ω ^∗ _d

updraught and downdraught relative mass fluxes

$ ν simple diffusion albedo

† long wave (earth) radiation

short wave (sun) radiation

[] ⁰ , [] ⁺ , [] ⁻ time t, t + 4t, t − 4t

NOTATIONS

Introduction

Operational Numerical Weather Prediction (NWP) models are nowadays a vital component in the preparation of weather forecasts. Such models solve numerically the equations of fluid mechanics, starting from given initial conditions and using some simplifying hypotheses.

Model fields are only computed at discrete points of a mesh, the values at these grid points representing the mean value of the fields over the area of the associated grid box. The size of the grid box is the model spatial resolution.

Forecasts longer than 2 or 3 days require the use of a global model (i.e. covering the whole earth), and subsequently the assimilation by the model of observation data over the same area. Seen the limited ground observation network, satellite information is also an important element helping to represent realistically the initial state of the atmosphere.

The mass of data to treat increases with the horizontal and vertical extension of the model, but also with its resolution; and end-users are generally more concerned by local features of the weather than averages over large areas.

Computer power has from the beginning imposed limitations on the extension in time and space and spatial resolution of the predictions – operational functioning imposes to produce results in reasonable time, at least in advance over the predicted phenomena.

In order to reach higher resolution over the regions of interest, the following two solutions are common practice:

• the use of variable mesh global models, where the mesh is finer over some regions;

• the use of overlapping models, where Local Area Models (LAMs) are computed with a high resolution, while receiving boundary conditions from a global model or a wider LAM.

LAMs are used essentially to provide short term (up to 2 days) forecasts with high resolution over a small domain.

The model we were working on – Arp` ege-Aladin – is a LAM receiving its initial state and boundary con- ditions from the global area model Arp` ege , which itself has a continuously variable mesh, with its highest resolution over France.

The equations describing the evolution of mean quantities also contain source terms, representing the aggre- gate effect of processes occurring at scales smaller than the mesh size. As the small scale processes play in fluid mechanics an essential role in energy dissipation, they cannot be ignored; but by definition, no detailed information is available about them.

The solution is to parameterize these “subgrid” phenomena, building physical representations which translate the statistical effects of subgrid phenomena on the mean large scale fields. As there is by definition very little information available at subgrid scale, the only choice is to approximate the global behaviour of small scale processes with, beside the large scale mean, subgrid statistical information (about orography, soil, vegeta- tion, and climate) and using generally tunable parameters. This is the role of the “physical part” of the model.

Parameterization proceeds locally, treating information over the vertical of each grid point, independently of the model horizontal geometry. This allows to develop packages usable at various scales. For instance, the LAM Arp` ege-Aladin uses the same physical package as the global model Arp` ege .

The quick progression of the computing power and the arrival soon of second generation METEOSAT weather satellites which should deliver more precise observation data, makes that LAMs of always higher resolution can be used.

This increasing resolution – also resulting in smaller time steps – implies specific adaptations of the physical

parameterisations, as the hypotheses made for large grid boxes loose their validity when the size of the boxes

INTRODUCTION

becomes comparable to the size of convective clouds systems – i.e. a few km.

In this resides the main objective of this work: the physical parameterisations developed for the global model Arp` ege , which were also used in Arp` ege-Aladin , need now to be reviewed for the high resolution.

Even though the essential adaptations concern the deep convection scheme, our work also describes all param- eterisations of the operational model, as the convective scheme is a part of a bigger ensemble, and must be seen in relation to this ensemble.

Part I reviews the general notions of meteorological modelling, focusing on the way they are used in the Arp` ege-Aladin model and in our own developments.

In part II we bring a needed contribution to the model documentation, with a description of all operational physical parameterisations other than deep convection.

Part III focuses on the deep convection scheme. After a general description of the present state of the scheme – with a separate chapter on the treatment of horizontal momentum which was one of our contributions – we discuss different features of the scheme and move it to a wider context, also comparing it with the Arakawa- Schubert scheme.

Our goal being to apply the model to increasing resolutions, we analyse the limitations of the present scheme which should be solved for this purpose.

We then introduce two developments proposed in the discussion: the introduction of prognostic variables for convective activity, and the consideration of significant convective mesh fractions.

Validation of these modifications and behaviour assessment experiments in single column model and for two cases in 3D model at different resolutions – including tests with the global Arp` ege model – are then presented.

A third development – the introduction of prognostic condensed phases – was found very suitable, but it is presently under study by other people.

Beside these enhancements, the reduction of the mesh size below 7 km normally requires to leave the hydro-

static approximation in the dynamics. There are then two additional large scale model variables, and their

potential exploitation in the physical package is quickly envisaged in the conclusions.