Page 1© Crown copyright 2005 Parametrization of the effects of Orography Andy Brown.

© Crown copyright 2005 Page 1

Parametrization of the effects of Orography

Andy Brown


Outline

Effects of small-scale hills on the (area-averaged) boundary layer Drag

Effective roughness length parametrizations Recent developments and alternative approaches

Other effects

Parametrization of the effects of larger-scale hills – and effects on the boundary layer

Small scale hills Wavelength less than around 6km – typically to short to excite gravity waves Usually within boundary layer (but not SBL?)


Turbulent form drag and its parametrization


Turbulent form drag

Neutral, inviscid flow over a hill would give perturbations in phase with the hill and hence no drag

BUT stress perturbations close to the surface displace streamline perturbations downstream, and lead to a pressure drag

Linear theory (e.g. Belcher et al., 1993)

Use of enhanced “effective” roughness lengths to represent the effects of turbulent form drag in many NWP models

4

2 2*

( )2

( )m

pi

u hF u

u h


Experimental support for effective roughness length approach

Grant and Mason (1990) Llanthony valley, South Wales Flow normal to approximately 2D ridges

Hignett and Hopwood (1994) Caersws, Mid-Wales Flow over approximately isotropic 3D hills

Both experiments suggested that area-averaged wind profile over hills was logarithmic and consistent with enhanced roughness length total stress (shear stress plus pressure drag) on surface


Hignett and Hopwood (1994) : Caersws

Flat case U = (u*/k) ln(z/z0)

Hilly case U = (u*

eff/k) ln(z/z0eff) (above crests but still within BL)


Calculation of effective roughness lengths

Total force on surface = turbulent stress + pressure drag ~ undisturbed turbulent stress + pressure drag

(1)

Well above hills, have quasi-homogeneous bl and

(2)

Assume that at a height hm (which increases with hill wavelength), (2) is valid, wind is unchanged from undisturbed value and is related to undisturbed stress through log-law with vegetative roughness length

(3)

From (1) and (3), can calculate z0eff

*

0

logeff

eff

u zu

z

*0 *

0 0

log logeff

m meff

u h huu

z z

2 2 2

* * *0eff

px pxu u F u F Pressure dragparametrizationrequired


Initial tendency BL budget (pre-z0eff)

-BL tendency Dynamics-BL tendency


Momentum Budget Residuals

Budget Residual Jan 95 New Gravity Wave Drag

–low level wave-breaking

–flow blocking

–trapped lee wavesEffective roughness

Budget Residual Dec 93


MSLP Zonal Mean Errors - Day 3

Zonalisation offlow prior toGWD & ORchange in

Jan95


Improvements in Global Model PerformanceDay 1 MSLP RMS errors & model cycles

G10

New GWD

O.Rough

G14

4Adv

CMT

1D-Var

TOVS

G27

New Dynamics

HadAM4 Physics

G33

4D-Var

G19

3D-Var ATOVS

G32

AIRS

G34

HadGEM1 Physics

G15

Resol.

60km

30L


More recent work on form drag parametrization


Recent work

What about stability effects? Can effective roughness length parametrizations possibly

work in shallow SBLs when the whole concept of hills being immersed within the boundary layer might break down?

Effects of gravity waves in the stable boundary layer? Are ‘long-tails’ in boundary layer representing some of the

effects of orography?

Directional effects in regions of anisotropic topography?

Possible replacements for effective roughness length parametrizations


Stability effects

Effects of low hills

Flow speed-up and surface drag as a function of stability - theory, observations, numerical modelling

Additional effects of larger hills

How do non-linear effects such as separation, drainage currents, pooling of cold air in valleys affect the drag?

Are effective roughness length still a useful concept for parametrization?

Are waves within the stable boundary layer a significant issue?


Linear theory for effects of stability on speed-up and drag

Neutral results for flow speed-up and drag

Effects of stability (Hunt, Richards and Brighton, 1988; Belcher and Wood, 1996)

Consider effects due to changes in undisturbed velocity profile and surface stress, changes in h

m, and also dynamic buoyancy effects on

perturbations in the outer region.For moderate levels of stability, dominant effect is increase in shear across middle layer increasing speed up and pressure drag.For higher stabilities increasing shear effect may be `capped' by middle layer depth reaching boundary layer top. Dynamic effects of buoyancy in outer region then decrease speed up and pressure drag.

0

0

20

0 0

( ') ( ') ( )

( ') ( ) ( ')

m

i

u z u z u hS

u z u h u z

4

2 2*

( )2

( )m

pi

u hF u

u h


Experimental results on speed-up

Both Frank et al., 1993 and Coppin et al., 1994 found fractional speed-upincreasing above neutral value for moderate stabilties, then appearing to asymptote to a constant value at higher stabilities


Neutral Stable

Variation of pressure drag withstability affected by similar considerations (Belcher and Wood, 1996). This variation is not currently well-represented in NWP parametrizations.

Numerical results for effects of stability on speedup and drag

Consistent with theory and observations

Extend to bigger hills. Large number of numerical simulations performed varying

stability hill height hill wavelength spacing (packed or isolated) 2D ridges / 3D hills


Streamfunction from example stable simulation (surface buoyancy flux = -0.001m2s-3) as a function of time

Interval = 10 m2s-1

between 0 and 50 m2s-1,50 m2s-1 thereafter.Regions with streamfunctionnegative are shaded.


Flow over isolated 2D ridges

Form drag remains significantin stable conditions - absolutevalues comparable to the neutral values for slopes up to 0.3

For bigger slopes, get somereduction compared to neutralvalue (more noticeably with packed ridges when get pooling of stagnant air in valleys)

BLACK: NEUTRAL; BLUE: STABLE


tau13 from simulations of flow over packed 2D ridges of varying heightWavelength = 2000 mSurface buoyancy flux of -0.0005 m2s-3

20m hill 300m hill


Results from simulations of flow over packed 2D ridges of varying heightWavelength = 2000 mSurface buoyancy flux of -0.0005 m2s-3

Horizontally averaged stress Boundary layer depth


Boundary layer depth is similar to (slightly smaller than) that expected for a homogeneous boundary layer with the same surface temperature and momentum flux.

Encouraging for the use of effective roughness length parametrizations

For homogeneous boundary layer, expect depth to scale as (u*L/f)1/2

(Zilitinkevich, 1972). Try normalizing hilly boundary layer depths using this scale (where u* and L are calculated using total momentum flux at surface i.e. Pressure drag included).


STABLE NEUTRAL

Parametrization of total drag on ridges

BLUE LINE : drag on flat surface (z0=0.1m) as a function of stability

RED LINE : total drag on ridged

surface (z0=0.1m) with p-t-h of 200m as a function of stability

GREEN DASHED : drag on flat surface with enhanced roughness (z0

eff=1.0m) as a function of stability

Effective roughness length independent of stability would not be too bad an approximation


Waves within the stable boundary layer

Repeat of simulations of stable boundary layer flow over a low ridge, but with wind no longer normal to ridge

= 2 km, Peak to trough height = 20 m, Boundary layer depth = 350 m



Force on surface follows cosine squared variation (as neutral) except when component of flow across ridge becomes small enough to allow waves

Force is then much bigger



This case not stable enough for waves

Phase lines of vertical velocity plot vertical

Mean flow momentum flux small through most of boundary layer



Magnitude of cross-ridge component of flow reduced so that Froude number is now small enough to permit waves

Phase lines of vertical velocity plot slope

Mean flow momentum flux significant throughout boundary layer, and consistent with surface pressure drag (star)


Stability Effects Summary

Fractional speed-up and non-dimensional drag both increase at first with increasing stability due to the increasing shear, then decrease due to dynamical stability effects

The area-averaged boundary layer remains reasonably similar to that over a homogeneous surface, suggesting that an effective roughness length approach to parametrization remains promising

Always likely to excite waves in the SBL from ridges (Fourier modes) aligned closely parallel to the wind. Are these a significant player in the momentum budget?

Are ‘long tails’ commonly used in SBL parametrizations implicitly representing effects of orographically-induced gravity waves and/or of enhanced turbulent mixing due to drainage currents etc.?


Experiment in region of anisotropic topography

Loch Cluanie, Scottish Highlands

Deliberately chosen as a region of approximately 2D orography (E-W ridges)

Horizontal scale 5-9 km

Peak-to-trough height 600 m


Experiment in region of anisotropic topography

Composite near neutral sonde profiles for cases with flow within 30 degrees of parallel and normal to ridges

Parallel : blue (18 cases) still have logarithmic profile effective roughness of 8 m

Normal : red (23 cases) deeper logarithmic layer (>2

km) effective roughness of 47 m


Directionally dependent drag

How does the drag on an infinite two-dimensional ridge depend on wind direction?

Is this infinite ridge limit a relevant one in reality? How elongated does a hill have to become before it acts as

an infinite ridge? Are the Caersws or Loch Cluanie results more typical?


Drag on anisotropic 3d hills

How anisotropic does a hill have to become before it acts like a two-dimensional ridge?

Consider ellipsoidal hills and independently vary

wind direction aspect ratio of hills (=1 for

isotropic hill; infinity for 2D ridge)


1) For isotropic hillsthe magnitude of thedrag is independent ofwind direction

2) For 2D hills, the magnitude of the drag is a strong function of wind direction (approx. cosine squared of angle between wind andnormal to ridge)

3) With an aspect ratioof 2, the results alreadylie closer to the 2D ridgeresult than they do to theisotropic hill result


Directional Effects Summary

Directional dependence rapidly becomes important as an isotropic hill is elongated into a ridge

For low hills, can recover this result by taking 2D FFT of the 3D orography, and summing the 2D drag results

NWP application? Could make effective roughness length a function of wind direction to

capture some of the directional effects Effects might still be fairly weak, as even if subgrid orography locally

looks quite anisotropic, it is likely to look more isotropic again if averaged over a larger area


Why move away from effective roughness lengths?

Rather indirect parametrization (so, for example, difficult to link to gravity wave parametrization)

To leading order, scalar transfer should be unaffected by small-scale hills. However, effective roughness lengths significantly reduce the near-surface winds, and have to use effective scalar roughness lengths to “undo” this effect

<Wind>

<Stress>Flat simulation z0=0.1m

Area-averages from hilly simulation, h=400m, =3000m, z0=0.1m

1d simulation z0eff=25m


Wood et al. (2001)

Extra orographic stress term added to momentum equations with orographic stress profile specified using surface pressure drag parametrization and exponential decay (on scale related to wavelength)

Able to provide required orographic drag without excessive slowing of near-surface winds

Currently under test at Met Office

Variant of scheme (Beljaars et al., 2004) with further simplifications to allow implicit solving within the boundary layer scheme under test at ECMWF

/z lx pxF e min ,

3izl


Other effects of small scale hills


Orographic effects on heat and moisture

Currently many NWP models have no (explicit) representation of the effects of subgrid orography on heat and moisture transports

Should they have? Altered large-scale cloud and precipitation in region of significant

subgrid orography? e.g. Leung and Chan (1998), Terra (2004)

Effects of orography on convective triggering (forced ascent; elevated heat source)?

Investigate through simulations across a range of resolutions (climate → O(2km))

European Alps Maritime Continent


Parametrization of the effects of larger-scale hills


Gravity waves and flow blocking

In this talk, have deliberately concentrated on the effects of boundary layer scale hills

In principle, gravity wave and flow blocking parametrizations represent the effects of larger scales and different mechanisms

In practice, issues inextricably linked Lack of knowledge of relative importance in reality of different scales

and mechanisms to drag Implicit tuning of one scheme against another Did effective roughness lengths look so important in the Met

Office model due to the lack at that time of a low-level flow blocking scheme?

Numerical interactions e.g. flow blocking and boundary layer schemes acting in the same place (and solved separately)


Gravity waves and flow blocking

Higher level flow passes over mountain and produces

propagating gravity waves

Low level flow deflected around mountain – flow

blocking

From Lott and Miller, 1997


Angular momentum budget

January 2001, 31 ECMWF 24 hour forecasts SSO incorporates parametrized torque due to gravity waves and

flow blocking Significant compared to BL torque, especially at low resolution Apparently optimum BL torque may depend on how we parametrize

SSO torque (and vice versa)

January 2001 T159

-40

-20

0

20

40

Bud

get t

erm

s (

1018

Nm

)

90N 90SEq

AMFCRESSSOBLResidual

January 2001 T511

-40

-20

0

20

40

Bud

get t

erm

s (

1018

Nm

)

90N 90SEq


Importance of different scales

Variation of resolved orographic drag on Alps with model resolution (125km to 4km)

Further similar studies planned to provide further information on the relative importance of different scales and mechanisms

e.g. get to high enough resolution to explicitly model effects of boundary layer scale hills and larger scale hills at the same time

Smith et al. (2005)


Key questions

What should be the relative importance of different scales and mechanisms (flow blocking, gravity waves, turbulent form drag, boundary layer drag over flat terrain)?

Can the numerical implementation be improved?

Effects of subgrid orography on clouds and moisture – should we be doing more?

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