Mountain Meteorology

Naresh KumarMountain Meteorology Cell,

National Weather Forecasting Centre

What is mountain meteorology

It is the branch of meteorology that focuses on the weather and climate of orographic regions.

Orography is the term used to describe undulations on the surface of the Earth of any size and shape, from small hills to major mountain ranges that span continents.

When the winds encounter orographic barriers, lee waves come into the picture.

Lee waves, in meteorology are waves in a stream of air when the wind moves over mountains.

Cont….Usually a horizontal turbulence is generated at the lee side of the first mountain (following the air stream), so called rotor (circulation of flow about a horizontal or nearly horizontal axis that is usually associated with flow over the lee side of a barrier, such as a mountain range).

Lee waves always occur in groups on the lee side of mountains. In totality, we get the activities in hilly region in the following figure:

Where mountain has been shown by 1, flow of wind by 2, rotor by 3, lee waves by 4 and typical clouds by 5 & 6.

Mountain Wave Turbulence

Cont…

Produces the most violent turbulenceOccurs in two regions to the lee of mountains:

a) Near the ground and

b) Near the tropopause

Turbulence at and below mountain top level is associated with rotors

Turbulence near tropopause associated with breaking waves in the high shear regions just above and below trop

Orographic lift

Orographic lift occurs when an air mass is forced from a low elevation to a higher elevation as it moves over rising orographic barriers.

As the air mass gains altitude it quickly cools down adiabatically (Adiabatic changes in temperature occur due to changes in pressure of a gas while not adding or subtracting any heat),

which can raise the relative humidity to 100% and create clouds and, under the right conditions, precipitation.

Cont…

Effects of orographic lifting are: Precipitation

Rain shadowing

Leeward winds

Associated clouds

Cont…

Precipitation:

Precipitation induced by orographic lift occurs in many places throughout the world.

Examples include:The windward slopes of Khasi & Jayantia Hills see over 11000 mm (Mawsynram located about 15 km north-west of Cherrapunji in the state of Meghalaya) of rain during the Southwest Monsoon SeasonThe Western Ghats that run along India's western coast.

Cont…Rain Shadow:The highest precipitation amounts are found slightly upwind from the prevailing winds at the crests of mountain ranges, where they relieve and therefore the upward lifting is greatest.

As the air descends the lee side of the mountain, it warms and dries, creating a rain shadow.

On the lee side of the mountains, sometimes as little as 25 km away from high precipitation zones, annual precipitation can be as low as 200 mm per year. e.g. The Himalayas block moisture from the Tibetan Plateau.

Cont…Leeward winds

Downslope winds occur on the leeward side of mountain barriers when a stable air mass is carried over the mountain by strong winds that increase in strength with height. Moisture is removed and latent heat released as the air mass is orographically lifted. As the air mass descends, it is compression heated. The warm foehn wind (A warm dry wind coming off the lee slopes of a mountain range, especially off the northern slopes of the Alps) or Nor'wester depending on the region,

Cont…Associated clouds:As air flows over mountain barriers, orographic lift can create a variety of cloud effects.

Orographic fog is formed as the air rises up the slope and will often envelope the summit. When the air is humid, some of the moisture will fall on the windward slope and on the summit of the mountain

Rotor cloud is sometimes formed downwind and below the level of the ridge. It has the appearance of the cumulus cloud type but it is caused by a turbulent horizontal vortex, i.e. the air is very rough.

Fundamentals of mountain wavesI. Basic forces that give rise to gravity waves are buoyancy (Archimedes'

principle states that a fluid will exert an upward force on an object immersed in it equal to the weight of the fluid displaced by the object) restoring forces.

II. If a stably stratified air parcel is displaced vertically (i.e., as it ascends a mountain barrier) the buoyancy difference between the parcel and its environment will produce a restoring force and accelerate the parcel back to its equilibrium position.

III. The energy associated with the buoyancy perturbation is carried away from the mountain by mountain waves.

IV. Mountain waves forced by mountains often ‘breakdown’ due to convective overturning in the upper levels of the atmosphere, in doing so exerting a decelerating (to reduce speed) force on the large-scale atmospheric circulation, i.e., a drag.

V. The basic structure of a Mountain wave is determined by the size and shape of the mountain and by vertical profiles of wind speed and temperature.

VI. A physical understanding of gravity waves can be got using linear theory, i.e., the gravity waves are assumed to small-amplitude.

Mountain Waves under Stable Conditions

Inviscid (flow without friction), Adiabatic Governing Equations

kBDt

uD ˆ

0Dt

DB

0 u

Conservation of

momentum

energy

mass

ukBDt

uD

2ˆ

BDt

DB 2

Flow Past an 2D Obstacle

)(xhzx

huw

)(xhz

xz

)(0 xhznu on

n

Linear gravity-wave theoryAssumptions:•Consider two-dimensional airflow in an x-z plane over a ‘ridge’•Waves are linear, i.e. small amplitude•Ridge is sufficiently narrow that the Coriolis force can be neglected•WKBJ assumption: scale heights of background quantities such as density, temperature, and velocity, are longer than a gravity wave vertical wavelength.•Steady-state•Boussinesq flow: density differences are sufficiently small to be neglected, except where they appear in terms multiplied by g•Atmosphere is inviscid

Cont…

022

2

2

2

wlz

w

x

w

See Smith 1979;Houze 1993; Palmer et al. 1986

Scorer parameterU

Nl

z

U

UU

Nl

1

2

2

2

22

The linearized momentum equation can be reduced to a single equation for the vertical velocity

)(zU is the speed of the basic state flow)(zN is the Brunt-Vaisala or buoyancy frequency

Cont…kxhh sin0

Lk /2

222 klm

Consider an infinite periodic ridge in which i.e. sinusoidal terrain

is the horizontal wavenumber with L the width of the ridge

)(Re mzkximzkxi BeAew Solutions to the previous momentum equation can be written as

A and B are complex coefficients and Re denotes the real part

is the vertical wavenumber

iklm 22 NLUlkBeAeew zzikx /or Re

NLUlkBeAew mzkximzkxi /or Re

Defining

the solution may be written as

kxAew z sin

)sin( mzkxAw

Upper boundary condition implies B=0

Radiation condition implies B=0 (i.e., the perturbation energy flux must be upward)

Cont…k>l (i.e. narrow-ridge case)

(or equivalently U/L>N, i.e. high frequency)Evanescent solution (i.e. fading away)

k<l (i.e. wider mountains) (or equivalently U/L<N, i.e. low frequency)

Wave solution

0wu

•waves decay exponentially with height•vertical phase lines•no momentum transport

•energy/momentum transported upwards•waves propagate without loss of amplitude•phase lines tilt upstream as z increases

)sin( mzkxAw kxAew z sin

Durran, 2003

Mountain flow regimes

•linear/flow-over regime (Nh/U small)

Non-dimensional height: Nh/U U: upstream velocityh: mountain heightN: Brunt-Vaisala frequency

•non-linear/blocked regime (Nh/U large)

Non-dimensional mountain length: NL/UL: mountain length

h

•waves cannot propagate (NL/U small)•waves can propagate (NL/U large)

Flow processes governed by horizontal and vertical scales (in absence of rotation)

Thanks