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The Nature of the Wind. Why doth ye’ wind blow?. MET/OCEAN apply Newton’s 1 st Law ( applies in fixed frame only ). equations are p.u.m. F = ma. F/m = a. What is acceleration (in terms of velocity)?. D v/ D t = change in velocity/change in time. F/m = D v/ D t .

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slide2

Why doth ye’ wind blow?

MET/OCEAN apply Newton’s 1st Law (applies in fixed frame only)

equations are p.u.m.

F = ma

F/m = a

What is acceleration (in terms of velocity)?

Dv/Dt = change in velocity/change in time

F/m = Dv/Dt

What are the forces acting on an air parcel?

pressure gradient

friction

gravitation

and what else??

Coriolis + Centrifugal (rotational effects)

slide3

Atmosphere is (in part) thermally driven: e.g. 3 Cell Model

H

H

H

H

H

H

polar front

(surface trough)

sinking

(warms)

rising

H

Polar easterlies

convergence

60N

sinking

L

L

sinking

Westerlies

V

divergence

30N

Northeast trades

sfc winds

rising

convergence

Low pressure

(cools)

sfc winds

L

L

Rotating

Non-Rotating

*Studies show 1-cell model unstable

*Uniformly covered with H2O

*development of mid-lat cyclones

*rotating

*ITCZ (convergence/rising motion)

*Sun directly overhead at Eq

*Actual airflow more complicated….

slide4

Just above the top of the boundary layer the atmosphere is close to

geostrophic balance…

1. parcel begins to accelerate due to pgf

pgf

2. Coriolis kicks in (to right of motion)

3. As parcel accelerates, Coriolis increases

low

4. As Coriolis increases balances with pgf

(constant wind – no net force)

high

FCoriolis= pgf

initial unbalanced flow

equilibrium

This balance only applies to ‘straight’ isobars

slide5

What influences the wind in the PBL?

  • Driven by large-scale horizontal pressure/temperature gradients
  • Impacted by surface roughness characteristics
  • Earth’s rotation (Coriolis)
  • Diurnal temperature cycle at the surface (PBL stratification)
  • Entrainment of air above the PBL
  • Horizontal advection of momentum & heat
  • Large-scale convergence/divergence
  • Clouds and precipitation
  • Topography

w

slide6

new equilibrium

no net force

Near the sfc (above sfc layer up to 1 km or so)

Ekman Spiral

Ffr

FCoriolis= pgf

1. Parcel in geostrophic balance.

apply friction

2. Apply friction (disrupt balance).

3. Winds decelerate, Coriolis weakens.

4. PGF causes flow to deflect toward low

pressure.

high

low

5. New force balance established

This balance only applies to ‘straight’ isobars

geostrophic

z

x-isobaric toward low pressure

x

y

slide7

Lower atmosphere is referred to as the troposphere (~ 15 km)

The planetary boundary layer (PBL) is confined to the lower part of the atmosphere (~0-3 km) over which the impact of the earth’s surface can be important.

slide8

The typical atmosphere close to the ground is strongly dependent on solar and terrestrial radiation, reflection, and absorption which in turn depend on cloud cover, terrain properties, cloud thickness, water vapor content and winds.

At night, or as the sun gets low on the horizon, the ground cools and in turn cools the air above. This process continues until sunrise when the characteristic nocturnal inversion (temperature increasing with height) reaches its peak. The largest changes take place during clear, calm and dry atmospheric conditions.

Diurnal variation in atmospheric variables is one of the key characteristics of the boundary layer over land.

Over oceans, the boundary layer depth varies relatively slowly in space and time. Water has a large heat capacity, meaning that it can absorb large amounts of heat from the sun with relative little temperature change.

slide9

Things like frictional drag, solar heating, and evapotranspiration generate turbulence of various-sized eddies

thermally driven

shear driven

z

A good forecast (e.g., wind) is often critically dependent on accurate estimates of surface fluxes

slide10

The planetary boundary layer over land consists of three major parts.

Mixed layer

Unstable conditions with strong upward heat flux from the surface of the Earth and low wind speeds, the planetary boundary layer is associated with buoyant thermals (unstable parcels of air) rising from the surface layer. During these unstable conditions, which usually occur during daytime, the planetary boundary layer is called the mixed layer.

Nocturnal stable boundary layer

Radiational cooling of the air just above surface tend to create a low level inversion with relatively ‘stable’ conditions. The depth where temperatures increase from the surface of the Earth up to the inversion level is called the stable boundary layer and ranges from about 100 m to 500 m deep.

slide11

10 km

Free Atmosphere

1 km

Convective

Mixed Layer

Residual Layer

Mixed Layer

stable boundary layer

surface layer

Noon

Sunset

Midnight

Sunrise

Noon

Residual layer

 The residual layer is the part of the atmosphere where mixing still takes place as a result of air flow, although heat fluxes from the surface of the Earth are small.

The surface layer is the area most influenced by surface properties like heat fluxes etc..much of what I’ll be talking about today is relevant to this layer only.

winds are ~ geostrophic

slide12

1 cm

molecular

transfer

turbulent

transfer

TOTAL EFFECTIVE

TURBULENT

FLUX

0.2

0

K m/s

Turbulence by itself cannot transfer heat (or momentum, moisture) across the interface between the atmosphere / ocean or atmosphere / Earth. There are some other mechanisms responsible for the transport of these variables in the lowest few millimeters of the atmosphere (laminar boundary layer).

Molecular conduction transfers heat between the surface and the lowest part of the atmosphere. Once in the air, turbulence takes over to transport heat to greater depths in the atmosphere. A similar argument applies for the transfer of momentum and moisture in the atmosphere.

slide13

The structure of the atmospheric boundary layer is influenced by the underlying surface and by the stability of the PBL

(same stability)

Surface roughness determines to a certain extent the amount of turbulence production, the surface stress and the shape of the wind profile.

slide14

Stability influences the structure of turbulence. In an unstably stratified PBL (e.g. during day-time over land with an upward heat flux from the surface) the turbulence production is enhanced and the exchange is intensified resulting in a more uniform distribution of momentum, potential temperature and specific humidity.

In a stably stratified boundary layer (e.g. during night-time over land) the turbulence produced by shear is suppressed by the stratification resulting in a weak exchange and a weak coupling with the surface.

slide15

potential temperature

q

NOTE SCALE!

u

wind speed

Entrainment

PBL TOP

inversion layer

LLJ

mixed layer

convective PBL profiles

stable PBL profiles

~200 m

~1500 m

sfc layer

0

~150 m

u

q

u

q

vigorous mixing (sfc heating)

neutral

nightime

(sharper gradients)

radiational cooling

slide16

Why parameterize the low-level PBL wind?

Using a mean wind value for a site will mask the variation in wind speed. As wind power generated depends upon the cube of the wind speed this may seriously affect the estimate of wind power available over a year.

This problem may be overcome by describing the wind speed probability distribution for the year.

Use of statistical tools is difficult (e.g., length of sample can impact on the results – ‘representativeness’)

Data would be more useful if it could be described by a mathematical expression.

Varying levels of urban canopy parameterizations are frequently employed in atmospheric transport and dispersion codes in order to better account for the urban effect on the meteorology and diffusion. Many of these urban parameterizations need building related

parameters as input.

slide17

stationary

‘Representing’ the wind profile

f(stability) 1-D (hz homog)

PBL is often generalized by considering 3 basic stability regimes (in reality not this simple!)

Convective boundary layer (buoyancy generated turbulence, heated surface/sunny conditions)

Stable boundary layer

Near neutral boundary layer(shear/friction generated

turbulence, windy and cloudy)

Look at NNBL (not all that common however!) (ABOVE CANOPY)

Atmospheric boundary layer behavior is a complex function of terrain and soil characteristics, and the vertical fluxes of heat, momentum and moisture. More is known about properties very close to the ground and during neutral stratification than for either highly stable or unstable conditions.

slide18

No net buoyancy

sink

rise

neutral

1.0 km

Tparcel < Tobserved

Tparcel > Tobserved

height

observed lapse rate

(stable)

dry lapse rate

~10 C/km

0.1 km

9

8

11

10

6

12

5

7

temperature (C)

slide19

Power Law Profile (Prandtl)

power law should be carefully employed since it is not a physical representation of the surface layer and does not describe the flow nearest to the ground very well

(i.e. should only be used for heights above the roughness elements where the flow is free)

slide20

Logarithmic Profile Law (NNBL only, or z < 10 m)

Turbulent mixing in the atmosphere may be considered in a similar way to molecular mixing (this is called K theory)

simple laws?

  • The increase of wind speed with height in the lowest 100m can be described by a logarithmic expression (i.e., assumes that the wind variation with height is inversely proportional to the height).

represents the effect of

wind stress on the ground

(depends on sfc and

wind magnitude)

slide21

Both the log law and the power law are simplified expressions of the actual wind profile. They are valid in flat homogeneous terrain.

They do not include the effects of topography, obstacles or changes in roughness or stability.

  • When either of these 2 simple laws do apply, they are intended
  • for the lower part of boundary layer called the surface layer (i.e.
  • lowest ~50-100 m or so but above the canopy and in flat homo-
  • geneous terrain).
  • Wind direction is assumed to change little with height
  • Effects of earth rotation are assumed to be minimal
  • Wind structure is determined by surface friction and the vertical
  • temperature gradient.
slide22

If the atmosphere is not stable, then turbulent eddies will be stretched (unstable) or flattened (stable) which will affect the wind profile.

In situations where the atmosphere is not neutral, the log law equation can be modified by multiplying by a dimensionless coefficient which depends on atmospheric stability.

  • The roughness of a flat and uniform surface can be characterized
  • By:
  • the average height of the various roughness elemenets
  • areal density of the elements
  • shape of the elements
  • flexibility and mobility of the elements

Above too complicated for a generalized and simple description…

Use a couple of characteristics only determined from wind profile

slide23

Roughness Length zo

Usually calculated from a least-square fit of the log wind profile

Won’t work within the ‘canopy’

Varies by over 5 orders of magnitude!

Terrain Classification in Terms of Effective Surface Roughness Length, ZO

ZO (m)Terrain Description (~1/30 height of the roughness elements)

0.0002 Open sea, fetch at least 5km

0.03 Open flat terrain; grass, few isolated obstacles

0.10 Low crops, occasional large obstacles; x'/h > 20*

0.25 High crops, scattered obstacles, 15 < x'/h < 20*

0.50 Parkland, bushes, numerous obstacles, x'/h 10*

0.5-1 Regular large obstacle coverage (suburb, forest)

slide24

In reality, the PBL is more often thermally stratified

(non-uniform temperatures and thus buoyancy mixing is now

important in addition to mechanical)

Similarity Theory…(an extension of the NNBL stuff show previously)

A few of the instruments used to sample the PBL…

  • Portable Automated Mesonet (PAM)
  • Wind profilers
  • Doppler Sodar
  • Tethersonde Atmospheric Sounding System
  • Boundary layer observing tower
  • Surface flux measurement system
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