The Nature of the Wind

Talk Outline

A. Big picture (Why the wind blows)

B. The global circulation

C. Large-scale force balance above the boundary layer

D. The planetary boundary layer (PBL)

i. wind

ii. friction

iii. turbulence (mechanical and thermal)

iv. structure and stability

E. Wind parameterization

F. Surface characteristics

G. Recent work

PBL

atmosphere

3 km

How do we identify areas/regions that are favorable for wind energy (commercial)?

Are there certain features associated with wind-prone regions (e.g., terrain, water, etc.)?

GLOBAL CIRCULATION

General Circulation: Conceptual Models of the Atmosphere

*non-rotating rotating

*Uniformly covered with H2O

*Sun directly overhead at Eq

higher tropopause

sfc winds sfc winds

GOOD MODEL?

Hadley Cell

Low pressure

high

high

*thermally driven

isobars

or…. How thermal energy is redistibuted in the atmosphere

ok for tropics maybe…

p = RT?

sfc winds

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

rising

sinking

rising

sinking

*Uniformly covered with H2O

*Sun directly overhead at Eq

divergence

convergence

convergence

sfc winds

H H H

polar front

30N

60N

(surface trough)

*Studies show 1-cell model unstable

*ITCZ (convergence/rising motion)

LL

*development of mid-lat cyclones

Northeast trades

Polar easterlies

Westerlies

(cools)

(warms)

H

H H H

LL

*Actual airflow more complicated….

sinking

low pressure

Non-Rotating Rotating

Reality…

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.

80-90% of the mass of the atmosphere is in the troposphere!

from Doswell

Looking at the lowest 2 km…

winds ~ geostrophic

planetary boundary layer

wind turbine

increasing friction

Above the top of the boundary layer the atmosphere is close togeostrophic balance…

high

low

FCoriolis= pgf

pgf1. parcel begins to accelerate due to pgf

2. Coriolis kicks in (to right of motion)

3. As parcel accelerates, Coriolis increases

4. As Coriolis increases balances with pgf

initial unbalanced flow equilibrium

(constant wind – no net force)

This balance only applies to ‘straight’ isobars

Not quite this simple in reality as geostrophic balance does not describe how we arrive at a balanced flow!

Assume constant PGF

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

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

low

FCoriolis= pgf

high

apply friction

new equilibriumno net force

1. Parcel in geostrophic balance.

2. Apply friction (disrupt balance).

3. Winds decelerate, Coriolis weakens.

4. PGF causes flow to deflect toward low pressure.

Ffr

5. New force balance established

Ekman Spiral

This balance only applies to ‘straight’ isobars

zgeostrophic

yx

x-isobaric toward low pressure

Assume constant PGF

isobars

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

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

zshear driven (e.g., nighttime,cloudy/stable daytime conditions)

thermally driven

high reflection!

more absorption

DAYTIME BOUNDARY LAYER

Noon NoonSunset SunriseMidnight

1 km

10 km

Free Atmosphere

surface layer

ConvectiveMixed Layer

Mixed Layer

stable boundary layer

Residual Layer

Residual layer

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

The surface layer (~lowest 10% of PBL) is the area most influenced by surface properties like heat fluxes etc..much of what I’ll be talking about coming up is relevant to this layer only.

winds are ~ geostrophic

radiational cooling

peak heating

similar characteristics

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

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

(same stability)

increasing roughness length

“no-slip lower boundary”

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.

well-mixed

Wind speed increases with height more rapidly in a stable PBL

deep mixingshallow/less mixing

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 (e.g., for modeling/parameterizations).

Provides estimates of the wind speed (at a level and locale) where none exists

Ultimately will help with the ‘siting’ of wind instrumentation

Why parameterize the low-level PBL wind?The wind profile can be, to a first order, be represented by simple relationships (combo of empircal and physical!)

Power Law Profile (Prandtl)

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

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

zR = height of uR (~10 m)

f(friction)

D typically taken to 0

NWS winds

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).

Logarithmic Profile Law (NNBL only)

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

represents the effect of wind stress on the ground

(depends on sfc and wind magnitude)

simple laws?

u*/k ~ uRln(zR/z0)

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.