dynamical meteorology

8/10/2019 Dynamical Meteorology

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Teaching Week 1 Dynamical Meteorology Page 1of 6

Teaching Week 1 - Dynamical Meteorology

Just as water flows in a stream, wind flows over the Earth's surface in a similar a fashion. Smoothflow is a preference however we all know that due to mountains and other obstructions wind flows aresubject to many local variations some of which can be hazardous to the control of a pilot's aircraft.

1.1 Measurement of Wind

Obtaining a true measurement of surface wind speed and direction is difficult owing to the roughnessof the ground, the type of surface and the proximity of buildings as well as the Stability of theatmosphere (See Teaching Week 4 - Stability of the Atmosphere).

1.1.1 Surface Roughness

The surface over which the wind blows affects its speed. Rough surfaces, such as areas with treesand buildings, will produce more friction and turbulence than smooth surfaces such as lakes or opencropland. The greater friction means the wind speed near the ground is reduced.

(Source: http://www.energy.iastate.edu/renewable/wind/wem/wem-08_fig08)

The approximate increase of speed with height for different surfaces can be calculated from thefollowing equation:

v2= v-! x (h2/h1)n

where v., is the known (reference) wind speed at height h., above ground, v2is thespeed at a second height h2, and n is the exponent determining the wind change. Values for n arelisted in the following

table for different types of wind cover. If the wind comes across a fallow crop field, you do not have toreach as high for greater wind speeds as you would in a forest or suburb.

ground cover n

smooth surface ocean, sand .10

low grass or fallow ground .16

high grass or low row crops .18

tall row crops or low woods .20

high woods with many trees suburbs, small towns .30

Here is an example of how this method is used. Suppose you are interested in buying ananemometer and have taken measurements for a year with a wind speed instrument on a 3 metretower in an area of low woods. The average speed is 19 km/h. You want to estimate the speed at theplanned 10 metre height of the standard World Meteorological Organisation (WMO) anemometermeasurement.

In your calculation v is equal to 19 km/h, h., is 3 metres, and h2is 10 metres. Since your surroundingsconsist of low woods, the correct value for n is .20. Plugging these values into the formula, theaverage wind speed at 10 metres is:

v2= 19km/h x (10m/3m)20


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v2= 19 x (3.33)20

v2= 19 x 1.27

v2= 24.17 km/h

Again, this method only provides a rough estimate of wind speeds, not a precise value, it is mostuseful when using average and not instantaneous wind speeds. In addition, this formula should only

be used for relatively flat terrain because hills and mountains often have unpredictable influences onwind characteristics.

Lastly, within dense vegetation, such as a forest or an orchard, a new effective ground level isestablished at approximately the height where the branches of adjacent trees touch. Below this levelthere is little wind in a dense cornfield, this height would be the average corn height. In a forest, itwould be the average height of the tree canopy, and so on. When using the wind speed equation allheights should be expressed above the effective ground level.

1.1.2 Trees and Buildings

Trees and buildings are the most common obstacles to wind in the vicinity of potential site for

measuring wind speed and direction. They act to disturb the air both upwind and downwind of theobstruction by reducing wind speed and increasing turbulence.

(Source :http://www. energy. iastate.edu/renewable/wind/wem/wem-08_power. html)

1.2 Wind and Pressure

The building blocks of meteorology are based upon the relationship between pressure and wind,

(commonwealthBureau of Meteorology, 2003 Aviation Meteorology, Wind p47)

1.2.1 Buys Ballot's Law

Large scale wind flow and the relationship to pressure can be described via the Buys Ballot law. If anobserver stands with back to the wind the lower pressure is on the right in the southern hemispherewith comparatively higher pressure on the left. This law was formulated in 1857 by the Dutchmeteorologist Buys Ballot.

This law only applies to large scale wind flow and becomes invalid for smaller scale wind flows likekatabatic winds and sea and land breezes. (See Teaching Week 7 - Mesoscale Meteorology).

1.3 Coriolis Force

An apparent force is created as a result of the Earth's rotation. This apparent force deflects the wind


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from a straight path across the Earth's surface. This force is known as the Coriolis force, named afterthe French mathematician.

The principle is the same on the earth. Moving objectswill appear to have been deflected to the left in thesouthern hemisphere and to the right in the northernhemisphere. The deflections are imperceptible for

objects like footballs travelling short distances, butthey are important over long distances. Correctionshave to be made for artillery shells, for example, orthey will not hit their target. Pilots must also makenavigational corrections to their flight plans.

The atmosphere spins with the earth as though it werea solid body. If it didn't there would be extremely strongwinds, particularly at the equator, where a point on theearth is moving at 1670 km/hr because of the earth'srotation.

(Source: How to Forecast, Bureau of Meteorology)

Any movement of the air relative to the earth is thewind. If a parcel of air at point X in the southernhemisphere moves towards the equator, it is moving toregions where the movement of the earth is greaterand, to a person on the earth, the parcel of air willappear to be moving more slowly, and so have beendeflected westward. Conversely, if the parcel of airmoves toward the pole, it is moving to areas where themovement of the earth to the east is slower, and so the

air is apparently deflected eastwards, once again to theleft of its direction of motion. In the northernhemisphere, the deflections are to the right.

1.3.1 Properties of the Coriolis Force

it acts perpendicularly to the direction of motion; deflecting motion to the left in the southernhemisphere and to the right in the northern hemisphere.

it is directly proportional to the wind speed; zero when the air is stationary and at a maximum whenthe wind speed is at a maximum.

the magnitude depends on latitude; such that it is zero at the Equator and a maximum at thepoles.

Consider the difference between say 15 and 30 degrees south (1613 - 1446 = 167 km/h) and thedifference between 75 degrees south and the pole (432 - 0 = 432 km/h). The deflection is clearlygreater closer to the South Pole.

The Coriolis force -2Q x VRacts at right angles to the direction of motion and has the components offorce:

Cx= 2 v Sin - 2 w Cos

CY= 2 u Sin

Cz= 2 u Cos where = the angular speed of rotation of the Earth = 7.292 x 10-5

s-1

and u =zonal velocity, v = meridional velocity and w = vertical velocity and = latitude.


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1.4 Pressure Gradient Force

The differences which exist between high pressure and low pressure areas on the Earth's surfacedrive the movement of air. The greater the pressure difference, the greater the pressure gradientforce is, which in turn means air will move in a faster fashion.

the cause of air movement is an unequal horizontal pressure distribution; the excess pressure

at one

point causing air to move away from it in the general direction of lower pressure.

isobars are lines of equal pressure and are shown on a mean sea level pressure (MSLP)analysis.

distance between the isobars indicates the pressure gradient which is the change of pressureper unit distance from one place to another at the same horizontal level.

the PGF (pressure gradient force) acts perpendicular to the isobaric flow directed from highpressure to low pressure.

( Source: Australian Ultraflight Federation)

The pressure gradient force PGF = - 1/P where = the standard sea level density of air = 1.225kg m3 and P is the distance between two isobaric surfaces of nominal pressures.


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1 millibar = 1 hectopascal. Hectopascal (hPa) is the standard unit of pressure in Australianmeteorology. An isobar is a contour line of equal atmopheric pressure.

1.5 Frictional Force

According to Meteorology & Navigation, Thom, 1992, wind flow is retarded by frictional forces (nearthe Earth's surface). A depth of approximately 2000 to 3000 feet is the depth of the atmosphere towhich frictional forces act. This depth is known as the frictional layer or the boundary layer.

1.5.1 Results of Frictional Retardation

The Coriolis force is reduced as a result of frictional effects and no longer counters the pressuregradient force. The wind therefore flows slightly across the isobars in the direction of the PGF that istowards lower pressure. The angle is determined by the strength of the friction force, which in turn isdetermined by the roughness of the Earth's surface.

Over the sea, where friction is less than that over land, the surface wind speed is reduced to abouttwo-thirds the wind above the boundary layer and the flow is at an angle of about 10 degrees to theisobars. Over the land, the surface wind may be only half or even one-third of the wind above the

boundary layer and the cross-isobar angle of the flow would be approximately 25 to 30 degrees.The balance of forces for straight isobars with friction is illustrated below.

is the angular deflection Of the Wind. (Source: The Australian Weather Book, Colls & Whitaker,1990)


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When friction is included, the balance of forces in the southern hemisphere is depicted above, for lowand high pressure respectively. (Source: Manual of Aviation Meteorology, Commonwealth Bureau of

Meteorology, 2003, pg 49). Ideally wind should flow directly across isobars from high to low pressure.In reality though, wind some 2000 to 3000 feet above the Earth's surface, usually flows parallel to theisobars, whilst the surface wind blows slightly across the isobars.

1.6 Useful URLs

http://www.classzone.com/books/earth_science/terc/content/visualizations/es1904/es1904page01.cfm?

http://www.ems.psu.edu/~fraser/Bad/BadCoriolis.html

http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml

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