Lena M. Tallaksen

Appendix D and E; Dingman

GEO3020/4020

Lecture 1: Meteorological elements

Meteorological elements

2

Symbols, e.g. wind

3

4

is determined by the energy and mass transport at the surface:

Weather

Meteorological variables are used to describe the weather and to calculate the components of the energy and water balance equation.

Meteorological elements

5

• Precipitation• Radiation• Air temperature• Air humidity• Wind• Air pressure

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Meteorological variables

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RadiationLand-surface water balances is linked with energy balance through E (evaporation).

In the water balance equation there are usually two unknown, S and E. To close the water balance equation, we need to know evapotranspiration.

Evapotranspiration can be calculated using the energy balance equation.

Energy balance is linked with radiation budget through Rn (net radiation).

Rn is usually calculated using the radiation budget equation.

It is therefore import to show the procedure for calculation of Rn.

8

App. D.1 - Physics of radiant energy

• Stefan-Boltzmann Law:– All matter at a temperature above absolute zero radiates

energy in the form of electromagnetic waves that travel at the speed of light. The rate is given by Stefan-Boltzmann Law:

Qr: energy per unit surface area and per unit time [E L-2 T-1]

T: absolute temp. [°K]

: Stefan-Boltzmann constant = 5.67×10-8 [W m-2 K-4]

: emissivity [-]– Table D-1 gives values of ( = 1 for a blackbody)

1)-(D 4TQr

9

Table d1

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Physics of radiant energy• Wave length and frequency of radiation are inversely

related:

– : wavelength [L] – f: frequency [T-1]– c: speed of light = 2.998×108 [m s-1]

– Only radiation in the near-ultraviolet (wavelength 0.2 - 0.4 m), the visible (0.4 - 0.7), and the infrared (0.7 - 80 m) ranges plays a role in the earth’s energy balance and climate.

2)-(D cf

11

Solar radiation reaches Earth surface0.2-3.0m

Longwave radiation>4m

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Physics of radiant energy

• Planck’s law (equation is not shown)– Wavelength of the energy emitted by a radiating surface

decreases as its temperature increases

• Wien’s Displacement law– Wavelength at which max energy radiation occurs,max[m],

is related to absolute temperature, T [K] via Wien’s law,

max·T = 2897 (D-3)

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Physics of radiant energyElectromagnetic energy is transmitted through a vacuum

undiminished. But when it strikes matter, portion of it may be transmitted, reflected or absorbed.

• Absorption fraction of the incident energy at wavelength that is absorbed by a surface, this energy raises the temperature of the matter and/or causes a phase change (melting or evaporation)

• Reflection this energy does not affect the matter and continues traveling undiminished in a new direction

• Transmission this energy does not affect the matter and continues traveling undiminished in the original direction

Albedo – the reflectance integrated over visible wavelength (0.4 to 0.7 m).

Table D-2

=1

14

30% 70%

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Table D-2

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Daily clear-sky solar radiation

• Important contributor to the energy balance at the earth surface;

• Difficult to measure;• Method for estimating it on a horisontal and slope

surface at an arbritary place is given in Appendix E.

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18

Extraterrestrial Radiation on a horizontal plane

Extraterrestrial Radiation – radiation at the top of the atmosphere

• Solar constant – the average radiation flux on a plane perpendicular to the solar beam at the upper surface of the atmosphere:Isc = 1367 W m-2 = 118.1 MJ m-2 day-1 = 2.0 cal cm-2 min-1

• Extraterrestrial radiation on a plane tangent to the earth surface depends on

– The radiation on a plane perpendicular to the solar beam– The angle of the tangent plane relative to the solar beam;

function of latitude, season and time of the day

– Instantaneous extraterrestrial radiation flux,

– Daily solar flux, = integration of between sunrise and sunset.

'ETk

'ETK '

ETk

Equations (E-6) and (E-7)

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Radiation on a horizontal plane at the earth surface

1. Direct Radiation at the earth surface

As the solar radiation passes through the atmosphere, the energy is reduced due to absorption and reflection by the gaseous and solid particles,

where is the total atmospheric transmissivity [-]

2. Diffuse Radiation at the earth surface

About one-half of the energy scattered from solar beam reaches the surface as diffuse radiation,

where s = attenuation of the solar beam due to scattering by water vapor and permanent atmospheric constituents

3. Global radiation

8)-(E ''ETdir KK

14)-(E 5.0 ''ETsdif KK

19)-(E '''dirdifg KKK

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Radiation on a horizontal plane at the earth surface

4 Backscattered Radiation• Of the solar radiation striking the surface, a portion given by

albedo, , is reflected back to the atmosphere (i.e. )

• Of the reflected radiation, about half is reflected again from atmosphere to the surface,

5 Total clear sky solar radiation flux,

20)-(E 5.0 ''gsbs KK

'gs K

21)-(E 25.05.05.0

...

5.05.0

5.0

radiation tteredbackscksca radiation global

'2

'''

'''

''

'

ETsss

gsETsET

gsdifdir

bsg

cs

K

KKK

KKK

KK

K

'csK

21

Radiation on a sloping plane

• Total radiation flux at the surface

Since only the direct (beam) radiation is dependent on slope and aspect, the total clear-sky solar radiation flux on a slope is

where the extraterrestrial radiation on sloping surface, KET, is computed from by considering slope, position, etc.

• Slope factor

''''bsdifETcs KKKK

'ETK

27)-(E 'cs

cssl K

Kf

26)-(E ''bsdifETcs KKKK

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Empirical adjustments

• The total daily clear sky radiation flux at the surface , are derived from

• Empirical relationships (adjusting for the effect of clouds and vegetation) have been developed, e.g.

where global short wave radiation on the surface and , Extraterrestrial Radiation, n = actual sunshine hour and N= max sunshine hour (can be read from table for a given location and season).

'csK

21)-(E ...

5.0 '''

gsgcs KKK

'gK

N

nbaKK ETg

''

'ETK

23

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Relation between K, KET, Kcs, Kin

• KET = Extraterrestrial (potential) solar radiation• Kcs = clear sky short wave radiation flux on a horizontal surface on earth• Kin = adjusted Kcs for slope, aspect, clouds and vegetation• K = net flux of solar energy entering the surface, e.g. snowpack

• Normally K < Kin < Kcs < KETKET = extraterresytrial (potential) solar radiation

Kin = measured solar radiation

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Summary

• = Extraterrestrial Radiation on a horizontal plane

• = Extraterrestrial Radiation on a sloping plane

• = Total daily clear sky incident radiation on a horizontal

plane at the earth surface

• = Total daily clear sky incident radiation on a sloping

plane at the earth surface

• = global short wave radiation at the earth surface

• = Backscattered Radiation

'ETK

ETK'csK

csK

'gK

'''dirdifg KKK

'bsK

What are the relations among them?

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Structure of the atmosphere• Composition• Vertical structure: Pressure-temperature relation

Ideal gas law

– P = atmospheric pressure [kPa]

– Ta = air temperature [K]

– a = mass density of air [kg m-3]

– Ra = gas constant [0.288]

As a consequence of this law, an increase (decrease) of pressure is always accompanied by an increase (decrease) in temperature and density

5)-(D aa

a T

PR

27

• Fig D-2

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• Adiabatic cooling

Cooling of air due to rising and without losing heat

• Dry adiabatic lapse rate

If no condensation occurs, the rising air cools at a fixed rate of 1 °C/100m

• Moist adiabatic lapse rate

If condensation occurs, the rising air cools at a fixed rate of 0.65 °C/100m

Adiabatic rising

Fig D-6

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Water vapour• Vapor pressure

– The partial pressure of water vapor is called (actual) vapor pressure, ea (or just e)

– The maximum vapor pressure = the saturation vapor pressure, e*

where e* in kPa, T in °C

water vapor content higher than e* results in condensation

– The actual vapor pressure, ea, can be determined from the relative humidity, Wa=ea/e*.

7)-(D 3.237

3.17exp611.0*

T

Te

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• Fig D-3

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Water vapour

• Absolute humidity, ρv – The mass concentration of water vapour in a volume of air

(vapour density) [kg m-3]• Applying gas low for water vapor

6)-(D aa

a T

PR

e = vapour pressure [kPa]v = absolute humidity, [kg m-3]Ta = air temperature in KRv = gas constant for vapour [0.463]Ra = gas constant for air [0.288]

v

a

R

R622.0

Molecular weight of water vapour is 0.622 times the molecular weight of air

8b)-(D 622.0

av

Pe

8a)-(D va

v T

eR

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Water vapor• Specific humidity

• Relative humidity

• Dew point temperature

The temperature to which a parcel with a given vapor pressure has to be cooled in order to reach saturation

9)-(D 622.0

P

eq

a

v

10)-(D *a

aa e

eW ea is actual vapor pressure

3.237

3.17exp611.0

d

da T

Te

Td is dew point temperature

11)-(D )ln(00421.00708.0

4926.0)ln(

e

eTd

*aaa eWe

saturation vapor pressure*ae

• Precipitation• Radiation• Air temperature• Air humidity• Wind• Air pressure

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Meteorological variablesMeasurements

Measuring humidity 

• Hygroscopic substances

The length of a substance (hair) is sensitive to humidity. Calibrated against relative humidity.

• Psykrometer

composed of two thermometers, one dry and one wet at the ball. Evaporation from the wet thermometer ball

requires energy and the temperature drops. This difference increases with decreasing humidity.

Calibrated against relative humidity.

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Measuring radiation 

• Pyrheliometer direct solar beam normal to the angle of incidence

• Pyranometer shortwave radiation from a whole hemisphere

•  Albedometer shortwave net radiation measured using an upward and downward facing pyranometer

• Pyrgeometer longwave radiation• Pyrradiometer short- and long wave radiation

from a whole hemisphere• Netto radiometer net short- and long wave

radiation

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• Precipitation• Radiation• Air temperature• Air humidity• Wind• Air pressure

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Meteorological variablesAutomatic weather station (Aanderaa)

Measuring wind 

• Subjective judgement

Rough estimate based on the influence

wind has on its environment in a period

of 10 minutes (Beaufort score).

• Instrumentation

Windspeed: Anemometer (horisontal velocity)

Wind direction: Weather wane, wind socks

Measured at an altitude of 10 meters in a

flat, open terrain, where the distance to the nearest obstacle is at least 10 times the

high of the obstacle.

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Wind - speed and direction

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39

40

Zveg

Zd

Z0

velocity