1. GEO3020/4020 Lecture 1: Meteorological elements
Repetition

2. Weather is determined by the energy and mass transport at the surface:
Meteorological variables are used to describe the weather and to calculate the components of the energy and water balance equation.

3. Meteorological variables
Precipitation
Radiation
Air temperature
Air humidity
Wind
Air pressure

4. Radiation
Why do we want to calculate the radiation budget at the land surface?

5. 70%
30%

6. 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.

7. Summary = Extraterrestrial Radiation on a sloping plane
= 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
= global short wave radiation at the earth surface
= backscattered radiation (= )
and

8. 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).

9. Relation between K, Kin, Kcs, KET
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 < KET
KET = extraterrestrial (potential) solar radiation
Kin = measured solar radiation

10. Structure of the atmosphere
Composition
Vertical structure
Pressure-temperature relation (Ideal gas law)
Adiabatic lapse rate (dry & wet)
Vapour
Vapour pressure, ea
Sat. vapour pressure, ea*
Absolute humidity, ρv
Specific humidity, q = ρa/ρv
Relative humidity, Wa = ea/ea*
Dew point temperature, Td
The mass concentration of water vapour in a volume of air (vapour density) [kg m-3]

11. Meteorological variables Measurements
Precipitation
Radiation
Air temperature
Air humidity
Wind
Air pressure
Selve hytten er hvitmalt for å reflektere mest mulig solstråling, og skal plasseres i et åpent område, helst ikke i le av eller for nær bygninger og lignende hindringer som gir skygge.
Underlaget under hytten skal være kortklipt gress. For eksempel kan asfalt ett sted og en fuktig myr et annet sted gi helt forskjellige målinger, særlig på varme, solrike sommerdager.
Veggene i hytten er ikke helt tett, slik at det er godt ventilert og luften kan bevege seg fritt gjennom hytten.
Termometeret er plassert inne i hytten, to meter over bakken.
Inni hytten er termometeret beskyttet slik at solen ikke skinner direkte på det og varmer det opp, og det er også skjermet mot nedbør

12. GEO3020/4020 Lecture 2: I. Energy balance
Lena M. Tallaksen
Chapter & 7.3.4, Appendix D.4; Dingman

13. 70%
30%

14. Albedo is the
shortwave reflectance

15. Shortwave radiation input, K
Net solar radiation, K
K = Kin - Kout = Kin·(1-a) (5-27)
Where K is net flux of solar energy entering the body
Kin – flux of solar energy incident on the surface (= global radiation)
Kout – reflected flux
a – albedo, depends on the properties of the surface
K can be measured by pyranometers, but more common to estimate
Kcs represents the clear-sky shortwave radiation flux
Kin, adjusted for the slope and aspect:
Λ, latitude, J day of year,
b, slope inclination angle, a, slope azimuth angle
C, fraction of sky covered with clouds
F, fraction of sky obscured by forest canopy,
are functions

16. Shortwave radiation input, K
The function is derived using the concept of equivalent latitude,
The function , the effect of cloud cover can be estimated using empirical relations like, or
The function effect of forest canopy, an example for pine,
The albedo, a, changes with location, season, vegetation, ….

17. Practical considerations
Empirical equation for Shortwave radiation
C = fraction of sky covered with clouds
KCS = total daily clear sky incident radiation on a horizontal plane at the earth surface

18. Longwave radiation exchange, L
Net longwave radiation – equals to incoming atmospheric longwave radiation minus the portion of that reflected and the radiation flux emitted by the surface
L = Lin – Lout = Lat – (1-es)Lat - Ls (7-28)
where:
Lat - incoming atmospheric longwave radiation flux,
Ls - outgoing radiation from the surface
es - emissivity of surface
L, Lat, Ls can be measured by pyranometers, but more common to estimate using equations like:
eat - emissivity of the atmosphere and canopy
es - emissivity of the surface
σ - Stefan-Boltzmann constant
Tat ,Ts – temperature of the atmosphere and water surface

19. Longwave radiation exchange, L
Combine the two equations (5.35 and 5.36) we get:
where
s, Stefan-Boltzmann constant (4.90×10-9 MJ m-2 day-1 K-4)
Tat, effective radiating temp of atmosphere and canopy (˚C)
Ts, temperature of surface (˚C)
Table D-1 for es values, the question remains how to calculate eat.

20. Table d1

21. Longwave radiation exchange, L
Clear sky, no forest canopy
Cloudy sky, no forest canopy
Cloudy sky, forest canopy (general equation)
where ea is near surface saturation atmospheric vapor pressure
and Ta is air temperature in °C, F is the ratio of the horizontally projected area of forest canopy to the total area of interest, C is degree of cloud cover

22. 30%
70%

23. Sensible heat, H Sensible-heat exchange by turbulent transfer, H:
and from equation (D-49)
where
ra = density of air;
Ca = heat capacity of air;
k = 0.4;
zd = zero plane displacement
height
z0 = surface-roughness height;
za = height above ground surface
at which va & Ta are measured;
va = windspeed,
Ta = air temperatures and
Ts = surface temperatures.

24. Zveg Z0 Zd
velocity

25. Latent heat, LE Latent heat exchange by turbulent transfer, LE
and from equation (D-42)
where
ra = density of air;
λv = latent heat of vaporization;
P = atmospheric pressure
k = 0.4;
zd = zero plane displacement
height
z0 = surface-roughness height;
za = height above ground surface
at which va & ea are measured;
va = horisontal windspeed,
ea = air vapor pressure
es = surface vapor pressure (measured at z0 + zd)

26. Exchange of (sensible) heat with the ground, G
Positive or negative depending on the temperature of the air and soil surface (often negligible compared to other terms).
If soil temperature is increasing downward (due to thermal energy stored during the summer) heat is transferred upwards at a rate:
kG is the thermal conductivity of the soil (E L-1 T-1 q-1), depends on soil texture, soil density, and moisture content and vary widely with season and place.

27. Water-advected energy, Aw (lakes)
Net water-advected energy Aw [E L-2 T-1] is found from:
where:
rw density of water [M L-3]
cw – specific heat of water [E M-1 θ-1]
w – average precipitation rate [L T-1]
SW and GW – surface water and ground water inflows and outflows
Ts – temperatures of the respective inflows and outflows [θ]
Heat input by rain, R (snowpack)
rainwater is first cooled to the snow temperature (Eq. 5-47a)
if the snow is below zero, then freezing may occur and latent heat realised (Eq. 5-47b)

28. Change in stored energy, ΔQ
Energy can be stored in e.g. a snowpack, lake or soil
Snow (warming phase)
Lake
where:
hm snow water equivalent
ci heat capacity of ice
V lake volume,
TL average lake temperature,
AL lake area.
subscripts 1 and 2 designate values at the beginning and end of Dt

29. Energy balance equation
where:
K net shortwave radiation
L net longwave radiation
LE latent heat transfer
H sensible heat transfer
G soil flux
Aw advective energy
ΔQ/Δt change in stored energy
Units: [EL-2T-1]

30. Calculation of evaporation using the energy balance method
Evaporation can be calculated solving for LE:
where:
LE has units [EL-2T-1]
E [LT-1] = LE/ρwλv
Latent Heat of Vaporization :
lv= (2.361 × 10-3) Ta

31. Lena M. Tallaksen Chapter 7. – 7.1.2, 7.3.6; Dingman
GEO3020/4020 Lecture 2: II. Evapotranspiration - Definitions - Governing factors - Measurements
Lena M. Tallaksen
Chapter 7. – 7.1.2, 7.3.6; Dingman

32. Global water balance
765
114
1141
1255
490
275
mm/year

33. Water balance for Norway, 1931 -60
Otnes & Ræstad, 1978

34. Evaporation - Norway

35. Global distribution of evaporation (cm)
Encyclopedia Britannica Inc.

36. Temporal variation – bare soil

37. Temporal variation – Lake Ontario

38. Evaporation and evapotranspiration
Summary
Evapotranspiration is a collective term for all the processes by which water in the liquid or solid phase at or near the earth’s surface (rivers and lakes, bare soils, and vegetative surfaces) becomes atmospheric water vapor.
Evapotranspiration is a second largest term in the global water balance; about 62% of precipitation that falls on the continents is evapotranspired.
Evapotranspiration is the term that links earth surface’s water balance and energy balance.
It is much more difficult to measure evapotranspiration than to measure precipitation and streamflow.
There are numerous methods/models available in calculating evapotranspiration, of which the most well-known methods will be discussed in the class.

39. Governing factors of evaporation
I. Meteorological situation
Energy availability
How much water vapour can be received
Temperature
Vapour pressure deficit
Wind speed and turbulence
Optimal conditions: ?

40. Governing factors of evaporation
II. Physiographic and plant characteristics
Characteristics that influence available energy
albedo
heat capacity
How easily can water be evaporated
size of the evaporating surface
surroundings
roughness (aerodynamic resistance)
salt content
stomata
Water supply
free water surface (lake, ponds or intercepted water)
soil evaporation
transpiration
The wind speed immediately above the surface.
The humidity gradient away from the surface.
The rate and quantity of water vapor entering into the atmosphere both become higher in drier air.
Water availability.
Evapotranspiration cannot occur if water is not available.

41. Evapotranspiration Measurements
Free water evaporation
Pans and tanks
Evaporimeters
Evapotranspiration (includes vegetation)
Lysimeters
Remote sensing

42. Definitions
Potential evapotranspiration, PE, is the rate at which evapotranspiration would occur from a large area completely and uniformly covered with growing vegetation which has access to an unlimited supply of soil water and without advection or heat-storage effects (i.e. the rate is depedent on the vegetation)
Actual evapotranspiration, ET, is the rate at which evapotranspiration occurs (i.e. describes all the processes by which liquid water at or near the land surface becomes atmospheric water vapor).

43. Pan evaporation methods
Epan = W – [V2-V1]
where
W = precipitation during Dt
V1 = the storage at the beginning of Dt
V2 = the storage at the end of Dt
For American Class-A pan, Kohler et al. (1955) developed an empirical equation to account for energy exchange through sides of a pan, and adjust daily pan evaporation, Epan, to free water evaporation, Efw [mm day-1] (Equations 7-41 and 7-42).

44. Pan evaporation methods
Pan coefficient
Elake/Epan = kp
where
k is a coefficient that varies with seasons and lake.
Its annual average over the US is about 0.7

45. Pan evaporation methods

46. Pan evaporation methods
Example of pan coefficient in the Yangtze River catchment in China 46

47. Lysimeter
One of the most reliable way of measuring potential or actual evapotranspiration is to use large containers (sometimes on the order of several metres across) called lysimeters;
Evapotranspiration is calculated by subtraction considering the different components of the water balance.
A lysimeter is most accurate when vegetation is grown in a large set up which allows the rainfall input and water lost through the soil to be easily calculated from the difference between the weight before and after a given period.

48. Lysimeter for measuring potential evapotranspiration
input (Rainfall R and Additional water A) and output (Percolated water P)
collected in the receiver, then PE can be estimated from the equation:
PE = R + A – P R A P

49. Lysimeter for measuring actual evapotranspiration
Figure. Schematic of a weighable gravitation lysimeter.

50. Estimation of evapotranspiration by remote sensing
Remote sensing has two potentially very important roles in estimating evapotranspiration (Engman, 1995).
First, remotely sensed measurements offer methods for extending point measurements or empirical relationships to much larger areas, including those areas where measured meteorological data may be sparse.
Secondly, remotely sensed measurements may be used to measure variables in the energy and moisture balance models of ET, such as as radiometric surface temperature, albedo, and vegetation index.