I.
Meteorological
Elements
II. Energy Balance
III. Evapotranspiration
GEO3020/4020
Evapotranspiration
•
•
•
•
•
Definition and Controlling factors
Measurements
Physics of evaporation
Estimation of free water evaporation, potential and actual evapotransp.
Processes and estimation methods for bare soil, transpiration,
interception
Weather
is determined by the energy and mass transport at
the surface:
Energy transport
LE: 15%
H: 60%
Oceans: 25%
Meteorological variables are used to describe the weather and to
calculate the components of the energy and water balance equation.
2
Meteorological variables
•
•
•
•
•
•
Precipitation
Radiation
Air temperature
Air humidity
Wind
Air pressure
3
Radiation
Why do we want to calculate
the radiation budget at the
land surface?
4
30%
70%
5
Summary
'
= Extraterrestrial Radiation on a horizontal plane
K ET
K ET = Extraterrestrial Radiation on a sloping plane
K cs'
= Total daily clear sky incident radiation on a horizontal
plane at the earth surface
K g'
= global short wave radiation at the earth surface
'
'
'
'
K g'  Kdif
 Kdir
 0.5   s  K ET
   K ET
K bs'
and
= backscattered radiation (= 0.5   s    K g' )
K sc'  K g'  Kbs'
6
• 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
7
GEO3020/4020
Lecture 2: I. Energy balance
II. Evapotranspiration
Energy balance equation
K  L  H  LE  G  Aw  Q / t  0
where:
K
L
LE
H
G
Aw
ΔQ/Δt
net shortwave radiation
net longwave radiation
latent heat transfer
sensible heat transfer
soil flux
advective energy
change in stored energy
Units: [EL-2T-1]
Bowen ratio = H/LE replace H = B∙LE
9
Controlling factors of evaporation
I. Meteorological situation
• Energy availability
• How much water vapour can be received
– Temperature
– Vapour pressure deficit
– Wind speed and turbulence
10
Controlling 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
11
Evapotranspiration
Measurements
Free water evaporation
- Pans and tanks
- Evaporimeters
Evapotranspiration (includes vegetation)
- Lysimeters
- Remote sensing
12
GEO3020/4020
Lecture 3: Free water Evaporation
Flux of water molecules over a surface
14
 zm  zd
1
vm   u*  ln 
k
 z0



(D - 22)
Zveg
Z0
Zd
velocity
15
Momentum, sensible heat and water vapour
(latent heat) transfer by turbulence (z-direction)
16
Steps in the derivation of LE
• Fick’s law of diffusion for matter (transport due to
differences in the concentration of water vapour);
• Combined with the equation for vertical transport of
water vapour due to turbulence (Fick’s law of
diffusion for momentum), gives:
DW V
0.622   a
k 2vm
LE 
 V 

DM
P
  za  zd
ln 
  z0



2
(e s - e m )
 (D - 42)
DWV/DM (and DH/DM) = 1 under neutral atmospheric conditions
17
Latent heat, LE
Latent heat exchange by turbulent transfer, LE
LE  K LE  va  es  ea 
(D - 45)
where
K LE
0.622   a
k2
 V 

P
  za  zd
ln 
  z0
where
a = density of air;
λv = latent heat of vaporization;
P = atmospheric pressure
k = 0.4;
zd = zero plane displacement
height



2
 (D - 43)
z0 = surface-roughness height;
za = height above ground surface
at which va & ea are measured;
va = windspeed,
ea = air vapor pressure
es = surface vapor pressure
(measured at z0 + zd)
18
Sensible heat, H
Sensible-heat exchange by turbulent transfer, H (derived based on
the diffusion equation for energy and momentum):
H  K H  va  Ts  Ta 
(D - 52)
where
K H    a  ca 
k2
  za  zd
ln 
  z0
where
a = density of air;
Ca = heat capacity of air;
k = 0.4;
zd = zero plane displacement
height



2

(D - 50)
z0 = surface-roughness height;
za = height above ground surface
at which va & Ta are measured;
va = windspeed,
Ta = air temperatures and
Ts = surface temperatures.
19
Selection of estimation method
•
•
•
•
Type of surface
Availability of water
Stored-energy
Water-advected energy
Additional elements to consider:
1) Purpose of study
2) Available data
3) Time period of interest
20
Estimation of free water evaporation
•
•
•
•
Water balance method
Mass-transfer methods
Energy balance method
Combination (energy +
mass balance) method
• Pan evaporation method
Defined by not accounting for stored energy
21
Mass-transfer method
Physical based equation:
LE  K LE  va  ea  es 
or
E  K E  va  ea  es 
Empirical equation:
E  (b0  b1  va )  ea  es  ref. Dalton (1802)
-
Different versions and expressions exist for KE and the
empirical constants b0 and b1; mainly depending on wind, va
and actual vapour pressure, ea
22
Calculation of evaporation using energy balance
method
Substitute the different terms into the following equation, the
evaporation can be calculated
LE  K  L  G  H  Aw  Q / t
(7 - 15)
K  L  G  H  Aw  Q / t
E
 w  v
(7 - 22)
where
LE has units [EL-2T-1]
E [LT-1] = LE/ρwλv
Latent Heat of Vaporization :
v= 2.495 - (2.36 × 10-3) Ta
[MJkg-1] or 2495 J/g at 0oC
23
Penman combination method
Penman (1948) combined the mass-transfer and energy balance
approaches to get an equation that did not require surface temp.:
I. Simplifies the original energy balance equation:
K LH
E
 w  v
(7B1 - 1)
thus neglecting ground-heat conduction G, water-advected energy
Aw, and change in energy storage Q/t.
II. The sensible-heat transfer flux, H, is given by:
H  K H  va  Ts  Ta 
(7B1 - 2)
I. + II. gives the Penman equation:
  ( K  L)  K E  wv  va  ea* 1  Wa 
E
 wv (   )
(7 - 33)
24
Penman equation – input data
• Net radiation (K+L)
(measured or alternative cloudiness, C or sunshine hours, n/N
can be used);
• Temperature, Ta (gives ea*)
• Humidity, e.g. relative humidity, Wa = ea/ea*
(gives ea and thus the saturation deficit, (ea* - ea)
• Wind velocity, va
Measurements are only taken at one height interval and data are
available at standard weather stations
25
GEO3020/4020
Lecture 4: Evapotranspiration
- bare soil
- transpiration
- interception
Lena M. Tallaksen
Chapter 7.4 – 7.8; Dingman
Influence of Vegetation
•
•
•
•
•
•
Albedo
Roughness
Stomata
Root system
LAI
GAI
Aerodynamic and surface resistance
27
Modelling transpiration
DW V
0.622   a
k 2vm
LE 
 V 

DM
P
  zm  zd
ln 
  z0



2
(e s - e m )
Rearrange to give:
LE 0.622   a DW V
k2
E

v (e - ea )
2 m s
V  w
P   w DM   z  z 
a
d

ln 
  z0 
and
E  K at  Cat  (e s - ea )
28
Atmospheric conductance, Cat
Cat 
vm
  zm  zd
6.25ln 
  z0



2
29
Penman equation – 3 versions
Orignal Penman
  ( K  L)    f (u )  ea* 1  Wa 
E
 wv (   )
Penman (physical based wind function)
  ( K  L)  K E  wv  va  ea* 1  Wa 
E
 wv (   )
Penman (atmospheric conductance)
  ( K  L)   a ca Cat  ea* 1  Wa 
E
 wv (   )
30
Penman-Monteith
Penman
  ( K  L)   a ca Cat  ea* 1  Wa 
E
 wv (   )
(7 - 55)
Penman-Monteith
  ( K  L)   a ca Cat  ea* 1  Wa 
E
(7 - 56)


Cat


 w v     1 

C

can  


where
”Big leaf” concept
Ccan  f s  LAI  Cleaf
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Interception: Measuring and Modelling
Function of:
i)Vegetation type and age
(LAI)
ii)Precipitation intensity,
frequency, duration and
type
Replacement or addition
to transpiration?
32
Estimation of potential evapotranspiration
Definition: function of vegetation – reference crop
Operational definitions (PET)
1.Temperature based methods (daily, monthly)
Empirical
2.Radiation based methods (daily)
Homogeneous, well watered surfaces, e.g. P-T
3.
Combination method (daily)
Penman or Penman-Monteith (Cleaf: no soil moisture
deficit)
4.
Pan methods
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Estimation of actual evapotranspiration (ET)
• Potential-evapotranspiration approaches
–
–
–
–
Empirical relationships between P-PET
Monthly water balance
Soil moisture functions
Complementary approach
• Water balance approaches
– Lysimeter
– Water balance for the soil moisture zone, atmosphere, land
• Turbulent-Transfer/Energy balance approaches
– Penman-Monteith
– Bowen ratio
– Eddy correlation
• Water quality approaches
34
GEO3020/4020
Lecture 10: Rainfall-runoff
processes
Lena M. Tallaksen
Chapter 9.1-9.2; Dingman
Streamflow response to
precipitation (rain or snow) input
• Basic aspect of catchment
response
– hillslope (and stream
network)
• Hydrograph separation
– The Base Flow Index (BFI)
• Linear reservoir model
• Mechanisms producing event
response
• (Rainfall-runoff modeling)
36
Definition of terms
Refer Table 9-1
- Time instants, t
- Time durations, T
37
Hydrograph separation
Flow components
Methods for continuous separation similarly divide the
total streamflow into one rapid, qef (event flow) and one
delayed component, qbf (base flow). The delayed flow
component represents the proportion of flow that
originates from stored sources (e.g. groundwater).
Rapid response
The Base Flow Index
BFI = Vbase flow /Vtotal flow
Isotopic and chemical
methods (Box 9.1)
6,50E+04
6,00E+04
5,50E+04
5,00E+04
4,50E+04
4,00E+04
Base flow
Linear reservoir model of
catchment response
• Box 9-2
– Catchment response time, T*
– Influence of storm size and timing
– Influence of drainage basin characteristics
• Summary of their influence is given in Table 9.2
39
Mechanisms producing event response
III. Subsurface flow
I. Channel precipitation
II. Overland flow (surface runoff)
A. Hortonian
B. Saturation excess
III. Subsurface flow
A. Saturated zone
1.
2.
Local groundwater mounds
Perched saturated zones
B. Unsaturated zone
1.
2.
Matrix (Darcian) flow
Macropore flow
40
Questions?
41