Repetition
GEO3020/4020
Lecture 3: Evapotranspiration(free water evaporation)
Flux of water molecules over a surface
2
3
Zveg
Zd
Z0
velocity
22)-(D ln1
0*
z
zzu
kv dm
m
Momentum, sensible heat and water vapour (latent heat) transfer by turbulence (z-direction)
4
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:
DWV/DM (and DH/DM) = 1 under neutral atmospheric conditions
5
42)-(D )e-(e
ln
622.0ms2
0
2
zzz
vk
PD
DLE
da
maV
M
WV
Lapse rates (stable, neural, unstable)
6
Actual lapse rate
7
Latent heat, LE
Latent heat exchange by turbulent transfer, LE
where
where
a = density of air;
λv = latent heat of vaporization;
P = atmospheric pressure
k = 0.4;
zd = zero plane displacement
height
45)-(D asaLE eevKLE
43)-(D
ln
622.02
0
2
zzz
k
PK
da
aVLE
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)
8
Sensible heat, H
Sensible-heat exchange by turbulent transfer, H (derived based on the diffusion equation for energy and momentum):
where
where
a = density of air;
Ca = heat capacity of air;
k = 0.4;
zd = zero plane displacement
height
52)-(D asaH TTvKH
50)-(D
ln
2
0
2
z
zz
kcK
da
aaH
z0 = surface-roughness height;
za = height above ground surface
at which va & Ta are measured;
va = windspeed,
Ta = air temperatures and
Ts = surface temperatures.
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
9
10
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
11
Water balance method• Apply the water balance equation to the water body
of interest over a time period t and solving the equation for evaporation, E
– W: precipitation on the lake– SWin and SWout: inflows and outflows of surface water– GWin and GWout: inflows and outflows of ground water– V change in the amount of stored in the lake during t
But: • Difficult to measure the terms• Large uncertainty in individual terms gives high uncertainty in E• Can however, give a rough estimate, in particular where E and
Δt is relative large
16)-(7 VGWSWGWSWWE outoutinin
12
Water balance methodApply the water balance equation to the water body of
interest over a time period t and solving the equation for evaporation, E
Data needed
Application
16)-(7 VGWSWGWSWWE outoutinin
13
Mass-transfer methodPhysical based equation:
or
Empirical equation:
- Different versions and expressions exist for the empirical constants b0 and b1; mainly depending on wind, va and ea
- If compared with physical based equation; b0=0 and b1=KLE
saaE eevKE saaLE eevKLE
(1802)Dalton ref. )( 10 saa eevbbE
Mass-transfer methodData needed
- va (dependent on measuring height)
- es (from Ts)
- ea (from Ta and Wa)
Application
- gives instantaneous rate of evaporation, but averaging is OK for up to daily values
- requires data for Ts
- KE varies with lake area, atmospheric stability and season
Harbeck (1962) proposed the empirical equation:
where AL is lake area in [km2], KE in [m km-1 kPa-1]
14
19)-(9 1069.1 05.05 LE AK
15
Eddy-correlation approach• The rate of upward movement of water vapor near the surface
is proportional to the time average of the product of the instantaneous fluctuations of vertical air movement, , and of absolute humidity, q’, around their respective mean values,
– Advantages• Requires no assumption about parameter values, the shape of the
velocity profile, or atmospheric stability
– Disadvantages • Requires stringent instrumentation for accurately recording and
integrating high frequency (order of 10 s-1) fluctuations in humidity and vertical velocity
For research application only
'au
21)-(7 '' quE aw
a
16
Energy balance methodSubstitute the different terms into the following equation, the evaporation can
be calculated
where
22)-(7 /
vw
w tQAHGLKE
15)-(7 / tQAHGLKLE w
Latent Heat of Vaporization :v= 2.495 - (2.36 × 10-3) Ta
LE has units [EL-2T-1]
E [LT-1] = LE/ρwλv
17
Bowen ratio
We recognize that the wind profile enters both the expression for LE and H. To eliminate the need of wind data in the energy balance approach, Bowen defined a ratio of sensible heat to latent heat, LE:
where is called the psychrometric constant [kPa K-1]
Needs measurements at two levels.
as
as
asv
asa
ee
TT
ee
TTPc
LE
HB
622.0
v
a Pc
622.0
18
Use of Bowen ratio in energy balance approach
• Original energy balance approach
• Replace sensible heat, H by Bowen ratio, B
• Substitute (7-23) into (7-22)
The advantage of (7-24) over (7-22) is to eliminate H which needs wind profile data
22)-(7 /
vw
w tQAHGLKE
23)-(7 EBLEBH vw
24)-(7 )1(
/
B
tQAGLKE
vw
w
Energy balance method
Data
Data demanding, but in some cases less a problem than in the water balance method (regional estimates can be used)
Application
- gives instantaneous rate of evaporation, but averaging is OK for up to daily values;
- change in energy stored only for periods larger than 7 days (energy is calculated daily and summed to use with weekly or monthly summaries of advection and storage);
- requires data for Ts (Bowen ratio and L);
- most useful in combination with the mass transfer method.
19
20
Penman combination methodPenman (1948) combined the mass-transfer and energy balance
approaches to arrive at an equation that did not require surface temperature data:
I. From original energy balance equation:
Neglecting ground-heat conduction, G, water-advected energy, Aw, and change in energy storage, Q/t, Equation (7-22) becomes
22)-(7 /
vw
w tQAHGLKE
1)-(7B1 vw
HLKE
21
Penman combination methodII. The sensible-heat transfer flux, H, is given by:
• Introduce the slope of saturation-vapor vs. temperature curve:
• Derive an expression for H:
I. + II. gives the Penman equation:
2)-(7B1 asaH TTvKH
3)-(7B1 **
as
as
TT
ee
8)-(7B1 *aa
aH
aE
aH eevK
vK
EvKH
33)-(7
)(
1)( *
vw
aaavwE WevKLKE
22
Penman combination method• Note that the essence of the Penman equation can be
represented as:
• The first term and second term of the equation represents energy (net radiation) and the atmospheric contribution (mass transfer) to evaporation, respectively.
• In many practical application, Ea is simplified as: f(va)(es-ea) and an empirical equations used for f(va).
34)-(7 )(E transfer mass)(Rradiation net an
E
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
23
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
24
GEO3020/4020
Lecture 4: Evapotranspiration- bare soil- transpiration - interception
Lena M. Tallaksen
Chapter 7.4 – 7.8; Dingman
26
Soil Evaporation
• Phase 1: Meteorological controlled
• Phase 2:
Soil controlled
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Influence of Vegetation
• Albedo• Roughness• Stomata• Root system• LAI • GAI
28
Transpiration
29
Resistance – ConductanceAerodynamic and surface
30
The influence of stomatal aperture on transpiration – leaf scale
31
Modelling transpiration
32
Rearrange to give:
)e-(e
ln
622.0ms2
0
2
zzz
vk
PD
DLE
dm
maV
M
WV
)e-(e
and
)e-(e
ln
622.0
as
as2
0
2
C KE
v
z
zz
k
D
D
P
LEE
atat
m
daM
WV
w
a
wV
Atmospheric conductance, Cat
33
ln25.6
2
0
zzz
vC
dm
mat
Orignal Penman (1948)
Penman (physical based wind function)
Penman (atmospheric conductance)
Penman equation – 3 versions
34
)(
1)( *
vw
aaavwE WevKLKE
)(
1)( *
vw
aaataa WeCcLKE
)(
1)()( *
vw
aa WeufLKE
Estimation of Cleaf
The leaf conductance is a function of:
1. Light intensity
2. CO2 level in the atmosphere
3. Vapour pressure difference (leaf – air)
4. Leaf temperature
5. Leaf water content
where Cleaf* is the maximum value (all stomata full opening; typical values are given in Table 7-5) and f(x) is a proxy used for each variable above.
35
72)-(7 * fTffKfCC aTvpinkleafleaf
Relative leaf conductance [0,1](ref. Fig. 7-13 and Table 7-6)
36
Penman-Monteith
Penman
Penman-Monteith
37
55)-(7
)(
1)( *
vw
aaataa WeCcLKE
where
56)-(7 1
1)( *
CLAIfC
CC
WeCcLKE
leafscan
can
atvw
aaataa
”Big leaf” concept
Evapotranspiration – measuring and modelling
38
• Single leaf or plant • Stand• Mixed vegetation• Regional scale• Seasonal variation in LAI (”big leaf”)
Interception
39
Function of:
i)Vegetation type and age (LAI)
ii)Precipitation intensity, frequency, duration and type
Interception measurements
40
i) Direct measurements
ii) Measurements of throughfall or net precipitation
Interception measurements
41
Measurements of throughfall or net precipitation
Experiemental site in the Huewelerbach catchment, Luxembourg (from TUDelft website)
42
43
Interception modelling
44
• Regression models (empirical equations)e.g. between interception loss (Ei) and
precipitation (R) for a given Δt
• Conceptual based modelse.g. Rutter water balance model which uses the
equation for free water evaporation to estimate interception losses.
- Requires meteorological data and vegetation characteristics.
Regression model to determine the net precipitation rate
45
The Rutter model
46
Regression model to determine S (as the point where the linear line crosses X)
47
48
Forest evapotranspirationExample 7- 8
Thetford forest (UK): 16.5 m, vind speed 3.0 m/sAtmospheric conductance: Cat = 23.2 cm/s
Transpiration rateSoil moisture deficit = 0 cmET=1.8 mm/day
Soil moisture deficit = 7 cmET=1.2 mm/day
Evaporation of intercepted waterET=54 mm/day (1 mm/0.45 hour)
Replacement or addition to transpiration ?
Estimation of potential evapotranspiration
49
Definition: function of vegetation – reference crop
Operational definitions (PET)
1.Temperature based methods (daily, monthly)
2.Radiation based methods (daily)
3.Combination method
4.Pan
50
Actual evapotranspiration
• Two extreme cases– In arid case, P <<PE, water limited
AE = P
– In humid case, P >>PE
AE = PE, energy limited
51
Long-term actual evapotranspiration as presented by Turc-Pike (mid), and Schreiber and Ol’dekop methods.
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
52
53
Complementary approach
• Based on heuristic arguments of Bouchet (1963)• Simply states that the potential and actual
evapotranspiration are not independent, but form a complementary relationship
Increase of wetness
ETa = 2 ETw - ETp
ETw = wet environment evapotr.ETp = potential evapotr.ETa = actual evapotr.
evap
otra
nspi
ratio
n
The above figure is identical to Fig 7-25 in the book
54
Soil moisture functions (hydrological water balance models)
Daily or monthly time step– General equation
– rel is the relative water content in the soil
– where fc is the field-capacity, pwp is the permanent wilting point
67)-(7 )( PETFET rel
68)-(7 pwpfc
pwprel
55
• Fig 7-24
fccritfc 8.0 fccritfc 8.0
56
Drying of soil moisture by 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
I. Meteorological Elements
II. Energy Balance
III. Evapotranspiration