Engineering Hydrology

for the Masters Programme

Water Science and Engineering

3 Evaporation

Prof. Dr. Stefan Uhlenbrook Professor of Hydrology

UNESCO-IHE Institute for Water Education

Westvest 7

2611 AX Delft

The Netherlands

E-mail: s.uhlenbrook@unesco-ihe.org

Acknowledgements

for the material used in this lecture

• Dr. Pieter de Laat, prof. Huub Savenije, UNESCO-IHE, Delft, The Netherlands (wrote the course note; some pictures)

• Prof. Tim Link, Idaho, USA (some PPT slides and pictures)

• Prof. Chris Leibundgut, University of Freiburg (some PPT slides and pictures)

Evaporation - Basics

• Huge energy transfer to the atmosphere (latent heat); condensation generates sensible heat

• Often estimated by solving the water balance (uncertain!)

• Very important variable of water balance, as worldwide about 75% of continental precipitation evaporates; in Europe 60% - 85%

• Most difficult variable to estimate for a whole catchment including its space-time variability

• Good estimations are needed for water balance studies, water resources assessments, effective agriculture and forestry, ecology etc.

• Sensitive to global changes: Climate change, deforestation, urbanisation, change of CO2 in atmosphere etc.

Consumptive water use by terrestrial ecosystems as seen in a global perspective

(Falkenmark in SIWI Seminar 2001).

percentages

Some Global Estimates Blue-Green

Water Flows

Objectives of this Lecture

• Coupled Water-Energy Balance

• Processes of evaporation

• Measurement of evaporation

• Estimation of evaporation

Exoatmospheric Radiation: ~1376 W m-2

~50% to 95% of radiation reaches the surface

Incoming Solar Radiation

(Solar constant;

not really constant!)

Radiation Balance (simplified!)

nLsN RR r1R

Net radiation RN : (neglecting storage of heat below the surface)

What will happen ?

Lake Desert

Earth’s Energy Budget Coupled Energy and Water Cycle

Surface Energy Balance

Incoming Energy = Outgoing Energy + D Storage per time step

Rn = lvE + H + G + DS/Dt

Rn: Net radiation

lE: Latent heat (= evapotranspiration; Etotal)

H: Sensible heat

G: Soil heat flux

DS/Dt: Change in storage

Assuming G and DS/Dt to be negligible: Rn = lE + H

Coupled Water-Energy Balance

• Watershed mass-balance P = Q + E + DS/Dt Know this!!

• Surface energy-balance Rn = H + lvE + G + DS/Dt Know this!!

Net Solar Radiation (Snet)

Snet = Sin – Sout

Sout = Sin (a)

Snet = Sin(1 – a)

Albedo (a) is the reflection coefficient (a := Sout / Sin )

Sin Sout

Snet

a

Typical Albedo Values

Surface Albedo (%)

Water 5-10

Dry soil 20-35

Wet soil 8-15

Grass 15-30

Dense spruce forest 5-10

Mixed conifer/hardwood 10-15

Hardwoods 15-20

Fresh snow 80-95

Old snow 40-70

Objectives of this Lecture

• Coupled Water-Energy Balance

• Processes of evaporation

• Measurement of evaporation

• Estimation of evaporation

Evaporation and

Transpiration

Processes

• Free-water evaporation

– Open water surfaces • Lakes, rivers, vegetation

surfaces (interception), soil surface

• Transpiration • Roots Stem Leaves Stomata Atmosphere

Symbols and Terminology (all values in mm per time step)

Evaporation E0 : open water evaporation (often the reference E)

Es : evaporation from soil

EI : interception evaporation

Transpiration ET : transpiration of living plants (and animals/humans)

Evapotranspiration := sum of all E-fluxes Epot : potential evapotranspiration (no moisture shortage)

Eact : actual evapotranspiration (can be lower than Epot

depending on moisture availability)

Free Water Evaporation

• Lakes, soil, saturated canopy - function of: – Available Energy

– Vapor Gradient

– Atmospheric Conductance

– Albedo

• Transpiration – additional function of: – Stomatal conductance

A note about resistance (R)

and conductance (C):

inverse quantities!

CR

1

Transpiration Process by which water vapor escapes

from living plants and enters the atmosphere

It includes water which has transpired

through leaf stomata

Very Difficult to Measure

Usually Lumped in with Total Evaporation

“Evapotranspiration” but “Total Evaporation” is the preferred term

Transpiration Process Consider the structure of a leaf

Epidermis

Epidermis

Cuticle

Cuticle

Mesophyll

Stomatal Pore

High Vapor Pressure

Low Vapor Pressure

Water vapor exits

when pore is open to let

carbon in (photosynthesis)

H2O

H2O

H2O

H2O

H2O

H2O

H2O

H2O

Resistance Analogs

Open Water Leaf

RH=100%

RH=100%

RH<100% RH<100%

Atmospheric

Conductance

Atmospheric

Conductance

Stomatal

Conductance

Relative

humidity

Evaporation from Soil

• If saturated, behaves like water – Depending on solar energy and vapor pressure of air

– Occurs normally for 1 to 3 days max • Depending on weather and soil conditions and characteristics

• If surface not saturated: – Evaporation in soil profile

– Air in soil pores ~es

0%

100%

Evap. ra

te

Bare Soil

Soil w/ Litter

0 5 10 15 Time (days)

Comparison of forested and deforested

areas Average annual water balances in forested and deforested areas in %

(Baumgartner, 1972). P = Precipitation Etotal = ES + EI + ET R = Runoff ES = Soil evaporation EI = Interception evaporation ET = Transpiration

P Etotal R

Expressed in % of Etotal

ES EI ET

Forests 100 52 48 29 26 45

Open

land

100 42 58 62 15 23

(from lecture notes, De Laat & Savenije 2008)

Energieflüsse

Challenges for understanding and

estimating TRANSPIRATION

• Very different for different plants

• Density and geometry of stomata and canopy

• Stomatal mechanics are bio-chemically controlled

• Environmental feedbacks: – Solar irradiance

– Air temperature

– Vapor pressure deficit

– Soil moisture

– CO2 in the atmosphere

• ETC!!

Evapotranspiration (ET) combination of Evaporation and Transpiration

• Potential (PET): A theoretical rate of ET when all surfaces have unlimited water supply

– Depends on surface albedo (% of energy reflected) and other meteorological parameters as well as the vegetation

• Actual (AET): The true rate of ET, of most interest to water managers

– Depends on plant, soil, and soil water properties and soil water availability

• Often done in practice: estimate PET for a defined land use and adjust with a crop coefficient (k)

• Consumptive use: mainly an irrigation term describing the “actual” (seasonal) consumption

Some PET and AET values

• PET from open water – Tropical regions 1500–3000 mm/a

– Mediterranean area 1000–1500 mm/a

– Humid temperate area 550–800 mm/a

– Cold humid or mountainous 300 mm/a or less

(in mm/a)

Comparison Eact (= AET) and Epot (= PET)

for cropped surface vs. bare soil

Fig. 3.1 Relative evapo(transpi)ration from an initially wet

(bare and cropped) surface during a rainless period.

Estimation of ET using crop factors

• In various handbooks crop factors kc are tabulated in relation to a particular ETref . The reference evaporation is often taken as the evaporation of an open water surface, Eo neglecting the storage of heat. In The Netherlands potential evapotranspiration of grass may then be estimated from

• This shows that the crop coefficient, kc is time-variant. FAO defines ETref as the potential evapotranspiration of short grass. It has to be noted that a different definition of ETref results in a different set of crop factors.

refcpot ET kET

period summer the for E 8.0ET opot

period winterthe for E 7.0ET opot

Terminology and Processes

Some Terminology

• Interception: The process by which precipitation falls on vegetative surfaces and is stored there.

• Gross rainfall (R): The rainfall measured above canopy or in open areas.

• Direct Throughfall (Rd): Proportion of rainfall that passes through the canopy without being detained (“free throughfall”).

• Canopy Throughfall (Rc): Proportion of rainfall that contacts the canopy before reaching the ground; can have different chemistry than Rd.

• Stemflow (Rs): The water that reaches the ground surface by running down trunks and stems; can have different chemistry than Rd.

• Net Throughfall (Rt): The rainfall that reaches the ground surface directly through canopy spaces, by canopy drip, and stemflow.

Terminology continued…

• Canopy Interception Loss (Ec): Water that evaporates from the canopy.

• Litter Interception Loss (El): Water that evaporates from debris and litter (in forests often 0.02 to 0.05R).

• Total Interception Loss (E): canopy + litter evaporation

Canopy Characteristics

• Storage Capacity (S): The depth of water that can be detained on a plant surface [0.5 – 5.0 mm, higher for conifers (up to 8 mm) or for solid precipitation (up to >25 mm)].

• Direct Throughfall Coefficient (p): Rd = R * p

• Drainage Coefficient (b): Proceeds at exponential rate relative to canopy saturation and reaches maximum (S).

65

70

75

80

85

90

95

100

0 25 50 75 100 125 150

Storm Size (mm)

Th

rou

gh

fall %

Ridge-top stand

Gum Springs watershed

Through fall as % of Storm Precipitation

Oak-Hickory Stands in Missouri Ozark

Jewitt, 2008

INTERCEPTION

• The initial processes that affect precipitation prior to ponding

and infiltration.

Interception represents a hydrologic “loss”

to the system (But, is loss the right word??)

• 10% - 40% of gross rainfall annually!

• Can have large seasonal variations

• Much more variable over short-term periods (event time scale) <0% to ~100%

• Highly dependent on rainfall frequency

• Negative interception ?! Fog/cloud interception and condensation can be significant

• Reduces rainfall intensity, but can increase it locally (channelizing of throughfall’) and, thus, can increase erosion

• Significant water storage (and loss) in snow-dominated systems

• Voluminous quantities of literature are available

• Interception reduces transpiration

Evap rate > transpiration in forests with large interception

Evap rate ~ almost transpiration (or less) in grasslands

Why? (Higher interception in forests compared to grassland)

• Throughfall chemistry

Dry deposition, thus increase of SO4, NO3, Cl, Ca, K, etc.

Leaching from leaves (mainly organic C)

• Effects on other biological processes

Epidemiology of fungal pathogens

Duration of leaf wetness key, but difficult to measure

Significant heterogeneity of wetting/drying within canopies

Interception represents a hydrologic

“loss” to the system (plan-soil-water system)

INTERCEPTION - VEGETATION CHARACTERISTICS

Interception capacity is a function of

Growth form: trees, shrubs, grasses

• coniferous trees intercept 25-35% of annual precipitation

• deciduous trees intercept 15-25% of annual precipitation, but just as

much as coniferous trees during the growing season

• grasses have high interception capacity during the growing but then

either die (annual plants) or lose mass (perennial plants); also they

are grazed and harvested (spring wheat intercepts 11-19% of

precipitation before harvest)

Jewitt, 2008

Brief Note on

Stemflow

• Stemflow, Rs, is generally low

• Conifers: <1% of gross precipitation

• Smooth barked trees: up to 5% gross precipitation; depends on geometry and structure of canopy etc.

• May play important role in nutrient delivery

• Big pain to measure, relative to canopy interception

(from A. Rodhe, Sweden)

Objectives of this Lecture

• Coupled Water-Energy Balance

• Processes of evaporation

• Measurement of evaporation

• Estimation of evaporation

Measuring Etotal

• Water Balance – Measure precipitation and streamflow (ignoring dS/dt !!)

E = P – R

– Examples: Precipitation in a catchment is 1000 mm/a, water yield is 600 mm/a, so E is 400 mm/a; ignoring storage changes (note, accumulation of errors!!)

• Micro-meteorological measurements

• Evaporation Pan – Measure daily rate of water drop in tank

– Estimate: E = kp x Epan

(determining pan coefficient kp is difficult)

• Lysimeters: Buried tanks growing with plants

– Measure precipitation in and drainage out

– and/or weigh tank

Evaporation pan: Class A pan

Evaporation pan: Class A pan

Class A pan

Class A pan

(Picture from Prof. Peter Troch)

Measuring evaporation of a lake

Estimation of evporation using a

Class A pan (simple example)

In a floating class A plan the water height at day one was at 6 AM

is 210 mm, and at the next morning (also at 6 AM) the water level

was estimated to a depth of 220 mm. During that day a

precipitation event of 15 mm occured. What was the evaporation?

mm/d 5E

mm/d 10mm/d 15E

ΔhPE w

Note: To calculate the evaporation from a Class A pan located on

the land surface, the pan coefficient needs to be considered (‘oasis

effect’).

panpanref EkE The coefficient varies between 0.35 and 0.85 depending on time

scale (day, month, or year), climate, soils etc.

Weight according

to Wild

Piche-Evaporimeter

Lysimeter Set-up

Fig. 3.7 Lysimeter with controlled water table

Excellent measurement of real E, in

particular if a weighted lysimeter is used

But,

Point measurement and regionalisation to

catchment scale is difficult

Soil column often not undisturbed (not

natural)

High experimental effort; costly in particular

for weighted lysimeters (the most useful

type!)

Lysimeter: pros and cons

Estimation of ET using a lysimeter

The only real measurement of ET from land!

Ea: Actual/real ET [mm d-1]

Po: Precipitation at the ground [mm]

percsoil: Percolation out of the soil column [mm]

DSsoil: Change of soil water content during

time step Dt [mm]

Dt: time step [d]

Δt

ΔSpercPEa

soilsoilo

The following variables were measured within 24

hours (7 AM – 7 AM): Precipitation 10 mm,

percolation 1 mm, and change of soil water content 3

mm (increase of soil water).

mm/d 6 Ea

1d

mm 3mm 1mm 10Ea

Δt

ΔSpercPEa

soilsoilo

Estimation of ET using a lysimeter

(a simple example)

Measurement of

through fall

Throughfall

Measurement

Measurement of

stem flow

Stemflow Measurement

Objectives of this Lecture

• Coupled Water-Energy Balance

• Processes of evaporation

• Measurement of evaporation

• Estimation of evaporation

Evaporation Estimation

Depends on:

Climate

1. Net radiation (atmosphere, albedo, exposition, topography etc.); energy is the most important parameter

2. VPD (relative humidity)

3. Temperature (more correctly temperature on evaporating surface: soil, water surface, or leaf)

4. Wind speed, transporting saturated air masses away

5. Soil water status/supply (moisture storage capacity)

Vegetation Characteristics

6. Height, canopy, roughness (atmos. conductance)

7. Species, age (stomatal conductance) • Response to environmental variables

Estimating Evaporation Some examples for widely used formulae

• Thornthwaite – PET of grass cover

– Uses Ta, heat index

• SCS Blaney-Criddle – Uses Ta, day length, crop and geographical coefficients

• Jensen-Haise – Uses T, Sin, VP, elevation

• …. there are many, many more empirical formulae (see text books or course note)!

• Penman-Monteith (most physically based approach) – Often used to calculate reference vegetation ET

– Uses climate and vegetation characteristics

– Widely accepted to be appropriate for different land uses

– Has many parameters, thus needs many observations

Example: Results of the application of the

Thornthwaite formula (for details see lecture notes)

Mansoura, Egypt

Tn J EP Dn Nn E E oC (-) mm/month d hr mm/month mm/d

Jan 13.3 4.4 26.4 31.0 10.4 23.7 0.8

Feb 14.0 4.8 30.1 28.0 11.1 26.0 0.9

Mar 16.3 6.0 42.7 31.0 12.0 44.2 1.4

Apr 19.6 7.9 66.0 30.0 12.9 71.0 2.4

May 24.4 11.0 111.2 31.0 13.6 130.2 4.2

Jun 26.1 12.2 130.2 30.0 14.0 151.9 5.1

Jul 26.6 12.5 135.6 31.0 13.9 162.3 5.2

Aug 27.0 12.8 141.1 31.0 13.2 160.3 5.2

Sep 25.8 12.0 126.2 30.0 12.4 130.4 4.3

Oct 22.9 10.0 95.8 31.0 12.0 98.9 3.2

Nov 19.9 8.1 68.8 30.0 10.6 60.8 2.0

Dec 15.2 5.4 36.5 31.0 10.8 34.0 1.1

J = 107.0, a = 2.4 Average = 3.0

Table 3.6 Example computation of ETTHORN

Comparison of different empirical

methods to estimate evaporation

Eo open water evaporation in mm/d

C Conversion constant

RN net radiation at the earth surface in W/m2

L latent heat of vaporization (L = 2.45*106 J/kg)

s slope of the temperature-saturation vapour pressure curve

(kPa/K)

es saturation vapour pressure deficit (kPa)

ed actual vapour pressure deficit (kPa)

γ psychrometric constant (γ = 0.067 kPa/K)

cp specific heat of air (cp = 1004 J/kg/K)

ρa air density (ρa = 1.2047 kg/m3 at sea level)

ra aerodynamic resistance (s/m), which is function of windspeed U2

s

r/eecsR

L

CE

adsapN

o

5.0U 54.0

245r

2

a

Open water evaporation: Equation of Penman

Required meteorological data (24 hour means at 2 m height):

Ta temperature of the air

RH relative humidity or actual vapour pressure

U2 windspeed

n/N relative sunshine duration or radiation

s

r/eecsR

L

CE

adsapN

o

Open water evaporation:

Equation of Penman

Evapotranspiration ET

Penman - Monteith equation

ra aerodynamic resistance (s/m)

rc crop resistance (s/m)

For a soil amply supplied with water rc reaches a minimum value and

Eact = Epot

Example aerodynamic resistance of grass:

Minimum value crop resistance grass

(crop well supplied with water)

rc = 70 s m-1

ac

adsapN

rr1 s

r/eecsR

L

CET

2

aU

208r

• Standard for estimating potential evapotranspiration (FAO).

• Suitable to directly estimate potential evapotranspiration, if the crop resistance is known (the one-step method), but it may also be used for estimating the reference crop evaporation in the two-step method.

• Definition of the reference crop:

The reference evapotranspiration, ETref, is defined as the rate of evapotranspiration from a hypothetical crop with an assumed crop height (12 cm) and a fixed canopy resistance (rc = 70 s.m-1) and albedo (r = 0.23) which would closely resemble evapotranspiration from an extensive surface of green grass cover of uniform height, actively growing, completely shading the ground and not short of water. With crop coefficients this ETref can be adjusted for other land uses.

Penman-Monteith Equation

Modelling total Eact using the Penman-Monteith

approach in a mountainous catchment (Ott and Uhlenbrook, 2004, HESS)

Modelling of Eact on a hourly base at a sunny

summer day

(Ott, Uhlenbrook 2004, HESS)

Mean annual PET for grass for Germany (German Hydrological Atlas)

Input parameters:

• sunshine duration

• air temperature

Calculated for every raster

cell on monthly basis and

summed up.

Min: in elevated areas (pre-

alpine and alpine mountains) =

350-400 mm a-1

Max: Upper Rhine valley =

>650 mm a-1

Difficulties to estimate areal ET

Irrigation

Land use change – Deforestation

Land use and land use change – Urbanisation

Land use – Intensive Agricultural Production

Take Home Messages • Coupled water-energy balance; evaporation is the

link!

• Differentiate between the processes/variables: Etotal, ES, EI, ET, ET, ETref, ETact, ETpot and different rainfall components in vegetated areas

• Note, importance and effects of interception

• Measurement of evaporation is difficult (i.e. different devices and techniques)

• Penman/Penman-Monteith equation is most accurate method to estimate evaporation (but needs a lot of input data …); it is a physically based method

• Areal estimation (space time variability!) of evaporation is even more difficult (i.e. different methods)

A note on units …

• Heat Fluxes are expressed in units of:

E L-2 T-1 (e.g. J m-2 s-1)

-or-

Energy per unit area per unit time (e.g. W m-2)

-or-

Power per unit area

The SI unit of Power is the Watt (W)

The SI unit of Energy is the Joule (J)

note: 1J = 1W x 1s