Energy Balance and Evapotranspiration MeasurementEnergy balance approach Boulet G., Chehbouni A., Braud I., Vauclin M., Haverkamp R., Zammit C. 2000. A simple water and energy balance

Energy Balance and Evapotranspiration

Measurement

Energy Balance and Evapotranspiration

MeasurementYu-Jun Cui

Ecole Nationale des Ponts et Chaussée, Paris, France

Jorge G. ZornbergThe University of Texas at Austin, USA

Yu-Jun CuiEcole Nationale des Ponts et Chaussée, Paris,

FranceJorge G. Zornberg

The University of Texas at Austin, USA

ABOUT THIS TOPIC- Multi-disciplinary

Unsaturated soil mechanics, meteorology, hydrogeology, agronomy etc.

- Broad application field

Analysis of drought effect, slope stability, agricultural soil compaction ; design and monitoring of evapotranpirativecover, etc…

- Application to be enhanced in geotechnical and environmental engineering

Only ONE paper submitted to this Symposium

OUTLINEEvapotranspiration background

- Solar Radiation

- Evaporation and Transpiration

Energy Balance Approach

- Background

- Case history 1: Boissy-le-Châtel (France)

- Case history 2: OII Superfund site (USA)

Direct measurement

- Background

- Case history: Monticello (USA)

Water balance approach

- Background

- Case history: Rocky Mountain Arsenal (USA)

Final remarks

Energy balance

Solar radiationEmission rate of the sun : 73 million W/m2

Portion on the top of the earth atmosphere : 1380 W/m2

30% scattered back to space

70% transmitted through the atmosphere

- 19% absorbed by gazes

- 51% transmitted down to the earth surface

Radiation balance :

( ) ( )[ ] ( )updownn LLaDSDSR −++−+=

S : direct shortwave radiation

D: diffuse shortwave radiation

L: Longwave radiation

a : earth albeto – reflected radiation

Soil water balance

( ) SRETRIP wtoffnt ++=+−

Water infiltration to the soil ground :

( ) ( )offntwt RETIPSRI ++−=+=

EvapotranspirationEvaporation : change in state of water from liquid to water vapor when the transfer of energy towards water increases the kinetic energy

Transpiration : evaporation from the vascular system of plants

Estimating evapotranspiration (Penman 1948):

γγρ

+∆+∆

= avwn ELRPET )/(1000

( )23.2374099+

=∆T

Pvs ( )( )100/8.0165.0 2uPPE vvsa +−=

( )

−

=42.58.67ln

87.42 zuu z

Evapotranspiration measurement

• Direct measurement

• Energy balance approach

• Soil water balance approach

Energy balance approach

GHLeRn ++=

zTkCH Hpa ∂∂

= ρSensitive heat transfer

zP

PkLLe vvv

∂∂

=ρεLatent heat transfer

(evaporation)

soilyTG

∂∂

= λSoil heat transfer


vvv PT

PT

LPCp

LeH

∂∂

=∂∂

== γε

β

β+−

=1

GRLe n

Bowen ratio β measurement

Water vapor perssureHygrometers ( dew point hygrometer in the system of Campbell Scientific)

Air temperatureThermocouples (chrome – constantan thermocouples in the Campbell Scientific)

Net radiation fluxNet radioameter

Bowen ratio β measurement

tdTC

S s∆= ( ) wwddwdds CCwCCC θρρρ +=+=

G(z = 0) = G(z = d) + S

Campbell Scientific

B023

Bowen ratio system(after Blight 1997)

Case History: Boissy-le-Chatel

Lodge

0.05

0.05

1.00Temperature monitoring zone

Drilling hole

Precipitation monitoring zone

(n 28)

J D

HG

E

F

A

CB

Garage

OfficeLivingroom

0 5 10 15m

Laboratory

Water collection zone

Station of meteorology

Measuring zone of water (Flux, Quantity)

Boundary of experimental drainage zone (615m )

Working house

Piezometer

Drainage network

TDR Probes

Legendes:

2

TDR Probes

After Cui et al. 2005 (in print)

-10

0

10

20

30

40

50

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/101/111/12

Date (day/month)

Air

tem

pera

ture

(°C

)

0

10

20

30

40

50

60

70

80

90

100

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12

date (day/month)

RH

(%)

0

50

100

150

200

250

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10

1/11

1/12

Date (day/month)

Prec

ipita

tion

(mm

/day

)

0

500

1000

1500

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10

1/11

1/12

Date (day/month)

Sola

r rad

iatio

n (J

/m²d

ay)

Field monitoring during the year 2003

0

5

10

15

20

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12

Date (day/month)

Win

d sp

eed

(m/s

)

0

10

20

30

40

50

60

70

80

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12

Date (day/month)

ETP

(mm

/day

)

0

5

10

15

20

25

1/1 1/2

1/3 1/4

1/5 1/6

1/7 1/8

1/9 1/10

1/11 1/12

Date (day/month)

Soil

tem

pera

ture

(°C

)

100 cm

50 cm

Field monitoring during the year 2003(continued)

-Darcy’s law for liquid phase :

-Fick’s law for vapor phase :

coupled through Pv to

zhkq w

w ∂∂

−=1

zPDq V

v ∂∂

−=2

∂∂

∂∂

+

∂∂

∂∂

=∂∂

zPD

zC

zhk

zC

th v

vvw

ww

∂∂

∂∂

+

−

∂∂

∂∂

=∂∂

zPD

zPPPL

tT

ztTC v

vv

eh λ

Determination of changes in Tsoil and θ

(after Wilson et al 1994)

Resolution method (Wilson et al’s equations)

• Attribute an initial value to β and determine the

corresponding values of H, G, PET and Le

• Calculate s and T by using H and Le definitions

• Lower boundary condition (T and hw ) known

• Resolution of Wilson et al’s equations

• repeat the calculations with another β value until an

admissible difference between calculated Le and PET

Temperature change at 0.5 m depth

8.0

9.0

10.0

11.0

12.0

13.0

14.0

0 5 10 15 20 25 30

Day(April, 1999)

Tem

pera

ture

(°C

)

Simulation

Measurement

(after Cui et al. 2005, in print)

Volumetric water content at 5 different depths

7

10

13

16

19

22

25

28

31

34

37

40

0 5 10 15 20 25 30

Day (April, 1999)

Vol

umet

ric w

ater

con

tent

(%)

Simulation15 cm25 cm35 cm45 cm55 cm

(Cui et al. 2005, in print)


Boulet G., Chehbouni A., Braud I., Vauclin M., Haverkamp R., Zammit C. 2000. A simple water and energy balance model designed for regionalization and remote sensing data utilization. Agriculture and forest meteorology 105, 117-132.

Shen Y.J., Kondoh A., Tang C.Y., Zhang Y.Q., Chen J.Y., Li W.Q., Sakura Y., Liu C.M., Tanaka T, Shimada J. 2002. Measurement and analysis of evapotranspiration and surface conductance of a wheat canopy. Hydrological Processes 16, 2173 –2187.

See also

Consideration of vegetation effect : LAI (Leaf Area Index)

Evapotranspirative Cover Systems

Evapotranspirative Cover Systems

Prescriptive CoverPrescriptive Cover(“Barrier” System)(“Barrier” System)

ET coverET cover(“Reservoir” System)(“Reservoir” System)

PrecipitationPrecipitationPrecipitation

EvapotranspirationEvapotranspirationEvapotranspirationOverland FlowOverland FlowOverland Flow

PrecipitationPrecipitationPrecipitation

PercolationPercolationPercolation

Overland FlowOverland FlowOverland Flow

MoistureStorageMoistureMoistureStorageStorage

PercolationPercolationPercolation

Case History: OII Superfund Landfill

Energy Balance ApproachEnergy Balance Approach

-50

0

50

100

150

200

250

Jan Feb Mar Apr May Jun Jul Aug Sep

Time

Liqu

id Q

uant

ity (m

m)

Infiltration

Evapotranspiration

Moisture Storage

Percolation

(E)( I )

(P)

(MS)

Monocover

Energy Balance Approach: Rooting DepthEnergy Balance Approach: Rooting Depth

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0 300 600 900 1200 1500

Rooting Depth (mm)

Perc

olat

ion

(%)

.

Baseline Case

Source: Zornberg et al. 2003

Energy Balance Approach: IrrigationEnergy Balance Approach: Irrigation

0

10

20

30

40

50

60

70

80

90

0 500 1000 1500 2000Irrigation (mm/year)

Perc

olat

ion

(%)

Baseline Case

Recommended irrigation (MWD)

Source: Zornberg et al. 2003

Direct measurement using a weighing lysimeter

Direct measurement using a weighing lysimeter

Sources: Benson et al. 2001, Waugh 2002

Monitoring of:

- Total weight, ∆W

- Precipitation, P

- Percolation, G

ET = P – (∆W + G)

Case History: Monticello (USA) Case History: Monticello (USA)

Sealing the Lysimeter Sealing the Lysimeter drainage capdrainage cap

Weighing lysimeters Weighing lysimeters for water storagefor water storage

Source: Waugh (2002)

Case History: Monticello (USA)Case History: Monticello (USA)


MonticelloVapor pressure deficit (VPD), Vapor pressure deficit (VPD), photosyntheticallyphotosynthetically active radiation active radiation (PAR), and transpiration rate of (PAR), and transpiration rate of P. P. smithiismithii measured July 6 on and measured July 6 on and adjacent to Lysimetersadjacent to Lysimeters


Water Balance ApproachWater Balance Approach

LysimeterDownSlope

30

Alldimensionsin meters20

0.6

10

5Perc.PipeSRO

Pipe

0.6

SRODiversion

Berm4 5

20

Source: Khire et al. (1997)

ET = P – G – S – Roff

Typical Lysimeter Cross-Section

Typical Lysimeter Cross-Section

LLDPEGeomembranePercolation

PipeExisting Slope (>2%)

EarthenBerm

Geocomposite Drain

20

EarthenBerm

Cover

InterimCover Soil

LLDPECutoff

RootBarrierLLDPE

Cutoff

Source: Khire et al. (1997)

Case History:Rocky Mountain Arsenal, USA




4 instrumented test covers•WCR moisture sensors•Lysimeter used to measure basal percolation•Weather station

•Temperature•Precipitation•Solar radiation•Wind speed

•Surface water runoff collection swales

WCR sensors

Moisture Content and Percolation Monitoring Results

Moisture Content and Percolation Monitoring Results

0

5

10

15

20

25

30

0 200 400 600 800 1000 1200 1400 1600 1800Time, days

Vol

umet

ric m

oist

ure

cont

ent θ

, %

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

Perc

olat

ion,

mm

θ(76 mm)θ(678 mm)

θ(1080 mm)

Percolation

Water Balance ApproachWater Balance Approach

0

100

200

300

400

500

600

700

0 200 400 600 800 1000 1200 1400 1600 1800Time, days

Cum

ulat

ive

annu

al a

mou

nt o

f wat

er, m

m Calculated ET from HYDRUSEstimated ET from water balance

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600 1800Time, days

Dai

ly e

vapo

trans

pira

tion,

mm

Calculated ET from HYDRUSEstimated ET from water balance

Comparison between ET estimated from water balance and ET calculated using HYDRUS:

- Significant daily discrepancies- Similar cumulative response

SummarySummary

SummarySummary• Among the various components of the water

balance, measurement of evapotranspiration has probably been the most difficult to quantify

• Direct measurement of evapotranspiration has been conducted using weighing lysimeters

• Quantification of evapotranspiration typically conducted using energy balance or water balance methods

• The current focus on evapotranspirative cover systems has brought renewed need for quantification of evapotranspiration

• Among the various components of the water balance, measurement of evapotranspiration has probably been the most difficult to quantify

• Direct measurement of evapotranspiration has been conducted using weighing lysimeters

• Quantification of evapotranspiration typically conducted using energy balance or water balance methods

• The current focus on evapotranspirative cover systems has brought renewed need for quantification of evapotranspiration

Final RemarksFinal RemarksSignificant improvements have been made regarding monitoring of evapotranspiration using direct methods (weighing lysimeter), energy balance methods, and water balance approaches. However, significant additional advances should be made towards integrating unsaturated soil mechanics with other areas such as meteorology, agronomy, and biology.

Significant improvements have been made regarding monitoring of evapotranspiration using direct methods (weighing lysimeter), energy balance methods, and water balance approaches. However, significant additional advances should be made towards integrating unsaturated soil mechanics with other areas such as meteorology, agronomy, and biology.

Grazie MilleGrazie Mille

Documents

Energy Balance and Evapotranspiration MeasurementEnergy balance approach Boulet G., Chehbouni A., Braud I., Vauclin M., Haverkamp R., Zammit C. 2000. A simple water and energy balance