ET Theory 101ET Theory 101

USCID WorkshopUSCID Workshop

http://http://biomet.ucdavis.edubiomet.ucdavis.edu

PMhrPMhr, , PMdayPMday, , PMmonPMmon

CUP, SIMETAW (DWR link)CUP, SIMETAW (DWR link)

R.L. Snyder, Biometeorology Specialist Copyright © Regents of the University of California

Methods of Heat TransferMethods of Heat TransferConductionConduction-- from molecule to moleculefrom molecule to molecule

Heat Heat SourceSource

ConvectionConvection -- by movement of by movement of heated airheated air

Metal barMetal bar

RadiationRadiation -- energy passing energy passing from one object to another from one object to another without a connecting mediumwithout a connecting medium

Long wave Long wave loss from loss from EarthEarth

Short wave Short wave gained from gained from the sunthe sun EarthEarth

Questions 1 and 2Questions 1 and 21. How many molecules

of air are in a cubic meter?

1. If six billion people count 1000 molecules per hour, it would take 511 million years to count the number of molecules in 1 m3

2.69 x 1025

26,900,000,000,000,000,000,000,000 molecules m26,900,000,000,000,000,000,000,000 molecules m--33

2. The air is mostly nitrogen? (T/F)?

2. Air is mostly empty space. Less than 0.1% of the volume is occupied by moleculesFalse

Horstmeyer, S. 2001. Weatherwise 54:20-27.

Questions 3 and 4Questions 3 and 43. At 30oC, velocities

N2 - 1709 Km h-1

O2 - 1603 Km h-1

CO2 - 1366 Km h-1

H2O - 2136 Km h-1

3. Which molecules move faster? A. nitrogen B. oxygen C. carbon dioxide D. water vapor

4. False! Less than 0.1% of volume is occupied. Air can hold more water.

4. When saturated, the air cannot hold more water vapor (T/F)?

Horstmeyer, S. 2001. Weatherwise 54:20-27.

Questions 5Questions 5

5. How many molecule collisions per second occur in a m3 of air?

5. There are about 595 trillion collisions per second between air molecules in a m3 of air.

595,000,000,000,000 collisions/sec595,000,000,000,000 collisions/sec

Occupy < 0.1% volumeOccupy < 0.1% volume

26,900,000,000,000,000,000,000,000 molecules m26,900,000,000,000,000,000,000,000 molecules m--33

Horstmeyer, S. 2001. Weatherwise 54:20-27.

Sensible Heat & TemperatureSensible Heat & Temperature

Lower temperature Lower temperature LessLess sensible heatsensible heat

Higher temperature Higher temperature MoreMore sensible heatsensible heat

HO

H

Water Molecules consistof one oxygen and twohydrogen atoms

Water Molecule

Methods of Heat TransferMethods of Heat TransferLatent Heat Latent Heat -- Chemical HeatChemical Heat

HO H

When water moleculesevaporate, sensible heat ischanged to latent heat andthe temperature drops

H O

H

When water moleculescondense, latent heat ischanged to sensible heatand the temperature rises

More Water Vapor More Latent HeatMore Water Vapor More Latent Heat

HH O

HH O

OH

H

H

HO

H HO

HH O

H

H

O

H

HO

H

HO

I am a free water vapor

moleculeEnergy breaks our hydrogen bonds and sets

us free

Latent heat

Questions 6 Questions 6

6.6. False, there is more False, there is more total heat in humid total heat in humid than in dry air to than in dry air to melt the ice creammelt the ice cream

6.6. Your ice cream will Your ice cream will melt faster at 35% melt faster at 35% RH than at 75% RH than at 75% RH (T/F)?RH (T/F)?

Which wet towel dries fastest?Which wet towel dries fastest?

30 % RH30 % RH 70 % RH70 % RH

TTaa = 30 = 30 ooCC

Adiabatic ProcessAdiabatic Process

Questions 7 Questions 7

7.7. Yes! But both the Yes! But both the temperature and temperature and vapor pressure vapor pressure must increase must increase

7.7. Is there evaporation Is there evaporation in a greenhouse in a greenhouse with 100% relative with 100% relative humidity?humidity?

following the following the saturation vapor saturation vapor pressure curve. pressure curve.

DiabaticDiabatic ProcessProcess

RadiationRadiation4TE εσ=

ε = 1.0 for a black body

ε < 1.0 for a gray body

σσ= 5.67 = 5.67 ×× 1010--88 W mW m--22 KK--11

TT = absolute temperature = = absolute temperature = ooC+273.15C+273.15

Blackbody spectral emittance for Sun and Earth

0

20

40

60

80

100

0.1 1 10 100

Wavelength (µm)

Sola

r Spe

ctra

l Em

ittan

ce (M

W m

-2 µ

m-1

)

6000 K 288 K Eart

h Sp

ectr

al E

mitt

ance

(W m

-2 µ

m-1

)

0

10

20

30

73,483,200 W m73,483,200 W m--22 390 W m390 W m--22

Direct Radiation (Direct Radiation (QQ))

•• Radiation that comes directly from the sun Radiation that comes directly from the sun

•• The amount of energy received per unit area is The amount of energy received per unit area is called “Irradiance” and the units are called “Irradiance” and the units are commonly W mcommonly W m--2 2 = J s= J s--11 mm--22..

•• The amount of energy received depends on the The amount of energy received depends on the angle of incidence of the radiationangle of incidence of the radiation

Direct beam radiation interception (W mDirect beam radiation interception (W m--22))

0o

60o

60o

30o

Qs500 433 250

QQss = Q = Q cos(cos(αα))

Diffuse Radiation (Diffuse Radiation (qq))

•• Solar radiation that is scattered by the sky and Solar radiation that is scattered by the sky and comes from all directions. comes from all directions.

•• During much of the day, about 10 to 15% of During much of the day, about 10 to 15% of the radiation received on a flat surface is the radiation received on a flat surface is diffuse radiation. diffuse radiation.

•• The diffuse radiation is nearly the same The diffuse radiation is nearly the same regardless of the surface orientation.regardless of the surface orientation.

•• The percentage of diffuse radiation is higher The percentage of diffuse radiation is higher near sunrise and sunset.near sunrise and sunset.

Direct and diffuse radiation (W mDirect and diffuse radiation (W m--22))

0o

60o

60o

30o

Qs

Qs+ q500

535

433

468

250

285

Rs = Qs + q

q ≈ 0.15 Qs on a horizontal sfc

0

10

20

30

0.1 1 10 100

Vegetation height (m)

Ref

lect

ion

(%)

AlbedoAlbedo

Net solar radiation (W mNet solar radiation (W m--22))

0o

60o

60o

30o

Qs

Qs+ q

α= 0.25

500

535

401

433

468

351

250

285

214

Net RadiationNet RadiationRn=(1-α)Rs+Lu+Ld

Rs=Qs+qRs

Rs Lu Ld

cloudy clearcloudy clear

LLuu + L+ Ldd = = --10 W m10 W m--22 to to LLuu + L+ Ldd = = --100 W m100 W m--22

Net radiation (W mNet radiation (W m--22))

0o

60o

60o

30o

Qs

Qs+ q

α= 0.25

RLn =-100

500

535

401

301

433

468

351

251

250

285

214

114

Net RadiometerNet Radiometer( )1n sd Ld LuR R R Rα= − + +

Soil Soil ((GroundGround)) Heat FluxHeat Flux

1TG Cz

∂= −

∂

0.0

0.5

1.0

1.5

2.0

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Volumetric Water Content

Ther

mal

Con

duct

ivity

(W m

-1K

-1)

SandyClayPeat

(b)

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=12

121 zz

TTCG

Soil Heat Flux Density Soil Heat Flux Density (G )(G )

Heat PlateHeat Plate

ThermocouplesThermocouples dd

GG

GG22

CCVV –– volumetric heat capacityvolumetric heat capacity

2f i

Vf i

T TG G C d

t t⎛ ⎞−

= + ⎜ ⎟⎜ ⎟−⎝ ⎠

SURFACE ENERGY BUDGETSSURFACE ENERGY BUDGETS

++

--+ - + -

MiscLEHGRn +++=

-+

Sensible Heat Flux DensitySensible Heat Flux Density

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=12

12

zzTTCH pκρ

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

hp r

TTCH 12ρ

hh

gzzr

=−

=12

1 κ

Latent Heat Flux DensityLatent Heat Flux Density

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

12

12

zzeeC

LE p

γρ

κ

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎟⎠

⎞⎜⎜⎝

⎛−=

w

p

reeC

LE 12

γρ

ww

gzzr

=−

=12

1 κ

Microclimate & Microclimate & EToETo

•• Fetch RequirementsFetch Requirements•• Shading Shading •• Wind blockingWind blocking•• Marine effectsMarine effects

Fetch Requirements (Indio)

98 m

83 m

N

ST8_1

ST7_1

ST7_1 and ST8_1 installed on March 24

Prevailing Wind Direction CIMIS 162

GRASS

Fetch (98 m Vs 181 m)

y = 1.00xR2 = 0.99

7.0

9.0

11.0

13.0

15.0

7.0 9.0 11.0 13.0 15.0

CIMIS ETo (mm)

Non

Idea

l ETo

(mm

)

Indio Station ST7_1

Empirical ETo Empirical ETo –– El Dorado Country ClubEl Dorado Country Club

Adjustments for Regional effectsWind Blockage

Sunrise-Sunset

Advection

Empirical EquationsCIMIS

Regional effects

El Dorado Country Club

y = 0.63xR2 = 0.72

0.0

2.0

4.0

6.0

8.0

10.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

CIMIS ETo (mm)

El D

orad

o E

To (m

m)

Torrey Pines Vs Mira Mar

y = 0.77xR2 = 0.72

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Mira Mar CIMIS ETo (mm)

Torr

ey P

ines

ET

o (m

m)

Temperature Model

y = -0.022x2 + 1.390xR2 = 0.885

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40Mira Mar CIMIS T (oC)

Torr

ey P

ines

T (o C

)

Wind Correction

y = 0.915xR2 = 0.667

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Mira Mar CIMIS Wind Speed (m s-1)

Torr

ey P

ines

W

ind

Spee

d (m

s-1

)

Torrey Pines ETo Model

y = 0.973xR2 = 0.980

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Mira Mar CIMIS ETo (mm)

Torr

ey P

ines

E

To (m

m)

R s & T d from Torry PinesT = -0.022*T C ^2 + 1.390*T C

U = 0.915*U C

Landscape CoefficientLandscape Coefficient

o

LL ET

ETK =

ETETLL -- measured measured ETEToo -- estimatedestimated

Dense Canopy Dense Canopy Light InterceptionLight Interception

Sparse Canopy Sparse Canopy Light InterceptionLight Interception

Some light reflected. Some light reflected. Increases sensible heat Increases sensible heat near the surface.near the surface.

Density CorrectionDensity Correction

0.000.00

1.201.20

0.800.80

0.400.40

Frac

tion

of M

axim

um

Frac

tion

of M

axim

um K

cK

c

00 2020 4040 6060 8080

CCGG Ground Cover (%)Ground Cover (%)

sin70 2

GCF π⎛ ⎞= ⎜ ⎟⎝ ⎠

-100

0

100

200

300

400

500

600

700

800

7 10 13 16 19 8 11 14 17 8 11 14 17Time

Ene

rgy

Flux

Den

sity

(W m

-2)

Rn LE H G

Sunflowers (Bari, Italy)

-200

0

200

400

600

800

2400 1200 2400 1200 2400 1200 2400 1200 2400 1200 2400

Flux

Den

sity

(W m

-2)

Rn LE H G2

24-Jun20-Jun

Citrus Energy Balance - Lindsay 2001

Net

Rad

i atio

n ( W

mN

et R

adi a

tion

( W m

-- 22))

Net Radiation

Transpiration 23 July

9.76 mm

Transpiration 26 July

14.66 mm

0.00.0

0.40.4

0.80.8

1.21.2

1.61.6

Time (h)Time (h)

Tra

nspi

r atio

n ( m

m h

Tr a

n spi

r atio

n ( m

m h

-- 11))

--200200

200200

600600

14001400

10001000

00 121266 24241818

Local Advection

0.0

0.2

0.4

0.6

0.8

1.0

Time of Drying

Fra

ctio

n of

Dai

ly E

Tc

SU

NR

ISE M

ID A

M

NO

ON

MID

PM

SU

NS

ET

Fog ContributionFog Contribution

Water Table ContributionWater Table Contribution

ETETc ETETcc c

No Water TableNo Water Table With Water TableWith Water Table

The EndThe End

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