REMOTE SENSING OF EVAPOTRANSPIRATION FOR WATER RESOURCES MANAGEMENT

BASIC PRINCIPLES

Ayse Kilic, University of Nebraska-Lincoln

Contributing Authors:

Baburao Kamble (UNL), Ian Ratcliffe (UNL), Richard Allen (UI)

University of Nebraska-LincolnGIS in Water Resources Lecture, 2014

• Landsat is a “Polar Orbiter” in a “sun synchronous” orbit (~11:00 am).

• Landsat orbits the poles every 90 minutes.

• We only get a ‘new’ image each 16 days for each spot on Earth.

Russia

Sochi

Each Landsat swath is 160 km wide

Recent Landsats• Landsat 8

• Launched February 11, 2013• 30 m pixel size for short-wave data• 100 m pixel size for thermal data• Revisit each 16 days

• Landsat 7• Launched February 1999• 30 m pixel size for short-wave data• 60 m pixel size for thermal data• Revisit each 16 days, 8 days after Landsat 8

• Landsat 5• Launched 1984 ended 2012• 30 m pixel size for short-wave data• 120 m pixel size for thermal data• Revisit each 16 days• Landsat 5 retired in 2012 (worn out), replaced by L8

What is Evapotranspiration?

Soil evaporation plus leaf transpiration

ET converts liquid water to vapor

ET consumes water from soil that must be replaced by rainfall or irrigation

ET from irrigation water is 90% of world-wide water consumption

Surface Temperature (8/29/2002) Western Nebraska

Temperature(°K)

Scottsbluff

There is much information in Surface Temperature. There is a huge amount of surface cooling by evaporation

Landsat 8 – 7/12/2013False Color Composite Bands 5/4/3 METRIC ETrF – 7/12/2013

ETr Fraction0.0

0.2

0.4

0.6

0.8

1.01.1

Evapotranspiration from 800 m diameter fields in Nebraska, USA

Some first processing of Landsat 8 images into Evapotranspiration

Landsat 8 -- Coastal area of Ventura, CA -- March 22, 2013

short-wave bands 6,5,4

Relative ET produced by METRIC following ‘sharpening’ of thermal data

Relative ET produced by METRIC

What do we use Evapotranspiration maps for?

• Better understanding of behavior of water consumption; timing. How it varies with vegetation type.

• Better water balances for hydrologic studies• Ability for improved water management • Ability for improved crop production• Knowledge of water consumption by crop

• Improved crop coefficient curves

• Reduction of Drainage and Salinity problems• Improvement in old irrigation projects

Irrigated fields in Nebraska

• ET is calculated as a “residual” of the energy balance. This requires both short-wave and thermal imagery.

• METRIC (Mapping EvapoTranspiration with high Resolution and Internalized Calibration)

ET = R - G - Hn

Rn

G

H ET

The energy balance includes all major sources (Rn) and consumers (ET, G, H) of energy

How do we determine ET from energy balance

Rn= Net Radiation

H= Sensible Heat Flux

G= Ground Heat Flux

ET= Latent Heat Flux

Net radiation from the sun is split into heating the air (H), heating the ground (G), or evaporating water (ET)

Vegetation Surface

ShortwaveRadiation

LongwaveRadiation

RS

RS

(Incident shortwave)

(Reflected shortwave)

RL

(Incident longwave)

(1-o)RL RL

(emitted longwave)

(reflected longwave)

Net Surface Radiation = Gains – Losses

Rn = (1-)RS + RL - RL - (1-o)RL

Surface Radiation Balance

Rs, and Rl are shortwave and long wave radiation, respectively. The arrows show the direction of energy flow (incoming-downward; outgoing-upward).

α is albedo (0 to 1) which is reflectance from the surface.

ε is emissivity term (0 to 1) which is the ability to emit long wave radiation.Black body is perfect emitter ( close to 1) whereas a grey body has emissivity less than 1.

What happens to Solar Radiation in the Atmosphere

H2O, O2, O3, N2O H2O, O2, O3, N2O

Direct Solar (Absorbed)Indirect

Longwave (Infrared) Radiation in the Atmosphere

H2O, CO2, CH4, CFC’s

4

What we want: At Surface Reflectance ρs,b

b,outb,in

b,ab,tb,s

TOA: Top of atmosphere

ρt,b at-satellite reflectance for band “b”

ρa,b “path” reflectance for band “b” that comes from molecules in the atmosphere

τin,b and τout,b are narrowband transmittances for incoming solar radiation and for surface reflected shortwave radiation

What satellite gives us: TOA Reflectance ρt,b

Incoming Transmissivity (ability to transport light)

C1-C5 = Generalized Coefficients fitted to MODTRAN and SMARTS2 models

Pair = mean atmospheric pressure, kPa (= f(elevation))W = precipitable water in atmosphere (= f(near surface vapor

pressure from weather station))Kt = turbidity (clearness) coefficient (default = 1.0)

qh = solar angle from nadir of horizontal surface

5432

1, coscosexp C

CWC

K

PCC

hht

airbin

Eq. has similar form to broadband

t equation of FAO-56, ASCE-EWRI

Outgoing Transmissivity

C1-C5 = Generalized Coefficients fitted to MODTRAN modelPair = mean atmospheric pressure, kPa (= f(elevation))W = precipitable water in atmosphere (= f(near surface vapor

pressure from weather station))Kt = turbidity (clearness) coefficient (default = 1.0)

qh = satellite angle from nadir of horizontal surface (0 for

Landsat)

543

t

air21b,out C

1

CWC

1K

PCexpC

TRANSMISSIVITY (FUNCTION OF WAVELENGTH)

Broadband Surface Albedo(Bulk Reflectance)

Wb = weighting coefficient that considers fraction of all potential solar energy at the surface over range represented by specific band. (Wb’s sum to 1.0)

weighting coefficients by Allen et al. 2006

7

1bbb,s w

Terms Band 1 Band 2 Band 3 Band 4 Band 5 Band 7 wb 0.254 0.149 0.147 0.311 0.102 0.036

0 0.4 0.6 0.8 1.2 1.6 2.0 2.4

Band: 1 2 3 4 5 7

Range for W5

Wavelength in Microns

0.103

Vegetation Indices

NDVI = (r4 - r3) / (r4 + r3)

SAVI = (1 + L) (r4 - r3) / (L + r4 + r3)

SAVIID = 1.1(r4 - r3) / (0.1 + r4 + r3)

For Southern Idaho: L = 0.1

We limit LAI 6.0

used to estimate the amount of vegetation on the surface which is then used to estimate aerodynamic roughness and thermal emissivity

Leaf Area Index (LAI):

r is usually

calculated at top of atmosphere

(Normalized Difference VI)

(Soil Adjusted VI)

LAI = 11SAVI3

NDWI = (r5 - r2) / (r5 + r2) (Normalized Difference Water Index)

Warning!!

NDVI = (r4 - r3) / (r4 + r3) (Normalized Difference VI)

• Please Note! that NDVI (and SAVI) are calculated using reflectances and not digital numbers and not radiances. The variables in the equations must be ‘normalized’ reflectances, by definition. Many novices and nonthinkers commonly compute NDVI using DN or radiance. DN is improper because its scale can change over time. In addition, both DN and radiance magnitudes will change with time of year as the sun angle changes.

• DN also changes with time of day. Reflectance is much more constant and consistent. One can use surface reflectance or top-of-atmosphere reflectance in the calculations. Results are usually similar since atmospheric attenuation is similar for both bands 3 and 4.

• We choose to use top-of-atmosphere in METRIC NDVI to be consistent with many other uses. However, using surface reflectance is probably slightly more consistent.

• Note also that NDVI computed from different satellite systems like MODIS will not be the same as from Landsat because of differences in band widths and centers.

Area just south of Albuquerque along Middle Rio Grande, New Mexico

NDVINega.0.0

0.2

0.4

0.6

0.8 +

0.0

1.0

2.0

3.0 +

LAI

290

300

310

320 +

Tsurface (K)

NDVIfalse color LAI

• Surface Emissivity• Surface Temperature

1

R

K

KT

c

1NB

2s

ln

Surface Temperature (Ts)

(Planck’s Law)

K1 K2

Landsat5 TM Band6 607.76 1260.56Landsat7 ETM+ Band6 666.09 1282.71

NB is the emissivity for the narrow band Landsat thermal band (10.45-12.42 μm wavelengths on Landsat 5, 10.31-12.36 μm wavelengths on Landsat 7, 10.5 – 11.2 μm wavelengths for band 10 on Landsat 8)K1 and K2 are constants Rc is the thermal radiance emitted from the surface in the narrow band, W/(m2 sr μm)Ts is surface temperature in K

K1 and K2 vary from image date to image date on Landsat 8. Therefore, you must read them from the Landsat header file that comes with the images.

eNB = 0.97 + 0.0033 LAI; for LAI < 3

Surface Emissivity

eNB = 0.98 when LAI 3

·       For water; NDVI < 0 and a < 0.47, eNB = 0.99 ·        For snow; NDVI < 0 and a 0.47, eNB = 0.99

Note that some bare rock may have emissivity as low at 0.90.The user can consult various emissivity libraries or measure.

Thermal Radiance from the Surface (Rc)

skyNBNB

pTc R

RLR

1

Rp is the path radiance in the Landsat thermal (narrow) band

that comes from molecules in the atmosphere Rsky is the narrow band thermal radiation emitted downward by a clear sky atmosphere (units are W/(m2 sr μm) )(we consider the 1- eNB component that reflects from the surface)

H2O, CO2, CH4, CFC’s

4

H2O, CO2, CH4, CFC’sH2O, CO2, CH4, CFC’s

44

For low aerosol conditions Rp=0.91, transmissivity τNB=0.866 and Rsky=1.32, based on comparisons with MODTRAN in southern Idaho (Allen et al. 2007). LT is the radiance calculated from the digital number for the thermal band.

Surface Temperature

Surface Temperature Image

Red – hot (500C)

Blue – cold (200C)

Surface Temperature Image

Pathfinder-Seminoe Reservoirs, WY

Surface Energy Budget EquationRn = G + H + lET

lET = Rn – G – H

Rn

G

H ET

Sensible Heat Flux is an Aerodynamic Process

Sensible Heat Flux (H) – SEBAL and METRIC

H = ( r × cp × dT) / rah

rah = the aerodynamic resistance from z1 to z2

HrahdT

z1

z2

dT = “floating” near surface temperature difference (K)

u* = friction velocity

k = von karmon constant (0.41)

ku

z

z

rzhzh

ah

*

)()(1

2

12ln

Advantage:dT is inverse calibrated (simulated) (free of Trad vs. Taero and free of Tair)

Advantage:dT and rah ‘float’ above the surface and are ‘free’ of zoh and some limitations of a single source approach

We use electric analog to represent the heat flow (Ohm’s Law)

Near Surface Temperature Difference (dT)

• To compute the sensible heat flux (H), define near surface temperature difference (dT) for each pixel

dT = Tnear surface – Tair

dT = Tz1 – Tz2

• Tair is unknown

• SEBAL and METRICtm assume a linear relationship between Ts and dT:

dT = b + aTs

HrahdTz1

z2

Soil Heat Flux (G)• Current G functions :

LAI ≥ 0.5

LAI < 0.5

G = f(H) is after suggestion of Stull (1988) and development of Allen (2010, memo).

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7

G/Rn

ratio

LAI

G/Rn current Eq. 33b

G/Rn for moist surface

Surface Energy Balance

Rn = ET + H + G

ET = (Rn - H – G)/

ETrF = ET/ETr

• is Latent heat of vaporization (2.45 MJ per Kilogram). converts ET from Energy unit (W/m2) to an equivalent depth of water (mm)

• ETrF is fraction of reference ET and generally ranges from 0 to 1.0. • ETrF value of 1.0 means that the fraction of reference ET is 1.0, so

that the ET for that pixel equals the reference ET value. • ETr is the reference ET, which is the “tall” or alfalfa reference ET that

is usually calculated using the ASCE Penman-Monteith equation (ASCE 2005).

Objective: Manage depletions to the Ogalla Aquifer. ET from irrigation extracts substantial amounts of water from the aquifer and lowers the levels.

Nebraska state law- Recognized that surface and ground water must be managed together for sustainability of water resources.

Irrigators have to reduce ground water depletion to long term sustainable levels.

Central Platte Natural Resources District (NRD) has adopted the use of Landsat based ET

Example Applications of METRIC -Nebraska

Central Nebraska Irrigation District (CPNRD) – 2007 Monthly ET

Central Platte Natural Resource District

2011 2007 1997

Variation in ET among years (Month of July)

Monthly ET estimates from METRIC were averaged over about 20 fields.Monthly ET estimates were similar to measured ET.

Accuracy of ET maps

-- Bowen Ratio energy Balance System (BRBS) data by Dr. Suat Irmak, BSE

Imperial Valley

~15% of traditional water supply to agriculture now flows to San Diego/ Los Angeles

ET maps help determine impacts of the water transfers on agriculture and on the Salton Sea.

California

Mexico

USA

Graphic courtesy of R. Trezza, 2008

2011 ET Workshop – Boise, Idaho

Landsat ET has improved stream flows for endangered fisheries and to protect native American water rights

Montana

Graphic courtesy of J.Kjaersgaard, 2009

Montana/Wyoming

ET

Graphic courtesy of C.Kelly, 2012

• US Supreme Court – Montana v. Wyoming, No. 137, Original

• --METRIC ET maps were introduced to the US Supreme Court in November 2013 to document how much irrigation water the State of Wyoming consumes from the Yellowstone River System

ETrF Comparison Between Landsat 8 and Landsat 7

0.00 0.20 0.40 0.60 0.80 1.00 1.200.00

0.20

0.40

0.60

0.80

1.00

1.20

f(x) = 0.996841829339176 xR² = 0.999270214426201

Landsat 8

Land

sat 7

ETrF is the ‘relative’ ET rate (fraction of reference ET)

Computations by Babu Kamble, Ian Ratcliffe, Ricardo Trezza

Daily Reference Evapotranspiration for the Entire United States1951 – 2012 at 12 km gridBased on GridMET (Bias-Corrected NLDAS Data by J.Abatzoglou)

Reference Evapotranspiration represents potential ET rate when surface is covered with vegetation

Reference Evapotranspiration-Google

Reference Evapotranspiration-Google Earth Engine