1. Ayse Kilic, University of Nebraska-Lincoln
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-Lincoln
GIS in Water Resources Lecture, 2014

2. There are many satellites orbiting the earth
There are many satellites orbiting the earth. However, today we are going to focus on only one system: LANDSAT

3. Each Landsat swath is 160 km wide
Sochi
Russia
A little bit more about Landsat!!
Nebraska takes 6 landsat paths to cover Nebraska while it requires 50+ landsat paths to cover the entire country of Russia.
Landsat makes one orbit every nineny minutes. And it is always Eleven o’clock everywhere the Landsat is on planet earth.
Landsat orbits the poles every 90 minutes. And as Landsat orbits, the earth rotates so that every orbit Landsat sees a new path. And it is only after 16 days, Landsat sees the same location twice. Because Landsat is always has the sun looking over its shoulder, it is always 11 o’clock in the morning when landsat takes its picture.
Landsat is in the same location so as the sun. It is the earth rotating. L5,L7 has 8 detectors (whisk broom). L8 has 5000 detectors (push broom)
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.
Replace Idaho with Nebraska image

4. 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
60 m pixel size for thermal data
Revisit each 16 days, 8 days after Landsat 8
Landsat 5
Launched 1984 ended 2012
120 m pixel size for thermal data
Landsat 5 retired in 2012 (worn out), replaced by L8
Landsats 1, 2 and 3 only had short wave (MSS-multi spectral scanner). Starting with landsat 4, we had a thermal imager.
L4 was only used for about 3 years and L5 was better quality and replaced L4.
L6 never made the orbit due to a failed rocket launch.

5. What is Evapotranspiration?
Soil evaporation plus leaf transpiration ET converts liquid water to vapor
In case anyone does not know what ET is, it is the sum of transpiration from the plant and evaporation from the soil.
Consumption of liquid water into vapor either by evaporation from soil and/or transpiration by plants
We have to irrigate to replace ET from soil for maximum crop production
ET consumes water from soil that must be replaced by rainfall or irrigation
ET from irrigation water is 90% of world-wide water consumption

6. Surface Temperature (8/29/2002) Western Nebraska
This is what Landsat sees thorough its thermal imager. There is a huge amount of surface cooling by evaporation.
Irrigated fields are cooler than rangeland.
We use this phenomena to estimate ET.
Question: what do I have to do to boil a bottle of water?
2.45 Million Joules per liter to evaporate water.
Scottsbluff
There is much information in Surface Temperature. There is a huge amount of surface cooling by evaporation

7. Some first processing of Landsat 8 images into Evapotranspiration
Evapotranspiration from 800 m diameter fields in Nebraska, USA
Landsat 8 – 7/12/2013
False Color Composite Bands 5/4/3
METRIC ETrF – 7/12/2013
Every field has a different ET amounts.
Center pivot fields (64 hectare-160 acres)

8. Landsat 8 -- Coastal area of Ventura, CA -- March 22, 2013
This is the first ever Evapotranspiration product produced from Landsat 8 thermal imagery – ET members of the Landsat Science Team (Allen, Kilic, Huntington, Trezza, Anderson)
False color image on the left. ET map is on the right at 100 m resolution of thermal band. The center is thermal sharpened to the 30 meter using NDVI.
Relative ET produced by METRIC following ‘sharpening’ of thermal data
Relative ET produced by METRIC
short-wave bands 6,5,4

9. 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
What do we care about ET?
We use ET to understand where and how much water is consumed in the landscape.
Irrigated fields in Nebraska

10. How do we determine ET from energy balance
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)
Net radiation from the sun is split into heating the air (H), heating the ground (G), or evaporating water (ET)
Rn= Net Radiation
H= Sensible Heat Flux
G= Ground Heat Flux
ET= Latent Heat Flux
ET = R - G - H n R G H ET
The energy balance includes all major sources (Rn) and consumers (ET, G, H) of energy
Satellite can not see ET. It can only see the reflected radiation and thermal. Therefore, we use energy balance where ET is calculated as a residual.
We can estimate the three terms on the right of equation using either reflected or thermal data.

11. α is albedo (0 to 1) which is reflectance from the surface.
Epsilon. Emissivity
(1- Emissivity) = (1-0.97)) is the Reflectance.
(1- Emissivity) *Rl incoming = Reflected incoming long wave.
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.

12. Atmosphere What happens to Solar Radiation in the Atmosphere
Reflected
from Clouds
Reflected
to Space
Extraterrestrial
Scattered
to Space
Atmosphere
Absorption
H2O, O2, O3, N2O
Absorption
H2O, O2, O3, N2O
Sun is the source for the shortwave radiation. We call that extraterrestrial because it is beyond the atmosphere of the earth.
Not all the shortwave (photons) make the atmosphere. Some of hits molecules in the atmosphere and they scattered (bounces of in all direction).
Most of the photons that reach to the surface get absorbed by the surface.
Once it is absorbed it is no longer radiation. It is converted into heat (h), conducted by the soil (G) or used to vaporize the liquid water (LE).
Some photons when they hit the surface, they bounce, this is reflected.
The slide shows what happens to shortwave radiation in the atmosphere.
Analogy (basketball)
One fourth of the photons (20%) gets absorbed by the molecules or scattered in the atmosphere.
Of the 80% (80 units) of remaining reaches to the surface.
Scattered Reflected
Scattered
Reflected
Indirect
Direct Solar (Absorbed)

13. INFRA means FAR in LATIN. INFRARED longer than Red.

14. Reflection from Surface
Longwave (Infrared) Radiation in the Atmosphere
Emission = f (T ) 4
Emission lost to Space
Emission from Clouds
Atmosphere
Absorption by Clouds
Emission
The long wave radiation is emitted by atmosphere (H2O, CO2, CH4) and by the earth. Both atmosphere and earth emit long wave.
We are only interested in the long wave that comes from the earth. Satellites sees both longwave infared and has no choice and we need to separate these.
Absorption
H2O, CO2, CH4, CFC’s
Emission from Clouds
Reflection from Surface
Emission from Surface

15. What we want: At Surface Reflectance ρs,b
What satellite gives us: TOA Reflectance ρt,b
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

16. 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
τin,b and τout,b are narrowband transmittances (0-1).
transmittances is the ability to transport light.
Eq. has similar form to broadband
t equation of FAO-56, ASCE-EWRI

17. Outgoing Transmissivity
C1-C5 = Generalized Coefficients fitted to MODTRAN model
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 = satellite angle from nadir of horizontal surface (0 for Landsat)

18. TRANSMISSIVITY (FUNCTION OF WAVELENGTH)

19. 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)
Band:
Range for W5
Albedo (bulk reflectance). how many photons bounce?
Wavelength in Microns
weighting coefficients by Allen et al. 2006
0.103

20. Vegetation Indices LAI = 11SAVI3 NDVI = (r4 - r3) / (r4 + r3)
used to estimate the amount of vegetation on the surface which is then used to estimate aerodynamic roughness and thermal emissivity
NDVI = (r4 - r3) / (r4 + r3)
(Normalized Difference VI)
NDWI = (r5 - r2) / (r5 + r2)
(Normalized Difference Water Index)
SAVI = (1 + L) (r4 - r3) / (L + r4 + r3)
(Soil Adjusted VI)
For Southern Idaho: L = 0.1
SAVIID = 1.1(r4 - r3) / (0.1 + r4 + r3)
Leaf Area Index (LAI):
LAI = 11SAVI3
r is usually calculated at top of atmosphere
We limit LAI  6.0

21. 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.

22. Area just south of Albuquerque along Middle Rio Grande, New Mexico
false color
NDVI
LAI

23. Surface Emissivity
Surface Temperature

24. Surface Temperature (Ts) (Planck’s Law)
NB is the emissivity for the narrow band Landsat thermal band
( μm wavelengths on Landsat 5, 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.

25. Surface Emissivity eNB = 0.97 + 0.0033 LAI; for LAI < 3
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.

26. Thermal Radiance from the Surface (Rc)
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)
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.

27. Surface Temperature

28. Surface Temperature Image
Red – hot (500C)
Blue – cold (200C)

29. Surface Temperature Image
Pathfinder-Seminoe Reservoirs, WY

30. Surface Energy Budget Equation
Rn = G + H + lET
lET = Rn – G – H R n G H ET

31. Sensible Heat Flux is an Aerodynamic Process

32. Sensible Heat Flux (H) – SEBAL and METRIC
Advantage:
dT and rah ‘float’ above the surface and are ‘free’ of zoh and some limitations of a single source approach
H = (r × cp × dT) / rah
Advantage:
dT is inverse calibrated (simulated) (free of Trad vs. Taero and free of Tair)
dT = “floating” near surface temperature difference (K) H
rah dT z1 z2
rah = the aerodynamic resistance
from z1 to z2
Convective heat equation. We use electric analog to represent the heat flow. V=IR (I =current * resistance)
H= I
V = T (temperature is the same as voltage)
R= R (instead of resistor, we have aero dynamic resistance)
Temp = H* R
H = Temp/R = (difference in temp as is difference in voltage)
u* = friction velocity
k = von karmon
constant (0.41)

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

34. 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 H
rah dT z1 z2

35. 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).

36. 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).

37. Example Applications of METRIC -Nebraska
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
Why are we doing this? Manage depletions to the Ogalla Aquifer.
NRDs regulate pumping of groundwater.

38. Central Nebraska Irrigation District (CPNRD) – 2007 Monthly ET
Here is what ET looks like over the entire CPNRD. Peak Months are July and August.
Central Platte is using for managing surface ground water!! ET varies substantially because of the weather and cropping conditions.
Evapotranspiration increases gradually from May after crop emergence and growth through July and August as the vegetation start to transpire at a potential rate for most vegetation surfaces. August is usually the peak ET month with high incoming solar radiation, high temperatures, and large vapor pressure deficit that increase ET. ET shows variation throughout the district as a function of different ET rates of various land covers, including corn, soybean, invasive species, natural vegetation, etc. With physiological maturity, leaf aging and senescence, ET starts to decrease gradually in September and is minimal in October. With harvest in October, most of the ET in this month represents the soil evaporation component of ET. As shown in monthly ET maps, mapping ET on large scales can provide vital information on the progression of ET for various vegetation surfaces over time.
Central Platte Natural Resource District 38

39. Variation in ET among years (Month of July)
2011
2007
1997
Even individual fields vary from year to year. ET varies between years.

40. Accuracy of ET maps
Monthly ET estimates from METRIC were averaged over about 20 fields.
Monthly ET estimates were similar to measured ET.
One of the things we are doing is comparing METRIC with ground measurements. We have a research field with Bowen Ratio Energy Balance Systems
-- Bowen Ratio energy Balance System (BRBS) data by Dr. Suat Irmak, BSE

41. California 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.
80% of the Nation’s winter vegetables are grown in Imperial Valley.
Water is taken from the Colorado River through the All-American Canal to irrigate ½ million acres.
USA
Mexico
Graphic courtesy of R. Trezza, 2008

42. Montana
Landsat ET has improved stream flows for endangered fisheries and to protect native American water rights
How do we balance the amount of water taken for irrigation with the amount of water left in the river for fish habitat?
This is a view of the Flathead Indian Reservation.
2011 ET Workshop – Boise, Idaho
Graphic courtesy of J.Kjaersgaard, 2009

43. Montana/Wyoming
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
Montana sued Wyoming because they are evaporating too much water from Yellow stone river before it reaches montano. ET
Graphic courtesy of C.Kelly, 2012

44. ETrF Comparison Between Landsat 8 and Landsat 7
ETrF is the ‘relative’ ET rate (fraction of reference ET)
Remarkably good comparison (slope =0.997)
Computations by Babu Kamble, Ian Ratcliffe, Ricardo Trezza

45. Reference Evapotranspiration-Google
Reference Evapotranspiration represents potential ET rate when surface is covered with vegetation
Daily Reference Evapotranspiration for the Entire United States
1951 – 2012 at 12 km grid
Based on GridMET (Bias-Corrected NLDAS Data by J.Abatzoglou)

46. Reference Evapotranspiration-Google Earth Engine