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**SEBAL Expert Training Presented by The University of Idaho and**

The Idaho Department of Water Resources Aug , 2002 Idaho State University Pocatello, ID

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**The Trainers Richard G. Allen, University of Idaho,**

Kimberly Research Station Wim M. Bastiaanssen WaterWatch, Wageningen, The Netherlands Ralf Waters

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**SEBAL Surface Energy Balance Algorithm for Land Developed by**

Dr. Wim Bastiaanssen, International Institute for Aerospace Survey and Earth Sciences, The Netherlands applied in a wide range of international settings brought to the U.S. by Univ. Idaho in 2000 in cooperation with Idaho Department of Water Resources and NASA/Raytheon

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**Why Satellites? Typical method for ET: Satellite imagery:**

weather data are gathered from fixed points -- assumed to extrapolate over large areas “crop coefficients” assume “well-watered” situation (impacts of stress are difficult to quantify) Satellite imagery: energy balance is applied at each “pixel” to map spatial variation areas where water shortage reduces ET are identified little or no ground data are required valid for natural vegetation

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**Definition of Remote Sensing:**

The art and science of acquiring information using a non-contact device

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**SEBAL UI/IDWR Modifications**

digital elevation models for radiation balances in mountains (using slope / aspect / sun angle) ET at known points tied to alfalfa reference using weather data from Agrimet testing with lysimeter (ET) data from Bear River basin (during 2000) from USDA-ARS at Kimberly (during 2001)

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**How SEBAL Works SEBAL keys off: reflectance of light energy**

vegetation indices surface temperature relative variation in surface temperature general wind speed (from ground station)

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**Satellite Compatibility**

SEBAL needs both short wave and thermal bands SEBAL can use images from: NASA-Landsat (30 m, each 8 or 16 days) - since 1982 NOAA-AVHRR (advanced very high resolution radiometer) (1 km, daily) - since 1980’s NASA-MODIS (moderate resolution imaging spectroradiometer) (500 m, daily) - since 1999 NASA-ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) (15 m, 8 days) - since 1999

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**Image Processing ERDAS Imagine used to process Landsat images**

SEBAL equations programmed and edited in Model Maker function 20 functions / steps run per image

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**What Landsat Sees Land Surface Wavelength in Microns**

Landsat Band 6 is the long-wave “thermal” band and is used for surface temperature

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**What We Can See With SEBAL**

Evapotranspiration at time of overpass Oakley Fan, Idaho, July 7, 1989

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Uses of ET Maps Extension / Verification of Pumping or Diversion Records Recharge to the Snake Plain Aquifer Feedback to Producers regarding crop health and impacts of irrigation uniformity and adequacy

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Why Use SEBAL? ET via Satellite using SEBAL can provide dependable (i.e. accurate) information ET can be determined remotely ET can be determined over large spatial scales ET can be aggregated over space and time

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**Future Applications ET from natural systems ET from cities wetlands**

rangeland forests/mountains use scintillometers and eddy correlation to improve elevation-impacted algorithms in SEBAL hazardous waste sites ET from cities changes in ET as land use changes

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Reflected

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**Net Radiation = radiation in – radiation out**

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**ET is calculated as a “residual” of the energy balance**

Energy Balance for ET ET is calculated as a “residual” of the energy balance ET = R - G - H n R G H ET Basic Truth: Evaporation consumes Energy The energy balance includes all major sources (Rn) and consumers (ET, G, H) of energy

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**Surface Radiation Balance**

Shortwave Radiation Longwave Radiation (1-eo)RL RL aRS (Incident longwave) (reflected longwave) RS RL (Reflected shortwave) (emitted longwave) (Incident shortwave) Vegetation Surface Net Surface Radiation = Gains – Losses Rn = (1-a)RS + RL - RL - (1-eo)RL

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Preparing the Image A layered spectral band image is created from the geo-rectified disk using ERDAS Imagine software. A subset image is created if a smaller area is to be studied.

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Layering – Landsat 7 Band 6 (low & high) Bands 1-5,7

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Layering – Landsat 5 Bands 1-7 in order

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**Final Layering Order – Landsat 5**

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**Creating a Subset Image**

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**Creating a Subset Image**

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**Obtaining Header File Information**

Get the following from the header file: Overpass date and time Latitude and Longitude of image center Sun elevation angle (b) at overpass time Gain and bias ofr each and (Landsat 7 only)

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**Applicable for these satellites and formats:**

Method A Applicable for these satellites and formats: Landsat 5 if original image in NLAPS format Landsat 7 ETM+ if original image is NLAPS or FAST

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**Locating the Header File for Landsat 7ETM+**

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**Locating the Header File for Landsat 5TM**

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**Acquiring Header File Information (Landsat 5 - Method A)**

GWT

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**Header File for Landsat 7 (bands 1-5,7)**

Biases Gains

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**Header File for Landsat 7 (band 6)**

Gains Biases Low gain High gain Header file information for band 6 – Landsat 7 ETM

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**Header File for Landsat 7 (latitude and sun elevation)**

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**Acquiring Header File Information (Method B)**

DOY GWT

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**Example of Weather Data**

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**Reference ET Definition File of REF-ET Software**

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**Ref-ET Weather Station Data**

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**Ref-ET Output and Equations**

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Reference ET Results

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**Calculating the Wind Speed for the Time of the Image**

For August 22, 2000: image time is 17:57 GMT Apply the correction: timage (Local Time) = 17:57 – 7:00 = 10:57 am Δt = 1 t1 = int 10+57/60 + ½ - 0 (1) + 1 = 12 hours 1

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**Estimate Wind Speed at 10:57 am**

Interpolate between the value for 12:00 (1.4 m/s) and the value for 13:00 (1.9 m/s) U = 1.4+( )[(10+57/60) – (10+1/2)] = 1.63 m/s To estimate ETr for 10:57 AM: Interpolate between the values for 12:00 (.59) and for 13:00 (.72) ETr = .59+( ) [(10+57/60) – (10+1/2)] = 0.65 mm/hr

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**Surface Radiation Balance**

Shortwave Radiation Longwave Radiation RS RL (1-eo)RL RL (Incident shortwave) (Incident longwave) (reflected longwave) (emitted longwave) aRS (Reflected shortwave) Vegetation Surface Net Surface Radiation = Gains – Losses Rn = (1-a)RS + RL - RL - (1-eo)RL

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**Flow Chart – Net Surface Radiation**

RS↓ calculator RL↑ model_09 RL↓ atoa model_03 TS model_08 eo model_06 rl model_02 Tbb model_07 Ll model_01 a model_04 NDVI SAVI LAI model_05 Flow Chart – Net Surface Radiation Rn = (1-a)RS↓ + RL↓ - RL↑ - (1-e0)RL↓

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**Radiance Equation for Landsat 5**

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**Radiance Equation for Landsat 7**

Ll = (Gain × DN) + Bias

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**Model 01 – Radiance for Landsat 7c**

Model for radiance – Landsat 7

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**Model 01 – Radiance for Landsat 5**

Enter values from Table 6.1 in Appendix 6 Model for radiance – Landsat 5

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**Writing the Model for Radiance**

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**Reflectivity Equation**

For August 22, 2000: Sun elevation angle () = , = (90 - ) = DOY = 235, dr = 0.980

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Model_02 - Reflectivity From Table 6.3

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**Writing the Model for Reflectivity**

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**Solar Radiation and Reflectance**

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**Albedo for the Top of Atmosphere**

atoa = Σ (wl × rl)

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**Model_03 - Albedo for the Top of Atmosphere**

From Table 6.4

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**Surface Albedo Equation**

path_radiance ~ 0.03 tsw = × 10-5 × z For Kimberly: z = 1195 meters, sw = 0.774

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**Model_04 - Surface Albedo**

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Surface Albedo Map Albedo: White is high (0.6) Dark blue is low (.02)

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**Surface Albedo for Bare Fields**

Two dark bare fields showing a very low albedo.

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**Typical Surface Albedo Valuse**

Fresh snow – 0.85 Old snow and ice – 0.70 Black soil – 0.14 Clay – 0.23 White-yellow sand – 0.40 Gray-white sand – 0.23 Grass or pasture – 0.25 Corn field – 0.22 Rice field – 0.22 Coniferous forest – 0.15 Deciduous forest – 0.20 Water – 0.348 (depending on solar elevation angle)

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**Incoming solar Radiation (Rs )**

Rs↓ = Gsc × cos q × dr × tsw Gsc solar constant (1367 W/m2) dr inverse squared relative Earth-Sun distance sw one-way transmissivity For August 22, 2000: Rs = W/m2

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

Vegetation Indices NDVI = (r4 - r3) / (r4 + r3) SAVI = (1 + L) (r4 - r3) / L + r4 + r3 For Southern Idaho: L = 0.1 SAVIID = 1.1(r4 - r3) / r4 + r3 We set LAI 6.0

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Model_05 – NDVI, SAVI, LAI

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NDVI Image Dark green – high NDVI Yellow green – low NDVI

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LAI Image Dark green – high LAI Yellow green – low LAI

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**Surface Emissivity (o)**

e0 = × ln(NDVI) For snow; a > 0.47, eo = 0.999 For water; NDVI < 0, eo = 0.999 For desert; eo < 0.9, eo = 0.9

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**Model_06 – Surface Emissivity**

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**Effective at Satellite Temperature**

K1 and K2 are given in Table 1 of the manual.

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**Model_07 – Effective at Satellite Temperature**

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Surface Temperature Systematic errors that largely self-cancel in SEBAL: 1) Atmospheric transmissivity losses are not accounted for. 2) Thermal radiation from the atmosphere is not accounted for. Fortunately, in SEBAL, the use of a “floating” air-surface temperature function and the anchoring of ET at well-watered and dry pixels usually eliminates the need to applyatmospheric correction.

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**Model_08 – Surface Temperature**

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**Surface Temperature Image**

Red – hot (600C) Blue – cold (200C)

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**Surface Temperature Image**

White – cold Dark red - hot

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**Outgoing Longwave Radiation (RL)**

RL↑ = eo σ T4 Where ε= emissivity T = absolute radiant temperature in degrees Kelvin = Stefan-Boltzmann constant (5.67 10-8 W / (m2 – K4)

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**Model_09 – Outgoing Longwave Radiation**

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**Outgoing Longwave Radiation Image and Histogram**

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**Selection of “Anchor Pixels”**

The SEBAL process utilizes two “anchor” pixels to fix boundary conditions for the energy balance. “Cold” pixel: a wet, well-irrigated crop surface with full cover Ts Tair “Hot” pixel: a dry, bare agricultural field ET 0

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**Incoming Longwave Radiation (RL)**

RL↓ = ea × σ × Ta4 a = atmospheric emissivity = 0.85 × (-ln tsw).09 for southern Idaho Ta Tcold at the “cold” pixel RL↓ = 0.85 × (-ln tsw).09 × σ × Tcold4 For August 22, 2000: tsw = 0.774, Tcold = K, RL↓ = W/m2

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**Net Surface Radiation Flux (Rn)**

Rn = (1-a)RS↓ + RL↓ - RL↑ - (1-eo)RL↓

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**Model_10 – Net Surface Radiation**

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**Net Surface Radiation Image and Histogram**

Light – high Rn Dark – low Rn

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**Surface Energy Budget Equation**

Rn = G + H + lET lET = Rn – G – H

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**Soil Heat Flux (G) G/Rn = Ts/a (0.0038a + 0.0074a2)(1 - .98NDVI4)**

G = G/Rn Rn Flag for clear, deep water and snow: If NDVI < 0; assume clear water, G/Rn = 0.5 If Ts < 4 oC and a > 0.45; assume snow, G/Rn = 0.5

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Model_11 – G/Rn and G

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**G/Rn Image and Histogram**

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**Soil Heat Flux Image and Histogram**

Light – high G Dark – low G

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**G/Rn for Various Surfaces**

Surface Type G/Rn Deep, Clear Water 0.5 Snow Desert – 0.4 Agriculture – 0.15 Bare soil – 0.4 Full cover alfalfa 0.04 Clipped Grass 0.1 Rock – 0.6 These values represent daytime conditions

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**Sensible Heat Flux (H) H rah dT H = (r × cp × dT) / rah**

dT = the near surface temperature difference (K). rah = the aerodynamic resistance to heat transport (s/m). H rah z2 dT z1

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**Friction Velocity (u*)**

ux is wind speed (m/s) at height zx above ground. zom is the momentum roughness length (m). zom can be calculated in many ways: For agricultural areas: zom = 0.12 height of vegetation (h) From a land-use map As a function of NDVI and surface albedo

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**Zero Plane Displacement (d) and Momentum Roughness Length (zom)**

The wind speed goes to zero at the height (d + zom).

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**Calculations for the Weather Station**

For August 22, 2000: zx = 2.0 m, ux = 1.63 m/s, h = 0.3 m, zom = 0.120.3 = .036 m u* = m/s u200 = 3.49 m/s

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**Iterative Process to Compute H**

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**Friction Velocity (u*) for Each Pixel**

u200 is assumed to be constant for all pixels zom for each pixel is found from a land-use map For agricultural fields, zom = 0.12h For our area, h = 0.15LAI zom = × LAI

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**Model_12 – Roughness Length**

Water; zom = m Manmade structures; zom = 0.1 m Forests; zom = 0.5 m Grassland; zom = 0.02 m Desert with vegetation; zom = 0.1 m Snow; zom = m For agricultural fields: Zom = LAI

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**Setting the Size of the Land-use Map**

Insert coordinates from LAI image

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**Aerodynamic Resistance to Heat Transport (rah) for Each Pixel**

z1 height above zero-plane displacement height (d) of crop canopy z1 0.1 m z2 below height of surface boundary layer z2 2.0 m

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**Model_13 – Friction Velocity and Aerodynamic Resistance to Heat Transport**

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**Near Surface Temperature Difference (dT)**

To compute the sensible heat flux (H), define near surface temperature difference (dT) for each pixel dT = Ts – Ta Ta is unknown SEBAL assumes a linear relationship between Ts and dT: dT = b + aTs

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How SEBAL is “Trained” SEBAL is “trained” for an image by fixing dT at the 2 “anchor” pixels: At the “cold” pixel: Hcold = Rn – G - lETcold where lETcold = 1.05 × ETr dTcold = Hcold × rah / (r × cp) At the “hot” pixel: Hhot = Rn – G - lEThot where lEThot = 0 dThot = Hhot × rah / (r × cp)

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How SEBAL is “Trained” Once Ts and dT are computed for the “anchor” pixels, the relationship dT = b + aTs can be defined.

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Graph of dT vs Ts Correlation coefficients a and b are computed

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Sensible Heat Flux (H) dT for each pixel is computed using: dT = b + aTs H = (r × cp × dT) / rah

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**Model_14 – Sensible Heat Flux**

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**Atmospheric Stability**

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**Stability Correction for u*and rah**

New values for dT are computed for the “anchor” pixels. New values for a and b are computed. A corrected value for H is computed. The stability correction is repeated until H stabilizes.

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**Instantaneous ET (ETinst)**

lET (W/m2) = Rn – G – H

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**Reference ET Fraction (ETrF)**

ETr is the reference ET calculated for the time of the image. For August 22, 2000, ETr = 0.65 mm/hr

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**Model_25 – Instantaneous ET and ETrF**

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**24-Hour Evapotranspiration (ET24)**

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**Seasonal Evapotranspiration (ETseasonal)**

Assume ETrF computed for time of image is constant for entire period represented by image. Assume ET for entire area of interest changes in proportion to change in ETr at weather station.

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**Seasonal Evapotranspiration (ETseasonal)**

Step 1: Decide the length of the season Step 2: Determine period represented by each satellite image Step 3: Compute the cumulative ETr for period represented by image. Step 4: Compute the cumulative ET for each period (n = length of period in days) Step 5: Compute the seasonal ET ETseasonal = ETperiod

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**ET - July-Oct., mm Montpelier, 1985**

Validation of SEBAL ET - July-Oct., mm Montpelier, 1985 Lysimeter 388 mm SEBAL 405 mm

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**ET - April-Sept., mm - Kimberly, 1989**

Validation of SEBAL ET - April-Sept., mm - Kimberly, 1989 Sugar Beets Lysimeter 718 mm SEBAL 714 mm

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**Conclusions ET can be determined for a complete year for large areas**

ET can be aggregated over space and time

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**The Future ET maps will be used to assess Irrigation Performance**

ET maps and associated products will be used to assess crop productivity

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The key is to look up !

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