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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: –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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Wavelength in Microns Landsat Band 6 is the long-wave “thermal” band and is used for surface temperature What Landsat Sees Land Surface

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Evapotranspiration at time of overpass Oakley Fan, Idaho, July 7, 1989 What We Can See With SEBAL

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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 –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 ET = R - G - H n R n G H ET The energy balance includes all major sources (R n ) and consumers (ET, G, H) of energy Basic Truth: Evaporation consumes Energy Energy Balance for ET

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Vegetation Surface Shortwave Radiation Longwave Radiation RSRS RSRS (Incident shortwave) (Reflected shortwave) RLRL (Incident longwave) (1- o )R L RLRL (emitted longwave) (reflected longwave) Net Surface Radiation = Gains – Losses R n = (1- )R S + R L - R L - (1- o )R L Surface Radiation Balance

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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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Bands 1-7 in order Layering – Landsat 5

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Final Layering Order – Landsat 5

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

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Header File for Landsat 7 (band 6 ) GainsBiases Low gain High gain

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Header File for Landsat 7 (latitude and sun elevation)

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DOY GWT Acquiring Header File Information (Method B)

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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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timage (Local Time) = 17:57 – 7:00 = 10:57 am t 1 = int 10+57/60 + ½ - 0 (1) + 1 = 12 hours 1 For August 22, 2000: image time is 17:57 GMT Apply the correction : Calculating the Wind Speed for the Time of the Image Δt = 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 ET r for 10:57 AM: Interpolate between the values for 12:00 (.59) and for 13:00 (.72) ET r =.59+( ) [(10+57/60) – (10+1/2)] = 0.65 mm/hr

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Vegetation Surface Shortwave Radiation Longwave Radiation RSRS RSRS (Incident shortwave) (Reflected shortwave) RLRL (Incident longwave) (1- o )R L RLRL (emitted longwave) (reflected longwave) Net Surface Radiation = Gains – Losses R n = (1- )R S + R L - R L - (1- o )R L Surface Radiation Balance

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R S↓ calculator R L↑ model_09 R L↓ calculator toa model_03 T S model_08 model_06 model_02 T bb model_07 L model_01 model_04 NDVI SAVI LAI model_05 R n = (1- R S↓ + R L↓ - R L↑ - (1- R L↓ Flow Chart – Net Surface Radiation

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Radiance Equation for Landsat 5

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L = ( Gain × DN ) + Bias Radiance Equation for Landsat 7

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Model 01 – Radiance for Landsat 7c

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Enter values from Table 6.1 in Appendix 6 Model 01 – Radiance for 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, d r = 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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toa = Σ ( × ) Albedo for the Top of Atmosphere

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Model_03 - Albedo for the Top of Atmosphere From Table 6.4

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Surface Albedo Equation sw = × × z For Kimberly: z = 1195 meters, sw = path_radiance ~ 0.03

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Model_04 - Surface Albedo

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

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Two dark bare fields showing a very low albedo. Surface Albedo for Bare Fields

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Fresh snow0.80 – 0.85 Old snow and ice0.30 – 0.70 Black soil0.08 – 0.14 Clay0.16 – 0.23 White-yellow sand0.34 – 0.40 Gray-white sand0.18 – 0.23 Grass or pasture0.15 – 0.25 Corn field0.14 – 0.22 Rice field0.17 – 0.22 Coniferous forest0.10 – 0.15 Deciduous forest0.15 – 0.20 Water0.025 – (depending on solar elevation angle) Typical Surface Albedo Valuse

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G sc solar constant (1367 W/m 2 ) d r inverse squared relative Earth-Sun distance sw one-way transmissivity R s↓ = G sc × cos × d r × sw For August 22, 2000: R s = W/m 2 Incoming solar Radiation (R s )

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Vegetation Indices NDVI = ( / ( ) SAVI = (1 + L) ( L + SAVI ID = 1.1( For Southern Idaho: L = 0.1 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) 0 = × ln(NDVI) For snow; > 0.47, o = For water; NDVI < 0, o = For desert; o < 0.9, o = 0.9

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Model_06 – Surface Emissivity

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Effective at Satellite Temperature K 1 and K 2 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 (60 0 C) Blue – cold (20 0 C)

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Surface Temperature Image White – cold Dark red - hot

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Outgoing Longwave Radiation (R L ) R L↑ = o σ T 4 Where ε= emissivity T = absolute radiant temperature in degrees Kelvin = Stefan-Boltzmann constant (5.67 W / (m 2 – K 4 )

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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 T s T air “Hot” pixel: a dry, bare agricultural field ET 0

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Incoming Longwave Radiation (R L ) R L↓ = a × σ × T a 4 a = atmospheric emissivity = 0.85 × (-ln t sw ).09 for southern Idaho T a T cold at the “cold” pixel R L↓ = 0.85 × (-ln sw ).09 × σ × T cold 4 For August 22, 2000: sw = 0.774, T cold = K, R L↓ = W/m 2

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Net Surface Radiation Flux (R n ) R n = (1- )R S↓ + R L↓ - R L↑ - (1- o )R L↓

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Model_10 – Net Surface Radiation

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Net Surface Radiation Image and Histogram Light – high R n Dark – low R n

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Surface Energy Budget Equation R n = G + H + ET ET = R n – G – H

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Soil Heat Flux (G) G/R n = T s / ( )(1 -.98NDVI 4 ) G = G/R n R n Flag for clear, deep water and snow: If NDVI < 0; assume clear water, G/R n = 0.5 If T s 0.45; assume snow, G/R n = 0.5

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Model_11 – G/R n and G

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G/R n Image and Histogram

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Soil Heat Flux Image and Histogram Light – high G Dark – low G

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Surface Type G/R n Deep, Clear Water0.5 Snow0.5 Desert0.2 – 0.4 Agriculture0.05 – 0.15 Bare soil0.2 – 0.4 Full cover alfalfa0.04 Clipped Grass0.1 Rock0.2 – 0.6 G/R n for Various Surfaces These values represent daytime conditions

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Sensible Heat Flux (H) H = ( × c p × dT) / r ah H r ah dT r ah = the aerodynamic resistance to heat transport (s/m). z1z1 z2z2 dT = the near surface temperature difference (K).

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Friction Velocity (u * ) u x is wind speed (m/s) at height z x above ground. z om is the momentum roughness length (m). z om can be calculated in many ways: –For agricultural areas: z om = 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 (z om ) The wind speed goes to zero at the height (d + z om ).

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Calculations for the Weather Station For August 22, 2000: z x = 2.0 m, u x = 1.63 m/s, h = 0.3 m, z om = 0.12 0.3 =.036 m u * = m/s u 200 = 3.49 m/s

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Iterative Process to Compute H

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Friction Velocity (u * ) for Each Pixel u 200 is assumed to be constant for all pixels z om for each pixel is found from a land-use map For agricultural fields, z om = 0.12h For our area, h = 0.15LAI z om = × LAI

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Model_12 – Roughness Length Water;z om = m Manmade structures;z om = 0.1 m Forests;z om = 0.5 m Grassland;z om = 0.02 m Desert with vegetation;z om = 0.1 m Snow;z om = m For agricultural fields: Z om = LAI

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Insert coordinates from LAI image Setting the Size of the Land-use Map

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Aerodynamic Resistance to Heat Transport (r ah ) for Each Pixel z 1 height above zero-plane displacement height (d) of crop canopy z 1 0.1 m z 2 below height of surface boundary layer z 2 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 = T s – T a T a is unknown SEBAL assumes a linear relationship between T s and dT: dT = b + aT s

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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: H cold = R n – G - ET cold where ET cold = 1.05 × ET r dT cold = H cold × r ah / ( × c p ) –At the “hot” pixel: H hot = R n – G - ET hot where ET hot = 0 dT hot = H hot × r ah / ( × c p )

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

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Graph of dT vs T s Correlation coefficients a and b are computed

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Sensible Heat Flux (H) dT for each pixel is computed using: dT = b + aT s H = ( × c p × dT) / r ah

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Model_14 – Sensible Heat Flux

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Atmospheric Stability

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Stability Correction for u * and r ah 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 (ET inst ) ET (W/m 2 ) = R n – G – H

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Reference ET Fraction (ET r F) ET r is the reference ET calculated for the time of the image. For August 22, 2000, ET r = 0.65 mm/hr

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Model_25 – Instantaneous ET and ET r F

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24-Hour Evapotranspiration (ET 24 )

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Seasonal Evapotranspiration (ET seasonal ) Assume ET r F 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 ET r at weather station.

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Seasonal Evapotranspiration (ET seasonal ) Step 1: Decide the length of the season Step 2: Determine period represented by each satellite image Step 3: Compute the cumulative ET r 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 ET seasonal = ET period

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

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

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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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