SEBAL Expert Training Presented by The University of Idaho and The Idaho Department of Water Resources Aug. 19-23, 2002 Idaho State University Pocatello, ID

The Trainers Richard G. Allen, University of Idaho, Kimberly Research Station rallen@kimberly.uidaho.edu Wim M. Bastiaanssen WaterWatch, Wageningen, The Netherlands w.bastiaanssen@waterwatch.nl Ralf Waters

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

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

Definition of Remote Sensing: The art and science of acquiring information using a non-contact device

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)

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)

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

Image Processing ERDAS Imagine used to process Landsat images SEBAL equations programmed and edited in Model Maker function 20 functions / steps run per image

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

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

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

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

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

Reflected

Net Radiation = radiation in – radiation out

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

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  

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.

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

Layering – Landsat 5 Bands 1-7 in order  

Final Layering Order – Landsat 5

Creating a Subset Image

Creating a Subset Image

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)

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

Locating the Header File for Landsat 7ETM+  

Locating the Header File for Landsat 5TM  

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

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

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

Header File for Landsat 7 (latitude and sun elevation)  

Acquiring Header File Information (Method B) DOY GWT  

Example of Weather Data

Reference ET Definition File of REF-ET Software

Ref-ET Weather Station Data

Ref-ET Output and Equations

Reference ET Results

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

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+(1.9-1.4)[(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+(.72-.59) [(10+57/60) – (10+1/2)] = 0.65 mm/hr

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  

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↓  

Radiance Equation for Landsat 5

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

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

Model 01 – Radiance for Landsat 5 Enter values from Table 6.1 in Appendix 6 Model for radiance – Landsat 5

Writing the Model for Radiance

Reflectivity Equation For August 22, 2000: Sun elevation angle () = 51.560, = (90 - ) = 38.440 DOY = 235, dr = 0.980

Model_02 - Reflectivity From Table 6.3

Writing the Model for Reflectivity

Solar Radiation and Reflectance

Albedo for the Top of Atmosphere atoa = Σ (wl × rl)

Model_03 - Albedo for the Top of Atmosphere From Table 6.4

Surface Albedo Equation path_radiance ~ 0.03 tsw = 0.75 + 2 × 10-5 × z For Kimberly: z = 1195 meters, sw = 0.774

Model_04 - Surface Albedo

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

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

Typical Surface Albedo Valuse Fresh snow 0.80 – 0.85 Old snow and ice 0.30 – 0.70 Black soil 0.08 – 0.14 Clay 0.16 – 0.23 White-yellow sand 0.34 – 0.40 Gray-white sand 0.18 – 0.23 Grass or pasture 0.15 – 0.25 Corn field 0.14 – 0.22 Rice field 0.17 – 0.22 Coniferous forest 0.10 – 0.15 Deciduous forest 0.15 – 0.20 Water 0.025 – 0.348 (depending on solar elevation angle)

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 = 812.2 W/m2

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) / 0.1 + r4 + r3 We set LAI  6.0

Model_05 – NDVI, SAVI, LAI

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

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

Surface Emissivity (o) e0 = 1.009 + 0.047 × 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

Model_06 – Surface Emissivity

Effective at Satellite Temperature K1 and K2 are given in Table 1 of the manual.

Model_07 – Effective at Satellite Temperature

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.

Model_08 – Surface Temperature

Surface Temperature Image Red – hot (600C) Blue – cold (200C)

Surface Temperature Image White – cold Dark red - hot

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)

Model_09 – Outgoing Longwave Radiation

Outgoing Longwave Radiation Image and Histogram

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

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 = 292.5 K, RL↓ = 311.0 W/m2

Net Surface Radiation Flux (Rn) Rn = (1-a)RS↓ + RL↓ - RL↑ - (1-eo)RL↓

Model_10 – Net Surface Radiation

Net Surface Radiation Image and Histogram Light – high Rn Dark – low Rn

Surface Energy Budget Equation Rn = G + H + lET lET = Rn – G – H

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

Model_11 – G/Rn and G

G/Rn Image and Histogram

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

G/Rn for Various Surfaces Surface Type G/Rn Deep, Clear Water 0.5 Snow 0.5 Desert 0.2 – 0.4 Agriculture 0.05 – 0.15 Bare soil 0.2 – 0.4 Full cover alfalfa 0.04 Clipped Grass 0.1 Rock 0.2 – 0.6 These values represent daytime conditions

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

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

Zero Plane Displacement (d) and Momentum Roughness Length (zom) The wind speed goes to zero at the height (d + zom).

Calculations for the Weather Station For August 22, 2000: zx = 2.0 m, ux = 1.63 m/s, h = 0.3 m, zom = 0.120.3 = .036 m u* = 0.166 m/s u200 = 3.49 m/s

Iterative Process to Compute H

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 = 0.018 × LAI

Model_12 – Roughness Length Water; zom = 0.0005 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 = 0.005 m For agricultural fields: Zom = 0.018 LAI

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

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

Model_13 – Friction Velocity and Aerodynamic Resistance to Heat Transport

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

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)

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

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

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

Model_14 – Sensible Heat Flux

Atmospheric Stability

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.

Instantaneous ET (ETinst) lET (W/m2) = Rn – G – H

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

Model_25 – Instantaneous ET and ETrF

24-Hour Evapotranspiration (ET24)

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.

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

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

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

Conclusions ET can be determined for a complete year for large areas ET can be aggregated over space and time

The Future ET maps will be used to assess Irrigation Performance ET maps and associated products will be used to assess crop productivity

The key is to look up !