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

2. The Trainers Richard G. Allen, University of Idaho,
Kimberly Research Station
Wim M. Bastiaanssen
WaterWatch, Wageningen, The Netherlands
Ralf Waters

3. 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

4. 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

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

6. 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)

7. 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)

8. 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

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

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

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

12. 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

13. 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

14. 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

17. Reflected

18. Net Radiation = radiation in – radiation out

19. 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

20. 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

21. 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.

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

23. Layering – Landsat 5
Bands 1-7 in order

24. Final Layering Order – Landsat 5

25. Creating a Subset Image

26. Creating a Subset Image

27. 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)

28. 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

29. Locating the Header File for Landsat 7ETM+

30. Locating the Header File for Landsat 5TM

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

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

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

34. Header File for Landsat 7 (latitude and sun elevation)

35. Acquiring Header File Information (Method B)
DOY
GWT

36. Example of Weather Data

37. Reference ET Definition File of REF-ET Software

38. Ref-ET Weather Station Data

39. Ref-ET Output and Equations

40. Reference ET Results

42. 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

43. 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

44. 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

45. 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↓

46. Radiance Equation for Landsat 5

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

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

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

50. Writing the Model for Radiance

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

52. Model_02 - Reflectivity
From Table 6.3

53. Writing the Model for Reflectivity

54. Solar Radiation and Reflectance

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

56. Model_03 - Albedo for the Top of Atmosphere
From Table 6.4

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

58. Model_04 - Surface Albedo

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

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

61. 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)

62. 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

63. 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

64. Model_05 – NDVI, SAVI, LAI

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

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

67. 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

68. Model_06 – Surface Emissivity

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

70. Model_07 – Effective at Satellite Temperature

71. 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.

72. Model_08 – Surface Temperature

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

74. Surface Temperature Image
White – cold
Dark red - hot

75. 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)

76. Model_09 – Outgoing Longwave Radiation

77. Outgoing Longwave Radiation Image and Histogram

79. 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

80. 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

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

82. Model_10 – Net Surface Radiation

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

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

85. 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

86. Model_11 – G/Rn and G

87. G/Rn Image and Histogram

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

89. 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

90. 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

91. 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

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

93. 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* = m/s
u200 = 3.49 m/s

94. Iterative Process to Compute H

95. 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

96. 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

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

98. 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

99. Model_13 – Friction Velocity and Aerodynamic Resistance to Heat Transport

100. 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

101. 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)

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

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

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

105. Model_14 – Sensible Heat Flux

106. Atmospheric Stability

107. 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.

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

110. 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

111. Model_25 – Instantaneous ET and ETrF

112. 24-Hour Evapotranspiration (ET24)

113. 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.

114. 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

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

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

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

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

120. The key is to look up !