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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 [email protected] Wim M. Bastiaanssen - PowerPoint PPT Presentation
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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
Wim M. Bastiaanssen
WaterWatch,Wageningen, The Netherlands
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:– 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 anon-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
Various amounts of reflection
Wavelength in Microns0 0.4 0.6 0.8 1.2 1.6 2.0 2.4
Band: 1 2 3 4 5 7
Visible Near Infrared
Landsat Band 6 is the long-wave “thermal” band and is used for surface temperature
What Landsat Sees
Land Surface
Evapotranspiration at time of overpass
Oakley Fan, Idaho, July 7, 1989
What We Can See With SEBAL
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– 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
ET = R - G - Hn
Rn
G
H ET
The energy balance includes all major sources (Rn) and consumers (ET, G, H) of energy
Basic Truth: Evaporation consumes Energy
Energy Balance for ET
Vegetation Surface
ShortwaveRadiation
LongwaveRadiation
RSRS
(Incident shortwave)
(Reflected shortwave)
RL
(Incident longwave)
(1-o)RL
RL
(emitted longwave)
(reflected longwave)
Net Surface Radiation = Gains – Losses
Rn = (1-)RS + RL - RL - (1-o)RL
Surface Radiation Balance
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
Bands 1-7 in order
Layering – Landsat 5
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)
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
Biases Gains
Header File for Landsat 7 (bands 1-5,7)
Header File for Landsat 7 (band 6)
GainsBiases
Low gain
High gain
Header File for Landsat 7 (latitude and sun elevation)
DOY
GWT
Acquiring Header File Information (Method B)
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
hours13112t 2
timage (Local Time) = 17:57 – 7:00 = 10:57 am
DSTperiodtimelocalimage
1 FlagtFlag2
1
t
tt
)(
int
ttt 12
t1 = 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
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
Vegetation Surface
ShortwaveRadiation
LongwaveRadiation
RS
RS
(Incident shortwave)
(Reflected shortwave)
RL
(Incident longwave)
(1-o)RL RL
(emitted longwave)
(reflected longwave)
Net Surface Radiation = Gains – Losses
Rn = (1-)RS + RL - RL - (1-o)RL
Surface Radiation Balance
RS↓ calculator
RL↑ model_09
RL↓ calculator
to
a model_03
TS model_08
model_06
model_02
Tbb model_07
L model_01
model_04
NDVI SAVI LAI model_05
Rn = (1-RS↓ + RL↓ - RL↑ - (1-RL↓
Flow Chart – Net Surface Radiation
LMINDNLMINLMAX
L
255
Radiance Equation for Landsat 5
L = (Gain × DN) + Bias
Radiance Equation for Landsat 7
Model 01 – Radiance for Landsat 7c
Enter values from Table 6.1 in Appendix 6
Model 01 – Radiance for Landsat 5
LMINDNLMINLMAX
L
255
Writing the Model for Radiance
rdESUN
L
cos
Reflectivity Equation
365
2DOYcos033.01d r
For August 22, 2000: Sun elevation angle () = 51.560, = (90 - ) = 38.440
DOY = 235, dr = 0.980
Model_02 - ReflectivityFrom Table 6.3
Writing the Model for Reflectivity
rdESUN
L
cos
Top of Atmosphere
Land Surface
Air
Sun
Satellite Sensor
Solar Radiation Reflectance at Land Surface
Reflectance at air
Solar Radiation and Reflectance
toa = Σ (×)
Albedo for the Top of Atmosphere
ESUN
ESUN
Model_03 - Albedo for the Top of Atmosphere
From Table 6.4
2
_
sw
radiancepathtoa
Surface Albedo Equation
sw = 0.75 + 2 × 10-5 × z
For Kimberly: z = 1195 meters,sw = 0.774
path_radiance ~ 0.03
Model_04 - Surface Albedo
Albedo: White is high (0.6) Dark blue is low (.02)
Surface Albedo Map
Two dark bare fields showing a very low albedo.
Surface Albedo for Bare Fields
Fresh snow 0.80 – 0.85Old snow and ice 0.30 – 0.70Black soil 0.08 – 0.14Clay 0.16 – 0.23White-yellow sand 0.34 – 0.40Gray-white sand 0.18 – 0.23Grass or pasture 0.15 – 0.25Corn field 0.14 – 0.22Rice field 0.17 – 0.22Coniferous forest 0.10 – 0.15Deciduous forest 0.15 – 0.20Water 0.025 – 0.348
(depending on solar elevation angle)
Typical Surface Albedo Valuse
Gsc solar constant (1367 W/m2)
dr inverse squared relative Earth-Sun distance
sw one-way transmissivity
Rs↓ = Gsc × cos ×dr × sw
For August 22, 2000: Rs = 812.2 W/m2
Incoming solar Radiation (Rs )
Vegetation Indices
NDVI = (/ ()
SAVI = (1 + L) (L +
91.0
59.0
69.0ln
IDSAVI
LAI
SAVIID = 1.1(
For Southern Idaho: L = 0.1
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)
0 = 1.009 + 0.047 × ln(NDVI)
For snow; > 0.47, o = 0.999
For water; NDVI < 0, o = 0.999
For desert; o < 0.9, o = 0.9
Model_06 – Surface Emissivity
Effective at Satellite Temperature
1ln
6
1
2
L
K
KTbb
K1 and K2 are given in Table 1 of the manual.
Model_07 – Effective at Satellite Temperature
Surface Temperature
25.00bb
s
TT
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↑ = o 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 RadiationImage 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↓ = a × σ × Ta4
a = atmospheric emissivity = 0.85 × (-ln tsw).09 for southern Idaho
Ta Tcold at the “cold” pixel
• RL↓ = 0.85 × (-ln sw).09 × σ × Tcold4
• For August 22, 2000: sw = 0.774, Tcold = 292.5 K, RL↓ = 311.0 W/m2
Net Surface Radiation Flux (Rn)
Rn = (1-)RS↓ + RL↓ - RL↑ - (1-o)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 + ET
ET = Rn – G – H
Soil Heat Flux (G)
G/Rn = Ts/(0.0038)(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 > 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
Surface Type G/Rn
Deep, Clear Water 0.5Snow 0.5Desert 0.2 – 0.4Agriculture 0.05 – 0.15Bare soil 0.2 – 0.4Full cover alfalfa 0.04Clipped Grass 0.1Rock 0.2 – 0.6
G/Rn for Various Surfaces
These values represent daytime conditions
Sensible Heat Flux (H)
H = (×cp × dT) / rah
HrahdT
rah = the aerodynamic resistance to heat transport (s/m).
ku
z
zln
r*
1
2
ah
z1
z2
dT = the near surface temperature difference (K).
om
x
x
z
z
kuu
ln
*
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 = 0.120.3 = .036 m
u* = 0.166 m/s
k
zuu om
200ln
*200
u200 = 3.49 m/s
Iterative Process to Compute H
omz
kuu
200ln
* 200
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 = 0.12hFor our area, h = 0.15LAIzom = 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 mFor agricultural fields: Zom = 0.018 LAI
Insert coordinates from LAI image
Setting the Size of the Land-use Map
ku
zz
rah
*
ln1
2
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 - ETcold
where ETcold = 1.05 × ETr
dTcold = Hcold × rah / ( × cp)
– At the “hot” pixel: Hhot = Rn – G - EThot where EThot = 0
dThot = Hhot × rah / ( × 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 = (×cp × dT) / rah
Model_14 – Sensible Heat Flux
10oC 10oC10oC
9oC9oC9oC
11oC 11oC11oC12oC
8oC
10oC
11oC
10oC 10oC
10oC
10oC9oC
: Direction of Force
StableNeutralUnstable
StableNeutralUnstable
100m
100m
The direction of force for an sudden movement of air
The tendency of air movement
Atmospheric Stability
ku
z
z
rzh
ah
*
)(1
2
2ln
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.
)200(0
200
200ln
*
mmmz
kuu
Instantaneous ET (ETinst)
ET (W/m2) = Rn – G – H
ET
hrmmETinst 3600)/(
r
inst
ET
ETETrF
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)
24_24 rETETrFET Path 39: Am. Falls -24-hour ET
8/07/00
9/08/01
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
n
irperiodrperiod i
ETFETET1
24
ETseasonal = ETperiod
0
100
200
300
400
500
Total
Lysimeter SEBAL
Validation of SEBAL
ET - July-Oct., mm Montpelier, 1985
SEBAL
405 mmLysimeter
388 mm
0100200300400500600700800
Total
Lysimeter SEBAL
Lysimeter
718 mmSEBAL
714 mm
Sugar Beets
Validation of SEBAL
ET - April-Sept., mm - Kimberly, 1989
Conclusions
ET can be determined for a complete year for large areas
ET can be aggregated over space and time
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Aug-98
Sep-98
Oct-98
Nov-98
Dec-98
Jan-99
Feb-99
Mar-99
Apr-99
May-99
Jun-99
Jul-99
Fra
cti
on
(-)
0
0.2
0.4
0.6
0.8
1
1.2
1.4R
elat
ive
soil
wet
nes
s (-
) Relative w ater supplyOverall consumed ratioRelative soil w etness
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 !