radiation in

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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
WaterWatch,
Wageningen, The Netherlands
[email protected]
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 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
V
i
s
i
b
l
e
N
e
a
r
I
n
f
r
a
r
e
d
Land Surface
Wavelength in Microns
0
0
.
4
0
.
6
0
.
8
1
.
2
1
.
6
2
.
0
2
.
4
B
a
n
d
:
1
2
3
4
57
V
a
r
io
u
s
a
m
o
u
n
t
s
o
fr
e
f
le
c
t
io
n
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
– 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
Energy Balance for ET
ET is calculated as a “residual” of the energy
balance
Rn
Basic Truth:
Evaporation
consumes
Energy
H
ET
ET = R n - G - H
G
The energy balance
includes all major
sources (Rn) and
consumers (ET, G, H)
of energy
Surface Radiation Balance
Shortwave
Radiation
Longwave
Radiation
RL
RS
aRS
(Incident
longwave)
(1-eo)RL
(reflected
longwave)
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)
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)
Biases
Gains
Low gain
High gain
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
 t image ( localtime) 1

t1  int 
  Flagperiod t  FlagDST
t
2


t 2  t1  t
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
t 2  12  1  13hours
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
(Incident
shortwave)
RL
(Incident
longwave)
aRS
(1-eo)RL
(reflected
longwave)
RL
(emitted
longwave)
(Reflected shortwave)
Vegetation Surface
Net Surface Radiation = Gains – Losses
Rn = (1-a)RS + RL - RL - (1-eo)RL
Flow Chart – Net Surface Radiation
Rn = (1-a)RS↓ + RL↓ - RL↑ - (1-e0)RL↓
a
model_04
atoa
model_03
RS↓
RL↑
calculator
RL↓
model_09
eo
calculator
TS
model_08
model_06
rl
model_02
NDVI
SAVI
LAI
model_05
Ll
model_01
Tbb
model_07
Radiance Equation for Landsat 5
 LMAX  LMIN 
Ll  
  DN  LMIN
255


Radiance Equation for Landsat 7
Ll = (Gain × DN) + Bias
Model 01 – Radiance for Landsat 7c
Model 01 – Radiance for Landsat 5
Enter values from Table 6.1 in Appendix 6
Writing the Model for Radiance
 LMAX  LMIN 
Ll  
  DN  LMIN
255


Reflectivity Equation
rl 
  Ll
ESUNl  cos  d r
2 

d r  1  0.033cos DOY

365

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
rl 
  Ll
ESUNl  cos  d r
Solar Radiation and Reflectance
Satellite Sensor
Sun
Reflectance
at air
Top of Atmosphere
Solar Radiation
Reflectance at Land Surface
Air
Land Surface
Albedo for the Top of Atmosphere
atoa = Σ (wl × rl)
ESUNl
wl 
 ESUNl
Model_03 - Albedo for the Top of Atmosphere
From Table 6.4
Surface Albedo Equation
a 
a toa  a path _ radiance
 sw
2
apath_radiance ~ 0.03
sw = 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
Old snow and ice
Black soil
Clay
White-yellow sand
Gray-white sand
Grass or pasture
Corn field
Rice field
Coniferous forest
Deciduous forest
Water
0.80 – 0.85
0.30 – 0.70
0.08 – 0.14
0.16 – 0.23
0.34 – 0.40
0.18 – 0.23
0.15 – 0.25
0.14 – 0.22
0.17 – 0.22
0.10 – 0.15
0.15 – 0.20
0.025 – 0.348
(depending on solar elevation angle)
Incoming solar Radiation (Rs )
Rs↓ = Gsc × cos  × dr × sw
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
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
 0.69  SAVI ID 
ln

0.59


LAI  
0.91
We set LAI  6.0
Some Vegetation Index
CLAIR Model (Clevers, 1991)
“Intrinsic” VIs
r
RVI  nir
r red
LAI  
DVI  r nir  r red
(obtained from ground measurements)
WDVI = WDVI for LAI  
……….
“New” Vis (…Soil line concept…)
SAVI 
……….
k  soil line 
r nir  r red )1  L)
r nir  r red  L)
L = soil adjustment factor (0.5)



a = Calibration factor !!
 r  r red )
NDVI  nir
r nir  r red )
WDVI  r nir  k r red

WDVI
ln  1 
a 
WDVI 
1
r nir( soil )
r red ( soil )
a
note
Author
0.252
0.530
0.485
0.34-0.54
Vegetative phase
Reproductive phase
Sugar Beet
Various Crops
Clevers, 1991
Clevers, 1991
Bouman et al, 1992
D’Urso, 2002
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 (eo)




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
Tbb 
K2
 K1 
ln
 1
 L6

K1 and K2 are given in Table 1 of the manual.
Model_07 – Effective at Satellite
Temperature
Surface Temperature
Ts 
Tbb
e
0.25
0
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
ea = 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-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
Deep, Clear Water
Snow
Desert
Agriculture
Bare soil
Full cover alfalfa
Clipped Grass
Rock
G/Rn
0.5
0.5
0.2 – 0.4
0.05 – 0.15
0.2 – 0.4
0.04
0.1
0.2 – 0.6
These values represent daytime conditions
Sensible Heat Flux (H)
H = (r × cp × dT) / rah
dT = the near surface temperature difference (K).
rah = the aerodynamic resistance to heat transport (s/m).
 z2 
ln 
z1 

rah 
u*  k
z2
dT
z1
rah H
Friction Velocity (u*)
ku x
u* 
 zx 

ln
 z om 
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
u 200
 200

ln
z om 

 u*
k
u200 = 3.49 m/s
Iterative Process to Compute H
Friction Velocity (u*) for Each Pixel
ku200
u* 
 200

ln
 z om 
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;
Manmade structures;
Forests;
Grassland;
Desert with vegetation;
Snow;
zom = 0.0005 m
zom = 0.1 m
zom = 0.5 m
zom = 0.02 m
zom = 0.1 m
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
 z2 
ln 
z1 

rah 
u * k




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 × lETr
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
The direction of force for an sudden movement of air
8oC
9oC
9oC
9oC
10 o C
9oC
10 o C
10 o C
10 o C
10 o C
10 o C
10 o C
12 o C
11 o C
11 o C
11 o C
10 o C
11 o C
100m
100m
U nstable
N eutral
S table
: Direction of Force
The tendency of air movement
U nstable
N eutral
S table
Stability Correction for u*and rah
u 200 k
u* 
 200
  m ( 200 m )
ln
 z0m 
 z2 
ln   h ( z2 )
z1 

rah 
u*  k
•
•
•
•
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
ETinst (mm / hr )  3600
l
lET (W/m2) = Rn – G – H
Reference ET Fraction (ETrF)
ETinst
ETrF 
ETr
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)
ET24  ETrF  ETr _ 24
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
ETperiod  ETr Fperiod  ETr24 i
i 1
(n = length of period in days)

Step 5: Compute the seasonal ET
ETseasonal =  ETperiod
Validation of SEBAL
ET - July-Oct., mm Montpelier, 1985
500
400
300
200
100
Lysimeter
SEBAL
388 mm
405 mm
0
Total
Lysimeter
SEBAL
Validation of SEBAL
ET - April-Sept., mm - Kimberly, 1989
Sugar Beets
800
700
600
500
400
300
200
100
0
Lysimeter
SEBAL
718 mm
714 mm
Total
Lysimeter
SEBAL
Conclusions

ET can be determined for a complete year
for large areas

ET can be aggregated over space and time

ET maps will be used to assess Irrigation
Performance

ET maps and associated products will be
used to assess crop productivity
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Relative w ater supply
Overall consumed ratio
Relative soil w etness
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Aug- Sep- Oct- Nov- Dec- Jan- Feb- Mar- Apr- May- Jun- Jul98 98 98 98 98 99 99 99 99 99 99 99
Relative soil wetness (-)
Fraction (-)
The Future
The key is to look
up !
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