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:– 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 !