METRIC: High Resolution Satellite Quantification of Evapotranspiration

Transcription

1 Copyright, R.G.Allen, University of Idaho, 2005 METRIC: High Resolution Satellite Quantification of Evapotranspiration University of Idaho, Kimberly, Idaho Part Two Energy Balance Co-developers and Collaborators: R. Allen, M. Tasumi, R. Trezza, W. Bastiaanssen, T. Morse, W. Kramber, J. Wright

2 Calculation of the Energy Balance R n H ET G 200 miles 4 million acres with 30 m resolution

3 Energy balance gives us actual ET Surface Energy Balance: Rn ET is calculated as a residual of the energy balance (radiation from sun and sky) H (heat to air) ET Basic Truth: Evaporation consumes Energy ET = R - G - H n G (heat to ground) The energy balance includes all major sources (R n ) and consumers (ET, G, H) of energy

4 True Color southcentral Idaho August 14, 2000 Thousand Springs North Dairy area (lots of corn, alfalfa) Twin Falls recent burn 100 miles basalt Wood River Valley Burley Craters of the Moon Lake Walcott

5 False Color southcentral Idaho August 14, 2000 Red indicates active vegetation Thousand Springs North Dairy area (lots of corn, alfalfa) Twin Falls recent burn 100 miles basalt Wood River Valley Burley Craters of the Moon Lake Walcott

6 Surface Temperature southcentral Idaho August 14, 2000 Thousand Springs North Twin Falls recent burn basalt Wood River Valley Temperature ( o C) Burley Craters of the Moon Lake Walcott

7 Net Radiation southcentral Idaho August 14, 2000 Thousand Springs North R n H ET G Twin Falls recent burn basalt Wood River Valley Net Radiation (W/m 2 ) Burley Lake Walcott Craters of the Moon

8 Ground Heat Flux southcentral Idaho August 14, 2000 R n H ET Thousand Springs North G Twin Falls recent burn basalt Wood River Valley Soil Heat Flux (W/m 2 ) Burley Craters of the Moon Lake Walcott

9 Heat Flux to Air southcentral Idaho August 14, 2000 R n H ET Thousand Springs North G Twin Falls recent burn basalt Wood River Valley Sensible Heat (W/m 2 ) Burley Craters of the Moon Lake Walcott

10 Instantaneous ET southcentral Idaho August 14, 2000 R n H ET Thousand Springs North G Twin Falls recent burn Wood River Valley Latent Heat (W/m 2 ) 0 basalt Burley Craters of the Moon Lake Walcott

11 24-hour ET southcentral Idaho August 14, 2000 Thousand Springs North Evapotranspiration (mm/day) Twin Falls recent burn basalt Wood River Valley ETr Fraction Burley Craters of the Moon Lake Walcott

12 METRIC tm -ERDAS submodel for sensible heat and ETrF

13 METRIC tm -ERDAS submodel for solar radiation in mountains

14 METRIC tm Level One Robust set of equations and procedures For general application Applications manual includes instructions and recommendations Includes algorithms for application in mountainous terrain (Appendix 12) Accuracy requires Intelligence Insight Iterative Review METRIC tm is an Engineering Tool

15 METRIC tm Level Two Equations and procedures (potentially) modified and customized for each application area: Multiple dt functions for complex subareas Limits on dt function Customized lapse correction for dt Modification of soil heat flux computation Refined selection of hot pixel Excess aerodynamic resistance for sparse vegetation Available energy for water bodies

16 METRIC tm Level Two Customized modifications are as much in the operator behavior, care, understanding and judgement as in modification of equations Level Two requires even more Experience Understanding (of physics and processes) Insight Iterative Review Level two is not for general release

17 METRIC tm Level One Requirements Background in: hydrologic science or engineering (to know behavior of soil, vegetation and water systems) Environmental physics Radiative Aerodynamic Heat transfer Familiarity with Vegetation systems (to know what one is looking at and growth and canopy characteristics) Specific human activities (agriculture, irrigation, etc.) Remote Sensing Science and Applications Image Processing

18 Energy Balance Radiation

19 Disposition of Solar Radiation in the Atmosphere H 2 O, O 2, O 3, N 2 O H 2 O, O 2, O 3, N 2 O Indirect Direct Solar

20 Longwave (Infrared) Radiation in the Atmosphere 4 H 2 O, CO 2, CH 4, CFC s

21 Surface Radiation Balance Shortwave Radiation Longwave Radiation (Incident longwave) (emitted longwave) (Incident shortwave) (reflected longwave) (Reflected shortwave) R S αrs R L (1-ε o )R L R L Vegetation Surface Net Surface Radiation = Gains Losses R n = (1-α)R S + R L -R L -(1-ε o )R L

22 METRIC tm uses the following seven bands of the Landsat spectrum: Band 1 visible (blue) ( µ) Band 2 visible (green) ( µ) Band 3 visible (red) ( µ) Band 4 near infrared ( µ) Band 5 near infrared ( µ) Band 6 thermal ( µ) Band 7 near infrared ( µ)

23 Locating The 7 Spectral Bands Band 6 Bands 1-5,7

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

25 Combining Layers (bands) into a False Color Composite and Selecting the Subset Image

26 The Total Image and Subset Image

27 The Total Image and Subset Image R n = (1-α)R S + R L -R L -(1-ε 0 )R L (model_f08) Surface albedo α Incoming shortwave R S Outgoing longwave R L Incoming longwave R L (model_f03) spreadsheet (model_f07) (model_f07) At-satellite Reflectances ρ t,b (model_f02) Spectral radiance L λ (model_f01) Surface emissivities ε ΝΒ & ε ο (model_f05) NDVI SAVI LAI (model_f04) Surface temperature T S (model_f06)

28 Radiance Equation for Landsat LMAX LMIN L b = DN LMIN L b = Spectral Radiance, W/m 2 /sr/:m LMAX = Maximum W/m 2 /sr/:m in calibration LMIN = Minimum W/m 2 /sr/:m in calibration DN = digital number (0-255) or for most Landsat 7 images: L b = (Gain DN) + Bias

29 LMIN and LMAX for Landsat 5 Markham and Barker, 1986 Tasumi et al., 2003d (using Landsat 7) Chander and Markham, 2003) After 15, Jan, 1984 For 2000 After 5, May, 2003 Band W*m -2 *ster -1 *µm -1 Band W*m -2 *ster -1 *µm -1 Band W*m -2 *ster -1 *µm -1 Number LMIN LMAX Number LMIN LMAX Number Gain Bias

30 LMIN and LMAX for Landsat 7 W*m-2*ster-1*µm-1 Before July 1, 2000 After July 1, 2000 Band Low Gain High Gain Low Gain High Gain Number LMIN LMAX LMIN LMAX LMIN LMAX LMIN LMAX

31 Model F01 Radiance for Landsat 5 Enter values from Table 6.1 in Appendix 6

32 Solar Radiation and Reflectance Satellite Sensor Sun Reflectance from atmosphere non-reflected radiation is what is absorbed at the surface and part of the energy balance. Therefore it is important to calculate accurately. Top of Atmosphere Solar Radiation Air Reflectance at Land Surface Land Surface

33 Satellite Sensor ρt,b Esunb (varies by band) Top of Atmosphere τin,b τout,b (varies by band) (varies by band) ρs,b (varies by band) Land Surface

34 Surface Albedo Albedo is the total (summed) reflectance across all short-wave bands Old method (used in METRIC prior to 2004) used single broad-band correction for atmosphere α = α toa α τ path _ radiance 2 sw New method (used since 2004) uses atmospheric correction for each band

35 Reflectance at Satellite (toa) ρ t,b = ESUN π L b b cos θ d r Disposition of Solar Radiation in the Atmosphere H 2O, O 2, O 3, N 2O H 2 O, O 2, O 3, N 2 O Indirect Direct Solar D t,b ESUN b cos2 d r d r 2π = cos DOY 365 = Reflectivity (dimensionless) (0-1) for band b at the top of the atmosphere (at the satellite) = Potential Solar Radiation in band b = cosine of solar angle from nadir = inverse of square of relative distance from sun to earth For August 22, 2000: Sun elevation angle (β) = , θ = (90 - β) = DOY = 235, d r = 0.980

36 ESUN b for Landsat 5 and 7 W/m 2 /µm Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 7 Landsat Landsat

37 (new method) Reflectance at Surface Disposition of Solar Radiation in the Atmosphere H 2 O, O 2, O 3, N 2 O H 2 O, O 2, O 3, N 2 O D s,b D t,b D a,b τ in,b τ out,b ρ s,b = = Reflectivity (dimensionless) (0-1) for band b at the surface = Reflectivity (dimensionless) (0-1) for band b at the top of the atmosphere (at the satellite) = false Reflectivity (dimensionless) (0-1) for band b seen by satellite, but originating from scattered radiation in atmosphere = Atmospheric transmissivity for incoming radiation from sun in band b τ ρ t,b in,b ρ τ a,b out,b = Atmospheric transmissivity for outgoing reflected radiation from surface in band b (τ in,b < τ out,b ) Indirect Direct Solar

38 Disposition of Solar Radiation in the Atmosphere Reflectance at Surface H 2O, O 2, O 3, N 2O H 2O, O 2, O 3, N 2O Absorption, scattering and transmission of atmosphere can be modeled using complex radiation transfer models like MODTRAN. MODTRAN considers impacts of: water vapor profile temperature profile pressure profile typical aerosols and gases MODTRAN requires a Radiosonde for the day of the correction MODTRAN is not perfect assumes all pixels reflect the same energy (to be scattered) as the pixel analyzed does not account for thinning of atmosphere with changing elevation in an image Indirect Direct Solar

39 Incoming Transmissivity τ C P W by Tasumi and Allen, air 3 4 in,b = C1 exp + C5 K t cosθh cosθh C + C C 1 -C 5 = Generalized Coefficients fitted to MODTRAN and SMARTS2 models P air = mean atmospheric pressure, kpa (= f(elevation)) W = precipitable water in atmosphere (= f(near surface vapor pressure from weather station)) K t = turbidity (clearness) coefficient (default = 1.0) θ h = solar angle from nadir of horizontal surface Eq. has similar form to broadband τ equation of FAO-56, ASCE-EWRI Terms Band 1 Band 2 Band 3 Band 4 Band 5 Band 7 C C C C C ρ a,b

40 Outgoing Transmissivity by Tasumi and Allen, 2005 τ out,b = C P C W + C 2 air 3 4 C 1 exp + K t 1 1 C 5 C 1 -C 5 = Generalized Coefficients fitted to MODTRAN model P air = mean atmospheric pressure, kpa (= f(elevation)) W = precipitable water in atmosphere (= f(near surface vapor pressure from weather station)) K t = turbidity (clearness) coefficient (default = 1.0) θ h = satellite angle from nadir of horizontal surface (0 for Landsat)

41 Broadband Surface Albedo W b α = 7 [ ρ ] s,b wb b= 1 = weighting coefficient that considers fraction of all potential solar energy at the surface over range represented by specific band. (W b s sum to 1.0) Range for W Band: weighting coefficients by Tasumi and Allen, 2005 Wavelength in Microns Terms Band 1 Band 2 Band 3 Band 4 Band 5 Band 7 w b

42 Broadband Surface Albedo Albedo by EBT-BBT NDVI less than 0.65 NDVI 0.65 or more Albedo by updated m ethod NDVI less than 0.65 NDVI 0.65 or more MODTRAN based albedo MODTRAN based Albedo EBT-BBT = old method used in METRIC until 2004 (based on broad-band transmissivity) α α = toa α τ path _ radiance 2 sw

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

44 Typical Surface Albedo Values 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 (depending on solar elevation angle) (Data from Horiguchi, 1992)

45 Albedo for a water body is often < 0.05

46 Incoming Solar Radiation (R s ) (if it wasn t clear, we wouldn t have an image) R s = G sc cos θ d r τ sw G sc solar constant (1367 W/m 2 ) d r inverse squared relative Earth-Sun distance τ sw one-way broad-band transmissivity (τ sw is calculated using ASCE-EWRI, 2004) For August 22, 2000: R s = W/m 2

47 Vegetation Indices used to estimate aerodynamic roughness and thermal emissivity NDVI = (ρ 4 ρ 3 ) / (ρ 4 + ρ 3 ) (Normalized Difference VI) SAVI = (1 + L) (ρ 4 ρ 3 ) / (L + ρ 4 + ρ 3 ) (Soil Adjusted VI) For Southern Idaho: L = 0.1 SAVI ID = 1.1(ρ 4 ρ 3 ) / (0.1 + ρ 4 + ρ 3 ) Leaf Area Index (LAI): LAI ln = 0.69 SAVI ID We limit LAI 6.0 (based on form of Bastiaanssen) ρ is usually calculated at top of atmosphere

48 NDVI Image Dark green high NDVI Yellow green low NDVI

49 Yellow green low LAI LAI Image Dark green high LAI

50 Area just south of Albuquerque along Middle Rio Grande false color NDVI NDVI Nega. 0.0 LAI 0.0 LAI T surface (K)

51 Surface Emissivity (ε o and ε NB ) --for thermal (infrared) radiation METRIC uses two surface emissivities: ε 0 is the emissivity for the broad band spectrum and is used to compute the outgoing longwave radiation. ε NB is the emissivity for the narrow band spectrum and is used to compute the surface temperature.

52 Surface Emissivity ε NB = LAI; for LAI < 3 ε 0 = LAI; for LAI < 3 ε ΝΒ = 0.98 and ε0 = 0.98 when LAI 3 For water; NDVI < 0 and α < 0.47, ενβ = 0.99 and ε o = For snow; NDVI < 0 and α 0.47, ενβ = 0.99 and ε o = 0.985

53 4 Thermal Radiance (R c ) H 2 O, CO 2, CH 4, CFC s R c = L 6 τ R NB p ( 1 ε ) NB R sky R p is the path radiance in the µm band R sky is the narrow band downward thermal radiation for a clear sky (we consider the 1- ε ΝΒ component that reflects from the surface)

54 Surface Temperature (T s ) (Planck s Law) T s = ε ln NB R K c 2 K 1 + 1

55 ERDAS Model Surface Temperature

56 Surface Temperature southcentral Idaho August 14, 2000 Thousand Springs North Twin Falls recent burn basalt Wood River Valley Temperature ( o C) Burley Craters of the Moon Lake Walcott

57 Outgoing Longwave Radiation (R L ) R L = ε o σ T s 4 Where; ε 0 = broad band emissivity T s = surface temperature in degrees Kelvin σ = Stefan-Boltzmann constant ( W / m 2 / K 4 )

58 Outgoing Longwave Radiation Image and Histogram

59 Incoming Longwave Radiation (R L ) R L = ε a σ T a 4 ε a = effective atmospheric emissivity = 0.85 (-ln τ sw ).09 for southern Idaho T a T s (some METRIC applications have assumed T a everywhere = T s for the cold pixel) R L = 0.85 (-ln τ sw ).09 σ T cold 4 For August 22, 2000: τ sw = 0.774, T s = K, R L = W/m 2

60 Net Surface Radiation Flux (R n ) R n = (1-α)R S + R L -R L -(1-ε o )R L

61 Net Radiation southcentral Idaho August 14, 2000 Thousand Springs North R n H ET G Twin Falls recent burn basalt Wood River Valley Net Radiation (W/m 2 ) Burley Lake Walcott Craters of the Moon

62 Mr. SEBAL

63 Soil Heat Flux (G) via Bastiaanssen (1995): G/R n = T s ( α)(1 -.98NDVI 4 ) via Tasumi et al., (2003) from USDA-ARS data at Kimberly: G/R n = exp ( LAI) for LAI > 0.5 G/R n = 1.80 (T s 273)/ R n for LAI < 0.5 (~bare soil) and G = G/R n R n

64 Water Heat Flux (G) (midday) For clear, deep water If NDVI < 0; assume clear water G/R n = 0.5 (on average for moderately clear, moderately deep) For snow If T s < 4 o Cand α > 0.45; assume snow G/R n = 0.5 (very rough guess)

65 Water Heat Flux (G) (Appendix 10) For clear, deep water Monthly average G vs. Rn measured in a deep Japanese lake (mean depth of 21m) (data from Yamamoto and Kondo, 1968). Monthly evaporation from three Great Lakes (Derecki, 1981)

66 Water Heat Flux (G) American Falls, Reservoir, Idaho 2004 midday readings based on combination of eddy covariance and REBS Bowen ratio measurements. Tasumi and Allen, 2004, preliminary data, University of Idaho units for R n, H, LE, G are W/m 2. Wind speed, WS, is in m/s. Kc = Evap / ET r

67 Water Heat Flux (G) American Falls, Reservoir, Idaho hr averages based on combination of eddy covariance and REBS Bowen ratio measurements. Tasumi and Allen, 2004, preliminary data, University of Idaho units for R n, H, LE, G are W/m 2. Wind speed, WS, is in m/s. Kc = Evap / ET r

68 Water Heat Flux (G) American Falls, Reservoir, Idaho hr averages Energy Flux (W/m2) Hour Rn G H LE based on combination of eddy covariance and REBS Bowen ratio measurements. Tasumi and Allen, 2004, preliminary data, University of Idaho 1000 August, 2004 November, 2004 Energy Flux (W/m2) Hour Rn G H LE units for R n, H, LE, G are W/m 2. Wind speed, WS, is in m/s. Kc = Evap / ET r

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

70 Weather Data In METRIC, Weather Data are used for: Wind speed for sensible heat flux calculation Vapor pressure for incoming solar transmissivity (minor) Calculate Reference ET for Calibrating the Cold Pixel Extrapolate ET using Reference ET for: 24-hour period Days between Images

71 Hourly Weather Data

72 Computing Reference ET

73 Weather Data from USBR AgriMet In METRIC tm applications, Alfalfa Reference ET r is computed using the hourly ASCE Standardized Penman-Monteith Equation In Idaho, USBR AgriMet data are used high quality and consistent frequent sensor calibration and QC available via web generally good agricultural locations relatively long history

74 ET, mm/hour Kimberly Lysimeters - September 4,1990 Data from Dr. J.L Wright ASCE Standardized Penman-Monteith (tall reference) at Kimberly, Idaho Time of Day - hourly time step ET sz ( R n Etr Lys. 2 alfalfa vapor pressure deficit psychrometric constant = Cn G) + γ u T γ ( 1+ C u ) d 2 2 ( e s e a ) ET, mm/hour Kimberly Lysimeters -September 7, 1990 wind speed 0.10 slope, sat. vapor pressure curve Time of Day Etr Lys. 2 alfalfa

75 ASCE Standardized Net Radiation at Kimberly, Idaho - hourly time step Measured data by Dr. J.L. Wright, USDA-ARS

76 Calculating Wind Speed, ETr, and vapor pressure for the Satellite Overpass Time Data image = Data t ( Data Data ) t 2 t t 1 t image( Local time) t 1 Flag DST + t Flag period t 2 t 1 t + t 2 image ( local time) 1 = int + Flagperiod t FlagDST t = t1 2 + t

77 Wind speed profile and aerodynamic transfer

78 Sensible Heat Flux (H) H = (ρ c p dt) / r ah dt = the near surface temperature difference (K). r ah = the aerodynamic resistance to heat transport (s/m). r ah = z ln z u * 2 1 k z 2 z 1 dt r ah H u * = friction velocity k = von karmon constant (0.41)

79 Friction Velocity (u * ) (m/s) u * = ln ku x z z x om u x is wind speed (m/s) at height z x above ground. z om is the momentum roughness length (m). z om can be calculated in many ways: For agricultural areas: z om = 0.12 height of vegetation From a land-use map As a function of NDVI and surface albedo

80 Calculations for the Weather Station For Kimberly, Idaho, August 22, 2000: u * = ku x z ln z x om z x = 2.0 m, u x = 1.63 m/s, h = 0.3 m, z om = =.036 m u * = m/s

81 Calculations for the Weather Station u 200 = u * ln 200 z k om u 200 = 3.49 m/s

82 Friction Velocity (u * ) for Each Pixel u* = ku ln z om u 200 is assumed to be constant for all pixels z om for each pixel is found from a land-use map For agricultural fields, z om = 0.12h For our area, h = 0.15LAI z om = LAI

83 Daily Wind speed Maps by NOAA NCEP (could be considered)

84 Land-use Classification for Southern Idaho Pixel value Land-use type 0 Background (For estimating z om ) 1 Water 2 City and manmade structure 3 Vegetated field (at 8/22/00) 4 Forest at flat area 5 grassland 6 sage brush 7 bare soil includes both in field area and desert area 8 burned area 9 salty soil 10 basalt (dark gray) 11 basalt (black) 12 basalt (gray) 13 basalt (light gray) 21 mountain forest 22 mountain bare soil, dead grass, sage brush and other small vegetations

85 Land Classification- Paths 40 and 39

86 Friction Velocity (u * ) u * = ln x z u om x k Ψ m(x) Blending Height Need to account for instability zom values are assigned via landuse Assume windspeed at 200m (Blending Height) is a constant

87 Calculation of Aerodynamic Resistance (r ah ) r ah = ln z z 2 1 Ψ u * h(z 2 k ) + Ψ h(z Land Surface 1 ) Resistance, r ah H zero plane displacement (d) Need to account for instability z z2 = d 2.0m, + zt2 2, = T T2m = T 2 dt = T 1 - T 2 z = d + z 1 z = d, T = T 1 z1 = 0. 1m, T1 = T0.01m (z1 = 0.1m in METRIC, 0.01m in SEBAL)

88 Aerodynamic Resistance to Heat Transport

89 Aerodynamic Equations used in METRIC tm H = ( ρ c p )(T a1 T a1 ) / r ah r Ψ ah = Ψ Ψ z ln z 2 ns Ψ u * h( z k ) + Ψ h( 2 z 1 ) u * = T a1 T a2 = f (T s ) ln 200 z 0m u 200 k Ψ Correction for atmospheric instability h 1 + = 2ln ( z2 ) x 2 ( z 2 2 ) 2 1+ x( 200m) 1 x 200m 2ln ln + ( ) = + 2ARCTAN x( 200m) 2 2 Ψ h ( z2 ) = z L 5 2 m( 200m) ( ) 0. 5π m + ( 200m) m ( 200m) = z L 5 2 and x ( height) ( height) = 1 16 L 3 T0 L Cpairu = ρ air * k g H for stable

90 Near Surface Temperature Difference (dt) (The Genius of SEBAL) z 2 dt r ah H To compute the sensible heat flux (H), define near surface temperature difference (dt) for each pixel z 1 dt = T near surface T air dt = T z1 T z2 T air is unknown SEBAL and METRIC tm assume a linear relationship between T s and dt:

91 How METRIC tm is Trained METRIC tm is trained for each image by defining dt at the 2 anchor pixels: At the cold pixel: H cold = R n G -LE cold where LE cold = 1.05 λ ET r dt cold = H cold r ah / (ρ c p ) (in classical SEBAL, H cold = ~0 and T cold ~ T s is for water) At the hot pixel: H hot = R n G -LE hot where LE hot ~ 0 (if indicated by water balance) dt hot = H hot r ah / (ρ c p )

92 Cold Pixel: The coldest green Ag. Fields consume as much as 5% more than ET r (Corn, Beans, Sugar Beets, Alfalfa) ET (cold pixel) = 1.05ET r ET r F=1.05 METRIC Daily ET r F, Corn on Lysimeter, Kimberly

93 Selection of Anchor Pixels The METRIC tm process utilizes two anchor pixels to fix boundary conditions for the energy balance and to internally calibrate. Cold pixel: a wet, well-irrigated crop surface with full cover T s T air (but depends on ET r ) -- In classical SEBAL, T s ~T air at cold pixel, thus H ~ 0 -- In METRIC tm, ET ET r at cold pixel, thus H = R n G ET r Hot pixel: a dry, bare agricultural field ET 0

94 White K Red K Selecting the Cold Pixel Look for 0.5 m tall alfalfa (can you see it???)

95 Selecting the Hot Pixel Red 334 K Yellow K

96 Selecting the Hot Pixel

97 ET r F at the Hot pixel: (is it really zero?): The operator must direct METRIC concerning any residual ET at the hot pixel. ET r F can be estimated using the FAO-56 surface evaporation estimation procedure Bare soil water balance, MRG, /1/2002 2/1/2002 3/1/2002 4/1/2002 5/1/2002 6/1/2002 7/1/2002 Kc based on ETr 8/1/2002 9/1/ /1/ /1/ /1/ Precipitation (mm)

98 How METRIC tm is Trained Once T s and dt are computed for the anchor pixels, the relationship dt = b + at s is defined as linear. Magic (and genius ) of SEBAL

99 Sensible Heat Flux (H) Application of the linear dt function: dt for each pixel is computed as: dt = b + at s H = (ρ c p dt) / r ah

100 Iterative Process to Compute H Weather station u, z x, z om, u * H for each pixel dt H = ρcp r ah wind speed at 200 meters u 200 = u * z ln z k 200 0m ρ L = Cp u k g H 3 * T s friction velocity at each pixel u * = ku z ln z m ψ m (blending) ψ h (z1) ψ h (z2) r ah for each pixel r ah = z 2 ln z 1 u k * u * = z ln z k 200 0m u 200 Ψ m(200) Cold Pixel H cold =Rn-G-λET cold dt coe =H cold *r ah /(ρcp) Hot Pixel H hot =Rn-G dt hot = H hot *r ah /(ρcp) r ah z ln z = 2 1 Ψh (z2 ) u k * + Ψ h (z ) 1 dt for each pixel dt=at s +b

101 R n, G and H along MRG south of Albuquerque Rn G H (W/m2)

102 Surface Energy Budget Equation R n = G + H + LE LE = R n G H ET = LE / λ R n H ET n G

103 Evapotranspiration at time of overpass Oakley Fan, Idaho, July 7, 1989

104 Guilty Allen, Tasumi, Bastiaanssen, Trezza Idaho 2002

105 Measured vs METRIC Instantaneous ET -- Sugar Beets, 1989, Kimberly, ID 1 1:1 Line 6/24/90 SEBALID ET (mm/hour) /18/89 9/25/89 7/29/91 7/23/89 8/21/88 7/7/89 5/4/ /5/89 6/21/89 5/20/ Measured ET (mm/hour)

106 What about the rest of the day? (and month??) (and year????)

107 ET r F = Fraction of ET r = K c ET r F is consistent through the day ET, mm/hour Kimberly Lysimeters - July 07, 1989 Sugar Beets Time of Day Lysimeter 2 data by Dr. J.L. Wright, USDA-ARS ETrF ETrF (ET r F = ET c /ET r ) ETr Daily Average ETrF

108 ET r F = Fraction of ET r = K c Assumption: ET r F is consistent through the day ET, mm/hour Kimberly Lysimeters - August 4, Time of Day Sugar Beets ET ETrF ETr ETrF ET, mm/hour Kimberly Lysimeters - August 5, Time of Day Sugar Beets ET ETrF ETr ETrF ETo Daily Average ETrF ETo Daily Average ETrF ET, mm/hour Kimberly Lysimeters - August 6, Time of Day Sugar Beets ET ETrF ETr ETrF ET, mm/hour Time of Day Sugar Beets ET Kcr ETr ETo Kimberly Lysimeters - August 7, 1989 Daily Average Kcr Kcr ETo Daily Average ETrF

109 Extrapolation of Inst. to 24-hour ET : ET r F method - METRIC Sugar Beets and Potatoes ETrF for 1988 and 199 satellite dates 1.20 ETrF for Sugar Beets May to September, 1989, Data from Dr. J.L Wright 1.20 y = x R 2 = : ETrF at satellite time hour ETrF :1 line Average Daily ETrF Instantaneous ETrF at 11:00 am ET r F based on Lysimeter Data by Dr. J.L. Wright, USDA-ARS

110 EF = Evaporative fraction = Fraction of (R n -G) Assumption: EF is consistent through the day EF = ET c /(R n -G) Fluxes, Watts/m Kimberly, Idaho, Grass May 29, 1989 Data by Dr. J.L. Wright, Evaporative Fraction Hour of day Rn - G ET (grass) -1 Sensible Heat (H) Evaporative Fraction

111 Estimation ET using EF (clipped grass) for Satellite Days (Kimberly) Evaporative Fraction (EF) for Grass at Kimberly, :1 line 1.2 Daily average EF /4/89 6/21/89 4/18/89 6/5/89 723/89 7/7/ Instantaneous EF at Satellite Time

112 Use of EF vs. ET r F to Estimate 24-hr ET ET r F is less sensitive to regional advection effects ---- ET r captures most regional advection effects (advection: low afternoon RH, high afternoon T and wind) EF at Kimberly (Grass, 5/20/89) ET r F at Kimberly (Grass, 5/20/89) ET, Rn, (W/m 2 ) Advection EF ET (mm/hr) more stable ETrF during day and ETrF 1100 ~ ETrF :00 9:00 11:00 13:00 15:00 17:00 19:00 7:00 9:00 11:00 ETrF 13:00 15:00 17:00 19:00 ET Rn ET Grass(mm) ETr (mm) EF EF24 ETrF ETrF24

113 Kimberly 1989 Inst. ET ET cold = 1.05ET r ET cold = R n -G SEBALID ET (mm/hour) /18/89 5/20/89 6/5/89 6/21/89 9/25/89 5/4/89 Measured ET (mm/hour) ET r F 7/29/91 7/23/89 8/21/88 1:1 Line 6/24/90 7/7/89 1:1 Line Inst. SEBAL ET (mm/hour) using EF Method /21/89 5/20/89 4/18/89 6/5/89 7/23/89 9/25/89 8/21/88 5/4/89 1:1 Line 7/7/ Inst. Measured ET (mm/hour) EF 1:1 Line 24-hour ET SEBAL ET (mm/day) /18/89 6/5/89 5/20/89 6/21/89 9/25/89 5/4/ Measured ET (mm/day) 6/24/90 8/21/88 7/29/91 7/23/89 7/7/89 (METRIC) SEBAL ET (mm/day) - EF Method /5/89 6/21/89 4/18/89 5/20/89 Sugar Beets /25/89 8/21/88 5/4/89 7/23/89 7/7/ Measured ET (mm/day)

114 24-Hour Evapotranspiration (ET 24 ) ET = ET F ET 24 r r _ 24 Path 39: Am. Falls - 24-hour ET 8/07/00 (in EF method, ET 24 = EF x R n24 )

115 Seasonal Evapotranspiration (ET seasonal ) Interpolate ET r F between images (after cloud masking) (same principle as in constructing a crop coefficient curve). Assume ET for entire area of interest changes in proportion to change in ET r at weather station.

116 Seasonal Evapotranspiration (ET ) seasonal Compute the cumulative ET for period of interest: ET period = n ( ET ) rfi ETr i= 1 (n = length of period in days) 24i Compute the seasonal ET ET seasonal = ET period

117 Image Dates during 2000 Path 40 3/15/00 4/8/00 5/2/00 6/3/00 6/19/00 7/5/00 7/21/00 8/14/00 8/22/00 9/7/00 9/15/00 10/17/00 Path 39 3/16/00 4/1/00 5/3/00 6/4/00 6/20/00 7/6/00 7/22/00 8/7/00 8/23/00 9/8/00 9/16/00 10/18/00 Southern Idaho

118 Seasonal ET > 1000

119 Comparison of Seasonal ET by METRIC tm with Lysimeter ET (mm) - April-Sept., Kimberly, 1989 Sugar Beets Lysimeter 718 mm Total METRIC 714 mm Lysimeter SEBAL METRIC

120 Seasonal ET Cumulative ET in 1989 for Sugar Beets 800 Error = 2.5% /1/89 4/15/89 4/29/89 5/13/89 5/27/89 6/10/89 6/24/89 7/8/89 7/22/89 8/5/89 8/19/89 9/2/89 9/16/89 9/30/89 Cumulative ET (mm) from 4/1/89 SEBAL-ID Estimation Lysimeter Measurement

121 Comparison of Seasonal ET by SEBAL 2000 with Lysimeter ET (mm) - July-Oct., Montpelier, ID Lysimeter 388 mm Total SEBAL 405 mm Lysimeter SEBAL

122 False color, Daily, Monthly and Annual ET r F for an area along the MRG south of Albuquerque Daily 8/26/2002 Monthly August 2002 Annual 2002 ET (mm/yr) ETrF

123 False color, Daily, Monthly and Annual ET r F path 34, San Acacia, New Mexico to Colorado Daily 8/26/2002 Monthly August 2002 Annual 2002 ETrF All Images

124 Confirmation of ET from Remote Sensing with Independent Measurements is Highly Desirable Validation can be done anywhere in the world ( physics are physics everywhere) However, Ground data MUST be Accurate ( No Data are better than Bad Data )

125 Comparison with Lysimeter Measurements: Lysimeter at Kimberly (Wright) 12/17/01

126 Thermal Information for a small Lysimeter Field is Challenging AirPhoto Shortwave (30mx30m) Thermal (120mx120m) Private Fields Private Fields 143 m USDA Research Plots Lysimeter 2 Field (field crops) Lysimeter 1 Field 179 m 198 m Private Field USDA Research Plots (grass) Lysimeters 63 m 130 m Asphalt Road North Private Fields Figure 3. Plan view of Kimberly lysimeters and surroundings

127 Thermal Information for Lysimeter Field for a Good Image Overlay Airphoto of Lysimeter 2 field (left), Landsat TM true color at 6/21/89 (center), and Landsat TM thermal band at 6/21/89 (right). Yellow colored pixels in the right image are from one original thermal band pixel (120m 120m).

128 Inadequate Thermal Overlay on Small field Lysimeter 2 field airphoto (left), Landsat TM true color at 7/7/89 (center), and Landsat TM thermal band on 7/7/89 (right). Each colored pixel in the right image represented a different thermal pixel (120m x120m).

129 False color composites (TM bands 2,3,4) showing the side-by-side lysimeter fields at Kimberly for May 4 (left image) and July 23 (right image), 1989.

130 Kimberly, Idaho (Snake River basin) Kc = Ratio of ET to Ground-based Reference ET Comparisons between SEBAL Predictions and Lysimeter Measurements: Kimberly Sugar Beet Field Field irrigated 2 days prior, Lys. only 1 day prior (Lys. was wetter than field) Lysimeter data by Dr. J.L. Wright, USDA-ARS Thermal pixels were badly blurred by areas outside lysimeter field Very high winds in AM and missing wind speed data (estimated at 6 m/s) 0.0 Bare Soil 04-May 21-Jun 20-May 07-Jul 18-Apr 05-Jun Satellite Image Date 23-Jul 25-Sep Five-day average Lys. Kc Lys. Kc for the Image Date Kc ETfrom r Ffrom SEBAL METRIC

131 Measured vs Instantaneous ET (using METRIC) Satellite Reference ET Measured ET (1) METRIC SEBAL ID ET (2) Difference Normalized (3) Date Crop ET r(inst) ET (inst) ET r F (inst) ET (inst) ET r F ET (inst) Error (4) 1989 mm/hr mm/hr mm/hr mm/hr % 8/21/88 Potatoes /18/89 Sugar B /04/89 Sugar B /20/89 Sugar B /05/89 Sugar B /21/89 Sugar B /07/89 Sugar B /23/89 Sugar B /25/89 Sugar B /24/90 Peas /29/91 Alfalfa (1) Measured ET values were provided by Dr. James Wright, USDA/ARS (2) The METRIC SEBAL ID ET is the averge of four 30m x 30m pixels that were centered at the lysimeter (3) In "Difference" column, negative values indicated that SEBAL METRIC ID ET was lower than Lysimeter 2 ET. (4) Normalized error was calculated as 100*Difference ET (inst) / ETr (inst)

132 Kimberly, Idaho Periods between Satellites ET during period, mm Impact of using Kc from a single day to represent a period: Kimberly 1989 Sugar Beets, 1989 Kimberly, Idaho 0 04-May 21-Jun 20-May 07-Jul 18-Apr 05-Jun 23-Jul 25-Sep Lys. Kc on Sat. date x sum ETr Sum. all lysimeter meas. (Truth) SEBAL METRIC ET ET for for period Lysimeter data by Dr. J.L. Wright, USDA-ARS

133 Validation in the Bear River Basin 1985 Three lysimeters lysimeter = 7 day averages, only Irrigated meadow (sedges, native grasses) Harvested in July, grazed in August

134 Confirmation in the Bear River Basin ET by Lysimeters and SEBAL Montpelier, Idaho Ratio of ET to Reference ET hay cut lysimeter = 7 day averages, only July August Sept. Oct. Lysimeter SEBAL Day of Year Avg. Etc/Etr by lysimeter Ratio of Etc to Etr by SEBAL

135 Imperial Valley, CA via Landsat 7 Imperial Valley ET (mm) ET during January March, 2003

136 Annual ET for all of California Created by SEBAL- North America for 2002 using MODIS satellite imagery (resolution = 1 km)

137 Imperial Valley ET (mm) Imperial Irrigation District Total Annual ET - all areas Imperial Valley, CA via Landsat 7 ET during January March, ,959,000 1,950,000 2,046,000 2,085, Acre-Feet / year , SNA 1987 (low year)- approx ave via WB 1996 (high year)- approx.

138 Imperial Valley ET (mm) Imperial Valley, CA via Landsat ET during January March, 2003 Imperial Irrigation District Jan.-March ET - all areas Million cu. meters/ year UI (METRIC) 443 SNA (SEBAL)

139 ET in Mountains Solar Radiation Incident solar radiation (Wm -2 ) for a mountainous area (left). Landsat 7 ETM+ false color is depicted to the right

140 Use of DEM (slope, aspect) in radiation calculations (Mountain Model) R n Path 40, Row 30, 8/14/ SouthEast sloping surface (bare/grass) 2. NorthWest sloping surface (bare/grass) 3. NorthWest sloping surface (forest) T. Color F. Color Flat Model Mountain Model R n (W/m 2 )

141 Use of DEM (slope, aspect) in radiation calculations (Mountain Model) 24-hour ET Path 40, Row 30, 8/14/ SouthEast sloping surface (bare/grass) 2. NorthWest sloping surface (bare/grass) 3. NorthWest sloping surface (forest) T. Color F. Color Flat Model Mountain Model ET (mm)

142 METRIC tm -ERDAS submodel for solar radiation in mountains

143 Surface/Terrain Roughness In METRIC mountain model, roughness is increased in mountainous areas to account for terrain roughness (f (s, z)) A map of surface roughness z om (left) for 06/04/2000 for the area SE of American Falls. The Landsat 7 false color is shown at the right.

144 Where EF has advantage Hourly ground weather data are sparse or are of poor quality (use EF and base ET on R n computed from trig) A large, shallow water body is present (T for cold pixel) Regional advection is relatively small (to use EF) Large images are processed (i.e., MODIS)

145 Where ET r F has advantage Hourly ground weather data are available and are of good quality Tall, well watered vegetation is available for the cold pixel (ET cold ~ 1.05 ET r ) (otherwise, ET cold = f (NDVI) ) Regional advection is relatively large Congruency with the K c ET r procedure is useful Landsat or ASTER are used (high resolution, smaller coverage than MODIS)

146 Sensitivity (or lack of) for METRIC to: Atmospheric correction of reflectances using radiative transfer model (MODTRAN) Atmospheric correction of surface temperature using radiative transfer model (MODTRAN) Estimated aerodynamic roughness

147 Estimated 24 hour ET (mm/day), 7/21/2000, path 40/30, Agr. Area Only Model Sensitivity To Correction of Surface Temperature for Atmosphere Estimated ET using uncorrected Ts y = x R 2 = Estimated ET using corrected Ts (Predictions are not sensitive due to calibration at hot and cold pixels)

148 to Aerodynamic Roughness, zom Model Sensitivity --- Agricultural Areas (mm/day) if zom is double Est. ET Estimated 24 hour ET (mm/day), 7/21/2000, Agricultural Area y = x R 2 = (mm/day) if zom is half Est. ET Estimated 24 hour ET (mm/day), 7/21/2000, Agricultural Area y = x R 2 = Estimated ET with original z om (mm/day) Estimated ET with original z om (mm/day) (Predictions are not sensitive due to calibration at hot and cold pixels)

149 Est. ET if zom is 0.6m (mm/day) zom --- City Areas Estimated 24 hour ET (mm/day), 7/21/2000, City Area y = x R 2 = Est. ET with original z om (= 0.2m) (mm/day) Est. ET if zom is 0.05m (mm/day) Model Sensitivity Estimated 24 hour ET (mm/day), 7/21/2000, City Area y = x R 2 = Est. ET with original z om (= 0.2m) (mm/day) (Predictions are not sensitive due to calibration at hot and cold pixels)

150 Example of LEVEL TWO METRIC Applications

151 ET in Deserts

152 Solution: Add an extra resistance of about 5 s/m Sagebrush Desert Application Desert ET often becomes negative in summer --- problem with wind speed and r ah Satellites Observe high Ts Solar Radiation penetrates sparse vegetation to soil Very Hot Soil Soil is protected from Wind and heats up and H is overpredicted by the dt vs. Ts function

153 ET in Deserts: Challenge - negative values Surface parameters and fluxes for several desert samples on 06/20/2000 without an extra resistance Sample Hot Pixel Sage Brush Grass Albedo LAI (m 2 /m 2 ) NDVI z om (m) T s (K) Rn (Wm -2 ) G/Rn G (Wm -2 ) H (Wm -2 ) ETrF ET 24 (mm/day)

154 Magic Valley ET estimated using an extra resistance in desert for desert areas 10 rah (s/m) needs additionally y = x x x R 2 = Wind speed 200 (m /s) Final Extra resistance function for METRIC

155 Magic Valley ET estimated using an extra resistance in desert for desert areas ETrF MV 7/30 /2003 False color MV 7/30 /2003 normal resistance calc. MV 7/30 /2003 extra resistance as a function of u

156 ET in Deserts: Middle Rio Grande region

157 Path 34: West of Middle Rio Grande, New Mexico ETrF < ET (mm/d) < MRG True Color path 34 6/7/2002 MRG METRIC-ET (single dt function) 6/7/ > > 14.06

158 South of Albuquerque: ET from Agriculture and City areas is accurately estimated ETrF < ET (mm/d) < MRG True Color 6/7/2002 MRG METRIC-ET (single dt function) 6/7/ > > 14.06

159 Western-edge of image: ET from green agricultural areas seems accurate, however, very negative ET values for desert and for some dry, bare fields ETrF < ET (mm/d) < MRG True Color 6/7/2002 MRG METRIC-ET (single dt function) 6/7/ > > 14.06

160 Use of a dual dt function for desert areas F(max) dt(agric.) F(agric) dt (K) dt(desert) F(agric) dt (K) F(pixel) F(desert) F(desert) F(min) T(cold) Surface temperature (K) T(hot,desert) T(hot,agric.) Surface temperature (K) Creation of the dual dt function: (1) Select two hot pixels: one for a general agricultural bare soil and another from bright desert. (2) Develop two dt functions using the same cold pixel, as shown in the left figure. (3) A dt slope is interpolated for each pixel based on albedo of the pixel. * The dual-dt function is applied only to bare soils. All vegetated pixels use the basic agricultural dt function.

161 Western-edge of the image after some adjustment: Several possible causes of negative ET in desert: Error in G, z om, lapse-correction, dt function, variation in u, stability, emissivity, and hot-pixel-selection all affect ET. In the MRG, we have concluded that stability corrections and emissivity have small impact on ET estimate. Reducing z om improved estimations somewhat, and modification of G and use of a limit on dt had the most impact on reducing occurrence of negative ET in deserts. ETrF < ET (mm/d) < MRG METRIC-ET (with reduction in G) 6/7/2002 MRG METRIC-ET (with limit on dt) 6/7/ > > 14.06

162 More information at: (METRIC tm ) (SEBAL tm )

163