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Introduction to thermal - Balance System Basics

Z. (Bob) Su International Institute for Geo-Information Science and Earth Observation (ITC), Enschede, The Netherlands [email protected], www.itc.nl/wrs

Monday 29 June 2009, Lecture D1Lb3 • Learning Objectives

1. To understand basic concepts of surface radiation budget 2. To understand basic measurements to derive surface radiation components 3. To be able to derive surface radiation components using different information 4. To familiarize with retrieval of surface parameters Land-Atmosphere Interactions - Terrestrial , Energy and Carbon Cycles

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S Processes ( THERMAL INFRARED RADIATION is a form of electromagnetic radiation with a between 3 to 14 micrometers (µm). Its is much lower than visible flux. VIS

SOLAR AND TERRESTRIAL SPECTRUM NIR TIR UV MIR

SOLARWavelength (μm) TERRESTRIAL Source: J.-L. Casanova SOME DEFINITIONS

RADIANT : The of flow of electromagnetic energy, i.e., , Φ (, i.e., per second.)

RADIANT EMITTANCE: Radiant power emitted into a full sphere, i.e., 4π (), by a unit area of a source, expressed in watts per square meter. Synonym , flux, , E (W m-2)

RADIANCE: Radiant power, in a given direction, per unit per unit of projected area of the source, as viewed from the given direction. Note: is usually expressed in watts per per square meter, L (W m-2.sr-1) = M/π

IRRADIANCE: Radiant power incident per unit area upon a surface. Note: is usually expressed in watts per square meter, but may also be expressed in joules per square meter. Synonym: power density, flux, radiant flux, M (watts/m2).

Source: J.-L. Casanova GRAPHICAL REPRESENTATION OF E, L AND M

RADIANCE, L = E/π (Wm-2.sr-1)

IRRADIANCE, M (Wm-2)

EMITTANCE or EXITANCE, E (Wm-2)

Source: J.-L. Casanova SPECTRAL MAGNITUDES

ALL THESE MAGNITUDES ARE USUALLY EXPRESSED AS SPECTRAL MAGNITUDES, THAT IS TO SAY, REFERRED TO A WAVELENGHT

-1 -1 RADIANT POWER: Pλ (W.μm ) or (W.cm )

-2 -1 -1 -2 RADIANT EMITTANCE: Eλ (W.m .μm ) or (W.cm m )

-2 -1 -1 -1 -2 -1 RADIANCE: Lλ (W.m .sr . μm ) or (W.cm m .sr ) = Eλ/π

-2. -1 -1 -2 IRRADIANCE: Mλ (W.m μm ) or (W.cm m ).

cm-1 = number of wavelenghts per cm = 10,000 . (1/ λμm) e.g. 1 μm ~ 10,000 cm-1; 10 μm ~ 1,000 cm-1; 11 μm ~ 909.09 cm-1… Source: J.-L. Casanova Thermal emission- the Planck’s Law:

The theory to express the thermal emission is based on the concept: a black body is an object that absorbs all electromagnetic radiation at each wavelength that falls onto it. A black body however emits radiation as well, its magnitude depends onλ its , and is expressed by the Planck’s Law: λ −5 c1 B( ,TS ) = ⎛ c2 ⎞ exp⎜ ⎟ −1 ⎝ λTS ⎠

8 4 -2 -1 c1 = 1.19104·10 W µm m sr 4 c2 = 1.43877·10 µm K, are the first radiation constant (for spectral radiance) and second radiation constant, respectively, B (λ, Ts) is given in W m-2 sr-1 μm-1 if λthe wavelength is given in µm. Terminology in Thermal Remote Sensing

• Thermodynamic (kinetic) temperature • temperature • Directional radiometric surface temperature & Directional • Hemispheric broadband radiometric surface temperature & Hemispherical broadband emissivity

Source: J. Norman, and F. Becker, 1995 Thermodynamic (kinetic) temperature • Thermodynamic (kinetic) temperature (T) is a macroscopic measure to quantify the thermal dynamic state of a system in thermodynamic equilibrium with its environment (no ) and can be measured with a thermometer in good contact with it. • By maximizing the total entropy (S) with respect to the energy (E) of the system, T is defined as dS 1 = dE T

ƒ which is consistent with the definition of the absolute temperature by the ideal gas law PV = RT

ƒ where P is pressure, V , R the gas constant (R=kN0, k is , N0 number of molecules in a ). Brightness temperature

• Brightness temperature (Tb,i) is a directional temperature obtained by equating the measured radiance (Rb,i) with the over wavelength of the Planck’s black body function multiplied by the sensor response fi.

θ φ λ

λ 2 f (λ )C R , = R T θ ,φ = i λ 1 dλ b ,i ()()b ,i ()∫ 1λ ⎛ ⎛ C θ φ⎞ ⎞ 5 ⎜ exp ⎜ 2 ⎟ − 1⎟ ⎜ ⎜ T (), ⎟ ⎟ ⎝ ⎝ b ,i ⎠ ⎠

λ 2 λ f d λ = 1 ∫ i () is the detector relative response. 1λ Directional radiometric surface temperature & Directional emissivity

By applying the Kirchhoff law (energy α = A / I = 1 conservation) to a black body and a real (grey) λ λ λ body, the emissivity is defined - The emittance of a ρ = R / I = 0 real body is always lower than that of the black λ λ λ body at the same temperature. In order to measure α + ρ = 1 BLACK BODY its temperature using a radiometer, we need to λ λ introduce a factor called “emissivity”, < 1, to ε A = I = M (black body definition) equate its emittence to that of the block body. λ λ λ

α′λ = A′λ / Iλ < 1

ρ′λ = R′λ / Iλ > 0 Iλ: incident flux α +ρ =1 ′λ ′λ αλ: Aλ: absorbed flux As the body is in thermal equilibrium: A′ = M′ = α′ I λ λ λ λ ρλ: Rλ: reflected flux M′λ / α′λ = Iλ = Mλ GREY BODY ε: emissivity

M′λ = ελ. Mλ = ελ. M′λ / α′λ ελ = α′λ ελ = 1 - ρ′λ Directional radiometric surface temperature & Directional emissivity

• The spectralρ radiance (RR) measured by a directional radiometer is the sum of the emitted blackα bodyβ radiance modified by the emissivity and the reflected radiation withinθ anφ infinitesimal wavelength band. α λ α RR, (θ ,φ )= ε (θ ,φ )RB, (θ ,φ ) β π λ 2 ρπ / 2 α (α β ) () ( )α () + b, θ, , λ, cos L , sin d dβ ∫0 ∫0 φ λ α Sky radiance Bidirectional reflectance distribution functionα β α If the incident sky radiance is isotropic, we λhave α π β 2 π / 2 ρ θ b , ()()()()(), , , cos L , sin d d = ,φ L ∫0 ∫0 λ Therefore for opaque bodies λat thermal equilibrium,

ε (θ,φ)()=λ1−ρλ θ,φ

λ

λ Hemispheric broadband radiometric surface temperature & Hemispherical broadband emissivity

π π λ • A hemispheric radiometricε surface temperature is used to provide an λ λ θ estimate of the emitted φradiance (Rl) over a broad wavelength and the full hemisphere of view λ θ φ θ θ λ θ 2 / 2 φ 2 ε 4 Rl = ()()()(), RB, , sin cos d d d = λσTR ∫0 ∫∫0 1 In-Situ measurements of Balance- EAGLE/SPARC Campaign 2004, Barrax, Spain

- Situated in the area of La Mancha, in the west of the province of Albacete, 28 km from Albacete - Geographic coordinates: 39º 3’ N; 2º 6’ W - Altitude (above sea level): 700 m

Corn

Bare Soil

Water Body

Garlic

Green Grass

Vineyard

Reforestation The Canopy from Different Perspectives The Fundamental of Earth Observation Sensor Response (Sensor - Object Radiative Relationship) A. How much radiation is detected? B. When does it arrive? Sensor

Object Properties: Its range, its combined temperature Nadir & Emissivity (or reflectivity) ° 52° at different , at different spatial 23 resolution, at different , at different direction, at different atmosphere

Object A: A Passive Sensor System A+B: An Active Sensor System Factors Influencing the Emissivity ε

•The material (minerals, water etc.) • The surface geometry (roughness of the surface) • The wavelength of the radiation •The view angle

(Source: Sobrino et al., 2005) Spectral emissivity extracted from MODIS UCSB Emissivity Library

1.0

0.9

0.8 Water: Seawatr1 Vegetation: 106 0.7 108 121 Soil: e3101 0.6 e4643

Spectral emissivity eply3c7

0.5 800 1200 1600 2000 2400 2800 Wave number (cm-1) lwu

Surface thermal R lwu R

radiation − lwd R + swu

Atmospheric R lwd R

− swd R = swu

Reflected solar radiation n R R Surface Radiation Budget - Measurements

swd Solar Radiation R Net radiation Surface Radiation Budget - Measurements

1 3 CNR1 net radiometer:

Spectral response - Pyranometer: 305 to 2800 nm - Pyrgeometer: 5000 to 50000 nm 5μm − 50 μm 2 4 ()1μm = 1000 nm

Radiation components: 1. incoming short-wave radiation 2. surface-reflected short-wave radiation 3. incoming long-wave thermal infrared radiation 4. outgoing long-wave TIR radiation (whiteness): ratio of scattered to incident electromagnetic radiation EAGLE/SPARC Campaign 2004, Barrax, Spain

Barrax 2004 Radiation @ Vineyard

SW_inc

1200 SW_out 1000 800 LW_inc 600 400 LW_out 200 0 196 197 198 199 200 201 202 203 -200 EAGLE/SPARC Campaign 2004, Barrax, Spain

Radiation Components, Barrax, 15 July 2004 1200

1000

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600 SW_in SW_out LW_in

W/M^2 400 LW_out

200

0 0 50 140 230 320 410 500 550 640 730 820 910 1000 1050 1140 1230 1320 1410 1500 1550 1640 1730 1820 1910 2000 2050 2140 2230 2320 -200 EAGLE/SPARC Campaign 2004, Barrax, Spain

Exercise:

1. Calculate & plot the net radiation and explain what are the influencing factors 2. Explain the pattern of the radiation components 3. Calculate the statistics of the radiation components (mean, minimum, maximum, etc.) 4. Calculate the albedo from the radiation components 5. Check the energy balance and explain what you see How is the net radiation consumed?

R n = G 0 + H + LE + Δ S Δ S ≈ 0

Right hand side: 1. Soil (warming up of the soil layer) 2. flux (warming up of the air layer) 3. flux (phase change, evaporation and transpiration) 4. Heat storage and biological activities

n Wind

R H LE

0 G [α ,ε ,T0 , f c ] Locations of measurements

Dutch site Forest nursery INRA sites

garlic vineyard 1 4 2

corn 5 3 Bare soil

Wheat

~3 km Soil heat flux: measurements with soil heat flux plates

• The soil heat were measured with 4 soil heat fluxes buried at a depth of 1cm below surface, with two placed in the middle of the row and two under the vine and shaded.

• Soil heat flux plates: • SH1 and SH4 were in the shade • SH2 and SH3 were in the sunlit areas SH2 SH1 SH3 SH4 Soil heat flux: measurements with soil heat flux plates Sensible heat flux: scintillometer measurements

•Scintillometer, 2 Sets • Radiation components • Soil Heat flux plates Receiver • Temperature profile (air & soil)

Transmitter Scintillometer Data, EAGLE/SPARC Campaign 2004, Barrax, Spain

Vineyard Barrax 2004 Sensible heat fluxes Corn-C2 600 Reforestation-F1

500 Sunflow er-SF1

400 Bare-B1

300 corn-3D

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0 196 197 198 199 200 201 202 203 -100

-200 Scintillometer Data, EAGLE/SPARC Campaign 2004, Barrax, Spain

Barrax 2004 Fluxes @ Vineyard

Rnet

800 G_avg 600 400 H-LAS 200 196 197 198 199 200 201 202 203 0 LE_Rest. -200 -400 Sensible & latent heat fluxes: Measurements

Canopy level measurements:

Eddy covariance system (Gill 3D sonic + closed path Licor gasanalyser: CO2 and H2O + nitrogen reference gas + pneumatic mast + data loggers)

• Turbulence, sensible heat flux, H2O, CO2 fluxes • CO2 concentrations Flux data SPARC 2004

Eddy Correlation Data, 10 Min Average, July 2004

700 40

500 30

300 20

H W m-2 100 10 LE W m-2 Fc μmol m-2 s-1

-100 0

-300 -10

-500 -20 DOY 195-203 Energy balance components

800 Energy balance (60 minute average), Vineyard, Barrax 2004 700 600

500 H_ed 400 LE 300 Rn 200 G 100 H_las 0 -100 -200 196 197 198 199 200 201 202 203 Energy balance closure ?? (Sum of H and LE exceeds the available energy) 800 H_ed+LE_ed 10 minutes avera ge, Vine yard, Barrax 2004 600 R_avai

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0

-200 196 197 198 199 200 201 202 203 800 H_ed+LE_ed 600 60 minutes average, Vineyard, Barrax 2004 R_avai

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-200 196 197 198 199 200 201 202 203 Surface thermal radiation

Atmospheric thermal radiation 4 0 T ⋅

σ ⋅

ε −

Reflected solar radiation lwd R ⋅ e ε + swd Temperatur R ⋅

α Surface albedo emissivity Surface Radiation Budget - Parameterisation : : :

Solar Radiation − 0

α ε T 1 () = n R ENVISAT Remote sensing retrievals NOAA/AVHRR, LANDSAT, METEOSAT, MODIS MSG Weather prediction model outputs Radio sounding

Remote Sensing Data Regional Atmospheric State

Geographical Data Pre-processing

DN ⇒ Radiance/Reflectance at Sensor ⇓ Atmospheric correction Radiance/Reflectance at Surface

⇓ Inversion of radiative transfer models Albedo, Temperature, Emissivity, Vegetation Parameters, Roughness, Incoming Radiation Derived Surface Parameters/variables

• Incoming global radiation • Albedo • Vegetation cover, Leaf Area Index • Surface temperature • Emissivity • Roughness Components of reflected and scattered solar beams received at the satellite

sca I I mul s I ind I I dir

sky I Φ

φs, Ψs

θ, Ψ0 Incoming global radiation

• Input parameters: – Group 1: date, time, location (latitude) and DEM (elevation, slope, aspect) to compute solar declination, eccentricity, solar zenith angle for a horizontal surface, solar azimuth angle, solar zenith angle on slopes

– Group2: weather condition - Optical properties of the atmosphere (at

the time of calculation) Idr Ida In τ

Idm θz θz

Case: a Case: b Incoming global radiation

• Case a: use total

• I = Isc ⋅e0 ⋅cosθz ⋅exp(−m⋅τ )

• where Isc is the , e0 the eccentricity factor, θz solar zenith angle, m air , τ the optical depth Incoming global radiation (cont.)

Case b: use water-vapor / horizontal visibility

I = I n + I d 1 = I n + I dr + I da + I dm = ()I n + I dr + I da ⋅ ρ 1− g ⋅ ρa′ where the direct solar radiation is

In = 0.9751⋅ Isc ⋅e0 ⋅cos(θz )⋅τ r ⋅τ o ⋅τ g ⋅τ w ⋅τ a

etc. References: M. Iqbal (1983) An introduction to solar radiation, Academic Press, Toronto. p.188-191. R. Bird and R.L. Hulstrom (1980) Direct insolation models, Trans. ASME J. Sol. Energy Eng., 103, 182-192. R. Bird and R.L. Hulstrom (1981) A simplified clear sky model for direct and diffuse insolation on horizontal , SERI/TR-642-761, Solar Energy Research Institute, Golden, Colorado. Surface Albedo & NDVI

• Algorithms • - Calculate surface bidirectional reflectance of narrow band • - Derive surface broad-band albedo from narrow surface reflectance - Derive NDVI from band RED & NIR surface reflectance - (Ref. Lecture Jose Moreno) Surface temperature

• Algorithms

• Land surface temperature derived by using a theoretical split- window algorithm

• References: Sorino et al.(2004) λθ The radiative transfer equation for LST retrieval λθ ε θ • The at-sensor radiance forλ a given wavelength (λ) s: λθ ε λ at−sensor atm↓ λθ atm↑ L = []B ( ,TS ) + (1− )L τ + Lλθ

•where

– ελθ is the surface emissivity, –Bθ(λ, Ts) is the radiance emitted by a blackbody at temperature Ts of the surface, is the downwelling radiance, Latm↓ – λ τλθ is the total transmission of the atmosphere () and is the upwelling atmospheric radiance. All these magnitudes also depend on the observation angle θ. atm↑ Lλθ • According to Sobrino et al. (1996), the upwelling and downwelling atmospheric radiance can be substituted, respectively, by:

λ atm ↑ L = (1 − τ iθ )Bi (Ta )

atm ↓ L λ = (1 − τ i53 )B i (T a )

where Ta is the effective mean atmospheric temperature and τi53 is the total atmospheric path transmittance at 53 degrees. Split-window equations to derive land surface temperature

• Substituting both atmospheric in the radiative transfer equation, an algorithm involving can be obtained using a first-order Taylor series expansion of the Planck’s law and writing the equation for i and j (i and j being two different channels observed at the same angle, Split-Window method):

Ts = Ti+A(Ti-Tj)-B0+(1-εi)B1-Δεθ B2

where A and Bi are coefficients that depend on atmospheric transmittances, εi is the mean value of the of channels i and j, Δεθ is the spectral variation, Ti and Tj are the brightness temperatures for two different channels with the same view angle. This equation is the so-called split-window equation and gives a separation between the atmospheric and emissivity effects in the retrieval of surface temperature. The structure of the split-window and dual-angle algorithms with the final values of the coefficients calculated by the minimization process • Notation: • n: Nadir view; • f: Forward view; • SW: Split-Window Method (two spectral channels at the same observation angle) • quad: algorithm that includes a quadratic dependence on (Ti-Tj); • (1): AATSR Channel 1 (12 μm); • (2): AATSR Channel 2 (11 μm); • W: algorithm with water vapor content dependence; • ε: algorithm with emissivity dependence; • Δε: algorithm including spectral or angular emissivity difference. Emissivity

• Algorithms

• Estimation of surface emissivity using the theoretical model of Caselles and Sobrino (1989).

• References: • V. Caselles and J.A. Sobrino (1989) Determination of frosts in orange groves from NOAA-9 AVHRR data, RSE, 29:135-146. • E. Valor and V. Caselles (1995) Mapping land surface emissivity from NDVI: Application to European, African, and South American Areas, RSE, 57:167-184. • Sobrino and Soria (2006) Thresholds Method (NDVITHM)

• A simplified method based on the estimation of emissivity, ε, using atmospherically corrected data in the visible and near infrared channels (Sobrino and Raissouni, 2000), which considers three different type of pixels depending on the NDVI value: bare soil pixels (NDVI<0.2), mixed pixels (0.20.5). The NDVITHM have been applied for NOAA channels 4 and 5 (Sobrino et al., 2001) and for MODIS channels (Sobrino et al., 2003). • This method is also applied to AATSR thermal channels using the Salisbury's spectra (Salisbury and D’Aria, 1992) and the AATSR response functions to obtain the appropriate expressions to estimate absolute emissivity. The NDVI value have been calculated with the well-known equation that uses reflectivity values from the Red region (ρred) and Near Infrared (ρnir) region, according to: ρ ρ red − nir NDVI = ρ red + ρnir

• AATSR channels centred in 0.67 μm and 0.87 μm have been used for ρred and ρnir respectively. Thresholds Method (NDVITHM)

• The final expressions obtained for this method are for bare soil pixels (NDVI < 0.2),

• ε = 0.9825 -0.051 ρred • Δε = -0.0001 -0.041 ρred

• for mixed pixels (0.2 NDVI 0.5),

• ε = 0.971 + 0.018 fc • Δε = 0.006 (1 - fc )

• and for vegetation pixels (NDVI > 0.5), • • ε = 0.990

•with fc being the vegetation proportion, given by 2 ⎛ NDVI −NDVI ⎞ f = ⎜ min ⎟ c ⎜ ⎟ ⎝ NDVImax −NDVImin ⎠

• where NDVImin=0.2 and NDVImax=0.5. The main constraint of this method is that it can not be used to extract water emissivity values because it is not possible to apply the NDVI and fc equations for water pixels. Roughness

2 2 Z0 = Z0or + Z0vg Total roughness

1 Orographic roughness Z 0 or = ⋅ v p size

Vegetation roughness Z 0 vg = f ( h , f c )

(h - vegetation height, fc – fractional coverage) Questions:

1. What is surface radiation budget 2. List some methods to derive surface radiation components 3. What information is needed in order to derive surface radiation components using the above mentioned methods 4. What are the essential surface parameters in determination of surface radiation balance References/Further Readings

• Su, Z., Timmermans, W., Gieske, A., Jia, L., Elbers, J. A., Olioso, A., Timmermans, J., Van Der Velde, R., Jin, X.,Van Der Kwast, H., Nerry, F., Sabol, D., Sobrino, J. A., Moreno, J. and Bianchi, R., 2008, Quantification of land- atmosphere exchanges of water, energy and carbon dioxide in space and time over the heterogeneous Barrax

site, International Journal of Remote Sensing, 29:17,5215-5235. • Su, Z., J. Wen, and L. Wan, 2003, A methodology for the retrieval of land physical parameter and actual evaporation using NOAA/AVHRR data, Journal of Jilin University (Earth Science Edition), 33(sup.), 106-118. • Jia, J., Z.-L. Li, M. Menenti, Z. Su, W. Verhoef, Z. Wan, 2003, A practical algorithm to infer soil and foliage component temperatures from bi-angular ATSR-2 data, International Journal of remote Sensing, 24 (23), 4739– 4760. • Li, Z.-L., L. Jia, Z. Su, Z. Wan, R.H. Zhang, 2003, A new approach for retrieving precipitable water from ATSR-2 split window channel data over land area, International Journal of Remote Sensing, 24(24), 5095–5117. • Z. Wan, Y. Zhang, Q. Zhang, Z.-L. Li, 2004, Quality assessment and validation of the MODIS global land surface temperature, International Journal of Remote Sensing, 25(1), 261–274. • J. Sobrino, G. Soria, F. Prata, 2004, Surface temperature retrieval from Along Track Scanning Radiometer 2 data: Algorithms and validation, Journal of Geophysical Research, Vol. 109, doi:10.1029/2003JD004212. • J. Norman, F. Becker, 1995, Terminology in thermal remote sensing of natural surfaces, Agricultural and Forest Meteorology, 77, 153-166.