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A simple algorithm to estimate sensible heat flux from remotely sensed MODIS data a
b
C. O. Mito , R. K. Boiyo & G. Laneve
c
a
Department of Physics, University of Nairobi, PO Box 30197, Nairobi, Kenya b
Department of Physics, Kenyatta University, PO Box 43844, Nairobi, Kenya c
University of Rome ‘La Sapienza’, 00138, Rome, Italy
Available online: 18 Apr 2012
To cite this article: C. O. Mito, R. K. Boiyo & G. Laneve (2012): A simple algorithm to estimate sensible heat flux from remotely sensed MODIS data, International Journal of Remote Sensing, 33:19, 6109-6121 To link to this article: http://dx.doi.org/10.1080/01431161.2012.680616
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International Journal of Remote Sensing Vol. 33, No. 19, 10 October 2012, 6109–6121
A simple algorithm to estimate sensible heat flux from remotely sensed MODIS data
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C. O. MITO*†, R. K. BOIYO‡ and G. LANEVE§ †Department of Physics, University of Nairobi, PO Box 30197, Nairobi, Kenya ‡Department of Physics, Kenyatta University, PO Box 43844, Nairobi, Kenya §University of Rome ‘La Sapienza’, 00138 Rome, Italy (Received 17 March 2011; in final form 10 February 2012) Sensible heat flux (H) has a large impact on energy exchange between the surface and the atmosphere and, thus, affects climate change and climatic and hydrological modelling. In the past, remote sensing of H has been a major area of interest and, as a result, various methods have been established for its retrieval. However, large discrepancies between measured and simulated values of H have been observed over land surfaces because of various assumptions and simplifications. This article presents a generalized algorithm for the estimation of sensible heat flux that is suitable for a wide range of atmospheric and terrestrial conditions from Moderate Resolution Imaging Spectroradiometer (MODIS) data. Standard built-in atmospheric profiles in Fast Atmospheric Signature Code (FASCODE) together with atmospheric conditions obtained by periodic radio sounding, once a week, performed at the Broglio Space Centre in Malindi, Kenya, were used in simulating MODIS data at 11.03 and 12.02 µm wavelengths using PcLnWin software. This new approach improves the form of the Mito algorithm, developed to determine surface temperature, by removing some of the assumptions underlying the algorithm – for example, the assumption that air temperature T a is approximately equal to surface temperature T s . The resulting bulk aerodynamic resistance equation allows the formulation of a general algorithm for the determination of H, which takes into account the surface emittance effect, water vapour column (WVC), canopy properties, air temperature and different atmospheric stabilities. Unlike other conventional methods developed earlier for the determination of H, a prior knowledge of surface temperature as an auxiliary input is not necessary in this new algorithm. The estimates of sensible heat flux derived from MODIS using the proposed algorithm compared well with in situ measurements, giving a good correlation coefficient of r = 0.9.
1.
Introduction
Sensible heat flux, H, is the amount of heat energy transferred from the Earth’s surface to the atmosphere by conduction and convection due to the temperature difference between them. Through sensible heat flux, the land absorbs heat energy from the atmosphere or releases heat energy to the atmosphere, compensating the sharp temperature change in the atmosphere and regulating the local climate. Accurate determination of
*Corresponding author. Email:
[email protected] International Journal of Remote Sensing ISSN 0143-1161 print/ISSN 1366-5901 online © 2012 Taylor & Francis http://www.tandfonline.com http://dx.doi.org/10.1080/01431161.2012.680616
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sensible heat flux provides important scientific information for global energy change research and contributes greatly to the understanding of the dynamic transfers of water, energy and trace gases at the Earth’s surface (Watts et al. 1998). Information about sensible heat flux is also important in modelling and monitoring other energy balance components, including net radiation, latent heat flux and ground heat flux. Different techniques for estimating sensible heat flux have evolved in terms of method, instrumentation and computation. Direct measurements, using largeaperture scintillometers (LASs), eddy covariance techniques (ECTs) or surface renewal analysis (SRA), have been reported to have various limitations, including precision errors, the need for high expertise and high cost, with the latter limited to intensive field experiments (Watts et al. 2000). These methods also provide estimates of sensible heat flux with low temporal resolution. The use of mathematical models, on the other hand, has drawn mixed results in spite of the similarity in input variables (Allen et al. 2005). Remote-sensing technology, using high-resolution, multiband, multi-temporal and multi-angle remote-sensing instruments, has brought the hope of estimating sensible heat flux over different surfaces. Much effort has been devoted to investigating parameterization of sensible heat flux and to improving its accuracy using measurements at various spatial and temporal resolutions and over various land surfaces. Therefore, when compared with other methods, remote sensing has obvious superiority in estimating a real sensible heat flux over different surface conditions. However, a major challenge is in retrieving accurate and reliable values of sensible heat flux by this technique. The challenge consists of two tasks: the first is to retrieve accurate estimates of surface temperatures from satellite data and to extrapolate them temporally and the second is to relate estimates of sensible heat flux obtained over relatively large surfaces from satellite data, 1–16 km2 , to ground measurements usually representative of less than 0.1 km2 (Watts et al. 1998). Sensible heat flux depends directly on the difference between surface and air temperatures, and its accurate determination requires good knowledge of these parameters. Large-scale retrieval of surface temperature from satellite measurements in the thermal infrared (TIR) is not an easy task because of high heterogeneity over short distances, mainly due to vegetation, topography and soil physical properties and the complex relationship between atmosphere and the surface (Sobrino et al. 2008). Surface temperature varies spatially according to soil type, soil moisture, land use and land cover and temporally with time of the day and season of the year. Hence, the use of meteorologically obtained surface temperature to estimate sensible heat flux is inappropriate. Yamaguchi et al. (2004) analysed H in urban areas using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and Moderate Resolution Imaging Spectroradiometer (MODIS) data. The surface temperature observed using ASTER, air temperature measured at ground meteorological stations, net radiation estimated from solar irradiance derived from ASTER data and ground heat flux inferred from net radiation and surface types were used in the analysis. García et al. (2008) estimated H using the temperature vegetation dryness index (TVDI) and MODIS data. Their work assumed that ground heat flux was negligible. This assumption is not appropriate, because in some cases ground heat flux ranges from 10% to 50% of the net radiation, depending on the amount of vegetative cover. On a well-watered and full-vegetation-covered surface, ground heat flux is of the same order of magnitude as the sensible heat flux. A study has been carried out to estimate H using Advanced Very High Resolution Radiometer (AVHRR) data (Watts et al. 1998). The bulk aerodynamic formula was used with surface temperature
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retrieved by the general split window technique (GSWT) proposed by Ulivieri et al. (1994). Reasonable instantaneous estimates of H were obtained, although with a large scatter. As H has a large diurnal variation and is subject to significant variation from one day to another, a high-frequency repeat rate is required, and this is available only on wide-swath sensors on low Earth orbiting (LEO) satellites such as AVHRR on board the National Oceanic and Atmospheric Administration (NOAA) series satellites and MODIS on board the Terra and Aqua satellites. MODIS is a payload on polar orbiting satellites first launched into the Earth’s orbit by the NASA Goddard Space Flight Center on 18 December 1999 on board the Terra platform satellite and again on 4 May 2002 on board the Aqua platform satellite (Mallick et al. 2009). Some advantages of the instrument include its global coverage and high radiometric resolution (Xiong et al. 2008). Being on Terra and Aqua satellites, MODIS data can be acquired four times a day for the same area; Aqua passes south to north over the equator in the afternoon (at local time 1.30 p.m., ascending mode) and in the morning (at local time 1.30 a.m., descending mode), whereas Terra overpasses from north to south across the equator in the morning (at local time 10.30 a.m., descending mode) and in the afternoon (at local time 10.30 p.m., ascending mode) (Wang and Liang 2009). Terra is at an altitude of 750 km and has a cross- and along-track swath of 2330 and 10 km, respectively (Abreham 2009). Terra and Aqua MODIS instruments are effectively the same, although band 31 on the Aqua MODIS saturates at a temperature of about 60 K while that on the Terra MODIS saturates at ∼400 K (Hall et al. 2008). MODIS acquires data in 36 spectral bands ranging in wavelength from 0.4 to 14.4 µm and at varying spatial resolutions (2 bands at 250 m, 5 bands at 500 m and 29 bands at 1 km). These data improve our understanding of global dynamics and processes occurring on the land, in the oceans and in the lower atmosphere (Mito et al. 2006). Bands 1–19 and 26 are in the visible and near-infrared (NIR) range and the remaining bands are in the TIR range. The bands in the transparent atmospheric windows are designed for remote sensing of surface properties. Other bands are designed mainly for atmospheric studies (Wan and Li 1997). In this article, we present a general simple algorithm, suitable for a wide range of atmospheric and terrestrial conditions, to estimate sensible heat flux from MODIS data. The approach computes surface temperature, T s , by improving on the GSWT algorithm earlier proposed by Mito et al. (2006) and removing some of the assumptions made earlier. The improved algorithm retrieves T s by taking into account the surface and air temperature difference effects, water vapour and non-unitary surface emissivity. The resulting improved bulk aerodynamic resistance equation allows the formulation of a general algorithm for the determination of H, where prior knowledge of surface temperature as an auxiliary input is not required as in other already developed models.
2. Theoretical background 2.1 The surface energy balance components In places where there is no heating from the interior of the Earth, i.e. natural land surfaces, solar radiation becomes the only source of energy controlling most micrometeorological events in the layer of soil. In such places, the surface energy balance components are best described by the law of conservation of energy:
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(1)
where E denotes the change in energy, R is the net radiation (in W m−2 ), G is the ground heat flux (in W m−2 ), H is the sensible heat flux (in W m−2 ) and Le is the latent heat flux (in W m−2 ), on a globally averaged scale. E, which represents the planetary energy balance, is equal to 0, and, hence, equation (1) can be written as
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R = G + Le + H.
(2)
Sensible heat flux refers to the amount of heat energy transferred from the Earth’s surface to the atmosphere by conduction and convection due to the temperature difference between them. Heat is initially transferred into the air by conduction when air molecules collide with the surface molecules. As air warms, it circulates upwards via convection. Thus, the transfer of H is accomplished in a two-step process. Because air is a very poor conductor of heat, convection is the most efficient way of transferring heat into the air. Sensible heat flux is formulated in terms of the difference between surface temperature (T s ), usually not measurable directly at a given source height for heat transfer, and air temperature (T a ) at a reference height within the surface layer (Chehbouni et al. 1997): H=
ρCp (Ts − Ta ) , r
(3)
where ρ (kg m−3 ) is the air density, C p (J kg−1 K−1 ) is the specific heat capacity of air at constant pressure (1013 J kg−1 K−1 ) and r (s m−1 ) is the aerodynamic resistance. Net radiation refers to the difference between incoming radiation at all wavelengths and reflected short-wavelength radiation (≈0.15–4 µm) and both reflected and emitted long-wavelength (>4 µm) radiations. It is a key quantity for estimation of the energy budget and is used in various applications, including climate monitoring, weather prediction and agricultural meteorology (Bisht et al. 2005). The net radiation can, therefore, be expressed as the sum of four components: R = Rsd − Rsu + Rld − Rlu ,
(4)
where Rsd is the downward shortwave radiation (0.15–4 µm) from the Sun and the atmosphere, Rsu is the shortwave radiation reflected by the surface, Rld is the longwave radiation (>4 µm) emitted from the atmosphere towards the surface and Rlu is the longwave radiation emitted from the surface into the atmosphere. Ground heat flux is the amount of heat energy transferred from the Earth’s surface to the subsurface of the Earth, soil or water via conduction due to the temperature gradient between them. Heat is transferred downwards when the surface is warmer than the subsurface – positive ground heat flux. If the subsurface is warmer than the surface, then heat is transferred upwards − negative ground heat flux. Ground heat flux, G, is an important component of the Earth’s surface energy budget because it plays an important role in surface energy balance at the land–atmosphere interface and in meteorological modelling. It can be expressed as
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G = kg
(Ts − Td ) , z
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where kg is the thermal molecular conductivity of ground soil (W m−1 K−1 ), T d is the sublayer temperature (K), T s is the land surface temperature (K) and z is the depth of the subsurface layer (m). Latent heat flux, Le , refers to the amount of heat energy transferred from the Earth’s surface to the atmosphere that is associated with evaporation or transpiration of water at the surface and subsequent condensation of water vapour in the troposphere. When evaporation is taking place, we say there is a positive latent heat flux. This indicates that the surface is losing energy to the air above. This energy can be obtained as a residual when net radiation is balanced with the dissipation terms according to the law of conservation of energy. Estimation of Le is important for regional water balance studies, field irrigation studies and description of the atmospheric boundary layer, including atmospheric stability and weather forecasting. The term Le is of most interest for hydrological purposes. 2.2 Aerodynamic resistance Aerodynamic resistance describes the resistance to the transfer of heat and water vapour from vegetation upwards and involves friction from air flowing over vegetative surfaces. It is expressed according to the Monin–Obukhov similarity (MOS) theory as z−d z−d 1 − ψm ln − ψh , r = 2 ln k u zom zoh
(6)
where k (unitless) is the von Karman constant, equal to 0.41, u (m s−1 ) is the wind speed at the reference height z (m), zom (m) is the roughness length for momentum transfer, zoh (m) is the roughness length for heat transfer and d (m) is the height at which wind speed becomes essentially zero in the plant canopy – the zero plane displacement of the wind profile. ψ h and ψ m are stability corrections for heat and momentum, respectively. Reasonable estimates of aerodynamic properties, i.e. d, zom and zoh , have been obtained for several relationships as long as the surface is uniformly covered and fairly flat. Data have shown that for a wide variety of vegetation, these terms can be estimated from plant height, hc , as follows (Kustas 1989): ⎧ d = 23 hc ⎪ ⎨ zom = 18 hc . ⎪ ⎩z = 1 h om
(7)
80 c
Assuming that the stability conditions are measured to be nearly neutral, T s ≈ T a , i.e. where temperature, atmospheric pressure and wind velocity distributions follow nearly adiabatic conditions, ψ m = ψ h = 0 and equation (6) becomes ro =
z−d z−d 1 ln , ln k2 u zom zoh
(8)
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where ro is the aerodynamic resistance in neutral conditions. In such conditions, adjustment of wind speed data obtained from instruments placed at elevations other than the standard height of 2 m is done using a logarithmic wind speed profile: u2 = uz
4.87 , ln(67.8hc − 5.42)
(9)
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where u2 (m s−1 ) is the wind speed at 2 m above the ground surface and uz (m s−1 ) is the measured wind speed at z m above the ground surface. For stable and unstable conditions, various parameterizations of ψ m and ψ h have been developed on the basis of the MOS theory to estimate aerodynamic resistance (Liu et al. 2007). 3. Methodology 3.1 Surface temperature retrieval The GSWT proposed by Mito et al. (2006) was improved and found to be the most suitable for retrieval of surface temperature. This algorithm, whose concepts originate from Ulivieri et al. (1994), initially applied to AVHRR channels 4 and 5, has been proved to be very accurate when compared with several others and takes atmospheric effects into account, in particular, the water vapour column (WVC) amount and a nonunitary surface emissivity for MODIS bands 31 and 32. The corresponding brightness temperature equation yields Ts = T31 + β(a1 − 1)T31 + a2 (T31 − T32 ) + a3 (Ts − Ta ),
(10)
where coefficients aj (j = 1, 2, 3) are functions of the surface spectral emittances, the atmospheric water vapour content and the temperature profile of the atmosphere, respectively; expressions for a1 . . . a3 are reported elsewhere (Ulivieri et al. 1994), and T a is the standard air temperature at a height of 2 m, which can differ more or less significantly from T s , depending on the nature of the surface and on the climatological conditions. T 31 and T 32 are the brightness temperatures of MODIS bands 31 and 32, respectively. The term β, which does not vary greatly over temperature and spectral ranges of interest, results from linearization (Mito et al. 2006). In equation (10), the difference between surface temperature and air temperature at a height of 2 m is reflected in the retrieved temperature through the coefficient a3 . This effect, according to the surface condition, ranges from a few tenths of kelvin over waterbodies (T s − T a = 2−3 K, corresponding to 10% of the total error in the retrieved temperature) to 1 K on insulated bare soil (T s − T a = 10−20 K, corresponding to 25% of the total error in the retrieved temperature) (Ulivieri et al. 1985). In both Ulivieri et al. (1994) and Mito et al. (2006), T s has been assumed to be equal to T a for the sake of simplicity, the corresponding corrective term being almost independent of the other two. However, this assumption negates the concept of sensible heat flux as H depends on the difference between the two temperatures (equation (3)). In this article, this assumption is not made. If the mean emissivity in MODIS band 31, ε¯ 31 , is equal to the mean emissivity in MODIS band 32, ε¯ 32 , i.e. ε¯ 31 = ε¯ 32 = 1, the resulting retrieved surface temperature, Ts , is given from equation (10) as Ts = T31 + a2 (T31 − T32 ) + a3 (Ts − Ta ).
(10a)
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Combining equations (10) and (10a) then yields
Ts = T31 + a2 (T31 − T32 ) + β(a1 − 1)T31 + a2 − a2 (T31 − T32 ) + a3 − a3 (Ts − Ta ), (10b) and the following surface temperature (T s ) equation results after a little algebra:
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Ts = T31 + a2 (T31 − T32 ) + F1 (1 − ε¯ ) + F2 δε + F3 (1 − ε¯ )2 − (0.5δε)2 + F4 (Ts − Ta ), (11) where ε¯ and δε are the mean and the difference in mean emissivities of MODIS bands 31 and 32, respectively. F 4 = G4 /D, with
G4 = A1 A2 (c − 1) + (1 − ε) cA1 A2 E2 Z2 + E1 Z1 − A1 A2 E2 Z2 + E1 Z1
+ 0.5δε cA1 A2 E2 Z2 − E1 Z1 − A1 A2 E2 Z2 − E1 Z1
+ (1 − ε)2 − (0.5δε)2 (c − 1)A1 A2 E1 E2 Z1 Z2
(12)
and
D = cA2 − A1 + A2 E2 Z2 − E1 1 − A1 Z1 c + A1 E2 1 − A2 Z2 − E1 Z1 (1 − ε)
+ 0.5 A2 E2 Z2 + E1 1 − A1 Z1 c + A1 E2 1 − A2 Z2 + E1 Z1 δε
(1 − ε)2 − (0.5δε)2 , + A2 E1 E2 Z2 A1 Z1 − 1 c + A1 E2 E1 Z1 1 − A2 Z2 (13) a2 , F 1 , F 2 , F 3 , Ei = τi , Ai = 1 − τi , Z1 , Z2 , a3 , H1 , H2 , H3 and c are discussed elsewhere (Mito et al. 2006) and F 1 = H1 , F 2 = H2 and F 3 = H3 . δε is the difference in emissivities between MODIS bands 31 and 32. 3.2 Estimation of sensible heat flux From equations (3) and (11), we have
H = ρCp r−1 T31 + a2 (T31 − T32 ) + F1 (1 − ε) + F2 δε + F3 (1 − ε)2 − (0.5δε)2 −Ta + ρCp r−1 F4 (Ts − Ta ) (14) or H = ρCp r−1 h + ρCp r−1 F4 (Ts − Ta ),
(15)
where
h = T31 + a2 (T31 − T32 ) + F1 (1 − ε) + F2 δε + F3 (1 − ε)2 − (0.5δε)2 − Ta .
(16)
Again, substituting equation (11) into equation (15), we have H = ρCp r−1 h + ρCp r−1 F4 T31 + a2 (T31 − T32 ) + F1 (1 − ε) + F2 δε
+ F3 (1 − ε)2 − (0.5δε)2 − Ta + ρCp r−1 (F4 )2 (Ts − Ta )
(17)
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or H = ρCp r−1 h + ρCp r−1 hF4 + ρCp r−1 (F4 )2 (Ts − Ta ).
(18)
Therefore, by continuing this process n times, we eventually obtain Hn = ρCp r−1 h + ρCp r−1 hF4 + ρCp r−1 h(F4 )2 + ρCp r−1 h(F4 )3 + · · · + ρCp r−1 h(F4 )n−1 + ρCp r−1 (F4 )n (Ts − Ta )
(19)
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or Hn =
ρCp r−1 h((1 − F4 )n ) + ρCp r−1 (F4 )n (Ts − Ta ). (1 − F4 )
(20)
3.3 Aerodynamic resistance Determination of aerodynamic resistance requires information on aerodynamic properties of the canopy surface and atmospheric stability. In this article, the model developed by Choudhury et al. (1986) based on different atmospheric conditions was used to perform stability corrections for retrieval of sensible heat flux. In the model, the aerodynamic resistance, r, is expressed as r0 , (1 + η)p
(21)
5(z − d)g(Ts − Ta ) , Ta u2
(22)
r= where η is the stability factor defined as η=
where g is the acceleration due to gravity (9.8 m s−2 ), u is the wind speed (m s−1 ) and p assumes the following values for various stability conditions: p = 0, neutral; p = 0.75, unstable; p = 2, stable. The method has been found to give results that are in good agreement with the measured values (Liu et al. 2007), and is more convenient to use because no iteration is required (Watts et al. 2000). As the stability factor (η) in equation (22) depends on the difference between surface and air temperatures, it can be expressed as η=
5(z − d)g 2 2 T (1 − −T + a (T − T ) + F (1 − ε) + F δε+F ε) −(0.5δε) 31 31 32 1 2 3 a 2 Ta u2 5(z − d)g F4 (Ts − Ta ). (23) + Ta u2
Applying the same procedure n times as in §3.2, we finally get the following expression for the stability factor: ηn =
5(z − d)gh(1 − (F4 )n ) 5(z − d)g (F4 )n (Ts − Ta ) + Ta u2 (1 − F4 ) Ta u2
(24)
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and the corresponding value of r, rn , is therefore rn = 1+
5(z−d)g Ta u2
r0 h(1−(F4 )n ) (1−F4 )
+ (F4 )n (Ts − Ta )
p .
(25)
4. Assessment of the effects ρCp h(1 − (F4 )n ) + (F4 )n (Ts − Ta ) H = Hn (n→∞) = ro (1 − F4 ) p 5(z − d)g h(1 − (F4 )n ) n 1+ + (F4 ) (Ts − Ta ) . Ta u2 (1 − F4 )
(26)
Equation (26) is the general algorithm for the determination of sensible heat flux. From simulations, F 4 is highly sensitive to water vapour but is scarcely influenced by the surface emittance effect. It is always T s ) and the aerodynamic resistance is evaluated for p = 2 and, therefore, H becomes Hstable =
2 5(z − d)g h h ρCP 1+ . ro (1 − F4 ) Ta u2 (1 − F4 )
(29)
Finally, under unstable conditions, surface temperature is always greater than air temperature (T s > T a ). Aerodynamic resistance is evaluated for p = 0.75 and sensible heat flux can specifically be evaluated by the algorithm Hunstable
0.75 5(z − d)g h h ρCP 1+ = . ro (1 − F4 ) Ta u2 (1 − F4 )
(30)
Combining equations (28), (29) and (30), we obtain the following simple general algorithm for the determination of sensible heat flux: ρCP 5(z − d)g p H= k 1+ k , ro Ta u2
(31)
where all the symbols have previously been defined elsewhere in this article and
k = 1.06 T31 + a2 (T31 − T32 ) − Ta + k1 (1 − ε) + k2 δε + k3 (1 − ε)2 − (0.5δε)2 . (32) Equation (32) was solved by linear regression analysis with least-square-sum fitting using 21 sets of emissivity conditions (Mito et al. 2006). The variations of coefficients k1 , k2 and k3 with water vapour column are illustrated in figure 2. It is evident how they are scarcely influenced if the water vapour column is less than or equal to 3.0 g cm−2 , with k1 = 61.92, k2 = −125.47, k3 = 48.63 and a2 = 2.24 as the evaluated mean values 100 Functions, k1, k2 and k3
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4.3 Unstable condition
50 0 –50 –100 –150 0
1 2 3 4 5 Water vapour column (g cm–2)
6
Figure 2. k1 (∗ ), k2 (+) and k3 (×) functions versus water vapour column (WVC).
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of these functions in this water vapour range. For any realistic amount of atmospheric water vapour column above 3.0 g cm−2 , the following regressive relationships fit very well the behaviour of k1 , k2 and k3 versus water vapour content (w): ⎧ ⎨ k1 = −7.2w + 84 k = 23w − 180 . ⎩ 2 k3 = −4.4w + 66
(33)
The quantitative validation of the proposed algorithm was made using MODIS data in coincidence with in situ measurements of sensible heat flux, H. In the MODIS H processing, MODIS Calibrated Radiance (MOD021KM), emissivity product (MOD11_L2) and water vapour product (MOD05_L2) (available at ftp://ladsweb.nascom.nasa.gov) were used to retrieve H pixel by pixel. The in situ data were obtained from a series of field campaigns conducted by the University of Lleida, Spain, between 15 April 2004 and 26 July 2004 within the Ebro river basin, Spain (41◦ 18 04 N, 0◦ 21 51 W, elevation 150 m). The materials and method used in the determination of in situ sensible heat flux are described in detail elsewhere (Castellvi and Martínez-Cob 2005). In situ data were extracted to coincide as closely as possible with satellite overpass (nearest 30 min average). Validation results for neutral, stable and unstable atmospheric conditions are given in figure 3. The correlation coefficients for neutral, stable and unstable conditions are 0.8, 1.0 and 0.8, respectively, resulting in an overall correlation coefficient of 0.9 for the entire data.
MODIS-based sensible heat flux (W m–2)
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5. Validation results
250 r = 0.9 200 150 100 50 0 –50 –100 –100
–50 0 50 100 150 200 Measured sensible heat flux (W m–2)
250
Figure 3. Comparison between measured sensible heat flux and MODIS-based sensible heat flux over the Ebro river basin, Spain, for neutral (◦), stable ( ) and unstable (♦) conditions. r, correlation coefficient.
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6. Conclusions An algorithm for estimating sensible heat flux from remotely sensed MODIS data in two thermal bands IR1 (10.780–11.280 µm) and IR2 (11.770–12.270 µm) has been developed. It is possible to express sensible heat flux for various atmospheric stabilities as a function of surface emittance, canopy properties and air temperature. For any realistic amount of atmospheric water vapour column above 3.0 g cm−2 , the coefficients used to estimate sensible heat flux are further found to be linear functions of atmospheric WVC in addition to the other factors. Sensible heat flux has been validated with in situ data from the Ebro river basin, Spain, for the year 2004 for different days ranging from 15 April 2004 to 26 July 2004. MODIS-based sensible heat flux is highly correlated with measured sensible heat flux, with an overall correlation coefficient for all the three conditions being 0.9. Future work may involve estimation of other energy balance components, including latent heat flux, ground heat flux and net radiation, based on the results obtained from this algorithm. This will provide a greater insight into the reliability of the algorithm in evaluating the energy balance components and hence its applicability in modelling and monitoring these components. The advantage of this algorithm is that unlike other already developed methods, prior knowledge of surface temperature as an auxiliary input is not necessary. Acknowledgements The authors thank the Broglio Space Centre (BSC) in Malindi, Kenya, for providing the data set used in the simulation. They also recognize the efforts of Ontar Corporation (http://www.ontar.com) for providing the software, PcLnWin, used in simulating atmospheric effects in this article. The authors thank Dr Antonio Martínez from the University of Lleida, Spain, for providing validation data. References ABREHAM, A., 2009, Open water evaporation estimation using ground measurement and satellite remote sensing: a case study of Lake Tana, Ethiopia. Geo-Information and Earth Observation, 26, pp. 34–51. ALLEN, R.G., TASUMI, M., MORSE, A. and TREZZA, R., 2005, A Landsat-based energy balance and evaporation model in Western US Water Rights Regulation and Planning. Journal of Irrigation and Drainage Systems, 19, pp. 251–268. BISHT, G., VENTURINI, V., ISLAM, S. and JIANG, L., 2005, Estimation of net radiation using MODIS (Moderate Resolution Imaging Spectroradiometer). Remote Sensing of Environment, 12, pp. 52–67. CASTELLVI, F. and MARTÍNEZ-COB, A., 2005, Estimating sensible heat flux using surface renewal analysis and the flux variance method: a case study over olive trees at Sástago (NE of Spain). Water Resources Research, 41, W09422, doi:10.1029/2005WR004035. CHEHBOUNI, A., LOSEEN, D., NJOKU, E.G., LHOMME, J.P., MONTENY, B. and KERR, Y.H., 1997, Examination of difference between radiative and aerodynamic surface temperature over sparsely vegetated surfaces. Remote Sensing of Environment, 58, pp. 177–186. CHOUDHURY, B.J., REGINATO, R.J. and IDSO, S.B., 1986, An analysis of infrared temperature observations over wheat and calculation of latent heat flux. Agricultural and Forest Meteorology, 37, pp. 75–88. GARCÍA, M., FERNÁNDEZ, F., VILLAGARCÍA, L., PALACIOS-ORUETA, A., WERE, A., PUIGDEFÁBREGAS, J. and DOMINGO, F., 2008, Estimating latent and sensible heat
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