Estimation of net radiation flux distribution on the southern slopes of the central Himalayas using MODIS data

Atmospheric Research 154 (2015) 146–154

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Estimation of net radiation flux distribution on the southern slopes of the central Himalayas using MODIS data Pukar Man Amatya a,b,⁎, Yaoming Ma a, Cunbo Han a,b, Binbin Wang a,b, Lochan Prasad Devkota c a Key Laboratory of Tibetan Environment Changes and Land Surface Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, CAS Center for Excellence and Innovation in Tibetan Plateau Earth System Sciences, Beijing 100101, China b University of Chinese Academy of Sciences, Beijing 100049, China c Central Department of Hydrology and Meteorology, Tribhuvan University, Kathmandu 44618, Nepal

a r t i c l e

i n f o

Article history: Received 9 March 2014 Received in revised form 19 November 2014 Accepted 21 November 2014 Available online 28 November 2014 Keywords: Net radiation flux distribution MODIS DEM central Himalayas Nepal

a b s t r a c t Recent studies have highlighted the importance of the southern slopes of the Himalayas as a possible heating source driving the South Asian Summer Monsoon (SASM). The central Himalayas are characterized by a complex topography; consequently the measurements regarding land surface heat fluxes are scarce. In this study we tested the feasibility of deriving the regional net radiation flux, an essential component of the surface energy balance, from MODIS data. Three MODIS data scenes were used to derive net radiation flux, taking into account the effect of topography and a detailed extinction process within the atmosphere. This is the first time the regional net radiation flux distribution for the southern slopes of the central Himalayas has been derived from satellite data. The net shortwave radiation flux, net longwave radiation flux and net radiation flux from MODIS data agree well with field observations with mean relative errors of 6.19%, 7.72% and 6.60% respectively. We can therefore conclude that the aforementioned net radiation flux can reasonably be obtained using this method. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Net radiation flux, defined as the difference between total incoming and total outgoing radiation flux, is one of the key energy available at the earth's surface that drives photosynthesis, evaporation of water and heating of the soil and air (Blad et al., 1998; Rosenberg, 1983). It is also a key term of the surface energy balance and is important for agricultural, hydrological and climatic studies (Niemelä et al., 2001b). Most of the evapotranspiration models (Monteith, 1965; Nishida et al., 2003; Priestley and Taylor, 1972; Su, 2002) require an accurate estimation of net radiation flux given as direct input (Ryu et al., 2008). It is therefore vital to determine the spatial and temporal

⁎ Corresponding author at: Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Lincui Lu, 16 Haoyuan, Building 3, Beijing 100101, China. Tel.: +86 18810250513. E-mail addresses: [email protected], [email protected] (P.M. Amatya).

http://dx.doi.org/10.1016/j.atmosres.2014.11.015 0169-8095/© 2014 Elsevier B.V. All rights reserved.

variability of net radiation flux on local, regional and global scales. Generally net radiation flux is obtained from field measurements. However, in most countries direct measurements are unavailable or inaccurate, due to technical and financial constraints (Kjærsgaard et al., 2007; Sozzi et al., 1999). An alternative way to obtain net radiation flux is to combine atmospheric radiation models or field measurements with remote sensing (Wang et al., 2005). Various satellite remote sensing data such as Landsat (Goodin, 1995), Geostationary Operational Environmental Satellites (GOES) (Jacobs et al., 2002), Advanced Very High Resolution Radiometer (AVHRR) (Hurtado and Sobrino, 2001), and Moderate Resolution Imaging Spectro radiometer (MODIS) (Cai et al., 2007) have successfully been utilized to estimate net radiation flux. Since it is difficult to obtain meteorological variables solely from satellite data, certain ground-based observations are utilized to produce meteorological variables. Net radiation flux has also been obtained using radiative transfer models such as, MODTRAN (Ma et al., 2014a;

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Ma et al., 2011; Ma et al., 2014b) and SMAC (Ma et al., 2012; W. Ma et al., 2014), but these require radiosonde inputs, which are not readily available (Niemelä et al., 2001a). The MODIS multispectral sensor has been regarded as an effective tool for observation of the earth's surface and atmosphere state with high spatiotemporal resolution (Masuoka et al., 1998) enabling estimation of net radiation flux independent of ancillary data. Bisht et al. (2005) developed a parameterization scheme for the estimation of net radiation flux in the Southern Great Plains, USA using MODIS data. Hwang et al. (2013) built a MODIS stand-alone net radiation flux model and applied it to East Asia (including the Korean Peninsula and Japanese Archipelago). Ryu et al. (2008) combined various MODIS land and atmosphere products, developing a scheme to retrieve the four components of radiation and net radiation flux. Application of the above mentioned models is, however, limited to flat areas. Over flat terrain, downward shortwave radiation remains the same over a large area, so one measurement can represent the entire area. However, for mountainous terrain this assumption is invalid (Dozier and Frew, 1981), as variations in altitude, slope, orientation (aspect) and shadows cast by topographic features create strong local solar radiation gradients (Tovar-Pescador et al., 2006). Downward shortwave radiation on mountainous terrain can be divided into three parts: (i) direct radiation, which is strongly affected by atmospheric attenuation, illumination angle and shadowing, (ii) diffuse radiation, which is scattered out of the solar beam by gases and aerosols and (iii) radiation reflected to the surface from the surrounding terrain. The Digital Elevation Model (DEM) provides an opportunity to take into account the effect of topographic characteristics such as slope, aspect and shadowed area on the spatiotemporal variability of downward shortwave radiation. As clear sky solar radiation passes through the atmosphere, it is affected by various extinction processes (Yang et al., 2006). These parameters must be included in downward shortwave radiation estimation. Atmospheric effects are among the most difficult parameters to determine for the calculation of solar radiation (Flint and Childs, 1987). Many researchers have proposed models to estimate net radiation flux in mountainous terrain. Dozier (1980) presented a clear sky spectral solar radiation model combined with topographic calculations taken from digital terrain data. However, this requires in-situ measurement of global solar radiation to derive atmospheric variables such as atmospheric turbidity and water vapor. Proy et al. (1989) presented a solar radiation model which uses a digital terrain model to calculate topographic characteristics but does not consider the effect of the atmospheric attenuation of insolation. Dubayah (1992), Gratton et al. (1993) and Duguay (1995) successfully estimated net radiation flux using Landsat data and DEM, but these models use a radiative transfer model which requires atmospheric radiosonde measurements. Long et al. (2010) successfully estimated daily average net radiation flux using MODIS and DEM, but assumed transmissivity to be constant. In this study we used a net radiation flux calculation procedure developed to obtain the net radiation flux distribution in the complex topography of Mt. Qomolangma (Everest) (Chen et al., 2013). This model accounts for the effect of topographic characteristics using DEM according to the method suggested by Kumar et al. (1997). Yang et al. (2001) developed a broadband

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radiative transfer model based on Leckner's spectral model (1978). Evaluated among 21 broadband models, this was considered one of the best by Gueymard (2003a, 2003b). This model was used to include the extinction process, which takes place as solar radiation passes through the atmosphere. It requires surface pressure, precipitable water, ozone thickness and the Angstrom turbidity coefficient as inputs, all of which can be easily obtained from in-situ measurements as well as remote sensing. Elevated heating by the Tibetan Plateau (TP) has long been considered the primary driving force for the SASM (Flohn, 1968; Gu et al., 2015; Li and Yanai, 1996; Wu and Zhang, 1998). However, recent studies have shown that heating sources from the southern slopes of the Himalayas (Wu et al., 2012) and non-elevated areas south of the Himalayas (Boos and Kuang, 2013) are equally important for monsoonal circulation. In order to quantify these heating sources, net radiation flux estimation is vital. The main objective of this study is therefore to explore the feasibility of obtaining regional distribution of net radiation flux over the complex topography of the southern slope of the central Himalayas (i.e. Nepal) (Fig. 1) by combining MODIS data and DEM. 2. Theory and scheme The MODIS multispectral sensors onboard the National Aerodynamic and Space Administration's (NASA) Earth Observation System's (EOS) Terra and Aqua satellites have continuously monitored the earth's land, atmosphere and ocean states since December 1999 and May 2002 respectively. Various standard MODIS land, atmosphere and ocean products have been created by NASA and the United States Geological Survey (USGS). In this study we used MODIS products from the Aqua satellite as inputs for the net radiation flux model. One atmospheric and two land products were used for net radiation computation (Table 1). Surface reflectance of bands 1–7 with spatial resolution of 500 m were obtained from the MYD09GA land product. Land surface temperature with 1 km spatial resolution was obtained from the MYD11A1 land product. Pressure and precipitable water content with 5 km spatial resolution were obtained from the MYD07 level 2 (MYD07_L2) atmospheric product. All the products were resampled to 1 km spatial resolution in order to make them spatially continuous. The potential effects of slope and aspect were generated by using the Shuttle Radar Topographic Mission (SRTM) DEM (Jarvis et al., 2008). Chen et al. (2013) developed a DEM-based solar radiation model and successfully estimated net radiation flux in Mt. Qomolangma region using Landsat and DEM. This model utilizes DEM to calculate topographic characteristics, using a GIS-based model suggested by Kumar et al. (1997). It also calculates the radiation extinction process via Rayleigh scattering, aerosol extinction, ozone absorption, water vapor absorption and permanent gas absorption using a parameterization scheme suggested in a hybrid model by Yang et al. (2001). This hybrid model follows the Angstrom model (Angstrom, 1924) and separately parameterizes radiative extinctions of air using Leckner's Spectral model (Yang and Koike, 2005). In this study we used MODIS data to derive the regional net radiation flux distribution as opposed to the meso-scale coverage offered by Landsat. We have also refrained from using in-situ

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Fig. 1. Map of the study area, showing location of net radiation stations.

meteorological data. The model is described in detail in the subsections below. The net radiation flux can be obtained from: Rn ¼ K ↓ −K ↑ þ L↓ −L↑ ¼ ð1−r 0 ÞK ↓ þ L↓ −ε 0 σT 0

4


ð1Þ

where r0 is surface albedo, K↓ is downward shortwave radiation, K↑ is upward shortwave radiation, L↓ is downward longwave radiation, L↑ is upward longwave radiation, ε0 is surface emissivity and T0 is land surface temperature. Surface albedo was obtained from MODIS by combining narrow band spectral reflectance using the method proposed by Liang (2001): r 0 ¼ 0:160α 1 þ 0:291α 2 þ 0:243α 3 þ 0:116α 4 þ 0:112α 5 þ 0:081α 7 −0:0015 ð2Þ where α1–α7 is the reflectivity for bands 1–7 respectively. Surface emissivity ε0 was determined using the model of Valor and Caselles (1996): ε 0 ¼ εv f c þ εg ð1−f c Þ þ 4hdεið1−f c Þf c

0.015(±0.008) is the error and fc is the fractional coverage obtained using Carlson and Ripley (1997):

ð3Þ

where εv = 0.985(± 0.007) is the surface emissivity for full vegetation, εg = 0.96(±0.010) for bare soil, 〈dε〉 =

fc ¼

NDVI−NDVI min NDVI max −NDVI min

2

ð4Þ

where, NDVImin is the NDVI value for bare soil and NDVImax is the value for full vegetation. 2.1. Downward shortwave radiation The downward shortwave radiation in mountainous terrain can be expressed using Proy et al. (1989): K ↓ ¼ Ib þ Ir þ Id

ð5Þ

where Ib is direct radiation, Id is diffuse radiation and Ir is reflected radiation. 2.1.1. Direct radiation The solar irradiance outside the atmosphere is given by:

 2πdoy I0 ¼ S0 1 þ 0:0344 cos 365

ð6Þ

Table 1 MODIS data products used in this study. Product name

Product type

Parameter used

Temporal resolution

Spatial resolution

MYD09GA MYD07_L2 MYD11A1

Surface reflectance Atmospheric product Land product

Band 1, 2, 3, 4, 5 and 7 Pressure, precipitable water content Land surface temperature

1 day 1 day 1 day

500 m 5 km 1 km

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where S0 (1367 W/m2) is solar constant and doy is day of the year. The direct radiation received by an inclined surface depends on: (i) altitude due to variation in atmospheric transmittance (ii) the position of the sun and slope and aspect of the surface and (iii) whether or not the surface is in the shadow of the

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surrounding terrain. The effect of self-shadowing (due to its own slope) and shadow (cast by surrounding terrain) was considered using the HILLSHADE function with MODEL SHADOWS option (ArcGIS) (Burrough et al., 1998). This function provides a shaded relief map considering both local illumination angles (selfshadowing) and shadow. In areas affected by self-shadowing

Fig. 2. Distribution maps of net radiation flux over the central Himalayas: (a) 30 October 2012, (b) 6 November 2012 and (c) 3 December 2012.

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and shadow direct radiation was shut off, only diffused and reflected radiations are considered. Direct radiation was computed using Kumar et al. (1997): Ib ¼ I0  τ b  cosθ

ð7Þ

where τb is beam transmittance and θ is solar incidence angle calculated as: cosθ ¼ sin δð sin L coss− cos L sins cos γÞ þ cos δ coshð cos L coss þ sin L sin s cos γÞ þ cos δ sin γ sin s sinh

ð8Þ

absorption, Rayleigh scattering, and aerosol extinction, respectively, m = air mass, mc = pressure corrected air mass, a (radian) = solar elevation, ps = local pressure and p0 = 1.013 × 105 Pa, l is the thickness of the ozone layer (cm), β is the Angstrom turbidity coefficient, and w is the precipitable water. Precipitable water was obtained from the MYD07_L2. Ozone data was obtained from a decadal mean dataset of ozone thickness created using satellite products provided by the NASA/ GSFC Ozone Processing Team. The Angstrom turbidity coefficient was calculated using aerosol optical depth at 0.5 μm obtained

where δ is declination of the earth (in radians) obtained from:  δ ¼ 0:409 sin

L= s=

γ=

h=

 2πdoy −1:39 365

ð9Þ

latitude (in radians). slope (radians), where s = 0 for horizontal and s = π/2 for vertical surface (s is always positive and represents a downward slope in any direction). surface aspect angle (in radians), where γ = 0 for south, γ = ±π for north, γ = +π/2 for east and γ = −π/2 for west. π(t − 12)/12, is hour angle (in radians). t is the local solar time. h = 0 at noon, h is negative in the morning and h is positive in the afternoon.

Beam transmittance (τb) was calculated according to the parameterization scheme described in the hybrid model suggested by Yang et al. (2001):   τb ≈max 0; τ oz τw τ g τr τa −0:013

ð10Þ

  0:7136 τoz ¼ exp −0:0365ðmlÞ

ð11Þ

τw ¼ min½1; 0:909−0:036 ln ðmwÞ

ð12Þ

  0:3139 τg ¼ exp −0:0117mc

ð13Þ

    −6 2 3 −4:08 τ r ¼ exp −0:008735mc 0:547 þ 0:014mc −0:0038mc þ 4:6  10 mc

ð14Þ     2 −1:3 τ a ¼ exp −mβ 0:6777 þ 0:1464mβ−0:00626ðmβ Þ

ð15Þ

h i −1:253 m ¼ 1= sina þ 0:15ð57:296h þ 3:885Þ

ð16Þ

mc ¼ mps =p0

ð17Þ

where τoz, τw, τg, τr and τa are the radiative transmittance due to ozone absorption, water vapor absorption, permanent gas

Fig. 3. Comparison of derived results with field measurements for net shortwave radiation, net longwave radiation and net radiation flux over the central Himalayas, together with a 1:1 line.

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from GADS (Global Aerosol Dataset 2.2 a) software. Detailed descriptions of ozone and turbidity calculation can be found in Yang et al. (2006) 2.1.2. Diffuse radiation Diffuse radiation is the fraction of radiation scattered by gases and aerosols. At any given location, a portion of the sky may be obstructed by topography. Sky obstruction can result either from self-shadowing by the slope itself or shadow from adjacent topography (Dubayah and Rich, 1995). The diffuse component is modified by taking into account the proportion of the sky visible from the point of estimation (i.e., the sky view factor). This represents a small fraction in a deep valley and close to 1.0 on a large flat plain (Pierce et al., 2005). Therefore, it was not considered in this study. Diffuse radiation flux was computed using Gates (1980): 2

Id ¼ I0 τd ð cos sÞ =ð2 sin aÞ

ð18Þ

where τd is diffuse radiation transmissivity, and a is the solar altitude angle calculated as:

sin a ¼ sin L sin δs þ cos L cos δs cos h

151

where r0 is ground reflectance, s is slope, a is solar altitude angle, and τr is reflected radiation transmissivity calculated as follows: τr ¼ 0:271 þ 0:706τb

ð22Þ

2.2. Downward longwave radiation Brutsaert's (1975) parameterization method was used for the estimation of downward longwave radiation flux from clear skies, which is expressed as follows: L↓ ¼ ε a  σ  T a

4

ð23Þ

where σ is the Stefan–Boltzmann constant (5.67 × 10−8 Wm−2 K−4), Ta (K) is the near surface air temperature and εa is air emissivity for clear skies, obtained using an empirical formula:
0:14286 e εa ¼ 1:24 a Ta

ð24Þ

where Ta (K) is the near surface air temperature and ea (hpa) is actual vapor pressure, calculated using a parameterization scheme given by Oberhuber (1988):

ð19Þ 7:5ðT a −273:16Þ=ðT a −35:68Þ

where L is latitude, δs is solar declination and h is hour angle. τd was calculated using the equation given by Yang et al. (2006): n h io τd ≈ max 0; 0:5 τoz τg τ w ð1−τa τr Þ þ 0:013

ð20Þ

2.1.3. Reflected radiation Reflected radiation is expressed as the ground reflected radiation impinging on the slope after being reflected from other surfaces visible above the slope's local horizon. Reflecting surfaces are considered to be Lambertian. Reflected radiation was also computed using Gates (1980): 2

Ir ¼ r 0 I0 τ r ð sin sÞ =ð2 sin aÞ

ð21Þ

ea ¼ 611  10

ð25Þ

In order to make the model independent of in-situ meteorological data, near surface air temperature from the Global Land Data Assimilation System (GLDAS) (Rodell et al., 2004) Noah model (25 km resolution) was used, with a temporal resolution of 3 h. Air temperature from GLDAS was linearly interpolated to gain air temperature at satellite overpass. SRTM data was used to downscale the GLDAS air temperature to 1 km resolution using the procedure suggested on the MicroMet model (Liston and Elder, 2006) and verified by Cai et al. (2013) on Ili Basin area. The procedure for downscaling is as follows: (a) GLDAS air temperature was used to calculate the sea surface temperature (SST) using DEM and a vertical temperature lapse rate; (b) SST was resampled to 1 km using bilinear interpolation; and (c) air temperature was recalculated from SST. A temperature lapse rate

Table 2 Comparison between derived and measured net shortwave radiation, net longwave radiation and net radiation. Site

Tarahara

Date

30-Oct 2012 545 552 −7 1.27 −97 −100 3 3 448 452 −4 0.88

Derived net shortwave Measured net shortwave Error RE (%) Derived net longwave Measured net longwave Error RE (%) Derived net radiation Measured net radiation Error RE (%)

Patan 6-Nov 2012 465 440 25 5.68 −86 −79 −7 8.86 379 361 18 4.99

3-Dec 2012 422 450 −28 6.22 −106 −98 −8 8.16 316 352 −36 10.23

30-Oct 2012 507 530 −23 4.34 −159 −160 1 0.625 348 370 −22 5.95

Chainpur 6-Nov 2012 457 493 −36 7.30 −144 −146 2 1.37 313 347 −34 9.80

3-Dec 2012 442 503 −61 12.13 −147 −170 23 13.53 295 333 −38 11.41

30-Oct 2012 578 558 20 3.58 −171 −151 −20 13.25 407 407 0 0

Mean 6-Nov 2012 535 517 18 3.48 −170 −147 −23 15.65 365 370 −5 1.35

3-Dec 2012 436 494 −58 11.74 −150 −158 8 5.06 286 336 −50 14.88

6.19

7.723

6.60

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of −0.0052 °C/m was used according to research conducted in Nepal by Kattel et al. (2013) 2.3. Upward longwave radiation

and reflected radiation. The effect of altitude, slope, aspect and shadow on each shortwave radiation component was considered using DEM. Variations in atmospheric transmissivity due to ozone, aerosol and water vapor were also considered. All the major inputs required to run the model were obtained from

Upward longwave radiation flux was computed using the Stefan–Boltzmann equation: L↑ ¼ ε 0  σ  T 0

4

ð26Þ

where ε0 is surface emissivity and T0 is the land surface temperature obtained from MYD11A1. 3. Case studies and validation Three MODIS images taken on October 30, 2012 (13:10 local time), November 6, 2012 (13:35 local time) and December 3, 2012 (13:00 local time) over the central Himalayas were used in this study. The derived net radiation flux was validated using field observations made at three stations: Patan (29.42°N,80.51°E), Chainpur (29.54°N,81.20°E) and Tarahara (26.69°N,87.26°E). The locations of these stations are shown in Fig. 1. In-situ radiation flux data was averaged out at 30 minute intervals. The relative error (RE) was used to evaluate the results: RE ¼

jH derived −H measured j H measured

ð27Þ

where Hderived is the derived value and Hmeasured is the measured value The net shortwave radiation, net longwave radiation and net radiation fluxes derived from MODIS data over the central Himalayas agree well with field observations (Fig. 3), with mean RE of 6.19%, 7.72% and 6.60% respectively (Table 2). The distribution pattern of net radiation flux showed strong contrasts due to the different land surface features. Its value ranged from −155 W/m2 to 788 W/m2 in October, −167 W/m2 to 760 W/m2 in November and −190 W/m2 to 658 W/m2 in December (Figs. 2 and 4). Mean net radiation values were 405.97 W/m2 in October, 371.11 W/m2 in November and 283.86 W/m2 in December (Fig. 4). Net radiation flux decreased from October to December as the seasons changed from autumn to winter. 4. Conclusion Recent studies have highlighted the importance of heat release from the southern slopes of the Himalayas as a primary driving source of SASM. These findings are in contrast to the longstanding view that suggests seasonal heating from the TP as the primary driving factor. However, studies regarding land surface heat flux are nonexistent for these southern slopes. In this study we tested the feasibility of obtaining regional net radiation flux distribution, an important component of the surface energy balance over complex topography of the southern slope of the central Himalayas using MODIS data and DEM. We used a DEM based net radiation model (Chen et al., 2013) to obtain the regional net radiation flux distribution. Each net radiation flux component was separately parameterized. As our study area is characterized by a complex topography, shortwave radiation was divided into three components: direct, diffuse

Fig. 4. Net radiation frequency distribution over the central Himalayan area.

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remote sensing and climate model, nullifying the need to use insitu data. Comparison of our results with field measurements suggests that, this method constitutes a good approach for modeling net radiation flux over a complex topography of the southern slope of the central Himalayas. The derived net shortwave radiation flux, net longwave radiation flux and net radiation flux from MODIS data agree well with field observations with mean RE of 6.19%, 7.72% and 6.60% respectively. Hence, it forms a good base for studying heat and water exchange over this complex topographical region. However in order to understand the land–atmosphere interactions taking in this region, other surface energy balance components (sensible heat flux, latent heat flux and ground heat flux) need to be evaluated. This will be our next point of focus. Acknowledgment This work was under the auspices of the Chinese Academy of Sciences (XDB03030201), the National Natural Foundation of China (91337212 and 41275010), the CMA Special Fund for Scientific Research in the Public Interest (GYHY201406001) and EU-FP7 projects of “CORE-CLIMAX” (313085). We would like to thank the Department of Hydrology and Meteorology, Government of Nepal for providing data from Patan and Chainpur. We would also like to thank Dr. Xuelong Chen for productive discussions and for providing the TESEBS model. Lastly, we would like to thank Dr. Binod Dawadi, Mr. Subash Kandel and Mr. Rudra Timsina and family for their help in establishing and regularly maintaining the eddy covariance system in Tarahara, Nepal. References Angstrom, A., 1924. Solar and terrestrial radiation. Report to the international commission for solar research on actinometric investigations of solar and atmospheric radiation. Q. J. Roy. Meteorol. Soc. 50 (210), 121–126. Bisht, G., Venturini, V., Islam, S., Jiang, L., 2005. Estimation of the net radiation using MODIS (Moderate Resolution Imaging Spectroradiometer) data for clear sky days. Remote Sens. Environ. 97 (1), 52–67. Blad, B.L., Walter-Shea, E.A., Mesarch, M.A., Hays, C.J., Starks, P.J., Deering, D.W., Eck, T.F., 1998. Estimating net radiation with remotely sensed data: results from KUREX-91 and FIFE studies. Remote Sens. Rev. 17 (1–4), 55–71. Boos, W.R., Kuang, Z., 2013. Sensitivity of the South Asian monsoon to elevated and non-elevated heating. Sci. Rep. 3. Brutsaert, W., 1975. On a derivable formula for long-wave radiation from clear skies. Water Resour. Res. 11 (5), 742–744. Burrough, P.A., McDonnell, R., Burrough, P.A., McDonnell, R., 1998. Principles of Geographical Information Systems. Oxford University Press, Oxford. Cai, G., Xue, Y., Hu, Y., Guo, J., Wang, Y., Qi, S., 2007. Quantitative study of net radiation from MODIS data in the lower boundary layer in Poyang Lake area of Jiangxi Province, china. Int. J. Remote Sens. 28 (19), 4381–4389. Cai, M., Yang, S., Zhao, C., Zeng, H., Zhou, Q., 2013. Estimation of daily average temperature using multisource spatial data in data sparse regions of Central Asia. J. Appl. Remote Sens. 7 (1), 073478. Carlson, T.N., Ripley, D.A., 1997. On the relation between NDVI, fractional vegetation cover, and leaf area index. Remote Sens. Environ. 62 (3), 241–252. Chen, X., Su, Z., Ma, Y., Yang, K., Wang, B., 2013. Estimation of surface energy fluxes under complex terrain of Mt. Qomolangma over the Tibetan Plateau. Hydrol. Earth Syst. Sci. 17 (4), 1607–1618. Dozier, J., 1980. A clear-sky spectral solar radiation model for snow-covered mountainous terrain. Water Resour. Res. 16 (4), 709–718. Dozier, J., Frew, J., 1981. Atmospheric corrections to satellite radiometric data over rugged terrain. Remote Sens. Environ. 11, 191–205. Dubayah, R., 1992. Estimating net solar radiation using Landsat Thematic Mapper and digital elevation data. Water Resour. Res. 28 (9), 2469–2484.

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