A direct method for estimating net surface shortwave radiation from MODIS data

Remote Sensing of Environment 103 (2006) 115 – 126 www.elsevier.com/locate/rse

A direct method for estimating net surface shortwave radiation from MODIS data Bohui Tang a,b , Zhao-Liang Li a,c,⁎, Renhua Zhang a a

Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, China b Graduate School of the Chinese Academy of Sciences, China c TRIO/LSIIT(UMR7005 CNRS)/ENSPS, Bld Sebastien Brant, BP10413, 67412 Illkirch, France Received 30 August 2005; received in revised form 7 April 2006; accepted 8 April 2006

Abstract The Net Surface Shortwave Radiation (NSSR) is of primary interest in climate research because it controls the total energy exchange between the atmosphere and the land/ocean surface. The conventional methods for estimating NSSR rely on broadband satellite data such as Earth Radiation Budget Experiment (ERBE) wide-field-of-view planetary albedo. The spatial resolution of the current ERBE satellite data having nadir footprints larger than 30 km is too coarse. The primary objective of this study is to estimate NSSR using multispectral narrowband data such as Moderate Resolution Imaging Spectroradiometer (MODIS) data. A direct method was developed for narrowband-to-broadband albedo conversion, which links the narrowband apparent reflectance at the Top Of Atmosphere (TOA) to shortwave broadband albedo for clear and cloudy skies without performing any surface angular modeling. The conversion coefficients were derived as functions of the secant Viewing Zenith Angle (VZA) for a given Solar Zenith Angle (SZA) and a given interval of Relative Azimuth angle (RAA). The result of comparing the values of estimated MODIS TOA shortwave broadband albedos with those of the Clouds and the Earth's Radiant Energy System (CERES) data indicated that this direct method could predict TOA shortwave broadband albedo accurately with Root Mean Square (RMS) error between CERES observations and the estimated instantaneous MODIS TOA albedos less than 0.02. Based on more accurate radiative transfer model MODTRAN 4, the parameterization coefficients of Masuda et al. for the estimation of the NSSR from TOA broadband albedo were recalculated. The result showed that the coefficients should be categorized by land surfaces, ocean surface and snow/ice surface, respectively. Finally, the NSSR estimated from MODIS data was compared with the measurements of meteorological data for an extended period of time covering all seasons in a year 2003. The RMS error is less than 20 W/m2 for clear skies and 35 W/m2 for cloudy skies. © 2006 Elsevier Inc. All rights reserved. Keywords: Net surface shortwave radiation; Albedo; MODIS; CERES; Narrowband-to-broadband conversion

1. Introduction Net Surface Radiation (NSR) is the driving force for the surface energy balance and the transportation and exchange of all matters at the interface between the surface and the atmosphere. As a main component of NSR, the Net Surface Shortwave Radiation (NSSR) significantly affects the climatic forming and change. In addition, as an important factor in global and regional climatic models, an accurate estimation of the NSSR at the earth's ⁎ Corresponding author. Institute of Geographical Sciences and Natural Resources Research, CAS, China. Tel.: +86 10 6488 8989. E-mail address: [email protected] (Z.-L. Li). 0034-4257/$ - see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2006.04.008

surface is required. Up to now, many algorithms for estimating the net surface shortwave radiation have been proposed: particularly noteworthy are those of Pinker et al. (1985), Pinker and Tarpley (1988), Cess and Vulis (1989), Cess et al. (1991), Pinker and Laszlo (1992), Li et al. (1993a,b), Masuda et al. (1995), Rossow and Zhang (1995). A review of earlier approaches was given by Pinker et al. (1995). Many methods (Li et al. 1993a,b; Masuda et al., 1995), however, mainly focused on broadband satellite data such as Earth Radiation Budget Experiment (ERBE) wide-fieldof-view planetary albedo. It is well known that the spatial resolution of ERBE satellite data having nadir footprints larger than 30 km is too coarse for some applications. Pinker and Laszlo (1992) and Rossow and Zhang (1995) estimated NSSR from

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narrowband radiances such as the International Satellite Cloud Climatology Project (ISCCP) C1 data on a global scale. However, the spatial resolution of ISCCP C1 data is 280 km × 280 km. Furthermore, most current satellite data are narrowband spectra with higher spatial resolution. It is essential to estimate NSSR using multispectral narrowband satellite data with adequate spatial resolution. Fortunately, the Moderate Resolution Imaging Spectroradiometer (MODIS), one of the sensors in the National Aeronautics and Space Administration (NASA) Earth Observing System (EOS) Terra platform launched in 1999 and Aqua platform launched in 2002, provides comprehensive and frequent global earth imaging in 36 spectral bands and at variable spatial resolution with nadir footprints no more than 1 km. Furthermore, MODIS provides a series of products for various land/ocean applications. The work presented in this paper focuses on the retrieval of the net surface shortwave radiation from MODIS data. Li et al. (1993a) have derived a relationship between the outgoing shortwave flux at the Top Of Atmosphere (TOA) and the shortwave flux absorbed at the surface and proposed a parameterization to estimate the net surface shortwave radiation directly from measured albedos at the TOA. This parameterization was selected for the present study because its input parameters are only Solar Zenith Angle (SZA), water vapor amount and the TOA shortwave broadband albedo, which significantly simplified the procedure and introduced relative few sources of error. Taking into account most current satellites having only narrowband data with adequate spatial resolution, we propose to estimate the net surface shortwave radiation using multispectral narrowband data such as MODIS data instead of broadband satellite data such as ERBE data used by Li et al. (1993a,b) and Masuda et al. (1995). Consequently, the narrowband-to-broadband albedo conversion at the TOA must be performed first. Many method of converting TOA narrowband reflectance to broadband albedo need Bidirectional Reflectance Distribution Function (BRDF) (Doelling et al., 2000; Jacobowitz & Hucek, 1993; Laszlo et al., 1988; Li & Leighton, 1992; Li & Strahler, 1986; Lucht et al., 2000; Pinker & Laszlo, 1992; Strahler et al., 1999; Wanner et al., 1995), which have to be determined using accumulated observations during a period of time (i.e., 16 days for MODIS). The derived albedo, therefore, represents the average state for that period. In this paper, we develop a direct method of narrowband-to-broadband albedo conversion that links the narrowband apparent reflectance at the TOA to the total shortwave broadband albedo for clear and cloudy skies. This method can derive the TOA instantaneous shortwave broadband albedo from MODIS data. In addition, the coefficients in parameterization of Masuda et al. (1995), in the present study, will be recalculated using more accurate radiative transfer model MODTRAN 4 (Berk et al., 1998) rather than using LOWTRAN 7 (Kneizys et al., 1988) as Masuda et al. (1995) did. Section 2 describes the data used in this study. The methodology and issues related to the retrieval of the net surface shortwave radiations are presented in Section 3. Section 4 gives an example of estimating net surface shortwave radiation from MODIS data and a preliminary validation with in-situ measurements. The conclusion is drawn in Section 5.

2. Data Two kinds of satellite data were used in this study. One is multispectral narrowband MODIS data, and the other is broadband CERES data. The former was selected to estimate the net surface shortwave radiation and the latter was used to validate the TOA broadband albedo derived from MODIS data using the present narrowband-to-broadband albedo conversion method. In addition, some meteorological data were used to validate the estimation of net surface shortwave radiation. 2.1. MODIS satellite data MODIS is a passive imaging spectroradiometer, arranged in 36 spectral bands, which covers the visible and infrared regions. It is a high signal-to-noise instrument designed to satisfy a diverse set of oceanographic, terrestrial, and atmospheric science observational needs. As mentioned above, various products are provided by MODIS for many applications in the area of Earth science. The data we used are the MOD021KM, MOD03, MOD05_L2 and MOD35_L2 product files provided by the NASA Goddard Space Flight Center (GSFC) Distributed Active Archive Center (GDAAC) (http://edcimswww.cr.usgs.gov/). The MOD021KM products, calibrated Earth View data at 1KM resolution by the MODIS Characterization and Support Team (MCST), including the 250 m and 500 m resolution bands aggregated to appear at 1 km resolution, are TOA radiances and reflectances. The first seven spectral bands of MOD021KM listed in Table 1 are used in this study. The MOD03 products are the geolocation fields' data calculated for each 1 km MODIS Instantaneous Field of View (IFOV) for all daytime orbits. The geolocation fields include geodetic latitude, longitude, surface height above geoid, solar zenith and azimuth angles, satellite zenith and azimuth angles, and a land/sea mask for each 1 km sample. The solar zenith and azimuth angles, satellite zenith and azimuth angles are used to estimate net shortwave radiation in our present study. The MOD05_L2 products are the near-infrared total precipitable water data consisting of column water vapor amounts over clear land areas of the globe, and above clouds over both land and ocean. Water vapor estimates are also derived in MOD05_L2 products over clear ocean areas. The MOD35_L2 is cloud mask product which assigns a clear-sky confidence level (clear, probably clear, uncertain, cloudy) to each IFOV. All of these products mentioned above can be combined to retrieve the shortwave broadband albedos and to calculate the net surface shortwave radiation according to the parameterization of Li et al. (1993a). 2.2. CERES data The Clouds and the Earth's Radiant Energy System (CERES) is one of the highest priority scientific satellite instruments developed for NASA's Earth Observing System (EOS). The CERES instrument is based on the successful Earth Radiation Budget Experiment (ERBE) scanning radiometer but has better spatial resolution with 10 km for Tropical Rainfall Measuring Mission (TRMM) nadir FOV and 20 km for both Terra and Aqua nadir FOV. The CERES instrument is a broadband scanning

B. Tang et al. / Remote Sensing of Environment 103 (2006) 115–126 Table 1 Spectral ranges, center spectra and spatial resolutions of the first seven MODIS bands Band

1

2

3

4

5

6

7

Spectral range (nm) Center spectral (nm) Spatial resolution (m)

620– 670 646.5

841– 876 856.7

459– 479 465.6

545– 565 553.7

1230– 1250 1241.9

1628– 1652 1629.1

2105– 2155 2114.3

250

250

500

500

500

500

500

117

as determined from application of the relationship with ERBE measurements of the TOA fluxes and from upward and downward facing radiometers mounted on tower, Li et al. (1993b) showed that a single relationship was adequate, regardless of the presence or absence of cloud or the nature of the surface. The parameterization of Li et al. was based on a moderate absorbing aerosol and invariants in concentrations of trace gases. Consequently, Masuda et al. (1995) modified and extended the parameterization to allow for variations in atmospheric properties such as surface pressure, ozone amount, aerosol type and amount, and

radiometer, with three detector channels, 0.3 to 5.0 μm, 8.0 to 12.0 μm and 0.3 to 50 μm. Among various CERES products the Terra Single Scanner Footprint (SSF) (http://eosweb.larc.nasa. gov/JORDER/guest.html) is a unique product including both solar-reflected and Earth-emitted radiation from the TOA to the Earth's surface for studying the role of clouds, aerosols, and radiance in climate. The major data on the SSF are CERES FOV geometry and viewing angles, radiance and flux (both at TOA and at Surface), area statistics and imager viewing angles, and others. Note that the CERES shortwave TOA upward flux in SSF data set is the instantaneous reflected solar flux from the Earth-atmosphere at the colatitude and longitude position of the CERES footprint, which takes into account the non-uniform spectral shape of the shortwave instrument filter. In this study, the CERES shortwave TOA upward fluxes data are used to validate our Narrowband-tobroadband albedo conversion formula. 2.3. Meteorological data The experimental campaigns were conducted at the YuCheng field site, located in the center of the plain of Huanghai and Huaihe River, China (36°37′N, 116°36′E). The center area of the experiment is 0.2 km2 and the periphery area is 200 km2. The area has a semi-humid climate, with a mean annual temperature of 13.1 °C and a mean annual rainfall of about 610 mm. Most of the soil distributing in the area are sandy loam and silt loam and the primary vegetation is agricultural crop. Solar radiation data recorded every 10 s was stored as 30 min averages in 2003. The instruments are mounted on a tower at 60 m above ground level. The measurements include horizontal solar global and reflected radiation, upwelling longwave radiation, downwelling longwave radiation and net radiation, all of which were measured using pyranometer. The 30 min average net shortwave radiation is retrieved through the horizontal solar global radiation minus the reflected radiation. 3. Method 3.1. Retrieval of NSSR Based on the results of radiative transfer calculation, Li et al. (1993a) derived a relationship between the outgoing shortwave flux at the top of the atmosphere and the shortwave flux absorbed at the surface for clear skies and for four different cloud types. The input parameters were only Solar Zenith Angle (SZA) and water vapor amount. Compared the net surface shortwave fluxes

Fig. 1. Spectral reflectance curves of nine surface types used in MODTRAN simulation.

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Fig. 2. Curve fits of narrow-to-broadband conversion coefficients bi (i = 1, 7) in Eq. (8) as function of the viewing zenith angles for solar zenith angle = 0 and relative azimuth angle in forward direction.

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cloud height and cloud type that were not considered in the original parameterization. Considering the success of the parameterization of Li et al. (1993a,b) and Masuda et al. (1995) in the estimation of shortwave flux absorbed at the surface from TOA reflected flux, we have in the present study adopted their parameterization scheme for the determination of NSSR. Li et al. (1993a) showed that the flux absorbed at the surface (as) expressed as a fraction of the flux incident at the TOA could be related to the normalized outgoing flux at the TOA, r, by as ðl; w; rÞ ¼ a V −b V r

ð1Þ

where as is defined by as ¼

NSSRd 2 E0 coshs

ð2Þ

and r, representing the TOA broadband albedo, is defined by r¼

Fu d 2 E0 coshs

ð3Þ

in which E0 is the TOA solar irradiance at one astronomical unit, θs the solar zenith angle, d the Earth–Sun distance in astronomical units, and Fu the upward flux at the TOA.

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The interception α′ and slope β′ in Eq. (1) were expressed by aV¼ 1−a1 l−1 −a2 l−x −ð1−expð−lÞÞða3 þ a4 wy Þl−1

ð4Þ

and bV¼ ð1 þ a5 þ a6 lnl þ a7 wz Þ

ð5Þ

in which μ is the cosine of the solar zenith angle, w the precipitable water, a1–a7 are constants for various surfaces. In Li et al. parameterization, x, y, z, took the value 0.5 but they were free parameters in Masuda et al. parameterization. The TOA broadband albedo r and the precipitable water w that Li et al. (1993a,b) and Masuda et al. (1995) used come from the Earth Radiation Budget Experiment (ERBE) satellite data and the European Centre for Medium-Range Weather Forecast (ECMWF) data, respectively. However, the data we used are MODIS data, which are narrowband reflectances at the TOA. The narrowband reflectance must be converted to shortwave broadband albedo. 3.2. Narrowband-to-broadband albedo conversion Broadband albedo is a critical variable for many scientific applications. Many conventional methods for estimating broadband albedo from satellite data rely on a series of steps in the

Table 2 Coefficients of the TOA narrow-to-broadband conversions (Eqs. (8) and (9)) for different solar zenith angles in forward direction Solar Zenith Angle (°)

b0

b1

b2

b3

b4

b5

b6

b7

0

− 0.05403 0.02036 1.73271 0.16932 − 0.05393 0.03405 1.74286 0.33363 − 0.04717 0.03211 1.73526 0.29155 − 0.06510 0.07563 1.72955 0.60936 − 0.04840 0.04656 1.70345 0.26552 − 0.05594 0.06018 1.68794 0.23031 − 0.08365 0.12443 1.60598 0.32150 − 0.14794 0.27048 1.55063 0.46241

0.84088 2.49949 0.17257 0.34613 0.81169 2.38133 0.18870 0.34667 0.78668 2.64369 0.20550 0.32646 0.75695 2.38618 0.23451 0.32285 0.73721 1.77321 0.27161 0.33291 0.69302 1.37413 0.56141 0.24758 0.52101 3.76866 0.30130 0.32131 0.23680 6.26712 0.27384 0.34113

0.18487 0.34567 1.19778 0.70489 0.09114 1.10520 − 0.08161 1.05425 0.11821 0.98016 0.46313 0.62314 0.09025 0.73612 0.80797 0.59212 0.09098 2.42373 0.26188 0.42813 0.04902 6.66617 − 0.26487 0.48945 0.20470 6.82781 − 0.18111 0.40112 0.24933 1.12753 − 0.86731 1.70942

1.40413 2.88350 − 0.02851 0.51796 1.37593 3.22075 − 0.03073 0.49437 1.36837 8.78781 − 0.31940 0.41361 1.31840 3.95866 − 0.00547 0.44557 1.29230 3.73010 0.01101 0.43821 1.26768 3.18884 0.07170 0.41208 1.17619 3.00476 0.06978 0.42072 1.00386 3.24162 0.26817 0.35020

− 1.64202 − 5.60429 − 0.04349 0.53910 − 1.59514 − 5.39629 0.00410 0.52550 − 1.58457 − 11.52053 − 0.30227 0.47238 − 1.52716 − 5.63249 0.06709 0.47552 − 1.50695 − 3.92107 0.27028 0.44650 − 1.47995 − 2.96946 0.47417 0.38074 − 1.31026 − 3.89719 0.41114 0.38700 − 1.00917 − 3.05223 0.71117 0.33393

0.19707 − 1.30626 − 0.22705 1.09412 0.19221 − 2.10978 − 0.52258 0.89482 0.18723 − 2.48273 − 0.39247 0.75225 0.16408 − 2.01480 0.02937 0.60948 0.14319 − 4.22008 − 0.02978 0.43587 0.16009 − 4.14039 − 0.04511 0.49672 − 0.00664 − 3.82384 0.03775 0.42230 − 0.20956 − 1.46739 − 0.31201 0.70404

− 0.03715 0.39343 0.78731 0.35910 − 0.01136 0.15091 1.17408 0.22749 − 0.02421 0.31381 − 0.08602 0.99147 0.02624 0.66823 0.37354 0.31681 0.07579 0.70597 0.04214 0.37154 0.12810 0.06120 1.32410 0.04246 0.13764 0.24585 1.17798 0.16340 0.12883 3.52008 0.27741 0.33812

0.16918 −0.56029 0.45516 0.27905 0.14783 −0.05062 1.14425 0.11623 0.12043 0.20507 −0.07858 0.59902 0.06195 0.29240 −0.86485 1.69123 0.04049 0.39034 −0.47093 0.81975 0.00691 0.03508 1.86992 0.14504 0.04693 −0.75481 0.65163 0.24966 0.09424 −3.26873 0.37701 0.31917

10

20

30

40

50

60

70

c1 c2 c3 c4 c1 c2 c3 c4 c1 c2 c3 c4 c1 c2 c3 c4 c1 c2 c3 c4 c1 c2 c3 c4 c1 c2 c3 c4 c1 c2 c3 c4

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of MODIS simulated by MODTRAN are further normalized to spectral apparent band reflectances at the TOA, by qi ðl; lm ; /Þ ¼

kLi ðl; lm ; /Þd 2 lEsun;band− i

ð6Þ

where μ is the cosine of solar zenith angle, μν the cosine of viewing zenith angle, ϕ the relative azimuth angle, subscript i the MODIS band number, d the Earth–Sun distance in astronomical units, and Esun,band_i is the mean solar exoatmospheric irradiance at band i, which is expressed by Rl Esun ðkÞRSRi ðkÞdk ð7Þ Esun;band− i ¼ 0 R l 0 RSRi ðkÞdk Fig. 3. Comparison of the actual TOA total shortwave broadband albedos, for different types of surfaces and sky conditions, with these estimated using Eq. (8) with coefficients c1i–c4i stored in the look-up-table for solar zenith angle = 0 in forward direction.

processing chain, including scene identification, anisotropic correction, and narrowband-to-broadband albedo conversions (Li, 1996; Li & Leighton, 1992; Pinker & Laszlo, 1992). Errors associated with each step may be accumulated and significantly affect the accuracy of the final albedo products. According to the definition of the TOA broadband albedo given by Eq. (3), in the following simulations, the total TOA shortwave broadband albedo will be computed by running MOD TRAN 4 with different atmospheric and geometric conditions. The upwelling TOA radiances of the first seven bands of MODIS are simulated by running MODTRAN 4 once more with the same conditions and the corresponding sensor spectral response functions. Assume that the land surface is Lambertian, and then the upwelling TOA radiances Li(μ, μν, ϕ)of the first seven bands

where RSRi(λ) is the spectral response function of MODIS band i. Before running MODTRAN, note that it is critical to use the representative surface reflectance spectra in data simulation. Different surface reflectance spectra were collected from the ASTER spectral library (http://speclib.jpl.nasa.gov/). In our MODTRAN simulations, nine surface reflectance spectra were employed, including vegetation canopy, grassland, wetland, and sandy loam, barren-desert, urban, ocean water, fresh snow and sea ice, their spectral reflectances are shown in Fig. 1. Four types of aerosol models (rural, maritime, urban, and troposphere) with variable visibilities (10, 15, 23, 30 km) representing different aerosol loading, and six atmospheric profiles (tropical, mid-latitude summer, mid-latitude winter, subarctic summer, subarctic winter, and US76) representing different atmospheres were used in our investigations. In addition to clear sky conditions, three types of cloud models (cumulus, altostratus, and stratus) were considered in the simulation. As for the operational application, of course, more surface reflectance spectra and atmospheric profiles should be included to represent the variable surface and atmospheric conditions.

Fig. 4. CERES IFOV represented by each solid ellipses were projected onto MODIS imagery (CERES and MODIS data acquired on May 25, 2003).

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flection in forward, sideward and backward directions, respectively. A linear minimization procedure is applied to get conversion coefficients, b0–b7, in Eq. (8) for a given pairs of Viewing Zenith Angle (VZA) and Solar Zenith Angle (SZA) in forward, sideward and backward directions, respectively. To establish relationships between obtained coefficients b0– b7 and VZA, an exponential function as Eq. (9) is used bi ¼ c1i þ c2i =ð1 þ expðð1=cosðVZAÞ−c3i Þ=c4i ÞÞ

Fig. 5. Comparison of the actual TOA shortwave albedo derived from CERES data with that estimated from MODIS data: (a) for May 25, 2003 (b) for October 15, 2003.

Taking into account the angular dependence of apparent reflectance ρi and the maximum MODIS viewing zenith angle (less than 65° from nadir), six viewing zenith angles (0°, 33.56°, 44.42°, 51.32° 56.25°, 60°), eight solar zenith angles (0°, 10° 20°, 30°, 40°,50°,60°,70°) and three relative azimuth angles (0°, 60°, 120°) were used to compute TOA shortwave broadband albedo r and narrowband reflectance ρi, respectively. In total, 158,976 cases were taken into account in MODTRAN simulations. Given the simulation of these data pairs of TOA reflectance and broadband albedo, a linear relationship between r and ρi as described in Eq. (8) can be obtained by a nonparametric regression method. The result of linear conversion formula is used as r ¼ b 0 þ b 1  q1 þ b 2  q 2 þ b 3  q 3 þ b 4  q 4 þ b 5  q 5 þ b 6  q6 þ b 7  q7

ð8Þ

where r denotes the TOA shortwave broadband albedo, ρi the TOA narrowband reflectance of MODIS band i. Note that the variation of radiance with azimuth angle is weaker than that with zenith angle. Three coarse intervals with respect to Relative Azimuth Angle (RAA) were taken into account. Their ranges are 0–60°, 60–120° and 120–180°, representing approximately re-

ð9Þ

where c1i–c4i are constants for a given solar zenith angle 0°, 10°, 20°, 30°,40°, 50°, 60° and 70°, respectively. A very good fitting result is obtained. As an example, Fig. 2 shows the curve fits of the coefficient b0–b7 as function of secant VZA for SZA = 0 in forward direction. As noted, the fitting results are quite well with R-square all larger than 0.997. At this stage, it is hard to find a good relationship between coefficients c1i–c4i and SZA. A look-up table of coefficients c1i–c4i (i = 0, 7) for SZA at step of 2° is established and will be used in the following calculations. Table 2 shows an example of c1i–c4i (i = 0, 7) for SZA at step of 10° from 0° to 70° in forward direction. Similarly, the coefficients c1i–c4i are respectively obtained for sideward and backward directions (interest readers can contact us for them). Note that the radiance is not azimuthly dependent when SZA = 0. Fig. 3 shows, as an example for different types of surfaces and sky conditions, the comparison of the actual TOA total shortwave albedos and those estimated using Eq. (8) with the conversion coefficients b0–b7, which are obtained themselves using Eq. (9) and c1i–c4i stored in the look-up table for SZA = 0. The different RMS errors listed in Fig. 3 are due to estimating the albedos from radiances at different VZA. The results are quite good with RMSE less than 0.0076. Similar results are obtained for other solar zenith angles and relative azimuth angles. 3.3. CERES data validation of Narrowband-to-broadband albedo conversion In order to validate our method of Narrowband-to-broadband albedo conversion (Eq. (8)) described above, the CERES shortwave TOA upward flux, which is an estimate of the instantaneous reflected solar flux from the Earth-atmosphere at the surface colatitude and longitude position of the CERES footprint, is used in this study. Taking into account the data needed are TOA shortwave broadband albedos, the CERES Table 3 Error statistics of actual CERES and estimated MODIS TOA albedos for different atmospheric conditions and surface types on May 25 and October 15, 2003 Surface RMS error 2003-05-25 Clear Land Ocean

2003-10-15

Partly cloudy Overcast Clear

0.0106 0.0117 0.0084 0.0099

0.0148 0.0125

Partly cloudy Overcast

0.0112 0.0133 0.0097 0.0115

0.0236 0.0207

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Table 4 Coefficients for estimating the net surface shortwave radiation from the TOA broadband albedos with Eq. (1) Surface type

a1

a2

a3

a4

a5

a6

a7

x

y

z

Land Ocean Snow/ice

− 0.011 0.003 − 0.011

0.179 0.166 0.163

− 0.980 − 0.774 − 0.648

0.929 0.733 0.631

− 0.701 − 0.511 − 0.867

0.090 0.059 −0.013

0.846 0.637 0.927

0.478 0.342 0.510

0.052 0.067 0.060

− 0.020 − 0.034 0.018

TOA shortwave upward flux is first converted to TOA shortwave broadband albedo according to the expression below. r¼

Fu d 2 lS0

ð10Þ

where r denotes the TOA shortwave broadband albedo, Fu the CERES TOA shortwave upward flux, d the Earth–Sun distance in astronomical units, μ the cosine of solar zenith angle, and S0 is the solar constant taken here to be 1368 W/m2. Note that each SSF IFOV represents one scanner measurement. Measurements are taken every 0.01 s. However, only those IFOVs, which can be convolved with some imager pixels, are included on an SSF granule. The CERES data and the imager data used by CERES come from instruments that are located on the same satellite. Some valid imager names are Visible and Infrared Scanner (VIRS), MODISam (MODIS imager on Terra platform), and MODISpm (MODIS imager on Aqua platform). CERES provides a product named Number of imager pixels in CERES IFOV in SSF data set, which parameter is a count of the actual

number of imager pixels within the CERES IFOV. On the basis of the count of imager pixels within each CERES IFOV and the surface colatitude and longitude position of the CERES footprint, an appropriate number of 1-km MODIS pixels within the CERES footprint were selected to match the CERES-derived broadband albedo, their corresponding radiances were converted to broadband albedos using our Narrowband-to-broadband albedo conversion method and then the 1-km broadband albedos were averaged. Two different temporal MODIS imageries were conducted in this study to validate the method of Narrowbandto-broadband albedo conversion. One MODIS imagery was acquired on May 25, 2003, and the other on October 15, 2003. The CERES instantaneous IFOV projected onto MODIS imagery is illustrated in Fig. 4. Each ellipse represents one CERES IFOV including appropriate number of 1-km MODIS pixels in MODIS imagery. The scatter plots of the actual CERES TOA shortwave albedos and the estimated MODIS TOA shortwave albedos are shown in Fig. 5. The RMS error between CERES observations and the estimated instantaneous MODIS TOA albedos for imagery May 25, 2003 was 0.013, and that of the RMS error

Fig. 6. Histograms of the differences between estimated as and actual as. (a) land surfaces. (b) ocean surfaces. (c) snow/ice surfaces.

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Fig. 7. Map of the Net surface shortwave radiation flux derived from MODIS data on October 15, 2003.

for imagery October 15, 2003 was 0.015. The error statistics for different atmospheric conditions and scene types are listed in Table 3. In this study, clear sky was defined as no cloudy pixels within one CERES IFOV. Partly cloudy sky was defined as the percent of cloudy pixels under 50% within one CERES IFOVand the percent exceeding 50% defined as overcast. The result shows that our method of Narrowband-to-broadband albedo conversion can predict the TOA shortwave broadband albedo accurately. 3.4. Determination of parameters x, y, z, and a1–a7 To obtain the coefficients x, y, z, and a1–a7 in Eqs. (4) and (5), the values as and the relevant r are computed through running MODTRAN 4. The nine surface types employed in narrow-tobroadband conversion simulation are used. Twelve solar zenith angles (0°, 10°, 20°, 30°, 35°, 40°, 45°, 60°, 66°, 72°, 78°, 82°) except for the unreasonably very large solar zenith angles are used to compute radiative fluxes. Six standard atmospheric profiles in MODTRAN 4 (tropical, mid-latitude summer, mid-latitude winter, subarctic summer, subarctic winter, and US76), with the default column water vapor amounts of 4.11, 2.92, 0.85, 2.08, 0.42 and 1.42 g/cm2, respectively, are used in the present MODTRAN simulation. Four types of aerosol models (rural, maritime, urban, and troposphere) with variable visibilities (10, 15, 23, 30 km), respectively, representing different aerosol types and aerosol loading are also included. Cloud types were used as

same as narrow-to-broadband conversion simulation. In total, the simulations provide 2574 pairs of as and r. Values of the coefficients are obtained using nonlinear least square fitting. The surfaces are categorized to three groups: Land surface, Ocean surface, and Snow/ice surface. The coefficients of the land surface are obtained using 2124 pairs of as and r from six atmospheric profiles, seven land surfaces and twelve solar zenith angles. Similarly, based on each surface, different sets of coefficients are computed, respectively. The RMS errors in as compared to the detailed calculations for land surface, ocean surface, and snow/ice surface are 0.0054, 0.0036 and 0.0076, respectively, leading to the RMS errors of NSSR less than 10 W/m2. It should be pointed out that the RMS errors quoted here are the errors in the fitting process Table 5 Description of Symbols A, B, and C representing small, moderate, and large NSSR absorbed by surface in Fig. 7

Longitude (°) Latitude (°) SZA (°) VZA (°) RAA (°) Water vapor (g/cm2) TOA albedo NSSR (W/m2)

A (blue)

B (green)

C (red)

128.52 E 42.80 N 52.13 1.17 56.88 0.263 0.4982 267.4

116.60 E 36.60 N 49.66 56 55.29 1.049 0.2039 540.7

129.64 E 34.51 N 43.76 28.64 115.97 0.85 0.0829 721.9

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Fig. 8. Comparison between NSSR estimated from MODIS data and NSSR measured in situ at YuCheng field site during an extended period covering all seasons (January (a), April (b), July (c) and October (d)) in 2003.

and do not include errors in estimating the TOA albedo. The corresponding coefficients are given in Table 4 and the residual error plots are shown in Fig. 6. 4. Retrieval of net surface shortwave radiation flux The objective of the present work is to estimate the instantaneous net surface shortwave radiation flux merely using MODIS data. In the first step the instantaneous MODIS TOA spectral radiance was converted to TOA total shortwave albedo according to our narrowband-to-broadband conversion method. Then the instantaneous net surface shortwave radiation flux was computed using the parameterization mentioned above. An example of the retrievals of the instantaneous net surface shortwave radiation fluxes during TERRA satellite overpass on October 15, 2003 at 10:25 local time is shown in Fig. 7. Note that the current two EOS satellites data are good for retrieving instantaneous NSSR but may not be good enough to provide a daily average since Terra and Aqua overpass one same site only two times each day, respectively. Symbols A, B, and C, located in blue, green, and red colored area in Fig. 7, represent small, moderate, and large NSSR absorbed by surface, respectively. The atmospheric conditions for A, B, and C are cloudy, clear and clear, and the surface conditions are land, land and ocean, respectively. The values of the solar

zenith angle, viewing zenith angle and relative azimuth angle, the water vapor amount, the TOA albedo, and resultant NSSR for one representative pixel in each blue, green, and red colored area are listed in Table 5. To validate our method, Fig. 8 shows comparisons of the NSSR flux estimated from MODIS observations and measured at YuCheng field site during an extended period of time covering all seasons (January, April, July and October) in 2003 for clear and cloudy skies. 30 min means of ground data and a single MODIS pixel with 1 km resolution were used in the comparison. On the basis of the clear-sky confidence level assigned to each IFOV, clear and probably clear pixels assigned in MOD35_L2 were taken as clear, and uncertain and cloudy pixels in MOD35_L2 were taken as cloudy in our study. From this figure, we see that, except for a few points for which the NSSR estimated from satellite data are much larger than that measured in situ which is probably due to the effects of broken or inhomogeneous cloud, NSSR estimated from MODIS data is generally in good agreement with that measured in situ. The RMS error between estimated and measured NSSR is less than 20 W/m2 for clear skies and 35 W/m2 for cloudy skies in these comparisons. Furthermore, Fig. 9 shows histograms of the differences between NSSR estimated using our present method denoted as NSSRest and the tower measured NSSR (NSSRmeasured), and the differences between the NSSR (NSSRmasuda) estimated using

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Fig. 9. Histogram of the differences between NSSRmeasured measured in situ and NSSRestimated estimated using different methods (method 1: NSSR estimated using the method proposed in this paper and method 2: NSSR estimated using the parameterization coefficients of Masuda et al.) for clear and cloudy skies, respectively.

parameterization coefficients of Masuda et al. and NSSRmeasured for clear and cloudy skies with these four-month MODIS data. The bias and RMSE of the former are respectively 8.4 W/m2 and 16.3 W/m2 for clear skies, and 14.5 W/m2 and 30.2 W/m2 for cloudy skies; and those of the latter are respectively 21.8 W/m2 and 28.4 W/m2 for clear skies, and 31.3 W/m2 and 41.1 W/m2 for cloudy skies. The result demonstrates that coefficients of Masuda et al. overestimate the surface NSSR as LOWTRAN 7 usually underestimates the transmittance in radiative transfer model, which indicates that the present coefficients can improve the retrieval accuracy of the surface NSSR. It should be pointed out that there exist spatial and temporal scale differences between satellite and tower measurements in our study. The MODIS data are instantaneous with 1 km resolution while the tower measurements are 30 min means with IFOV about 0.01 km2. 5. Conclusions The net surface shortwave radiation flux constitutes the fundamental parameter that governs the climate of the lower atmosphere. Note that many current algorithms for deducing the net surface shortwave radiation mainly used broadband satellite data such as Earth Radiation Budget Experiment (ERBE) widefield-of-view planetary albedos. Considering the limitation of the spatial resolution of ERBE satellite data with nadir footprints beyond 30 km, we have proposed to use MODIS data with respect to high spatial resolution to estimate the net surface shortwave radiation. It is well known that MODIS is a multispectral sensor with 36 spectral bands. It is necessary to convert narrowband reflectance to broadband albedo at TOA. In the present study, we have developed a direct method of narrowband-to-broadband albedo conversion that links the narrowband apparent reflectance

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at the TOA with total shortwave broadband albedo for clear and cloudy skies without performing any surface angular modeling. This method can derive the TOA instantaneous shortwave broadband albedo from MODIS data. In order to validate our method of narrowband-to-broadband albedo conversion, wide-field-of-view CERES data from two days (May 25, October 15, 2003) were used. For matching the CERES-derived broadband albedo with one estimated from MODIS, an appropriate number of 1-km MODIS pixels within the CERES footprint were selected, their corresponding radiances were converted to broadband albedos using our narrowband-tobroadband albedo conversion method and then the 1-km broadband albedos were averaged. Compared the values of CERES albedos estimated using Eq. (10) with the mean values of the retrieved instantaneous MODIS TOA albedos within CERES IFOVs, the RMS errors between CERES observations and the estimated instantaneous MODIS TOA albedos are less than 0.02, which demonstrated that our conversional method is reasonably accurate. The parameterization coefficients of Masuda et al. for the estimation of the NSSR from TOA broadband albedo were recalculated using more accurate radiative transfer model MODTRAN 4 and nonlinear least square fitting. The RMS errors in as resulting from the land surface, ocean surface, and snow/ice surface are 0.0054, 0.0036 and 0.0076, respectively. Finally, some meteorological data measured at YuCheng field site for an extended period of time covering all seasons in 2003 were used to validate the resultant NSSR estimated from MODIS data. Except for few values, the RMS error between estimated and measured NSSR is less than 20 W/m2 for clear skies and 35 W/m2 for cloudy skies, which suggests that the current method is feasible and accurate. It should be noted that the retrievals of instantaneous radiation flux in this study were obtained under the assumption that the earth surface is Lambertian in estimating TOA apparent reflectances. The effects of the bidirectional reflectance on radiation flux are unavoidable. This assumption can be easily removed as long as we have a good understanding of the bidirectional reflectance distribution function in the near future. The instantaneous net surface shortwave radiation, certainly, can be accurately estimated if the bidirectional reflectance distribution function is considered in TOA narrowband reflectance to total shortwave broadband albedo conversion and the determining of the parameterization coefficients in running MODTRAN 4. The lack of knowledge on the characteristics of the bidirectional reflectance distribution function makes us simplify the process in this study. A further improvement to take into account the bidirectional reflectance will be worked on in the future. Acknowledgments The authors like to thank the Land Processes Distributed Active Archive Center (LP DAAC) for providing us with the MODIS data products, the NASA Langley Research Center Atmospheric Sciences Data Center for the distribution of the CERES SSF data, the ASTER science team for providing the ASTER Spectral Library data, the MODTRAN development

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