Bisht e Bras, 2010 - Estimation of net radiation from the MODIS data under all sky conditions - Southern Great Plains case study.pdf

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Keywords:Remote sensingMODISNet radiationAtmospheric energy balanceEnergy budget

ponent in the surface radiation budget. Numerous studies have developed

methodologies to estimate net radiation for clou

Remote Sensing of Environment 114 (2010) 15221534

Contents lists available at ScienceDirect

Remote Sensing o

.eNet radiation (Rn) at the Earth's surface drives the process ofevaporation, photosynthesis, and heating of soil and air. Rn is thedifference between the downwelling and upwelling radiation uxesat the surface, including longwave and shortwave. Downwellingshortwave radiation, RS, at the surface results from scattering,emission and absorption within the entire atmospheric column;while upwelling shortwave radiation can be estimated by RS andsurface albedo. Downwelling longwave, RL, and upwelling longwaveradiation, RL, are characterized by near-surface air temperature, airemissivity, land surface temperature (LST) and surface emissivity. Net

compared to ground-based measurements. The methodologies toestimate surface Rn or its components (RL, RL or RS) from satellitedata can be classied in two broad categories on the basis of the dataused: (i) near-surface data (e.g., land surface temperature, surfacealbedo, near-surface air temperature); (ii) Top Of the Atmosphere(TOA) radiation. Several empirical parameterizations have beendeveloped to estimate components of radiation budget from near-surface air temperature, humidity and land surface temperature(Brutsaert, 1975; Dilley & O'Brien, 1998; Idaso, 1981; Prata, 1996;Zillman, 1972). A review of such parameterization schemes toradiation and the overall surface energy budgdevelopment of the planetary boundary-layeheterogenous land surfaces is crucial tointeractions.

Corresponding author.E-mail address: [email protected] (G. Bisht).

0034-4257/$ see front matter 2010 Elsevier Inc. Aldoi:10.1016/j.rse.2010.02.007Remote sensing provides data pertaining to land and atmosphericstates with a high-spatial, but low-temporal resolution, when1. IntroductionSurface energy budgetClear daysCloudy dayssignicant challenge. In this paper, we present a framework to estimate instantaneous and daily average netradiation under all sky conditions from using the data from the MODerate Resolution ImagingSpectroradiometer (MODIS), onboard from the Terra satellites. Bisht et al. (2005) methodology is used forthe clear sky portion of the MODIS overpass; while for cloudy portion of the MODIS overpass an extension ofBisht et al. (2005) methodology is applied. The extension of Bisht et al. (2005) methodology utilizes theMODIS cloud data product (MOD06_L2) for cloud top temperature, cloud fraction, cloud emissivity, cloudoptical thickness and land surface temperature for cloudy days. The methodology is applied over theSouthern Great Plains (SGP) for a time period covering all seasons of 2006. During the MODIS-Terraoverpasses in 2006 over the SGP, only 24% of day-overpasses and 9% of night-overpasses had 75% or more ofthe study region as cloud free. Thus, this proposed study is applicable to a large portion of the MODIS-Terraoverpasses. The root mean square errors (RMSE) of instantaneous and daily average net radiation estimatedunder cloudy conditions using the MOD06_L2 product, comparing to ground-based measurements are37 Wm2 and 38 Wm2, respectively. The strength of the proposed methodology is that it can relyexclusively on remote sensing data in the absence of ancillary ground observations, thus it has a potential toestimate surface energy budget globally.

2010 Elsevier Inc. All rights reserved.et are important for ther. Its quantication overstudy landatmosphere

estimate shortwsatellite data isNiemel et al. (2radiance (for lonradiation) involrates dependenangle (Li et al.,Liang, 2009; Wa

l rights reserved.dy sky conditions from remote sensing sensors remains aReceived in revised form 1 February 2010Accepted 12 February 2010frameworks to estimate net radiation or its components (upwelling or downwelling longwave and/orshortwave radiation) from remote sensing data for clear sky conditions. Application of existingArticle history:Received 25 June 2009

Net radiation is a key comEstimation of net radiation from the MODGreat Plains case study

Gautam Bisht a,, Rafael L. Bras b

a Department of Civil and Environmental Engineering, Massachusetts Institute of Technolob The Henry Samueli School of Engineering, 305 Rockwell Engineering Center, Irvine, CA 9

a b s t r a c ta r t i c l e i n f o

j ourna l homepage: wwwdata under all sky conditions: Southern

5 Vassar Street, Building 48-212, Cambridge, MA, 02139, USA-2700, USA

f Environment

l sev ie r.com/ locate / rseave and longwave radiation and their application topresented in Ellingson (1995), Pinker et al. (1995),001a, b), and Diak et al. (2004). Studies using TOAgwave radiation) or TOA reectance (for shortwaveve developing a statistical regression that incorpo-ce on solar zenith angle and/or satellite viewing1993; Tang & Li, 2008; Tang et al., 2006; Wang &ng et al., 2005). Various remote sensing platforms

including Geostationary Operational Environmental Satellites(GOES), the Advanced Very High Resolution Radiometer (AVHRR),Landsat and the MODerate Resolution Imaging Spectroradiometer(MODIS) have been used to estimate components of the surfaceenergy budget (Bisht et al., 2005; Diak & Gautier, 1983; Gautieret al., 1980; Gratton et al., 1993; Jacobs et al., 2002; Lee & Ellingson,2002; Li et al., 1993; Ma et al., 2002; Nishida et al., 2003; Tang & Li,2008; Tang et al., 2006; Wang & Liang, 2009; Wang et al., 2005;Wang et al., 2009; Zhou et al., 2007).

The MODIS sensor, onboard of the National Aeronautics and SpaceAdministration's (NASA's) Terra and Aqua satellites, provides fre-quent global coverage in 36 spectral bands with spatial resolutions of250 m, 500 m and 1 km in various bands. Several studies have alreadyutilized data from the MODIS to evaluate hydrologic models (Brownet al., 2008; Parajka & Bloschl, 2008). In addition the MODIS data hasbeen assimilated to improve hydrologic and numerical weatherprediction models (Benedetti & Janiskova, 2008; Demarty et al.,2007; Huang et al., 2008; Pan et al., 2008; Zaitchik & Rodell, 2009).Estimates of various components of the surface energy budget fromthe MODIS could not only serve as forcings to drive hydrologic

in the study is used over the Southern Great Plains (SGP) for a timeperiod covering all seasons of 2006. Current methodologies ofestimating Rn from remotely sensed data, which are restricted toclear sky conditions only, discard a large portion of the MODISoverpasses. Table 2 lists the number of acceptable clear sky and totaloverpasses for the MODIS-Terra over the SGP during 2006. Anacceptable clear sky overpass is dened as one for which 75% of theSGP was cloud free, thus it is a satisfactory candidate to which a clearsky Rn estimation methodology can be applied over the cloud-freeportion of the overpass. Only 24% and 9% of the MODIS-Terraoverpasses during day and night, respectively, were under acceptableclear sky conditions; thus for a large share of remotely sensed data,Rn cannot be computed with existing methodologies. The outline ofthis paper is as follows. Section 2 presents a framework to estimatenet radiation under all sky conditions by separately treating clear andcloudy pixels within a MODIS overpass. The study site and the dataused, including ground measurement and the MODIS data products,are described in Section 3. The results for instantaneous and dailyaverage net radiation using the MOD06_L2 product for cloudy daysare presented in Section 4; along with a framework to estimate net

1523G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534models, but also evaluate them. Numerous studies have demonstratedthe application of point-scale net radiation estimates, as well as,spatially distributed net radiation maps, derived from remote sensingdata, to estimate evapotranspiration (Batra et al., 2006; Kim & Hogue,2008; Nishida et al., 2003; Norman et al., 2003; Venturini et al., 2008).Recent studies that have used the MODIS data products to estimatecomponents of the surface radiation are summarized in Table 1. Wanget al. (2005) and Bisht et al. (2005) used near surface the MODIS dataproducts to produce estimates of various components of the surfaceenergy budget for clear days. While Wang et al. (2005) estimatedupwelling longwave radiation only; Bisht et al. (2005) producedestimates of all components of net radiation. Tang et al. (2006) usedstatistical regression to estimate surface shortwave budget for clearand cloudy conditions based on top of the atmosphere (TOA)reectance. Both Tang and Li (2008) and Wang and Liang (2009)used regression analysis of TOA radiance to obtain surface longwavebudget for clear sky days.

Here, we extend the framework developed by Bisht et al. (2005)to produce estimates of all components of the surface energy budgetusing the MODIS cloud product (MOD06_L2) under cloudy condi-tions. The cloud parameters from the MOD06_L2 product that is usedin this study include cloud top temperature, cloud fraction, cloudemissivity and cloud optical thickness. In addition, surface temper-ature at 5-km spatial resolution from the MOD06_L2 is also used toestimate upwelling longwave radiation. The methodology presented

Table 1Studies using theMODIS data to estimate various components of surface energy budget.

Study Quantitiesestimated

Skycondition

MODIS data products

Wang et al.(2005)

RL Clear MOD11B1

Bisht et al.(2005)

RL, RL

, RLnet, RS,

RS, RSnet_L2, Rn

Clear MOD03, MOD04_L2, MOD07_L2,MOD11_L2, MOD43B1

Tang et al.(2006)

RS, RS

, RSnet Clear andcloudy

MOD21KM, MOD03, MOD05_L2,MOD35

Tang and Li(2008)

RL, RL, RLnet Clear MOD21KM, MOD03, MOD35

Wang and Liang(2009)

RL, RL

, RLnet Clear MOD21KM, MYD021KM, MOD03,MYD03, MOD06_L2, MYD06,MOD07_L2, MOD11C3

Proposed study RL, RL

, RLnet, RS,

RS, RSnet, Rn

Clear andcloudy

MOD03, MOD04_L2, MOD06_L2,MOD07_L2, MOD11_L2, MCD43B3

RL downwelling longwave radiation; RL

upwelling longwave radiation; RS

downwelling shortwave radiation; RS upwelling longwave radiation; RLnet netnetlongwave radiation; RS net shortwave radiation; Rn net radiation.radiation for all sky conditions. We conclude with a discussion andnal remarks in Section 5.

2. Methodology to estimate net radiation

An all sky conditions methodology to estimate instantaneous anddaily average net radiation from the MODIS data is presented in thissection; while Fig. 1 outlines the owchart of the proposedmethodology. The pixels within a MODIS overpass for this studyare classied as clear sky pixels if 1-km LST estimate is available fromMODIS land surface temperature and emissivity product(MOD11_L2). Bisht et al. (2005) algorithm, briey mentioned inSection 2.1, is applied for clear sky pixels. For cloudy pixels, a newalgorithm is proposed to estimate instantaneous net radiation that ispresented in Section 2.2. The new cloudy sky algorithm usesMOD06_L2 data along with statistical regressions developed toestimate near-surface air and dew temperatures from the MOD06_L2LST.

2.1. Instantaneous net radiation: clear sky pixels with 1-km MOD11_L2LST available

Estimation of net radiation for clear sky pixels uses the algorithmof Bisht et al. (2005) and is presented here concisely. At the Earth's

Table 2Number of acceptable clear sky days (i.e. 75% or more of study site had no cloud cover)for the MODIS onboard the Terra satellite for the Southern Great Plains during 2006.Values in the parenthesis indicate the total number of the MODIS-Terra overpasses forthe SGP region.

Month Number of acceptableclear day-overpasses

Number of acceptableclear night-overpasses

January 09 (40) 04 (41)February 08 (38) 00 (39)March 06 (42) 02 (44)April 14 (40) 06 (43)May 12 (42) 06 (44)June 08 (38) 04 (38)July 09 (42) 03 (44)August 01 (40) 01 (43)September 14 (40) 02 (41)October 15 (39) 04 (39)November 14 (41) 05 (42)December 09 (41) 05 (42)Full-year 118 (483) 43 (500)

Fig. 1. Flowchart to estimate instantaneous and daily average net radiation from the MODIS data for all sky conditions.

1524 G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534

1525G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534surface, instantaneous Rnclear [W m2] for clear sky conditions can beexpressed in terms of downwelling and upwelling radiations as:

Rclearn = RclearS R

clearS + R

clearL R

clearL

= RclearS 1 + RclearL RclearL1

where RSclear, RS

clear, RLclear and RL

clear are downwelling shortwaveradiation [Wm2], upwelling shortwave radiation [Wm2], down-welling longwave radiation [W m2] and upwelling longwaveradiation [Wm2] for clear sky respectively; and is land surfacealbedo.

A parameterization scheme developed by Zillman (1972) is usedto estimate downwelling shortwave radiation using near-surfacevapor pressure, e0 [hPa], and solar zenith angle, [rad], as

RclearS =S0 cos

2 1:085 cos + e0 2:7 + cos 103 +

2

where is 0.1 and S0, is the solar constant at the top of atmospheric, is1367 [Wm2]. Niemel et al. (2001a) and Bisht et al. (2005) haveshown that Zillman's (1972) scheme tends to overestimate the down-welling shortwave radiation, thus we propose using a value of 0.2.

Downwelling longwave radiation is obtained from air emissivity, a,and air temperature, Ta [K], at near surface; while upwelling longwaverequires surface emissivity, s [], and surface temperature, Ts [K]. Airemissivity is parameterized using a scheme proposed by Prata (1996).Near-surface vapor pressure, e0 [hPa], is computed from dew pointtemperature, Td [K], using ClausiusClapeyron equation (Rogers & Yau,1989).

RclearL = aT4a 3a

a = 1 1 + exp 1:2 + 3

q 3b

=46:5Ta

e0 3c

e0 = 6:11 expLvRv

1273:15

1Td

3d

RclearL = sT4s 3e

where =5.67108 [W m2 K4] is the SteffanBoltzmannconstant, Lv=2.5106 [J kg1] is the latent heat of vaporizationand Rv=461 [J kg1 K1] is the gas constant for water vapor.

Bisht et al. (2005) used the following MODIS data products:geolocation data (MOD03 at 1 km); aerosol depth (MOD04_L2 at10 km); atmospheric prole data (MOD07_L2 at 5 km); land surfacetemperature and surface emissivity (MOD11_L2 at 1 km); and landsurface albedo (MOD43B1 at 1 km). The methodology of Bisht et al.(2005) used air and dew point temperatures from the MOD07_L2 atthe vertical pressure level of 1000 hPa as surrogates for near-surfacetemperatures. The land surface temperature and surface emissivityare obtained from the MOD11_L2 product. The land surface albedo iscomputed as a linear combination of black-sky albedo, bs and white-sky albedo, ws, provided in the MOD43B1 data product as (Luchtet al., 2000):

= 1S ; bs + S ; ws 4

where [] is the aerosol depth and S(, ) is the isotropic fractionrepresenting the state of the atmosphere between the extreme cases ofcompletely direct (black-sky) and diffuse (white-sky) illumination. Alook up table for computing the isotropic fraction was available from the

MODIS albedo products homepage. The solar zenith angle and aerosoloptical depth are obtained from MOD03_L2 and MOD04_L2 dataproducts, respectively. For a detailed description of the algorithm toestimate clear skynet radiation, readers are referred to Bisht et al. (2005).

Tang and Li (2008) argued that approximating air and dewtemperatures at 1000 hPa as near-surface temperatures maybeinappropriate due to variations caused by Earth's terrain andsuggested using the hydrostatic assumption in the atmosphere toestimate near-surface temperatures. Thus, in this study, we assume ahydrostatic atmosphere assumption to extrapolate Ta and Td providedat the lowest vertical pressure level from the MODIS atmosphericprole product to estimate near-surface Ta and Td. The hydrostaticatmospheric assumption can be written as:

dpdz

= g

PLPSz

= g: 5

where PL is the lowest pressure level of the MODIS atmospheric prolemeasurement; while PS is the surface pressure level obtained from theMODISdata. Theambient lapse rate is assumed tobeequal to6.5 K/km(Cosgrove et al., 2003) and can be used to relate temperature at thelowest pressure level, TaL, and near-surface temperature, TaS, as:

dTdz

= 6:50 K=km

TLaTSaz

= 6:50 K=km6

Combining Eqs. (5) and (6) and rearranging the terms, near-surface air temperature can be estimated as:

TSa = TLa +

6:50 K=kmg

PSPL

: 7

Even though the above equation is strictly applicable to air temper-ature, we additionally use it to estimate near-surface dew temperature.Near-surface Td is used to compute air emissivity through Eqs. (3b), (3c)and (3d); which is eventually used to estimate downwelling longwaveradiation as Eq. (3a). Thus, the retrieval of RL

clear is not very sensitive tonear-surface dewtemperature and justiesour estimationof near-surfaceTd using an identical approach as given by Eq. (7).

2.2. Instantaneous net radiation: cloudy pixels with 1-kmMOD11_L2 LSTunavailable

The net radiation, Rncloudy [Wm2], for cloudy pixels is dened as:

Rcloudyn = RcloudyS 1 + RcloudyL RcloudyL : 8

Under cloudy skies, the downwelling shortwave radiation, RScloudy

[W m2], is estimated as a linear combination of the uxes from clearsky and cloudy sky, weighted by cloud fraction, according to theparameterization proposed by Slingo (1989) as:

RcloudyS = RclearS 1fc + fcec = cos

h i9

where fc [] is the cloud fraction and [] is cloud optical thickness.The downwelling longwave radiation for cloudy conditions, RL

cloudy

[W m2], is estimated as a combination of downwelling radiationfrom near-surface conditions and clouds as proposed by Forman andMargulis (2007); while the upwelling longwave radiation, RL

cloudy

[W m2], for cloudy conditions follows the similar approach as duringclear sky conditions given by:

Rcloudy = T4 + 1 T4 10aL a a a c c

land surface temperature generally gets hotter than the ambient airand vice-versa during the night. Thus, we propose conductingseparate regression analysis to estimate air temperature offsetsduring day- and night-overpasses (Eqs. (11a) and (11b)). Numerousattempts have been made to estimate daily dew temperature fromminimum, maximum and daily air temperature (Hubbard et al., 2003;Kimball et al., 1997). Since in the present study, we obtain Ta undercloudy conditions itself through a regression analysis, we proposeestimating Td directly from Ts as given in Eq. (11c) and (11d) for day-and night-overpasses, respectively. The procedure to estimate thetemperature offsets are presented in Section 4.1.

1526 G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534RcloudyL = sT4s 10b

where c [] and Tc [K] are cloud emissivity and cloud temperature,respectively.

The proposed methodology of estimating Rncloudy requires numer-ous parameters regarding clouds. The Terra-MODIS cloud productprovides cloud optical depth at 1-km spatial resolution (for Eq. (9));while cloud emissivity (for Eq. (10a)), cloud top temperature (forEq. (10a)) and land surface temperature (for Eq. (10b)) are availableat the 5-km spatial resolution. Ideally for Tc in Eq. (10a) cloud basetemperature should be used, but the Terra-MODIS cloud product onlyprovides estimates of cloud top temperature. The authors acknowl-edge that using cloud top temperature instead introduces uncertaintyin the estimation of downwelling longwave radiation. Computation ofdownwelling longwave radiation requires surface air and dewtemperature (Eqs. (3b), (3c), (3d) and (10a)), which under clearsky are available at 5-km resolution from the MOD07_L2. For cloudyconditions, we estimate Ta and Td by subtracting o_sets from 5-km LSTprovided by the MOD06_L2 product, Ts06_L2, as:

Ta = T06 L2s

daya if day overpass 11a

Fig. 2. ARM ground stations within the Southern Great Plains in Oklahoma and Kansas.Stations in circles, triangle and squares had SIRS station only, EBBR station; and bothSIRS and EBBR stations respectively. The dashed box shows the SGP domain for thisstudy to which the MODIS overpass data is reprojected.Ta = T06 L2s

nighta if night overpass 11b

Td = T06 L2s

dayd if day overpass 11c

Td = T06 L2s

nightd if night overpass 11d

where aday [K] and anight [K] are offsets for air temperature during day-and night-overpasses; while dday [K] and dnight [K] are offsets for dewtemperature during day- and night-overpasses. During the day, the

Table 3The MODIS products used in this study.

MODIS product Short name Spatial resolution Parame

Geolocation product MOD03 1 km Solar zeAerosol product MOD04_L2 10 km OpticalCloud product MOD06_L2 1 km Cloud o

5 km Cloud etempera

Atmospheric prole product MOD07_L2 5 km Air temLand surface temperature and emissivity MOD11_L2 1 km SurfaceAlbedo product MCD43B3 1 km White-2.3. Daily average net radiation

Daily average net radiation estimates are more meaningful totalsthan instantaneous net radiation estimates. Methodologies aimed toestimate evapotranspiration from remote sensing data require dailyaverage net radiation values (Batra et al., 2006; Nishida et al., 2003;Norman et al., 2003; Venturini et al., 2008). Bisht et al. (2005)suggested a sinusoidal model to estimate the diurnal cycle of netradiation, which closely follows the framework for retrieving thediurnal cycle of surface temperature proposed by Lagouarde andBrunet (1983). The daily average net radiation, Rnavg [W m2], in termsof the instantaneous (clear or cloudy) net radiation estimate obtainedat local satellite overpass time, tovp, is given as (Bisht et al., 2005):

Ravgn =2Rn

sin tovptrisetsettrise

12

where trise and tset corresponds to local time when Rn becomes positiveand negative, respectively. It should be pointed out that trise and tset arerelated to the local sunrise and sunset time; and were approximated as1 h after local sunrise time and 1 hbefore local sunset time, respectively.In the present work, daily average net radiation is estimated using asingle instantaneous net radiation retrieval. The authors acknowledgethat the sinusoidal approximation of net radiation may not accuratelycapture the diurnal variation of Rn for days when cloud cover waspresent during a portion or entire day. The use of data from polar-orbiting satellite only, as done in this study, highlights the limitation ofin retrievingdiurnal cycle of net radiation.Observations from theMODISsensor onboardofAqua satellitewould serve as additional data source toimprove the estimation of Rnavg and has been separately pursued by theauthors (Bisht and Bras, submitted for publication). But additionalremote sensing data from geostationary satellites is needed toaccurately capture the diurnal variation of net radiation.

3. Study site and data used

The proposed methodology of estimating net radiation undercloudy conditions from the MODIS data is applied over the SouthernGreat Plains region (SGP). The SGP covers southern part of Kansas andmost of Oklahoma, extending from 34.5 to 38.5N and95.5 to99.5W, as shown in Fig. 2. The dashed box in Fig. 2 corresponds to the

ters used Clear sky algorithm Cloudy sky algorithm

nith angle, latitude and longitude x xdepth xptical depth xmissivity, cloud fraction, cloud topture, and land surface temperatureperature and dew temperature xtemperature and surface emissivity xand black-sky albedo x x

grid, with interval of 0.009, to which each MODIS overpass data wasreprojected. The region has a relatively at terrain with heterogenousland cover (Batra et al., 2006). The Atmospheric Radiation Measure-ment (ARM) program funded by U.S. Department of Energy,maintains continuous measurements of various meteorological andsurface variables. In this study, we utilized data from Energy BalanceBowen Ratio (EBBR) stations and Solar and Infrared RadiationStations(SIRS). The spatial distribution of ground stations within the SGP,along with the data-typemeasured at each location, is shown in Fig. 2.EBBR stations provided measurements of air temperature and vaporpressure (which is used to compute dew temperature) at 2.05 mabove the land surface; while SIRS recorded upwelling and down-welling shortwave, as well as, longwave radiation. The local sunriseand sunset times for the study region are obtained from the website ofUS Naval Observatory, Astronomical Application Department (http://aa.usno.navy.mil/), which are used in estimating daily average netradiation.

A detail description about the MODIS data products used for clearsky algorithm is presented in Bisht et al. (2005). Additionally, in the

present study we utilize the MOD06_L2 product. In the MOD06_L2product, cloud top temperature, cloud emissivity and cloud fractionare estimated at 5-km resolution from a CO2 slicing technique usingthe MODIS channels 31 (11.03 m), 33 (13.34 m), 34 (13.64 m), 35(13.94 m) and 36 (14.24 m) (Menzel et al., 2006). Cloud opticalthickness is estimated at 1-km resolution from the MODIS channel 1(0.645 m) which exploits the fact that the reection function ofclouds at a nonabsorbing band in the visible wavelength region isprimarily a function of the cloud optical thickness (King et al., 1998).The 5-km LST available from the MOD06_L2 product is obtained fromvarious sources including the MOD11_L2 product, National Centersfor Environmental Prediction (NCEP) gridded analysis and DataAssimilation Ofce (DAO) data (for details see King et al. (1998)). InSection 4.1, we examine the accuracy of 5-km MOD06_L2 LST data.The various MODIS data products, along with their spatial resolutionand parameters used, are summarized in Table 3. All the MODIS dataproducts are available in Hierarchical Data Format (HDF) and areobtained from the NASA's Warehouse Inventory Search Tool (WIST)website.

atacomde

1527G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534Fig. 3. Comparison of 5-km land surface temperature (LST) from the MODIS cloud dobservation during day- and night-overpasses, respectively; panels (c) and (d) areoverpasses; and; panels (e) and (f) are comparison of MOD06_L2 LST against observed

minus observed values.product (MOD06_L2): panels (a) and (b) are comparison of MOD06_L2 LST againstparison of MOD06_L2 LST against observed air temperature during day- and night-w temperature during day- and night-overpasses. Bias is computed as LST-MOD06_L2

4. Results

4.1. Temperatures: land surface, air and dew

In this section, we compare the 5-km land surface temperatureobtained from the MOD06_L2 product against ground measurements.

Furthermore, the temperature offsets mentioned in Eqs. (11a), (11b),(11c) and (11d) to estimate air and dew temperature under cloudyconditions are also obtained. Direct measurements of LST weren'tavailable, thus measurements of upwelling longwave by SIRS stationswere converted to obtain surrogate observations of LST using Eq. (3e),while assuming a constant surface emissivity of 0.98. The scatter plot

Table 4Bias, root mean square errors (RMSE), correlation (R2) and number of data points for various quantities given or derived from the MODIS data and ground observations. Bias iscomputed as the MODIS data minus observed data.

MODIS data Observation data Overpass time Sky condition Bias RMSE R2 Number of data points

5-km land surface temperature from MOD06_L2 Land surface temperature Day Clear+Cloudy 1.62 3.80 0.95 8261Night Clear+Cloudy 0.19 2.54 0.97 8320

Near-surface air temperature (Ta) Day Clear+Cloudy 4.5 2.76 0.97 4710Night Clear+Cloudy 0.51 2.12 0.98 5240

Near-surface dew temperature (Td) Day Clear+Cloudy 16.01 5.00 0.86 3347Night Clear+Cloudy 7.18 4.94 0.87 2927

Near-surface Ta from MOD07_L2 Day Clear 3.47 2.93 0.95 590Night Clear 0.85 2.46 0.96 251

Near-surface Td from MOD07_L2 Day Clear 16.45 6.08 0.79 605Night Clear 8.73 3.17 0.94 256

1528 G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534Fig. 4. Comparison of 5-km land surface temperature (LST) from the MOD06_L2 producatmosphere assumption. Panels (a) and (b) are comparison of MOD06_L2 with near-surfacecomparison of MOD06_L2 with near-surface dew temperature from MOD07_L2 during dayt with near-surface air and obtained from the MOD07_L2 product under hydrostaticair temperature fromMOD07_L2 during day- and night-overpass; panels (c) and (d) are- and night-overpass.

between Ts06_L2 and ground observations is shown in Fig. 3(a) and (b)for day- and night-overpasses. The bias, root mean square error(RMSE) and correlation (R2) between Ts06_L2 and ground observationsare summarized in Table 4. In this study, the bias is computed as theMODIS data minus in-situ observations (the same denition is alsoused when we report values of bias from any other study). RecentlyWang et al. (2008) compared clear sky nighttime surface tempera-tures provided by another MODIS product, MOD07_L2 over eightground locations (six in U.S. and two in Germany). They reportedbiases in MOD07_L2 LST that varied between 3.38 [K] to 3.14 [K];while RMSE ranged from 1.97 [K] to 4.10 [K]. Thus, the surfacetemperature estimates from the MOD06_L2 are not only comparableto those obtained from theMOD07_L2, but have an advantage of beingavailable for all sky conditions, while MOD07_L2 LST are produced foronly clear sky pixels.

Air and dew temperatures, needed to compute downwellinglongwave radiation, are estimated as offsets from Ts06_L2. EBBRmeasurements of vapor pressure at 2.05 m above land surface areconverted to Td measurements for comparison purposes. Scatterplotof Ts06_L2 and Ta during day- and night-overpasses is shown in Fig. 3(c)and (d); while Fig. 3(e) and (f) shows the scatter plot between Ts06_L2

and Td for day- and night-overpasses. Bias, RMSE and R2 aresummarized in Table 4. The RMSE and R2 between Ts06_L2 and Ta forboth day- and night-overpasses are better than those between Ts06_L2

and Ts; while statistical agreement between Ts06_L2 and Td is not asstrong (higher RMSE and lower R2). Sensitivity analysis of down-

welling longwave radiation with respect to dew temperature hasshown that errors in Td up to 5 [K] (which of the order of RMSEbetween Ts06_L2 and Td) result in errors of about 15 [Wm2] in theestimation of downwelling longwave radiation, which are signicant.The present methodology could certainly benet from a moreaccurate estimate of dew temperature under cloudy conditionsbased solely on remotely sensed information in the future. Thetemperature offsets used in Eqs. (11a), (11b), (11c) and (11d) areestimated as biases from scatter plots as:

daya = 4:35 K 13a

nighta = 0:51 K 13b

dayd = 16:01 K 13c

nightd = 7:18 K : 13d

The above estimates of temperature offsets rely on ancillarysurface measurements and such measurements are sparse globally.We also present an alternate approach to estimate temperatureoffsets that does not require surface measurements. Thus, theproposed framework of estimating Rn can rely exclusively on remotesensing information when surface measurements regarding air anddew temperatures are absent. The comparison of near-surface air and

r clo

1529G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534Fig. 5. Error histograms between observed and estimated components of net radiation fo

(d) downwelling shortwave; (e) upwelling shortwave; and (f) net shortwave radiation. Biaudy overpasses: (a) downwelling longwave; (b) upwelling longwave; (c) net longwave;

s is computed as estimated minus observed values.

Fig. 6. Comparison of estimated and observed net radiation for cloudy overpasses.Circles and triangles represent day- and night-overpasses of the MODIS. Bias iscomputed as estimated minus observed values.

1530 G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534dew temperatures (using a hydrostatic assumption in the atmo-sphere) from the MOD07_L2 data with Ts06_L2, under clear skyconditions, are shown in Fig. 4. The temperature offsets computedas biases from the scatter plot as:

day; cleara = 3:47 K 14a

night; cleara = 0:85 K 14b

day; cleard = 16:45 K 14c

night; cleard = 8:73 K : 14d

where the superscript emphasizes that these offsets are obtainedunder clear sky conditions. The difference in temperature offsets

Table 5Bias, root mean square errors (RMSE), correlation (R2) and number of data points forvarious quantities given or derived from the MODIS data and ground observations. Biasis computed as MODIS data minus observed data.

Sky condition Componentof the surfaceenergy budget

Overpasstime

Bias RMSE R2 Number ofdata points

Cloudy RL Day+Night 0.28 19.34 0.95 3552RL Day+Night 1.05 16.11 0.98 3552

Net RL Day+Night 1.33 21.99 0.75 3552RS Day 25.64 66.52 0.92 1156

RS Day 5.41 19.14 0.81 1156

Net RS Day 20.24 54.89 0.93 1156Instantaneous Rn Day 35.16 50.58 0.95 1156

Night 5.23 17.72 0.33 2396Day+Night 7.91 37.44 0.99 3552

Daily average Rn 34.00 37.72 0.93 1152Clear RL Day+Night 3.87 20.79 0.93 1653

RL Day+Night 2.50 15.76 0.98 1653

Net RL Day+Night 6.37 19.37 0.86 1653RS Day 17.82 42.05 0.96 1097

RS Day 17.40 17.79 0.79 1097

Net RS Day 35.22 40.78 0.96 1097Instantaneous Rn Day 23.08 39.34 0.96 1118

Night 3.72 11.51 0.51 476Day+Night 16.19 34.60 0.99 1594

Daily average Rn 11.27 31.98 0.93 991obtained from surface measurements and the MOD07_L2 productduring the day and night are 1 [K] and 1.5 [K], respectively. InSection 4.2, the results regarding various components of the surfaceenergy budget under cloudy skies use temperature offsets obtainedfrom surface measurements, as presented in Eqs. (13a)(13d). Theoverall impact of using temperature offsets obtained under clear skyconditions (Eqs. (14a)(14d)) to estimate net radiation is alsopresented in Section 4.2.

4.2. Instantaneous and daily average net radiation: under cloudy skiescondition

Next, we present results of instantaneous Rn obtained using dataabout cloud properties and 5-km surface temperature from theMOD06_L2 product; along with geolocation (MOD03), surface albedodata (MCD43B3) and temperature offsets obtained in Section 4.1.Under clear sky conditions, a higher resolution 1-km LST MOD11_L2product is available and the MOD07_L2 provides direct estimates of Taand Td at 20 vertical pressure levels. The MODIS overpasses that weredeemed as under clear sky in 2006, listed in Table 2, were omittedfrom the analysis presented here.

The error histogram between estimated and in-situ measurementsof downwelling, upwelling and net radiation for shortwave andlongwave is shown in Fig. 5; while the summary of bias, RMSE and R2

are presented in Table 5.The biases from individual components of netradiation were not corrected before computing instantaneous netradiation. Tang and Li (2008) reported an overall bias, RMSE and R2 forclear sky RL for the Surface Radiation Budget Network (SURFRAD)locations in U.S. as 20.3 [W m2], 30.1 [W m2] and 0.91,respectively; while clear sky net longwave radiation, RLnet, statisticswere11.7 [Wm2], 26.1 [Wm2] and 0.94. Wang and Liang (2009)similarly estimated clear sky RL and clear sky RLnet for SURFRAD locationsinU.S. fromtheTerra andAqua satellites.Overall biasbyWangand Liang(2009) for RL and RLnet from the Terra satellite were0.40 [Wm2] and2.80 [Wm2];while RMSEwere 17.60 [Wm2] and 17.72 [Wm2].Thus, the longwave radiation estimates presented in this section arecomparable to those reported in literature, while having an addedadvantage of being availableunder cloudy conditions, though at a coarse5-km resolution. Wang et al. (2008) estimated net surface shortwaveradiation using TOA reectance and obtained RMSE under clear andcloudy skies of 20 [Wm2] and 35 [Wm2], respectively. The RMSEbetween the estimated and observed albedo (not shown here) is0.02Fig. 7. Comparison of daily average estimated and observed net radiation for cloudyoverpasses. Bias is computed as estimated minus observed values.

1531G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534[], which is9% of themean value; while the bias and R2 are less than1% of the mean value and 0.87, respectively.

The comparison of instantaneous Rn estimates with groundmeasurements during day- and night-overpasses are shown in Fig. 6.The bias, RMSE and R2, including day- and night-overpasses, are 10.46[Wm2], 38.70 [Wm2] and 0.99. The R2 between estimated andmeasured Rn during the night-overpass is signicantly lower (0.32)when compared to day-overpasses (0.95), as summarized in Table 4.Analysis shows that major source error in estimating instantaneous Rncomes from the over estimation of downwelling solar radiation whencompared to observations. The use of temperature offsets obtainedunder clear sky conditions only (Eqs. (14a)(14d)) has little impact onRn estimates, including day- and night-overpasses, with an overallbias, RMSE and R2 as 3.28 [W m2], 40.49 [W m2] and 0.99,respectively. Fig. 7 shows the scatter plot between estimated dailyaverage net radiation and ground observations. The bias, RMSE and R2

between estimated daily average net radiation and ground observa-tions were 22.75 [Wm2], 34.11 [Wm2] and 0.95. Overall theproposed methodology is successfully able to estimate instantaneousand daily average net radiation from MOD06_L2 for 2006. Further-more, when the use of ancillary ground measurements in estimatingtemperature offsets is excluded, the impact on Rn estimates is minor.

4.3. Instantaneous estimates of net radiation: Under all sky conditions

In 2006, a large portion of the MODIS-Terra overpasses over theSGP were contaminated by the presence of clouds. Only 24% of day-

Fig. 8. Error histograms between observed and estimated radiations for clear sky overpasses: (shortwave; (e) upwelling shortwave; and (f) net shortwave radiation. Bias is computed as eoverpasses and 9% of night-overpasses had 75% or more of the SGPregion as cloud free. Thus, the methodologies that focus on retrievingnet radiation during clear sky days are not applicable to a large portion

a) downwelling longwave; (b) upwelling longwave; (c) net longwave; (d) downwellingstimated minus observed values.

Fig. 9. Comparison of estimated and observed net radiation for clear sky overpasses.Circles and triangles represent day- and night-overpasses of the MODIS. Bias iscomputed as estimated minus observed values.

of the MODIS-Terra overpasses. In the previous section, we success-fully demonstrated that for cloudy days, the MOD06_L2 product canbe used to estimate Rn, albeit at a coarser 5-km spatial resolutionwhen compared to 1-km Rn estimates available under clear skyconditions. Before proceeding to present the framework of estimatingRn for all sky conditions, the results obtained using the approach ofBisht et al. (2005) under clear sky conditions for 2006 are presented

for the sake of completeness. Fig. 8 shows the error histogramsbetween estimate and in-situ measurements for the various compo-nents of longwave and shortwave energy budget; while Figs. 9 and 10present results for instantaneous and daily average Rn. The statisticalsummary of the results for components of the surface energy budgetunder clear sky conditions is given in Table 5.

It is then possible to use the high resolution (1-km) clear skiesalgorithmwith the lower resolution (5-km) cloudy skies algorithm tosuggest an all-sky conditions methodology to estimate instantaneousand daily net radiation as shown in Fig. 1. An example of this mergedframework to the MODIS-Terra overpass on 24th July, 2006, at 17:35UTC is shown in Fig. 11. Clouds are present in eastern and south-western part of the SGP and occupy23% the SGP domain. In Fig. 11(b) and (c), estimates of Rn are shown for the clear sky and cloudyregion of the image. Finally the merged Rn map is shown in Fig. 11(d).Similarly, Fig. 12 demonstrates the application of merged frameworkto estimate Rn when71% of the SGPwas covered with clouds for theMODIS-Terra overpass on 6th July, 2006 at 17:45 UTC. The strength ofthe proposed approach is that it can rely solely on remote sensing dataand thus can be applied to globally. In this study we have only utilizedthe MODIS data from the Terra satellite; data from the Aqua satellitewould provide an additional estimate of Rn.

5. Summary

The MODIS sensor on the Aqua and Terra satellites providesvarious data products about the Earth's land surface, atmosphere,cryosphere and ocean. The MODIS data products have large spatialfootprint as compared to sparse ground observations. The surfaceenergy budget plays a signicant role in landatmosphere

Fig. 10. Comparison of daily average estimated and observed net radiation for clear skyoverpasses. Bias is computed as estimated minus observed values.

1532 G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534Fig. 11. Instantaneous estimation of net radiation (Rn) from the MODIS-Terra for all sky condSGP; (b) estimate of Rn using clear sky algorithm (white region represents no data due to clonly; and (d) estimate of Rn for all sky conditions obtained by merging (b) and (c).itions on 24th July, 2006 at 17:35 UTC. (a) Cloud fraction fromMOD06_L2 data over theoud cover); (c) estimate of Rn using cloudy sky algorithm for the cloud covered portion

1533G. Bisht, R.L. Bras / Remote Sensing of Environment 114 (2010) 15221534interactions, thus numerous studies have attempted to estimate thesurface energy budget or its components from the MODIS data. Suchattempts until now have been mostly limited to cloud-free days andthus a large share of the MODIS overpasses is discarded. In this paperwe present a methodology that overcomes the restriction of cloud-free condition to estimate net radiation using the MODIS-Terra data.We employ the MODIS cloud product to provide information aboutcloud top temperature, cloud fraction, cloud emissivity, cloud opticalthickness and land surface temperature for cloud covered regionswithin a MODIS overpass. A statistical regression, using ancillaryground measurements, is applied to5-km MOD06_L2-LST in order toobtain near-surface air and dew temperatures. In absence of ancillaryground measurements, a similar statistical regression can be obtainedby using the MOD07_L2 product, thus presenting a framework thatcan exclusively utilize remote sensing information.

Downwelling shortwave radiation is obtained as a linear combi-nation of cloud-free and cloudy radiation weighted by cloud fractionfollowing the approach of Slingo (1989). The estimate of downwellinglongwave radiation has a component dependent on near-surfaceconditions along with an inuence of clouds as suggested by Formanand Margulis (2007). Upwelling shortwave and longwave radiationuses land surface albedo data and 5-kmMOD06_L2-LST data. In orderto appraise howwell the estimates of Rn from theMOD06_L2 perform,the methodology is applied over the SGP for 2006. The Rn estimatesfrom this study are shown to be comparable to other existingmethodologies, while apparently having an advantage of beingapplicable to cloudy days. Finally, a framework to estimate Rn fromtheMODIS under all sky conditions is proposed bymerging the higherresolution methodology (1-km) outlined by Bisht et al. (2005) forclear sky pixels of the overpass and the present low resolutionmethodology (5-km) for cloudy pixels. Two applications of the

Fig. 12. Same as Fig. 11 except for the MODIS-Teproposed methodology are demonstrated for the MODIS-Terraoverpass on 6th July, 2006 and 24th July, 2006 that had 71% and23% cloud cover for the SGP respectively. In Bisht and Bras (submittedfor publication), authors further examine the retrieval accuracy of thepresent all-sky Rn methodology using data from the SURFRADnetwork in U.S. which provides radiation observations at sevenlocations, apart from the SGP. Additional data from the MODIS-Aqua,along with an extension of the present framework to estimate Rn overthe Continental United States is also presented in Bisht and Bras(submitted for publication).

Acknowledgements

This work has been supported by the National Aeronautics andSpace Administration (contract NNG05GA17G), the National Oceanicand Atmospheric Administration (contract NA06OAR4310059) andthe Martin Family Society of Fellows for Sustainability at theMassachusetts Institute of Technology. The authors also thank twoanonymous reviewers for their helpful comments that eventually leadto an overall improvement of the manuscript.

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Estimation of net radiation from the MODIS data under all sky conditions: Southern Great Plains.....IntroductionMethodology to estimate net radiationInstantaneous net radiation: clear sky pixels with 1-km MOD11_L2 LST availableInstantaneous net radiation: cloudy pixels with 1-km MOD11_L2 LST unavailableDaily average net radiation

Study site and data usedResultsTemperatures: land surface, air and dewInstantaneous and daily average net radiation: under cloudy skies conditionInstantaneous estimates of net radiation: Under all sky conditions

SummaryAcknowledgementsReferences