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Estimation of Daytime Net Radiation from Shortwave Radiation Measurementsand Meteorological Observations
KAICUN WANG AND SHUNLIN LIANG
Department of Geography, University of Maryland, College Park, College Park, Maryland
(Manuscript received 1 February 2008, in final form 2 September 2008)
ABSTRACT
Changes in surface net radiation Rn control the earth’s climate, the hydrological cycle, and plant photo-
synthesis. However, Rn is not readily available. This study develops a method to estimate surface daytime Rn
from solar shortwave radiation measurements as well as conventional meteorological observations (or sat-
ellite retrievals) including daily minimum temperature, daily temperature range, and relative humidity, and
vegetation indices from satellite data. Measurements collected at 22 U.S. and 2 Tibetan Plateau, China, sites
from 2000 to 2006 are used to develop and validate the method. Land cover types include desert, semidesert,
croplands, grasslands, and forest. Site elevations range from 98 to 4700 m. The results show that the method
estimates Rn under clear and cloudy conditions accurately over a range of land cover types, elevations, and
climates without requiring local calibration. The results show that the method estimates Rn accurately. The
bias varies from 27.8 to 9.7 W m22 (63% in relative value) for different sites, and the root-mean-square
error ranges from 12.8 to 21 W m22 (from 15% to 19% in relative value) for different sites, with an average
of 16.9 W m22 (16% relative) for all sites. The correlation coefficient for all sites is about 0.99. The cor-
relation coefficient between the measured and predicted annual anomaly (year average subtracted from
multiyear average) in daytime Rn is as high as 0.91, demonstrating that the method accurately estimates long-
term variation in Rn.
1. Introduction
Surface net radiation Rn is the sum of incident down-
ward and upward shortwave and longwave radiation:
Rn 5 S# � S"1 L# � L"5 S#(1� a) 1 L# � L"
5 Sn 1 L# � L", (1)
where S# and S" are the surface downward and upward
shortwave radiation, L# and L" are the surface down-
ward and upward longwave radiation, a is surface al-
bedo, and Sn is surface net shortwave radiation.
The downward components of Rn are controlled by
solar zenith angle (i.e., time of day, season, and latitude),
cloud amount, atmospheric water vapor amount, and
aerosol loading; in turn, Rn demonstrates a substantial
daily and seasonal variation. The upward components of
Rn are controlled by ground surface characteristics in-
cluding snow/ice coverage, vegetation coverage, and soil
moisture content (Wang et al. 2005b, 2007b). Most
previous studies only focus on the changes in shortwave
radiation (e.g., Pinker et al. 2005; Wild et al. 2005),
presumably because longwave radiation is not conven-
tionally measured. The objective of this study is to de-
velop a new method to estimate Rn, especially for cli-
mate study.
Numerous studies estimated L# using conventional
meteorological observations (Malek 1997; Niemela
et al. 2001; Jin et al. 2006; Bilbao and de Miguel 2007;
Kjaersgaard et al. 2007b; Lhomme et al. 2007). Results
to date show that most methods require long-term
longwave radiation observations for local calibration
(Jin et al. 2006; Bilbao and de Miguel 2007; Kjaersgaard
et al. 2007a; Lhomme et al. 2007). Air temperature and
water vapor profile retrievals from satellite observations
have also been used to estimate L# (Ellingson 1995;
Diak et al. 2004; Bisht et al. 2005; Zhou et al. 2007).
Wang and Liang (2008) estimated L# using only Mod-
erate Resolution Imaging Spectroradiometer (MODIS)
top of atmosphere radiance, but their method is suitable
only for clear-sky conditions. Quantifying cloud effects
is the main difficulty in estimating L# under cloudy
Corresponding author address: Kaicun Wang, Department of
Geography, University of Maryland, College Park, College Park,
MD 20742.
E-mail: kcwang@umd.edu
634 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48
DOI: 10.1175/2008JAMC1959.1
� 2009 American Meteorological Society
conditions (Ellingson 1995). Satellite sensors can mon-
itor the temperature of the cloud top; however, the
cloud-base temperature is the critical parameter con-
trolling L# at the earth’s surface under cloudy condi-
tions. Accuracies of the various methods vary, with the
error ranging from about 10 to 20 W m22 for instanta-
neous clear-sky L#, degrading to 20–40 W m22 for
cloudy conditions (Diak et al. 2004).
Liang (2004), Wang et al. (2005a), Zhang et al. (2007),
and Wang and Liang (2008) calculated L" from surface
temperature Ts and broadband emissivity using the
Stefan–Boltzmann law. Wang et al. (2005a) and Jin and
Liang (2006) developed methods to estimate broadband
emissivity and L" from MODIS Ts products. However,
these methods are unsuitable under cloudy conditions
when Ts is unavailable.
Rather than estimating L# and L" individually to esti-
mate Rn, we propose to estimate Rn directly. Long-term
global surface solar shortwave radiation measurements
enable us to develop a new method to estimate Rn.
Kjaersgaard et al. (2007a) compared six existing models
for calculating daytime Rn from solar shortwave radia-
tion using meteorological data at two temperate sites.
They concluded that local calibration of the models with
at least 5 years of data is essential to obtain stable cal-
ibration coefficients. However, all six methods failed
to consider surface characteristics, such as vegetation
cover fraction, that have substantial effects on surface
energy partitioning into latent heat and sensible heat
fluxes (Wang et al. 2007c; Wang and Liang 2008), which,
in turn, affect Ts and L" (Wang et al. 2006, 2007b).
Therefore, based on analysis of available long-term
measurements, we propose a robust method to estimate
Rn from solar radiation data using satellite and con-
ventional meteorological observations. Surface incident
solar radiation is conventionally observed globally (e.g.,
Gilgen and Ohmura 1999; Wild et al. 2005) and can also
be estimated from satellite observations (e.g., Diak and
Gautier 1983; Pinker and Ewing 1985; Dedieu et al.
1987; Li et al. 1993; Ceballos et al. 2004; Liang et al.
2006, 2007). The strength of this method is that it ac-
curately estimates Rn for a wide variety of land cover
types and climates and a range of surface elevations,
without local calibration.
2. Data
The two most important criteria for data and site se-
lection in this study are 1) the quality of Rn data and the
corresponding meteorological observations and 2) the
long-term continuity of data; surface elevation, land
cover types, and climate zone of the sites are also con-
sidered. The 24 sites selected are the 14 Energy Balance
Bowen Ratio sites of the Enhanced Facility of the At-
mospheric Radiation Measurement (ARM) Program
supported by the U.S. Department of Energy, 7 Surface
Radiation Budget Network (SURFRAD) sites suppor-
ted by the National Oceanic and Atmospheric Adminis-
tration (NOAA), 1 AmeriFlux forest site, 1 Asian Auto-
matic Weather Station Network Project (ANN) site sup-
ported by the Global Energy and Water Cycle Experiment
(GEWEX) Asian Monsoon Experiment (GAME), and
1 site supported by the Japanese Experiment on Asian
Monsoons (JEXAM) and the Frontier Observational
Research System for Global Change (FORSGC), Uni-
versity of Tokyo, and Kyoto University (Table 1).
The nature of the ARM, SURFRAD, AmeriFlux,
ANN, and JEXAM projects ensures that the data are
some of the best quality currently available. The quality
of the data used in this study is carefully checked, and
quality control flags are supplied before the data are
released by data centers. The primary objective of
SURFRAD is to support climate research with accurate,
continuous, long-term measurements of the surface ra-
diation budget over the United States (http://www.srrb.
noaa.gov/), whereas ARM uses clustered measurements
over a limited area for process-oriented studies (http://
www.arm.gov/). GAME ANN was implemented to un-
derstand the role of the Asian monsoon in the global
energy and water cycle (http://aan.suiri.tsukuba.ac.jp/
aan.html). AmeriFlux aims to quantify spatial and tem-
poral variation in carbon storage in plants and soils, and
exchanges of carbon, water, and energy in major vege-
tation types; the accuracy of radiation measurements is
not as high as that of SURFRAD measurements.
The data used in this study are highly accurate in large
part because of well-calibrated sensors. Measurement
accuracy is about 6% for shortwave radiation measure-
ments and about 2.5% for longwave radiation for obser-
vations at the sites. The SURFRAD project and Gaize
sites (http://www.srrb.noaa.gov/surfrad/getcals.html;
Wang et al. 2004, 2005b) carefully calibrate their sensors
annually. All SURFRAD and ARM data are carefully
checked, and quality-control information is supplied
with the data (ftp://ftp.srrb.noaa.gov/pub/data/surfrad/
and http://www.archive.arm.gov/). Internet sites listed
in this paragraph provide sensor information and
measurement accuracies for all sites except the Gaize
site; Wang et al. (2004, 2005b) provide information on
the Gaize site.
We have successfully used data from SURFRAD,
ARM, AmeriFlux, and the Gaize site to validate radiation
and albedo retrievals and to estimate physical processes
confirming the data quality and accuracy. We have suc-
cessfully used radiation and meteorological data collected
by ARM and AmeriFlux to estimate evapotranspiration
MARCH 2009 W A N G A N D L I A N G 635
(Wang et al. 2007c; Wang and Liang 2008) and evap-
orative fraction and light use efficiency (Wang et al.
2006, 2008). Wang et al. (2008) used SURFRAD radi-
ation measurements to successfully validate satellite
shortwave and longwave radiation retrievals (Wang and
Liang 2008, manuscript submitted to Remote Sens.
Environ.). Wang et al. (2004) successfully used Gaize-
site shortwave radiation measurements to validate sat-
ellite albedo retrievals, and Wang et al. (2005a) used
Gaize longwave radiation measurements to develop a
satellite L" algorithm.
We selected sites for this study that include a number
of land cover types, climates, and elevations ranging
from 98 to 4700 m to ensure the applicability of our
method (Table 1). All sites are located in the United
States except for two sites located on the Tibetan Pla-
teau, China. Land cover types include desert, semides-
ert, cropland, grassland, and forests. Most sites selected
for this study are pasture and grassland. Collection of
accurate S" and L" over relatively low stand pasture
and grassland vegetation is considerably easier than
over high-stand forested areas, and therefore only one
forest site is included in this study. Because high-quality
desert datasets are scarce because of the difficulty in
collecting long-term continuous measurements over des-
ert, only one desert site (Desert Rock, Nevada) and one
semidesert (Gaize, China) site are included in this study.
The problem with deserts is that sensors are not
consistently maintained for long time periods. There-
fore, long-term continuous desert measurements are
seldom available. Previous experience shows that the
strong daytime solar radiation and low nighttime tem-
peratures affect the performance of pyrgeometers
(Wang et al. 2007a). To measure upward shortwave
radiation and longwave radiation accurately, the mea-
surement height is required to be about 10 m above the
surface. For forest sites (typically 20–40 m above the
ground surface), the tower is required to be very high.
Therefore, most forest sites do not supply upward ra-
diation measurements.
Except for the two Tibetan Plateau sites at which Ts
is measured directly, Ts is calculated from L" and L#measurements:
Ts 5 [L" � (1� «)L#]/s«� �1/4
, (2)
where s is the Stefan–Boltzmann constant (5.67 3 1028
W m22 K24) and « is the surface broadband emissivity,
which is obtained from MODIS narrowband emissivi-
ties in the thermal infrared region from the MODIS
day/night Ts products (Wang et al. 2005b):
TABLE 1. A description of the data measurement sites used in this study. Ratio Rn /Sn and RH are 30-min-average values. MODIS
NDVI is the 16-day averaged product. We calculated the multiyear average values from 30-min-average values to characterize the
climatological behavior of the sites.
Site Lat, lon Land cover
Height
(km) Rn /Sn NDVI RH (%) Project
Time
period
Hillsboro, KS: EF02 38.318N, 97.308W Grass 0.447 0.74 0.47 60 ARM 2002–06
Plevna, KS: EF04 37.958N, 98.338W Rangeland (ungrazed) 0.513 0.75 0.40 58 ARM 2002–06
Elk Falls, KS: EF07 37.388N, 96.188W Pasture 0.283 0.76 0.55 64 ARM 2002–06
Coldwater, KS: EF08 37.338N, 99.318W Rangeland 0.664 0.74 0.35 58 ARM 2002–06
Ashton, KS: EF09 37.138N, 97.278W Pasture 0.386 0.77 0.44 61 ARM 2002–06
Pawhuska, OK: EF12 36.848N, 96.438W Native prairie 0.331 0.77 0.53 62 ARM 2002–06
Lamont, OK: EF13 36.618N, 97.498W Pasture and wheat 0.318 0.77 0.45 58 ARM 2002–06
Ringwood, OK: EF-15 36.438N, 98.288W Pasture 0.418 0.73 0.43 57 ARM 2002–06
Morris, OK: EF18 35.698N, 95.868W Pasture 0.217 0.77 0.53 62 ARM 2002–06
El Reno, OK: EF19 35.568N, 98.028W Pasture (ungrazed) 0.421 0.76 0.50 59 ARM 2002–06
Meeker, OK: EF20 35.568N, 96.998W Pasture 0.309 0.77 0.50 60 ARM 2002–06
Cordell, OK: EF22 35.358N, 98.988W Rangeland (grazed) 0.465 0.74 0.38 55 ARM 2002–06
Cement, OK: EF26 34.968N, 98.088W Pasture 0.400 0.75 0.49 58 ARM 2002–06
Earlsboro, OK: EF27 35.278N, 96.748W Pasture 0.300 0.75 0.50 58 ARM 2003–06
Bondville, IL 40.058N, 88.378W Crop 0.213 0.78 0.38 66 SURFRAD 2000–06
Boulder, CO 40.138N, 105.248W Grass 1.689 0.67 0.29 45 SURFRAD 2000–06
Desert Rock, NV 36.638N, 116.028W Desert 1.007 0.63 0.15 25 SURFRAD 2000–06
Fort Peck, MT 48.318N, 105.108W Grass 0.634 0.70 0.23 58 SURFRAD 2000–06
Goodwin Creek, MS 34.258N, 89.878W Pasture land 0.098 0.78 0.54 63 SURFRAD 2000–06
‘‘Penn State,’’ PA 40.728N, 77.938W Crop, forest 0.376 0.76 0.48 64 SURFRAD 2000–06
Sioux Falls, SD 43.738N, 96.628W Grass land 0.473 0.77 0.41 66 SURFRAD 2003–06
Amdo, China 32.148N, 91.378E Grass land 4.700 0.72 0.12 55 GAME ANN 2000–03
Gaize, China 32.308N, 84.068E Desert 4.420 0.65 0.10 27 JEXAM 2001–03
Wind River, WA 45.828N, 121.958W Temperate
evergreen forest
0.371 0.83 0.83 68 AmeriFlux 2000–06
636 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48
«b 5 0.2122«29 1 0.3859«31 1 0.4029«32, (3)
where «29, «31, and «32 are MODIS narrowband emis-
sivities of bands 29, 31, and 32.
We used two global vegetation index products from
MODIS to characterize land vegetated surfaces: the
normalized difference vegetation index (NDVI) and the
enhanced vegetation index (EVI) (Huete et al. 2002).
The equations for the indices are
NDVI 5 (rnir � rred)/(rnir 1 rred) and (4)
EVI 5 2.5(rnir � rred)/(rnir 1 6rred � 7.5rblue 1 1.0),
(5)
where r is reflectance after atmospheric correction, the
subscript ‘‘nir’’ represents the near-infrared band (0.841–
0.876 mm), ‘‘red’’ represents the red band (at 0.620–0.670
mm), and ‘‘blue’’ is for the blue band (at 0.459–0.479 mm).
The MODIS team applies a compositing procedure to
provide a high-quality vegetation index product every 16
days (Van Leeuwen et al. 1999). Vegetation indices char-
acterizing vegetation coverage and greenness are regar-
ded as indicative of global biosphere health (Tucker et al.
1985). NDVI and EVI vary from 0 to 1 for most terres-
trial surfaces, excluding snow, ice, and water; the higher
the value is, the denser and greener is the vegetation.
3. Methods
Unlike longwave radiation, surface incident short-
wave solar radiation S# is conventionally observed glob-
ally. The Global Energy Budget Archive (GEBA) project
collects long-term solar shortwave radiation at more than
1500 stations worldwide (Gilgen and Ohmura 1999; Wild
et al. 2005). GEBA also evaluates data quality. The ratio
of Rn to daytime net shortwave radiation (Rn/Sn) is used
to estimate daytime Rn from shortwave radiation mea-
surements. Daytime is any time during which Sn exceeds
20 W m22. GEBA S# measurements enable calculation
of Sn with the help of surface albedo. At this time, long-
term albedo is available globally at a high spatial res-
olution of several kilometers and a relatively high
temporal resolution of one-half of a month (e.g., Pinty
et al. 2000; Pokrovsky et al. 2003; Schaaf et al. 2002;
Strugnell and Lucht 2001). Figure 1 shows an example
of a time series of Rn/Sn that has a substantial seasonal
variation. We selected albedo from ground measure-
ments to keep the scale of ground-measured and pre-
dicted Rn consistent. Therefore, we can get Rn by esti-
mating the ratio Rn/Sn.
In our previous studies, we showed that vegetation cover
fraction, which can be quantified by NDVI or EVI (Tucker
et al. 1985), substantially affects surface energy partition-
ing into latent heat and sensible heat fluxes (Wang et al.
2007c; Wang and Liang 2008), which in turn affects Ts and
L" (Wang et al. 2006, 2007b). Global long-term NDVI at
high spatial resolution (several kilometers) and a rela-
tively high temporal resolution (week or one-half of a
month) is available from multiple satellite sensors and
data centers (e.g., Los et al. 2005; Tucker et al. 2005; Jiang
et al. 2008; Swinnen and Veroustraete 2008).
To parameterize the ratio Rn/Sn and to estimate Rn,
we calculate the correlation coefficients between the
ratio and daily average, daily maximum, and daily
minimum air temperature (Ta or Ts), daily Ta (or Ts)
FIG. 1. An example of the time series of the ratio Rn /Sn of surface daytime Rn to net shortwave
radiation Sn using data collected at Hillsboro, KS (EF02).
MARCH 2009 W A N G A N D L I A N G 637
range, relative humidity (RH), and NDVI and EVI.
Table 2 lists the correlation coefficients. Among the
various measures, daily minimum temperature has the
highest correlation coefficient with the ratio, followed
by RH, vegetation index, and daily Ts (or Ta) range.
Relative humidity, air temperature, and diurnal tem-
perature (Ta or Ts) range (closely related to cloud
cover) are the key parameters controlling L#. The Ts,
diurnal temperature range (Ta or Ts), and vegetation
indices are the key parameters controlling surface en-
ergy partitioning and, in turn, L" (Wang et al. 2006,
2007c; Wang and Liang 2008). Diurnal temperature (Ts
or Ta) range (DTaR or DTsR), the difference between
daily maximum temperature and daily minimum tem-
perature, accounts for the complex effects of clouds,
surface daytime temperature dynamics, and soil mois-
ture on Rn.
The nearly linear relationship of Rn/Sn to daily Ta
range, daily minimum Ta, NDVI, and RH is illustrated
by one example in Fig. 2. Equation (6) estimates Rn:
(Rn/Sn) 5 a0 1 a1Tmin 1 a2DTR 1 a3VI 1 a4RH, (6)
where Tmin is daily minimum Ta (or Ts), DTR is daily Ta
(or Ts) range, VI is MODIS global NDVI or EVI pro-
duct with a spatial resolution of 1 km and a 16-day
temporal resolution, and RH is relative humidity. To
incorporate the elevation contribution, the Tmin used in
Eq. (6) is corrected to sea level by decreasing the tem-
perature by 6.58C for each 1-km increase in elevation.
The relationships between Rn/Sn and DTaR, Ta min,
VI, and RH are not exactly linear (Fig. 2). Thus, none of
the parameters of DTaR, Ta min, VI, and RH can in-
dividually account for the variance in Rn/Sn, although
the four parameters in combination estimate the vari-
ance in Rn/Sn with greater accuracy. The results de-
scribed in section 4 substantiate this. We also performed
the regression analysis with the square of the terms in
addition to the linear terms without substantially im-
proving the results. Therefore, only linear regressions
are used in this paper.
4. Results analysis
The data collected at 24 sites have two purposes. We
used the Amdo, Bondville, Desert Rock, EF02, EF07,
EF12, EF15, EF18, EF19, Fort Peck, ‘‘Penn State,’’ and
Sioux Falls data to derive the coefficients in Eq. (6), and
we validated the coefficients with the Boulder, Gaize,
EF04, EF08, EF09, EF13, EF20, EF22, EF26, EF27,
Goodwin Creek, and Wind River data. Table 3 lists the
derived coefficients.
TABLE 2. A summary of the correlation coefficient between the ratio Rn/Sn and daily average air temperature (Ta daily), daily
maximum (or minimum) air temperature (Ta max or Ta min), DTaR, daily average land surface temperature (Ts daily), daily maximum
(or minimum) land surface temperature (Ts max or Ts min), DTsR, Sn, RH, NDVI, and EVI.
Site Ta daily Ta max Ta min DTaR Ts daily Ts max Ts min DTsR NDVI EVI RH
EF02 0.45 0.47 0.55 20.16 0.38 0.36 0.56 20.29 0.36 0.39 0.32
EF04 0.34 0.34 0.54 20.4 0.32 0.3 0.57 20.4 0.45 0.49 0.55
EF07 0.47 0.42 0.62 20.38 0.41 0.37 0.65 20.44 0.64 0.61 0.51
EF08 0.25 0.25 0.45 20.4 0.19 0.18 0.48 20.38 0.48 0.5 0.61
EF09 0.44 0.43 0.57 20.3 0.38 0.36 0.61 20.4 0.33 0.32 0.49
EF12 0.53 0.52 0.65 20.33 0.5 0.48 0.69 20.39 0.67 0.67 0.51
EF13 0.42 0.39 0.57 20.37 0.34 0.31 0.59 20.43 0.35 0.33 0.47
EF15 0.43 0.42 0.58 20.32 0.4 0.39 0.62 20.33 0.63 0.64 0.55
EF18 0.48 0.46 0.6 20.31 0.41 0.4 0.63 20.37 0.53 0.5 0.5
EF19 0.4 0.39 0.57 20.37 0.31 0.28 0.62 20.53 0.64 0.64 0.56
EF20 0.4 0.38 0.55 20.37 0.33 0.29 0.61 20.48 0.65 0.65 0.63
EF22 0.39 0.33 0.54 20.42 0.34 0.28 0.58 20.39 0.16 0.33 0.43
EF26 0.4 0.39 0.53 20.32 0.33 0.3 0.62 20.41 0.42 0.39 0.61
EF27 0.38 0.34 0.52 20.34 0.31 0.27 0.62 20.46 0.61 0.59 0.58
Bondville, IL 0.45 0.45 0.57 20.19 0.43 0.41 0.61 20.36 0.4 0.39 0.37
Boulder, CO 0.02 0.07 0.09 20.02 0.04 0.08 0.27 20.18 0.31 0.34 0.48
Desert Rock, NV 20.32 20.32 20.21 20.42 20.32 20.3 20.12 20.43 0.38 0.38 0.65
Fort Peck, MT 0.08 0.06 0.21 20.28 0.06 0.06 0.24 20.22 0.19 0.18 0.28
Goodwin Creek, MS 0.34 0.32 0.53 20.5 0.23 0.17 0.57 20.63 0.33 0.31 0.73
Penn State, PA 0.43 0.4 0.54 20.18 0.4 0.37 0.58 20.24 0.42 0.44 0.49
Sioux Falls, SD 0.17 0.16 0.29 20.3 0.15 0.13 0.34 20.34 0.17 0.17 0.43
Amdo, China 0.78 0.77 0.88 20.68 0.64 0.62 0.9 20.69 0.63 0.64 0.74
Gaize, China 0.57 0.56 0.65 20.61 0.45 0.4 0.68 20.63 0.52 0.51 0.72
Wind River, WA 20.07 20.09 0.11 20.3 20.07 20.09 0.14 20.29 20.03 0.13 0.4
Average of all 0.36 0.35 0.50 20.35 0.31 0.28 0.54 20.41 0.45 0.45 0.53
638 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48
As expected, the coefficients listed in Table 3 indicate
the importance of NDVI (or EVI) in accounting for the
variation in L" and Rn. Air humidity and temperature
(Ta or Ts) are generally considered to account for most
of the variation in L#. This is also the case in this study,
because RH and Ta (Ts) are the dominant terms for Rn
in Eq. (6) (Table 3). DTR is a measure of the effect of
soil moisture on Ts dynamics and L". Therefore, a2 is
more important when Ts is used in Eq. (6). In statistical
terms, Ta (Ts), DTaR (DTsR), and RH are all related to
cloud cover and its effects on Rn. The focus of this study
is on estimating daytime average Rn under both clear-
and cloudy-sky conditions because variations in per-
centage cloud cover are likely to occur over the course
of a day. Figure 3 shows an example of measured and
predicted Rn from daily minimum Ts, DTsR, NDVI, and
RH. Equation (6) predicts Rn using the same coeffi-
cients at the 24 sites. Table 4 summarizes the statistical
parameters of the comparison of predicted and mea-
sured Rn at the 24 sites.
Equation (6) and the Table 3 coefficients accurately
estimate Rn for a range of land cover types, surface
FIG. 2. An example of the ratio Rn/Sn as a function of DTaR, (Ta min), NDVI, and RH using data collected at
Earlsboro, OK (EF27) from 2003 to 2006.
TABLE 3. The fitted parameters in Eq. (6) and the statistics for all 24 sites. Equation (6) is used to predict daytime Rn at all 24 sites using
the parameters shown in the following columns. The correlation coefficients and RMSE between measured and predicted daytime Rn are
given in the last two rows.
Combinations of parameters
NDVI, Ts min,
DTsR, RH
NDVI, Ta min,
DTaR, RH
EVI, Ts min,
DTsR, RH
EVI, Ta min,
DTaR, RH
a0 0.5749 0.5129 0.5842 0.5195
a1 0.0026 0.0025 0.0026 0.0024
a2 20.0018 0.0000 20.0018 0.0001
a3 0.1299 0.1401 0.1813 0.1944
a4 0.2053 0.2604 0.2063 0.2651
Correlation coef 0.99 0.99 0.99 0.99
RMSE 16.9 (6%) 17.6 (7%) 17.0 (6%) 17.8 (7%)
MARCH 2009 W A N G A N D L I A N G 639
elevations, and climates without local calibration (Table
4). The bias varies from 27.8 to 19.7 W m22 (63%
in relative value) for different sites. The root-mean-
square error (RMSE) varies from 12.8 to 21 W m22 (from
5% to 9% in relative value) for different sites and an
average of 16.9 W m22 (6% in relative value) for all sites,
and the correlation coefficient is about 0.99 for all sites.
Wang et al. (2007c) and Wang and Liang (2008)
demonstrated that EVI better quantifies vegetation
cover fraction because EVI is less dependent on soil
type. Therefore, EVI may be more accurate in parame-
terizing Rn; however, EVI is only available after 2000
(Salomonson et al. 1989). NDVI is used to estimate Rn
when EVI is unavailable. Our previous studies also show
that Ts is directly related to L", whereas the relationship
between Ta and L" is indirect (Wang et al. 2005b, 2007b).
However, satellite Ts retrieval is not available under
cloudy conditions. Therefore, we also provide an equa-
tion using Ta.. Table 3 also shows that other combina-
tions of temperatures, vegetation index, and relative
humidity produce similar results. The results with Ts
demonstrate slightly better overall statistical parameters.
Changes in Rn impact a host of factors, including tem-
perature, precipitation, meteorological patterns, and
sea level (Charlson et al. 2005). Therefore, predicting
long-term variation in Rn, such as year-to-year variation
and decadal variation, is important. To examine the
applicability of the method to climate study, we com-
pare the annual abnormality (year average subtracted
from multiyear average) in measured and predicted
daytime Rn. The results, shown in Fig. 4, demonstrate
that Eq. (6) predicts the annual abnormality in daytime
Rn accurately, with a correlation coefficient between
measured and predicted annual abnormality as high as
0.91. This suggests that Eq. (6) accurately monitors
long-term change in Rn.
5. Conclusions and discussion
Changes in Rn broadly affect the earth’s climates, the
hydrological cycle, and plant photosynthesis. Existing
studies focus on solar shortwave radiation (to the ex-
clusion of longwave radiation), because it is readily
available from conventional measurements (whereas
longwave radiation is not). Methods to estimate long-
wave radiation and Rn are essential for climate studies.
Current methods to estimate L# suffer from the diffi-
culty of quantifying cloud effects. The estimation of L"requires Ts as a key input datum, which is unavailable
under cloudy conditions. In addition, previous studies
demonstrate that it is essential to locally calibrate the
existing models with at least 5 years of data to achieve
stable calibration coefficients.
Rather than estimating L# and L" separately, we es-
timate Rn directly. The new method accurately estimates
daytime Rn from solar radiation measurements using
data collected at 24 sites over a range of land cover types,
climate zones, and surface elevations. The method is
based on our previous research on land energy parti-
tioning into surface latent heat flux and sensible heat flux
and their interactions with Ts and L" (Wang et al. 2006,
2007b,c; Wang and Liang 2008). We use NDVI (or EVI),
which are parameters related to vegetation cover frac-
tion and soil moisture, to estimate Rn from solar radia-
tion measurements. The results show that an equation to
estimate Rn is suitable for all sites. The bias varies from
27.8 to 19.7 W m22 (63% in relative value),
and RMSE varies from 12.8 to 21 W m22 (from 5% to
9% in relative value) with an average of 16.9 W m22
(6% in relative value) for all sites, with a correlation
coefficient of about 0.99 for all sites. The accuracy im-
proves upon those in previous studies (e.g., Diak et al.
2004; Kjaersgaard et al. 2007a). The proposed method is
suitable for a range of land cover types, surface eleva-
tions, and climate zones without local calibration.
Another advantage of the proposed method is that it
relies only on conventional meteorological observations
and global available satellite data. DTR is used in the
parameterization proposed here. When Ts is used in the
proposed method, the effect of DTsR is very small, so
that it is not necessary to incorporate it in the parame-
terization. When using air temperature, DTaR accounts
for about 3% variation of Rn, by our calculations.
FIG. 3. Scatterplot of measured and predicted daytime Rn cal-
culated with Eq. (6) and daily minimum land surface temperature
(Ta min), daily land surface temperature range (DTR), RH, and
NDVI using data collected at Pawhuska, OK (EF12) from 2002 to
2006.
640 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48
The method is based on the analysis of daily net ra-
diation, daily meteorological observations, and satellite
daily Ts or 16-day vegetation indices. Our validation
results demonstrate that this method works well for
predicting daytime daily Rn and annual Rn variation.
The correlation coefficient between the measured and
predicted annual abnormality is as high as 0.91, indi-
cating that this method accurately estimates long-term
variation in Rn. At this time, the long-term datasets of
the input data required by the proposed method are
globally available. These data can be used to derive
global, long-term Rn. For example, GEBA provides S"at more than 1500 stations (Gilgen and Ohmura 1999;
Wild et al. 2005). At this time, long-term albedo is
available globally at high spatial resolution (several
kilometers) and a relatively high temporal resolution
(one-half of a month) (e.g., Pinty et al. 2000; Pokrovsky
et al. 2003; Schaaf et al. 2002; Strugnell and Lucht 2001).
A number of satellite sensors and data centers provide
global long-term NDVI datasets at high spatial resolu-
tion (several kilometers) and a relatively high temporal
resolution (week or one-half of a month) (e.g., Los et al.
2005; Tucker et al. 2005; Jiang et al. 2008; Swinnen and
Veroustraete 2008).
To validate the proposed data, we used the site
measurements and satellite observations at the spatial
resolution of 1 km. We believe our method will work
well for relatively large spatial resolutions because the
relationships between Rn and Sn, water vapor, vegeta-
tion coverage, and temperature do not significantly vary
with spatial scales.
Acknowledgments. Shortwave radiation, net radiation,
and corresponding meteorological observations were
obtained from the NOAA SURFRAD project (ftp://ftp.
TABLE 4. A summary of the fitted statistics from Eq. (6) using daily minimum land surface temperature (Ta min), DTsR, RH, and NDVI.
The same coefficients are used for all 24 sites.
Site Correlation coef RMSE (W m22) Bias (W m22) Rn (W m22) RMSE/Rn Bias/Rn
EF02 0.99 21.0 21.6 284.4 0.07 20.01
EF04 0.99 15.8 5.7 281.3 0.06 0.02
EF07 0.99 15.8 20.9 283.8 0.06 0
EF08 0.99 14.6 0.7 286.7 0.05 0
EF09 0.99 15.5 4.3 280.1 0.06 0.02
EF12 0.99 14.8 2.3 300.7 0.05 0.01
EF13 0.99 17.3 9.7 298.2 0.06 0.03
EF15 0.99 14.5 21.5 275.2 0.05 20.01
EF18 0.99 17.2 0.3 285.6 0.06 0
EF19 0.99 14.0 1.2 301.0 0.05 0
EF20 0.99 13.8 0.7 286.5 0.05 0
EF22 0.99 17.6 2.6 282.1 0.06 0.01
EF26 0.99 13.9 21.9 304.4 0.05 20.01
EF27 0.99 16.2 24.0 292.7 0.06 20.01
Bondville, IL 0.99 16.4 6. 9 223.3 0.07 0.03
Boulder, CO 0.99 16.9 27.8 243.1 0.07 20.03
Desert Rock, NV 0.98 17.8 27.6 267.0 0.07 20.03
Fort Peck, MT 0.99 17.2 3.5 190.0 0.09 0.02
Goodwin Creek, MS 0.99 12.8 0 254.0 0.05 0
Penn State, PA 0.99 16.4 1.2 201.0 0.08 0.01
Sioux Falls, SD 0.98 20.8 2.6 221.4 0.09 0.01
Amdo, China 0.99 13.4 2.5 276.1 0.05 0.01
Gaize, China 0.98 15.1 4.4 258.8 0.06 0.02
Wind River, WA 0.99 16 4.2 292.5 0.05 0.01
FIG. 4. A comparison of the measured and predicted annual
abnormality in daytime Rn calculated with Eq. (6), the coefficients
listed in Table 2, and data collected at the 24 sites described in
Table 1.
MARCH 2009 W A N G A N D L I A N G 641
srrb.noaa.gov/pub/data/surfrad/), the ARM Program of
the U.S. Department of Energy (http://www.archive.arm.
gov/), the AmeriFlux network (http://public.ornl.gov/
ameriflux/data-get.cfm), and the GAME ANN project
(http://aan.suiri.tsukuba.ac.jp/aan-center.html). MODIS
satellite data were obtained online (http://redhook.gsfc.
nasa.gov/;imswww/pub/imswelcome/plain.html). This
study was supported in part by NASA Grant
NNX08DC53G and NOAA Grant NA07NES4400001.
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