Estimation of Daytime Net Radiation from Shortwave Radiation

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: [email protected]

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


«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).


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


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%)


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.


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.


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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