Global atmospheric downward longwave radiation over land surface under all-sky conditions from 1973 to 2008



[1] In this article, we first evaluate two widely accepted methods to estimate global atmospheric downward longwave radiation (Ld) under both clear and cloudy conditions, using meteorological observations from 1996 to 2007 at 36 globally distributed sites, operated by the Surface Radiation Budget Network (SURFRAD), AmeriFlux, and AsiaFlux Projects. The breakdown of locations is North America (20 sites), Asia (12 sites), Australia (2 sites), Africa (1 site), and Europe (1 site). Latitudes for these sites range from 0° at the equator to ±50°; elevation ranges from 98 to 4700 m, and six different land cover types are represented (deserts, semideserts, croplands, grasslands, forests, and wetlands). The evaluation shows that the instantaneous Ld under all-sky conditions is estimated with an average bias of 2 W m−2 (0.6%), an average standard deviation (SD) of 20 W m−2 (6%), and an average correlation coefficient (R) of 0.86. Daily Ld under all-sky conditions is estimated with a SD of 12 W m−2 (3.7%) and an average R of 0.93. These results suggest that these two methods could be applied to most of the Earth's land surfaces. Accordingly, we applied them to globally available meteorological observations to estimate decadal variation in Ld. The decadal variations in global Ld under both clear and cloudy conditions at about 3200 stations from 1973 to 2008 are presented. We found that daily Ld increased at an average rate of 2.2 W m−2 per decade from 1973 to 2008. The rising trend results from increases in air temperature, atmospheric water vapor, and CO2 concentration.

1. Introduction

[2] Surface downward longwave radiation (Ld) is one of four components in the surface radiation balance driving weather, climate, and environmental change. While surface shortwave radiation has long been measured globally [Gilgen and Ohmura, 1999], Ld is not conventionally observed due to the higher cost of pyrgeometers used for Ld measurement, and more difficult challenges of instrument calibration and quality control [Enz et al., 1975; Udo, 2000; Sridhar and Elliott, 2002; Duarte et al., 2006].

[3] Water vapor is the dominant emitter of longwave radiation in the atmosphere. Brutsaert [1975] developed a physically rigorous parameterization with surface water vapor pressure and air temperature (Ta) to estimate clear-sky Ld based on the standard atmospheric model, i.e., the U.S. 1962 standard atmosphere. The rational for calculating clear-sky Ld with surface meteorological observations of Ta and relative humidity (RH) is that approximately 80% of Ld arises from the lowest 500 m of the atmosphere, and more than 50% of the Ld comes from the lowest 100 m of the atmosphere under clear-sky conditions [Schmetz, 1989]. Numerous studies estimate Ld using meteorological observations of RH and Ta [Brunt, 1932; Idso and Jackson, 1969; Brutsaert, 1975; Idso, 1981; Prata, 1996; Malek, 1997; Niemelä et al., 2001; Iziomon et al., 2003; Jin et al., 2006]. The calibration results of these studies differ substantially because most methods were validated and calibrated for a limited range of climate regions with data collected over short time periods [Bilbao and de Miguel, 2007; Kjaersgaard et al., 2007; Lhomme et al., 2007; Choi et al., 2008]. For example, Kjaersgaard et al. [2007] summarized the Brunt [1932] equation-derived coefficients calibrated for different regions. In this study, we use long-term Ld observations to evaluate the ability of the two methods to predict Ld for a range of climate and land cover types.

[4] Retrievals of Ta and water vapor profiles from satellite observations are also used to estimate Ld [Ellingson, 1995; Diak et al., 2004; Bisht et al., 2005; Zhou et al., 2007]. These methods depend on the accuracy of satellite retrievals of Ta and the water vapor profile in the surface layer of the atmosphere, which still have substantial uncertainties [Ellingson, 1995; Wang and Liang, 2009]. Radiance observations by satellite at the top of atmosphere are used to estimate Ld under clear-sky conditions [Tang and Li, 2008; Wang and Liang, 2009]; however, this method is not suitable for cloudy conditions because clouds are opaque in the thermal infrared region. Quantifying cloud effects also presents a major difficulty in estimating Ld under cloudy conditions [Ellingson, 1995]. Satellite sensors cannot monitor cloud base temperature, which controls cloud contribution to Ld under cloudy conditions. Diak et al. [2004] showed that the accuracies of the various methods for estimating Ld vary, with an error ranging from about 10–20 W m−2 for instantaneous clear-sky Ld, degrading to 20–40 W m−2 for cloudy conditions.

[5] Reliable cloud cover fraction measurement can be obtained from meteorological observation or satellite cloud detection products [Ackerman et al., 2008], and is more accurate than satellite retrieval of cloud characteristics such as cloud liquid water path, cloud base height and cloud base temperature [Ellingson, 1995; Diak et al., 2004]. Most existing empirical methods use cloud cover fraction to quantify cloud effects on Ld. If the cloud fraction can quantify the influence of clouds on Ld, estimation of Ld under cloudy conditions is far easier. This study further investigates the ability of the cloud fraction to estimate Ld.

[6] When ground measurements are used to perform local calibration of the parameterization [Bilbao and de Miguel, 2007; Kjaersgaard et al., 2007; Lhomme et al., 2007; Choi et al., 2008], the coefficients differ [e.g., Kjaersgaard et al., 2007]. However, few studies address the effect of measurement error on the model calibrations. Ground measurements of Ld often have significant errors [Enz et al., 1975; Udo, 2000; Sridhar and Elliott, 2002; Duarte et al., 2006]. Long-term measurements collected in this study provide data to quantify ground measurement error.

[7] This study has four major objectives. First we evaluate the two most accepted methods to estimate Ld using long-term measurements collected for a range of climate regimes and land covers between 1996 and 2007. Second, we investigate whether cloud fraction can quantify the cloud effect on Ld. Third, we try to quantify the effect of instrument calibration error on the method calibrations. Finally, we calculate decadal variation in Ld globally using hourly meteorological observations at 3200 stations from 1973 to 2008.

[8] This article is organized as follows: after the introduction, the data used in this study is described. Section 3 describes the methods, followed by their evaluation in section 4. Section 5 applies the methods to calculate decadal variation in Ld globally from 1973 to 2008. The last section is contains the discussion and conclusions.

2. Data

[9] We use surface incident shortwave and longwave radiation data and corresponding meteorological observations, such as air temperature and relative humidity, collected at 36 sites to evaluate two empirical methods of estimating global surface downward longwave radiation, Ld (Table 1): 7 sites of the Surface Radiation Budget Network (SURFRAD) supported by the National Oceanic and Atmospheric Administration, 20 AmeriFlux sites, 7 AsiaFlux sites, 1 Asian Automatic Weather Station Network Project (ANN) site supported by the Global Energy and Water Cycle Experiment Asian Monsoon Experiment (GAME AAN), and 1 site supported by the Japanese Experiment on Asian Monsoons and the Frontier Observational Research System for Global Change, University of Tokyo and Kyoto University. Table 1 summarizes site information. Land cover types of the sites include desert, semidesert, croplands, grasslands, forests and wetlands. The elevations of the sites vary from 98 m to 4700 m. Table 1 also supplies the annual average of daytime RH, Ta, Ld, and data collection dates at each site. The data period covers 1995 to 2007 and each site has at least 1 year's worth of data. The latitude of the sites varies from the equator to ±50° (Figure 1).

Figure 1.

Location of 36 sites used in this study. Red circles represent the 7 SURFRAD sites, green circles represent the 20 AmeriFlux sites, blue circles represent the 7 AsiaFlux sites, and magenta circles represent the 2 Tibetan Plateau sites where surface elevation is higher than 4000 m.

Table 1. A Description of Site Conditionsa
SiteCountryLand Cover TypeLat. (deg.)Long. (deg.)Elevation (m)Time PeriodLd (W m−2)Ta (°C)RH (%)InstrumentNetwork
  • a

    Abbreviations are as follows: Ld, multiyear daytime longwave radiation; RH, multiyear average daytime relative humidity; Ta, multiyear daytime air temperature.

BondvilleUSACropland40.06−88.372131996–200733015.167Eppley pyrgeometerSURFRAD
BoulderUSAGrassland40.13−105.2416891995–200729114.644Eppley pyrgeometerSURFRAD
Desert RockUSADesert grassland36.63−116.0210071998–200731422.623Eppley pyrgeometerSURFRAD
Fort PeckUSAGrassland48.31−105.106341996–20072969.958Eppley pyrgeometerSURFRAD
Goodwin CreekUSAGrassland34.25−89.87981996–200736120.761Eppley pyrgeometerSURFRAD
Penn StateUSACropland40.72−77.933761998–200732213.363Eppley pyrgeometerSURFRAD
Sioux FallsUSACropland43.73−96.624732003–200731813.564Eppley pyrgeometerSURFRAD
Bukit SoehartoIndonesiaForest−0.86117.04202001–200244328.377Kipp and Zonen CNR 1AsiaFlux
Fujiyoshida ForestJapanEvergreen forest35.45138.761030200033715.273Kipp and Zonen CNR 1AsiaFlux
LaoshanChinaLarch forest45.28137.4234020022915.461Eppley pyrgeometerAsiaFlux
Mae KlongThailandDeciduous forest14.5898.842312003–200441926.864EKO MR-40AsiaFlux
PalangkarayaIndonesiaForest2.35114.04302002–200543328.271Kipp and Zonen CNR 1AsiaFlux
SakaeratThailandEvergreen forest14.49101.925432001–200341925.968Kipp and Zonen CNR 1AsiaFlux
TomakomaiJapanForest42.74141.521402001–20033179.472EKO MR-40AsiaFlux
Howard SpringsAustraliaSavanna−12.50131.20792001–200640928.959 FLUXNET
Ghanzi grassBotswanaGrassland−21.5021.341131200336529.228 FLUXNET
Ghanzi mixedBotswanaMixed−21.5021.341131200337628.823 FLUXNET
Campbell RiverCanadaEvergreen forest49.87−125.303001999–20023189.379 FLUXNET
Dongtan 2ChinaWetlands31.55121.9032200535917.174 FLUXNET
Dongtan 3ChinaWetlands31.52121.9732200535217.973 FLUXNET
Dongtan 1ChinaWetlands31.52121.9632200536217.872 FLUXNET
HartheimGermanyEvergreen forest47.947.602012005–200634514.270 FLUXNET
Walnut Gulch KendallUSAGrassland31.74−109.9415312004–200631020.429 FLUXNET
Santa Rita MesquiteUSASavanna31.82−110.8711202004–200634322.828 FLUXNET
Black HillsUSAEvergreen forest44.16−103.6517002002–200730211.949Kipp and Zonen CNR 1AmeriFlux
Fort PeckUSAGrassland48.31−105.106342000–200727910.461Kipp and Zonen CNR 1AmeriFlux
Goodwin CreekUSAGrassland34.25−89.97702002–200635220.969Kipp and Zonen CNR 1AmeriFlux
BondvilleUSACroplands40.01−88.293001996–200732914.171Kipp and Zonen CNR 1AmeriFlux
Morgan MonroeUSADeciduous forest39.32−86.412751999–200333717.162Kipp and Zonen CNR 1AmeriFlux
Ozark MissouriUSADeciduous forest38.74−92.202202004–20062695.948Kipp and Zonen CNR 1AmeriFlux
BrookingsUSAGrasslands44.34−96.805102004–200631313.269Kipp and Zonen CNR 1AmeriFlux
Walker BranchUSADeciduous forest35.96−84.293702001–200734917.462Kipp and Zonen CNR 1AmeriFlux
Wind River CraneUSAEvergreen forest45.82−121.903711998–200632812.571Kipp and Zonen CNR 1AmeriFlux
Willow CreekUSAEvergreen forest45.81−90.085201998–20063037.479Kipp and Zonen CNR 1AmeriFlux
AmdoChinaDesert grassland32.2491.6347001999–20032481.145Eppley pyrgeometerGAME AAN
GaizeChinaGrassland32.384.0644202001–20032443.829Eppley pyrgeometer 

[10] The primary objective of SURFRAD is to support climate research with accurate, continuous, long-term measurements pertaining to the surface radiation budget over the United States. Three-minute average data are downloaded, checked against quality control standards and processed into daily files that are distributed in near real time by anonymous FTP and the WWW ( SURFRAD sites have the longest collection periods and the sensors are carefully calibrated. Augustine et al. [2000] provided the detailed information on SURFRAD sites and sensors. Both AsiaFlux and AmeriFlux are part of the global FLUXNET project that aims to quantify the spatial and temporal variation in carbon storage in plants and soils, and the exchange of carbon, water, and energy in major vegetation types. AmeriFlux and AsiaFlux sites provide both 30- and 60-min average data. GAME ANN was implemented to understand the role of the Asian monsoon in the global energy and water cycle. The Amdo (GAME AAN) and Gaize sites, on the Tibetan Plateau, provide 30- and 60-min average data, respectively. Information on sensor and measurement accuracies for all sites, except the Gaize site, is available at the Websites listed in the Acknowledgments. Wang et al. [2004, 2005] provided Gaize site information.

[11] Two brands of pyrgeometers are used to measure Ld: the Eppley, and Kipp and Zonen CNR 1 pyrgeometers. The Kipp and Zonen CNR 1 pyrgeometer has a spectral response region from 5 μm to 50 μm, and the Eppley pyrgeometer is sensitive to the spectral range from 3.0 to 50 μm. The difficulty in accurately estimating Ld is due in large part to instrument calibration error. DeLuisi et al. [1992] showed that differences between Ld measurements from different instruments may exceed ±10 W m−2 based on the results of Baseline Surface Radiation Network (BSRN) broadband infrared radiometer intercomparison at FIRE II. An experiment carried out in southeastern Spain indicated that the systematic error on incoming longwave radiation as measured by pyrgeometers may extend to ±5 W m−2 due to variable solar radiation and wind speed [Pérez and Alados-Arboledas, 1999].

3. Methods

[12] Surface downward longwave radiation (Ld)is typically estimated by first determining the clear-sky radiation (Ldc), and then correcting for cloud fraction. The general form of the Ldc equation is

equation image

where ɛa is atmospheric emissivity, and σ = 5.67 × 10−8 W m−2 K−4 is the Stefan-Boltzman constant. Most empirical methods estimate the atmospheric emissivity using water vapor pressure or Ta or both. The Brunt [1932] and Brutsaert [1975] equations are the best two parameterizations of many. Although coefficients are different for different regions, Sridhar and Elliott [2002] (for Oklahoma), Duarte et al. [2006] (for Ponta Grossa, Brazil), Kjaersgaard et al. [2007] (for Denmark), Lhomme et al. [2007] (for Andean Altiplano), and Rizou and Nnadi [2007] (for Florida) agreed that the Brutsaert [1975] method predicts Ldc the best; while Sugita and Brutsaert [1993] (for Kansas) and Kjaersgaard et al. [2007] (for Denmark) pointed out that the Brunt [1932] equation provided a similar result to the Brutsaert [1975] equation. Bilbao and de Miguel [2007] (for Valladolid, Spain) and Choi et al. [2008] (for Florida) further noted that the Brunt [1932] equation performs slightly better than the Brutsaert [1975] equation. Therefore, we evaluate only the Brunt and Brutsaert equations with ground-based measurements. The Brunt [1932] equation is

equation image

The Brutsaert [1975] model takes the form

equation image

where ea is water vapor pressure at reference level.

[13] The coefficients of the Brunt [1932] equation used in this study are a1 = 0.605 and a2 = 0.048 [Sellers, 1965], and the universal coefficients of Brutsaert [1975] equation are b1 = 1.24 and b2 = 1/7. We compared the performance of the coefficients proposed by Bilbao and de Miguel [2007], Kjaersgaard et al. [2007], Lhomme et al. [2007] and Choi et al. [2008], and found that Brunt's coefficients performed better.

[14] The cloud fraction is used to quantify the cloud effects on Ld. Among the parameterizations of cloud effect on Ld [e.g., Choi et al., 2008], the Crawford and Duchon [1999] method is regarded as the best by many authors [Duarte et al., 2006; Kjaersgaard et al., 2007; Lhomme et al., 2007; Choi et al., 2008]:

equation image

where f is cloud fraction. When cloud fraction is not available from observations, Crawford and Duchon [1999] suggest calculating f with

equation image

where Sd is surface incident shortwave radiation from observations, and Sdc is the theoretical incident shortwave clear-sky radiation under the same conditions except that cloud conditions may vary. We calculate Sdc with the model developed by Yang et al. [2001], and recommended by Gueymard [2003], Paulescu and Schlett [2004], and Madkour et al. [2006]. The method was improved by Yang et al. [2006], and its FORTRAN code is available at The input data required by the Yang et al. [2006] method includes the date, solar zenith angle, ozone and aerosol concentration, and relative humidity.

4. Evaluation

[15] Our validation results summarized in Table 2 demonstrate that equation (4) accurately estimates instantaneous Ld under all-sky conditions. One example in Figure 2 shows how well the predicted instantaneous 3-min average all-sky Ld matches the measured all-sky Ld at the SURFRAD Goodwin Creek site from 1996 to 2007 (Figure 2). Both Brunt [1932] and Brutsaert [1975] parameterizations on clear-sky Ld produce similar results at the Goodwin Creek site and other sites (Table 2). Instantaneous Ld is defined as the Ld estimates at the time scales of the radiation and meteorological data released by the data centers, such as 3-min average for SURFRAD sites and 30- or 60-min average for other sites. Instantaneous Ld is estimated with an average standard deviation (SD) of 20 W m−2 (6%), an average coefficient of 0.86 and an average bias of 2 W m−2 (0.6%), exceeding the accuracy of Diak et al. [2004].

Figure 2.

Comparisons of the measured and predicted 3-min average Ld by equation (4) with the clear-sky parameterization followed by Brunt [1932] and Brutsaert [1975] from 1996 to 2007 at the SURFRAD Goodwin Creek site.

Table 2. A Summary of the Statistics of the Comparison of the Measurements and Predictions of Instantaneous Downward Longwave Radiation Using Brunt [1932] and Brutsaert [1975] Clear-Sky Parameterizationsa
SiteMean LdBrunt MethodBrutsaert Method
  • a

    The biases, standard deviations, and longwave radiation (Ld) values are in watts per meters squared. Instantaneous Ld is defined as the Ld estimates at the time scales of the radiation and meteorological data released by the data centers such as 3-min average for SURFRAD sites and 30-min average or 60-min average for other sites.

Desert Rock314.315.316.40.947.017.20.94
Fort Peck295.65.422.00.933.323.90.93
Goodwin Creek361.10.415.80.964.315.90.96
Penn State322.0−−
Sioux Falls318.33.518.70.964.820.70.96
Bukit Soeharto443.0−7.417.50.44−1.716.00.50
Fujiyoshida Forest337.
Mae Klong419.1−9.816.80.80−3.715.30.83
Howard Springs409.35.618.50.8311.918.30.84
Ghanzi grass364.717.023.00.6416.624.10.63
Ghanzi mixed375.9−0.923.70.58−4.827.30.55
Campbell River317.6−−9.519.60.83
Dongtan 2359.04.714.40.987.414.20.98
Dongtan 3351.812.117.20.9715.317.00.97
Dongtan 1362.25.520.60.948.520.40.95
Walnut Gulch Kendall309.816.621.30.8810.022.40.88
Santa Rita Mesquite342.60.322.80.88−
Black Hills301.52.621.60.91−0.622.60.92
Fort Peck278.822.331.90.8620.635.00.86
Goodwin Creek351.617.822.60.9322.723.00.93
Morgan Monroe337.
Walker Branch349.1−4.719.40.91−2.720.00.91
Wind River Crane328.2−8.819.70.83−6.920.30.83
Willow Creek302.6−−8.923.60.93
Average of all sites337.

[16] The time scales of the instantaneous Ld in Table 2 vary by site. To be consistent, we averaged the data into daily averages. Because cloud fraction is calculated from solar radiation, only daytime data are shown. Figure 3 provides the results at seven SURFRAD sites and one Tibetan Plateau site. Comparing the measured and predicted daily all-sky Ld at all sites demonstrates that daily Ld is estimated with an average SD of 12 W m−2 (3.7%), an average correlation coefficient of 0.93 and an average bias of 2 W m−2 (0.6%) (Table 3). To investigate the ability of equation (4) to predict daily all-sky Ld, we calculated the linear regressions for each site:

equation image

where Ld,meas is the measured Ld and Ld,pre is the predicted Ld using equation (4). The slope a and the b-intercept of the regression line are shown in Table 3. The slope is equal to unity and the intercept is zero for perfect parameterizations. Our analysis shows that the Brunt [1932] and Brutsaert [1975] parameterizations are comparable, and that the Brunt [1932] equation is slightly better in term of the SD and slope (Table 3).

Figure 3.

Comparisons of the daily measured and predicted Ld by equation (4) with the clear-sky parameterization of Brunt [1932] (red circles) and Brutsaert [1975] (blue circles) at (a) SURFRAD Bondville, (b) SURFRAD Boulder, (c) SURFRAD Desert Rock, (d) SURFRAD Peck Fort, (e) SURFRAD Goodwin Creek, (f) SURFRAD Penn State, (g) SURFRAD Sioux Falls, and (h) the GAME AAN Amdo site. Periods of the site data are shown in Table 1. The statistics of the comparisons are shown in Table 3.

Table 3. Same as Table 2, Except for Daily Downward Longwave Radiationa
SiteBrunt MethodBrutsaert Method
  • a

    The slope (S) and intercept (I) of the linear regression are also supplied (see equation (6)). The biases and SDs are in watts per meters squared.

Desert Rock14.88.30.981.00−
Fort Peck4.315.70.970.8830.51.718.50.970.8154.3
Goodwin Creek−−
Penn State−2.710.90.981.003.4−2.612.60.980.9133.6
Sioux Falls1.814.10.980.9418.
Bukit Soeharto−7.310.00.280.25334.5−
Fujiyoshida Forest2.710.30.970.991.84.811.80.960.9127.5
Mae Klong−−−13.8
Howard Springs6.413.50.900.975.812.814.00.890.9123.4
Ghanzi grass16.89.10.961.33−−56.3
Ghanzi mixed−−
Campbell River−9.815.90.890.9331.8−
Dongtan 25.911.90.991.07−30.68.411.60.981.01−12.3
Dongtan 312.714.10.981.09−44.015.513.80.981.02−23.5
Walnut Gulch Kendall17.613.80.961.11−51.610.711.80.970.98−2.8
Santa Rita Mesquite0.88.00.971.06−21.1−
Black Hills2.013.20.960.9220.9−2.514.10.970.8449.3
Fort Peck20.527.80.920.7554.418.431.80.920.6874.6
Goodwin Creek17.914.30.971.04−−8.1
Morgan Monroe−6.411.30.980.9426.0−4.714.70.980.8651.1
Walker Branch−4.716.50.961.002.4−3.817.90.960.9134.8
Wind River Crane−9.714.80.890.8363.1−
Willow Creek−−9.519.30.970.8067.0
Average of all sites1.512.20.930.9613.70.913.10.930.8841.0

[17] The Brunt [1932] equation tends to overestimate Ld when Ld is low at high elevations, such as at Amdo and Gaize Tibetan Plateau sites, and the Brutsaert [1975] parameterization performs better at these sites (Figure 3 and Table 3). When site elevation is less than 1000 m, Brunt [1932] is better in terms of bias, SD, slope and intercept. The two sites near the equator (Bukit Soeharto, 0.86°S, 117.04°E and Palangkaraya drained forest site, 2.35°N, 114.04°E, see Table 1) have rather low correlation coefficients and low linear regression slopes due to the very small seasonal variation in Ld (<100 W m−2) compared to about 400 W m−2 at other sites (Figure 3). The biases and SDs (and their relative values) for these sites are small (Table 3). Studies show that the methods work well for humid conditions [e.g., Choi et al., 2008] in Florida, USA; however, there are no published studies for sites near the equator. Because Ld primarily comes from the surface layer of the atmosphere, the low-latitude air temperature and water vapor profile are similar to higher-latitude areas. The measurement errors at the sites may contribute to the worse comparison results.

[18] The quality of the Ld measurements is a very important factor in controlling the comparison between measurements and predictions of Ld. SURFRAD and AmeriFlux share three common sites: Boundville, Fort Peck and Goodwin Creek (Table 1). The distances between the SURFRAD and AmeriFlux sites are small and land cover and elevation are comparable; however, the differences in the bias at the SURFRAD and AmeriFlux sites are as large as 20 W m−2 with SURFRAD data that is believed to have better quality. We infer that the variations in bias are mainly caused by the systematic error from instrument calibrations. AmeriFlux has three similar wetland sites in China (Dongtan), and the bias of these sites vary from 6 W m−2 to 13 W m−2. The biases of the two Ghanzi sites in Botswana have differences of 17 W m−2.

[19] Because the conditions at each site vary little over the period of a few years, we expect the comparison statistics to be similar; therefore, we attribute most of the annual variation in bias to systematic measurement error. Changes in the land cover types and weather may also affect the bias; however, we believe this effect is small because there is no substantial change in land cover or annual dry-wet seasonal change for the study sites. Using long-term measurements collected at SURFRAD sites and some AmeriFlux sites, we calculated the annual bias of the comparisons of the measured and predicted daily Ld. Figure 4 shows the results at nine sites where at least 9-year data are available. The variations of annual bias of AmeriFlux Bondville and Fort Peck sites may reach up to 30 W m−2 and the variations are much larger than those at SURFRAD sites, explaining the poor prediction results at the AmeriFlux sites. Therefore, we did not include AmeriFlux Bondville, Fort Peck and Goodwin Creek data when calculating the all-site averages (last line in Tables 2 and 3).

Figure 4.

The annual bias (in watts per meters squared) in the comparisons between measurements and predictions of daily downward longwave radiation by Brunt [1932] (red line) and Brutsaert [1975] (blue line) at the nine sites. The variation in the annual bias of the comparison mainly results from measurement errors of downward longwave radiation.

[20] We conclude that the systematic measurement errors are primarily due to sensor calibration error produced by the effect of solar radiation and wind speed on pyrgeometers. Dutton [1993] pointed out that the absolute accuracy of the pyrgeometers has never been universally established to be better than +5% or 10 W m−2. Wardle and McArthur [1987] suggest that, under the optimum conditions, the root mean square error of pyrgeometer flux error is as large as 5% or 10 W m−2. This study further demonstrates that these errors are not necessarily random, such as the error caused by in situ calibrations. We calculate the SD of the annual bias of the nine sites, which varies from 3 to 12 W m−2, with an average of 5 W m−2. This is similar to the biases shown in Tables 2 and 3 for different sites and the average of their absolute values, about 7 W m−2.

[21] The average slope of all the sites for the Brunt [1932] clear-sky parameterization is 0.96, including the two sites near the equator, where the linear regression is not well defined because of the relatively stable daily Ld. If we exclude the two low-latitude sites, the average slope is 1.0, with a SD of 0.07; the slope is 0.91 with a SD of 0.07 for the Brutsaert [1975] equation. This demonstrates that the Brunt [1932] clear-sky parameterization combined with the Crawford and Duchon [1999] cloud parameterization works well to predict global Ld, especially for surface elevations less than 1000 m. The combination of the Brutsaert [1975] clear-sky parameterization and the Crawford and Duchon [1999] cloud parameterization works better for higher-elevation regions.

[22] The optimal way to calculate daily Ld is to average instantaneous Ld calculated from the instantaneous Ta and RH measurements using equation (4); however, in most cases, we only have daily averages of Ta and RH from conventional meteorological observations. In these cases, daily Ld was calculated using daily averaged Ta, RH, and cloud fraction with equation (4), then compared with measurements. The results are nearly the same as the results shown in Figure 3 and Table 3 (graph and data not shown to avoid repetition); therefore, daily Ld can be accurately calculated from the daily average of Ta and RH.

5. Decadal Variation in Global Ld

[23] In section 4, we found that the Brunt [1932] equation and the Brutsaert [1975] equation work well for a range of climate regimes and land cover types and elevations. The Brunt [1932] equation is more accurate than the Brutsaert [1975] equation for elevations less than 1000 m, while the Brutsaert [1975] equation is more accurate at elevations higher than 1000 m.

[24] In this section, the two methods are applied globally to estimate decadal variation in Ld using hourly meteorological observations. The Brunt [1932] equation is used for stations where surface elevation is less than 1000 m, and the Brutsaert [1975] equation is used for stations where surface elevation is exceeds 1000 m. The Crawford and Duchon [1999] parameterization is used to calculate the cloud effect on Ld. Since cloud cover fraction is available during both daytime and nighttime, we will discuss the decadal variation in daily Ld.

[25] The Integrated Surface Hourly (ISH) Database released by National Climate Data Center is used in this study. The database is derived from data exchanged under the World Meteorological Organization (WMO) World Weather Watch Program according to WMO Resolution 40 (Cg-XII) [WMO, 1996]. Data from over 9000 stations are typically available and accessible through the NCDC ftp server ( The database undergoes extensive automated quality control by the Air Weather Service, and over 400 algorithms are applied automatically to correctly “decode” the synoptic data, and to eliminate many of the random and systematic errors found in the original data. Data are generally available for 1929 to the present, with data sets from 1973 to the present being the most complete. In this study, we use data collected at about 3200 stations where data are available for 300 months at least from the period of 1973–2008.

[26] The data over U.S. and Canada are not reported here because the cloud observation method has changed from human visual assessment to instrument measured during the 1990s [Dai et al., 2006]. Satellite-derived cloud products have better global coverage. However, current long-term satellite cloud products often contain spurious signals resulting from satellite changes, sensor calibration [Trenberth and Fasullo, 2009], and satellite view geometry [Evan et al., 2007].

[27] To investigate the long-term variation in Ld, the linear trend is derived from the monthly Ld anomaly using the Mann-Kendall trend test method [Mann, 1945; Kendall, 1955]. The trends that passed the 95% significant confidence test are shown in Figure 5. As a result of global warming, Ld increases almost everywhere, while at the high latitudes in the Northern Hemisphere it increases at a higher rate. The global averaged trend is 1.9 W m−2 per decade. Prata [2008]-derived clear-sky Ld increased at a average rate of 1.7 W m−2 per decade from 1964 to 1990 using radiosonde data from 150 globally distributed stations. The meteorological observations have a much higher density (about 3200).

Figure 5.

Linear trend of daily Ld over 3200 global stations where data are available for at least 300 months (25 years) during the period 1973–2008. One point in the figure represents one station, and the color of the points shows the values of trend in Ld at the stations. The linear trend is calculated from the Mann-Kendall trend test method. Only the stations that passed the 95% confidence test are shown.

[28] Figure 6 shows that the increases in Ta and atmospheric water vapor concentration are the most important parameters controlling long-term variation of Ld. Although relative humidity remains stable (the global average trend of relative humidity is less than 0.1% per decade), it has substantial spatial variation. The trend of relative humidity is negatively correlated with the trend in Ta. This indicates that a trend toward drought where Ta increases at a higher rate. The contribution of variation in cloud is much less (the correlation between the trend in cloud cover fraction and Ld is about 0.11).

Figure 6.

The scatterplots of linear trends in Ld as a function of trends in air temperature (red) and water vapor pressure (green) at the stations shown in Figure 5. One point in the figure represents one station. The correlations of the trends in air temperature, relative humidity, and water vapor pressure are also shown.

[29] The dominant emitters of longwave radiation in the atmosphere are water vapor, and to a lesser extent, carbon dioxide. The water vapor effect is parameterized in this study, while the CO2 effect on Ld is not. The effect of CO2 can be accurately calculated with an atmosphere radiative transfer model given the concentration of atmospheric CO2. Prata [2008] showed that under the 1976 U.S. standard atmosphere, current atmospheric CO2 contributes about 6 W m−2 to Ld, and if atmospheric CO2 concentration increases at the current rate of ∼1.9 ppm yr−1 [Intergovernmental Panel on Climate Change, 2007], this will contribute to an increase of Ld by ∼0.3 W m−2 per decade. Therefore, the total variation rate in Ld is 2.2 W m−2 per decade.

6. Conclusions and Discussion

[30] In this study, we first evaluated the Brunt [1932] equation and the Brutsaert [1975] equation to calculate Ldc and the Crawford and Duchon [1999] cloud parameterization to account for the cloud effect on Ld. These methods were evaluated with long-term observations from 1996 to 2007 at 36 globally distributed sites. The evaluation shows that the instantaneous Ld under all-sky conditions can be estimated with an average bias of 2 W m−2 (0.6%), an average SD of 20 W m−2 (6%) and an average R of 0.86. Daily Ld can be estimated with a SD of 12 W m−2 (3.7%), and an average R of 0.93. This study demonstrates that the annual systematic error of Ld can reach up to 30 W m−2, with an average SD of 5 W m−2, which is similar to the average of absolute values of the bias for different sites.

[31] The two parameterizations work well for a range of climate regimes and land cover types and elevations. The Brunt [1932] equation is more accurate than the Brutsaert [1975] equation for elevations less than 1000 m, while the Brutsaert [1975] equation is more accurate at elevations higher than 1000 m.

[32] We then applied these methods to globally available meteorological observations to estimate decadal variation in Ld. Long-term variation in global Ld under all-sky conditions are reported in this study at about 3200 stations from 1973 to 2008. We found that daily Ld increased at an average rate of 2.2 W m−2 per decade from 1973 to 2008. The increase in Ld is mainly due to the increase in air temperature, water vapor and CO2 concentration.

[33] In this study, Ld is calculated from meteorological observations. This article gives a first estimate of long-term variation in Ld from 1973 to 2008 under all-sky conditions. The major uncertainty may be caused by the change in cloud characteristics, such as cloud type, base height and temperature. Because the contribution of variation in clouds to long-term variation in Ld is very small, we believe the trend reported in this study is reliable.


[34] The ground-based longwave radiation and other meteorological observations were obtained from AsiaFlux (, GAME AAN (, AmeriFlux (, the global FLUXNET project (, and SURFRAD ( The integrated hourly meteorological observations are downloaded from the National Climate Data Center ( The study is partially funded by NASA (grant NNX08AC53G).