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ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 29, NO. 4, 2012, 675–689 Estimation of Hourly Solar Radiation at the Surface under Cloudless Conditions on the Tibetan Plateau Using a Simple Radiation Model LIANG Hong 1,2 ( ), ZHANG Renhe 1 ( ), LIU Jingmiao 1,3 ( ), SUN Zhian 4 ( ), and CHENG Xinghong 5 ( ) 1 Chinese Academy of Meteorological Sciences, Beijing 100081 2 Graduate University of Chinese Academy of Science, Beijing 100049 3 Institute of Atmospheric Environment, China Meteorological Administration, Shenyang 110016 4 Centre for Australian Weather and Climate Research, Australian Bureau of Meteorology, Melbourne, Australia 5 Public Weather Service Center, China Meteorological Administration, Beijing 100081 (Received 19 August 2011; revised 19 December 2011) ABSTRACT In this study, the clear sky hourly global and net solar irradiances at the surface determined using SUNFLUX, a simple parameterization scheme, for three stations (Gaize, Naqu, and Lhasa) on the Tibetan Plateau were evaluated against observation data. Our modeled results agree well with observations. The correlation coefficients between modeled and observed values were > 0.99 for all three stations. The relative error of modeled results, in average was < 7%, and the root-mean-square variance was < 27 W m 2 . The solar irradiances in the radiation model were slightly overestimated compared with observation data; there were at least two likely causes. First, the radiative effects of aerosols were not included in the radiation model. Second, solar irradiances determined by thermopile pyranometers include a thermal offset error that causes solar radiation to be slightly underestimated. The solar radiation absorbed by the ozone and water vapor was estimated. The results show that monthly mean solar radiation absorbed by the ozone is < 2% of the global solar radiation (< 14 W m 2 ). Solar radiation absorbed by water vapor is stronger in summer than in winter. The maximum amount of monthly mean solar radiation absorbed by water vapor can be up to 13% of the global solar radiation (95 Wm 2 ). This indicates that water vapor measurements with high precision are very important for precise determination of solar radiation. Key words: solar radiation, numerical simulation, Tibetan Plateau Citation: Liang, H., R. H. Zhang, J. M. Liu, Z. A. Sun, and X. H. Cheng, 2012: Estimation of hourly solar radiation at the surface under cloudless conditions on the Tibetan Plateau using a simple radiation model. Adv. Atmos. Sci., 29(4), 675–689, doi: 10.1007/s00376-012-1157-1. 1. Introduction Solar radiation is of great importance for under- standing the land–atmosphere energy exchange pro- cess; it affects the change and evolution of the land surface processes (Oliphant et al., 2003; Wei and Wang, 2004). For example, the change of soil temper- ature and humidity, snowmelt, plant evapotranspira- tion, and photosynthesis processes are closely linked to variations in solar irradiance. Solar radiation at the surface is a clean and affordable energy source. Development and utilization of this renewable energy source requires the accurate estimation of special dis- tribution of the solar energy and its accurate forecast Corresponding author: LIU Jingmiao, [email protected] © China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of Atmospheric Physics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2012

Estimation of hourly solar radiation at the surface under cloudless conditions on the Tibetan Plateau using a simple radiation model

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ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 29, NO. 4, 2012, 675–689

Estimation of Hourly Solar Radiation at the Surface under

Cloudless Conditions on the Tibetan Plateau

Using a Simple Radiation Model

LIANG Hong1,2 (� �), ZHANG Renhe1 (���), LIU Jingmiao∗1,3 (���),SUN Zhian4 (���), and CHENG Xinghong5 (���)

1Chinese Academy of Meteorological Sciences, Beijing 100081

2Graduate University of Chinese Academy of Science, Beijing 100049

3Institute of Atmospheric Environment, China Meteorological Administration, Shenyang 110016

4Centre for Australian Weather and Climate Research,

Australian Bureau of Meteorology, Melbourne, Australia

5Public Weather Service Center, China Meteorological Administration, Beijing 100081

(Received 19 August 2011; revised 19 December 2011)

ABSTRACT

In this study, the clear sky hourly global and net solar irradiances at the surface determined usingSUNFLUX, a simple parameterization scheme, for three stations (Gaize, Naqu, and Lhasa) on the TibetanPlateau were evaluated against observation data. Our modeled results agree well with observations. Thecorrelation coefficients between modeled and observed values were > 0.99 for all three stations. The relativeerror of modeled results, in average was < 7%, and the root-mean-square variance was < 27 W m−2.

The solar irradiances in the radiation model were slightly overestimated compared with observation data;there were at least two likely causes. First, the radiative effects of aerosols were not included in the radiationmodel. Second, solar irradiances determined by thermopile pyranometers include a thermal offset error thatcauses solar radiation to be slightly underestimated.

The solar radiation absorbed by the ozone and water vapor was estimated. The results show thatmonthly mean solar radiation absorbed by the ozone is < 2% of the global solar radiation (< 14 W m−2).Solar radiation absorbed by water vapor is stronger in summer than in winter. The maximum amount ofmonthly mean solar radiation absorbed by water vapor can be up to 13% of the global solar radiation (95W m−2). This indicates that water vapor measurements with high precision are very important for precisedetermination of solar radiation.

Key words: solar radiation, numerical simulation, Tibetan Plateau

Citation: Liang, H., R. H. Zhang, J. M. Liu, Z. A. Sun, and X. H. Cheng, 2012: Estimation of hourly solarradiation at the surface under cloudless conditions on the Tibetan Plateau using a simple radiation model.Adv. Atmos. Sci., 29(4), 675–689, doi: 10.1007/s00376-012-1157-1.

1. Introduction

Solar radiation is of great importance for under-standing the land–atmosphere energy exchange pro-cess; it affects the change and evolution of the landsurface processes (Oliphant et al., 2003; Wei andWang, 2004). For example, the change of soil temper-

ature and humidity, snowmelt, plant evapotranspira-tion, and photosynthesis processes are closely linkedto variations in solar irradiance. Solar radiation atthe surface is a clean and affordable energy source.Development and utilization of this renewable energysource requires the accurate estimation of special dis-tribution of the solar energy and its accurate forecast

∗Corresponding author: LIU Jingmiao, [email protected]

© China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of AtmosphericPhysics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2012

676 ESTIMATION OF HOURLY SOLAR RADIATION ON THE TIBETAN PLATEAU VOL. 29

in both short- and long-term periods.Many studies (Li et al., 1995; Gautier and Lands-

feld, 1997; Lain et al., 1999; Ba et al., 2001; Zhanget al., 2002) have shown that surface radiation can beaccurately determined by satellite measurements com-bined with a few other meteorological parameters suchas solar zenith angle, precipitable water, and cloud mi-crophysical properties. Therefore, the calculation ofthe surface radiation budget may not require detailedestimation of all the radiative transfer processes in theatmosphere. In addition, many studies (e.g., Wengand Gao, 1995; Shazly, 1996; Zhao and Chen, 2000; Juet al., 2005) have shown that surface radiation can beaccurately obtained by empirical calculation methodsestablished by the surface radiation measurements anda few meteorological variables. However, the empiri-cal coefficients of such approaches usually vary withtime and space; it is hard to universally apply thesemethods to determine solar irradiances in different cli-matic regions. In the past several decades, many stud-ies have focused on estimations of daily and monthlymean of the solar irradiance, while studies that havefocused on determination of hourly or instantaneouslysolar radiation are rare.

Most early studies concentrated on the assessmentor estimation of solar irradiance at the surface usinghistorical observational data, satellite measured data,or model analysis data. The methods developed arehardly used in the forecast of the solar irradiance inshort and long term due to the limitation of localiza-tion or restrict of input data. To forecast solar radia-tion, a numerical weather prediction (NWP) model isused because it not only produces 7–10 days weatherforecast but also predicts the radiation field for thesame time period. However, current NWP modelsare not accurate enough to meet this requirement be-cause the radiation calculations in these models areperformed at a low time frequency due to computa-tional limits. For example, the model integration timestep is usually 400–750 seconds, but radiation calcu-lations are only performed at 1- or 3-h intervals inmost global NWP or climate models (Morcrette et al.,2008; Manners et al., 2009). Radiation is computa-tionally the most expensive process in an NWP model,and currently, computer power adequate to allow ra-diation to be calculated at each model time step isnot available. Although the 3-h radiation calculationsgreatly reduce time-consuming calculations in modelsimulations of the diurnal cycle of solar radiation, 3-hintervals are not well suited to modeling due to rapidchanges in the atmospheric conditions.

To improve this deficiency, Sun et al. (2007) devel-oped a simple radiation model, known as SUNFLUX,based on their radiative transfer model, SES2, for fast

yet accurate determination of instantaneous solar ra-diation at the surface. SUNFLUX uses all input dataavailable in a NWP model or obtainable from satel-lite measurements as an online scheme in a NWP orclimate model or as an offline scheme for determina-tion of solar irradiance at any time and location. Thescheme has been tested using the observational datafrom three atmospheric radiation measurements sta-tions located in three different climate regions (ARM,http://www.arm.gov). The accuracy of the global so-lar irradiance at the surface determined by this schemeis 7% higher, better than other schemes (Sun et al.,2007). Because the calculations of the surface solarirradiance are greatly simplified compared with thoseof a full radiative transfer model, it is much more eco-nomic to use in a global model. Offline schemes aremore complicated than early empirical models, buttheir accuracy is much better than those of empiricalmodels.

In this study, we further evaluated the SUNFLUXscheme using the observational data collected on theTibetan Plateau (i.e., the Plateau), and we used thisscheme to investigate solar radiation characteristics inthis region.

The Tibetan Plateau is the highest topographicfeature in the middle of the Eurasian Continent, withaverage height of 4500 m above the mean sea level, andit has important roles in global and regional weatherand climate systems (Ding, 1992; Zhang et al., 2011).The surface heat flux on the Plateau is essential forthe occurrence of the abrupt seasonal change of thegeneral circulation there and for the persistence of theAsian monsoon (Ye and Wu, 1998). Solar radiationplays a crucial role in the thermal features of the at-mosphere over the Plateau. Because of the scarcity ofsolar irradiance measurements and the uneven spatialdistribution of radiation observation stations, numeri-cal simulations are essential for understanding the sur-face radiation budget on the Plateau. Moreover, thePlateau is one of the regions of China where the solarenergy resource is the most abundant. Therefore, itis important to accurately estimate solar irradiance inthis region.

2. Data, model and methodology

2.1 Data

The data input to the SUNFLUX model includethe following parameters: total column ozone amount,carbon dioxide mixing ratio, surface albedo, surface airpressure, solar zenith angle, and precipitable water va-por (PW). To accurately determine the surface solarradiation and validate the scheme, the sites selectedfor this study measured the following data simultane-

NO. 4 LIANG ET AL. 677

ously: PW, solar radiation, and surface air pressure.Only three stations (Gaize, Naqu, and Lhasa) on thePlateau meet this condition. Gaize (32.31◦N, 84.06◦E,4394 m) is located in the western part of the Plateau,and the land surface at the site is rather flat and ho-mogeneous (Wang et al., 2004). Because of the highelevation of Gaize site, the surface pressure is ∼ 590hPa, half of that at the sea level. The aerosol opticaldepth in the visible spectrum is very stable around 0.1throughout the year (Zhang et al., 2003), which is closeto the background value of clear air over land. In addi-tion, anticyclonic systems often dominate the region,so cloudless days are common throughout the year.These conditions suggest that Gaize may be an idealobservational site to validate the model results undercloudless conditions. Naqu (31.48◦N, 92.06◦E, 4477m) is located in the north-central part of the Plateau,and its topography is high-altitude, hilly terrain withmore complex land surface features than Gaize. Theair mass here is approximately half of that at the sealevel. Lhasa (29.67◦N, 91.13◦E, 3650 m) is located inthe south-central part of the Plateau. This observationsite is located at the Lhasa River valley, surroundedby mountain ranges with relative height differencesgreater than 1000 m. Surface air pressure at Lhasais ∼ 650 hPa. The aerosol optical depth in the visiblespectrum at Naqu and Lhasa is ∼ 0.2, slightly largerthan at Gaize (Zhang et al., 2003). The regions on thePlateau where Gaize, Naqu, and Lhasa are located aresub-arid and subhumid (Yan et al., 2002). Therefore,the three locations differ in latitude, altitude, climaticcondition, and topography, making them favorable fortesting and comparing model results.

Water vapor does strongly absorb solar irradiance,and its distribution is highly variable in both space andtime. The uncertainties of the water vapor measuredby radiosonde and retrieved by Moderate-ResolutionImaging Spectroradiometer (MODIS) on the Plateauhave been discussed in many studies (e.g., Takagi etal., 2000; Liu et al., 2005, 2006). Lack of precise andcontinuous water vapor observations is one of the ma-jor sources of error in numerical weather predictionmodels (Liu et al., 2005). The traditional techniquefor water vapor measurements is to launch radioson-des, normally twice daily. This method is not only ex-pensive but also poor in both spatial coverage and tem-poral resolution. The observational technique, basedon the Global Positioning System (GPS) and is sen-sitive to the spatial and temporal distribution of thewater vapor content in the atmosphere, has made itpossible to retrieve precise and continuous estimatesof water vapor with spatial density governed by thenumber of receivers deployed (Bevis et al., 1994; Wangand Zhang, 2008). The accuracy of GPS-derived PW

has been shown to be near that of measurements bya water vapor radiometer and better than that of ob-servations from radiosonde (Liou et al., 2001; Sapucciet al., 2005; Guerova et al., 2005; Baelen et al., 2005;Liu et al., 2005; Pacione and Vespe, 2008). The ad-vantages of GPS-derived PW include data availableunder all weather conditions, high temporal resolu-tion (5-min to 2-h intervals), high accuracy (< 3 mmin PW), and long-term stability (Wang and Zhang,2008). All of these advantages make the GPS-derivedPW data very appealing for use in the calculations ofsolar irradiances. The PW measurements by GPS anddata processing were previously described in Liu et al.(2005) and Liang et al. (2010). The temporal reso-lution for PW used in this study is 30-min intervals.Daily total column ozone amounts were acquired inreal time from the Total Ozone Mapping Spectrome-ter (TOMS, http://toms.gsfc.nasa.gov/teacher/ozoneoverhead.html) for global coverage with 1◦ (lat)×1.25◦

(lon) resolution. The TOMS total ozone column ob-servations agree very well with data from an ensem-ble of Dobson and Brewer instrument ground stationsaround the world (McPeter and Labow, 1996; Kroonet al., 2006). The ozone values at the three sites usedin this study were determined by linear interpolationfrom TOMS data. The annual mean carbon dioxidemixing ratio observed at Waliguan, a global back-ground atmosphere station on the Plateau, was used inthe calculations. The carbon dioxide mixing ratio wasacquired from The World Data Centre for GreenhouseGases website (WDCGG, http://gaw.kishou.go.jp/wdcgg/). Surface air pressure and temperature datawere obtained from the China Meteorological DataSharing Service System (MDSS, http://cdc.cma.gov.cn/).

We acquired solar radiation data from ground mea-surements. An automatic weather station (AWS) wasinstalled at Gaize and began operation in October1997 as a part of the Japanese Experiment on theAsian Monsoon (Wang et al., 2004). We acquired totaldownward and upward solar radiation (0.3–2.8 μm)measured at 5-second intervals from upward-lookingand downward-looking high-precision pyranometers(MS-802, EKO instruments Trading Co., Ltd., Japan)mounted on a 1.5-meter-high horizontal platform. Thedatasets were averaged hourly to reduce random error.All radiation sensors are calibrated and serviced everyyear (Liu et al., 2005). We acquired solar radiationmeasurements at Naqu and Lhasa from the MDSS.The datasets were also averaged hourly to reduce ran-dom error. Only global solar radiation observationswere available for Naqu. For the Lhasa site, global,reflected, and diffuse solar radiation observations wereacquired.

678 ESTIMATION OF HOURLY SOLAR RADIATION ON THE TIBETAN PLATEAU VOL. 29

Surface albedo is an important parameter fordetermination of surface radiation budget. Surfacealbedo at Gaize and Lhasa sites was calculated us-ing hourly total downward and upward solar radiationdata. The MODIS global land surface albedo product(MCD43B3, version 5.0) with spatial resolution 1 km× 1 km and 8-day time interval 8 days was acquiredfor the Naqu site. MODIS surface albedo data wereacquirede from a website (ftp://e4ftl01.cr.usgs.gov/MOTA/). Wang et al. (2004) showed that MODISglobal land surface albedo meets an absolute accuracyrequirement of 0.02 and has no distinctive bias com-pared with the ground-measured albedo.

The data collected in 2001 and 2003 at Gaize,2003 at Naqu and from 2001 to 2008 at Lhasa wereused in this study. The data (collected under clearsky conditions) were sorted based on the total cloudfraction records available four times per day from themeteorological stations. If the total cloud fractionsat 0200 LST, 0800 LST, 1400 LST and 2000 LSTwere all < 0.1, then the day was assumed clear anddata during daylight hours were selected. Some of thedata selected under these conditions, however, wereinevitablely contaminated by presence of clouds.

2.2 Radiation model

The SUNFLUX model was developed based on aseries of calculations using a radiative transfer modelSES2 (Sun, 2008, 2011) for various atmospheric condi-tions. To ensure that the SUNFLUX model could beused globally, the total column values of three majorabsorbing gases (H2O, CO2, and O3) were varied tocover all possible values occurring in the global atmo-sphere. The effects due to N2O, CH4, and O2 wereimplicitly considered, and the changes in mixing ratiosfor these minor species were not included in the SUN-FLUX model. In facts, the radiative effects due tothese minor species were very small. Houghton et al.(2001) have suggested that from the years 1750 to 2000CH4 mixing ratio increased from 750 to 1750 ppb andN2O mixing ratio increased from 270 to 315 ppb. Theradiative effects due to the adding CH4 and N2O wereonly 0.48 W m−2 and 0.15 W m−2, respectively. In ad-dition, the solar zenith angle and surface albedo signif-icantly impacted the radiation at the surface and wereexplicitly considered in the model. The Rayleigh scat-tering was treated explicitly in the SUNFLUX model.The value of the solar constant was set to 1360.8 Wm−2 (Kopp and Lean, 2011) in the model. To developthe scheme, the concept of separation of variables wasused to deal with each variable individually and thepolynomial fitting methods were employed to createregression equations (Sun et al., 2007). Table 1 showsthe SUNFLUX model input variables. Notably, the

Table 1. The SUNFLUX model input variables.

Variables Definitions Unit

PW Precipitable water vapor cmO3 Total ozone amount DU

CO2 Carbon dioxide density ppmvθ Solar zenith angle degreeα0 Surface albedo —P0 Surface pressure hPa

Table 2. Division of spectral bands of the SUNFLUXscheme and major absorbing species in each band.

Band Spectral range (μm) Species

A 0.2–0.5 O3

B 0.5–0.83 O3, H2O, O2

C 0.83–5.0 H2O, CO2, CH4, N2O

radiative effects of aerosols were not included in themodel in this study.

Table 2 presents the SUNFLUX model radiationband structure and absorbing species in each spectralband. The three major species (H2O, CO2, and O3)have different absorbing spectra. Note that CH4, N2O,and O2 were considered implicitly in the scheme asmentioned above. The use of three distinct bands forthe model was expected to provide a more accuraterepresentation of Rayleigh scattering and gas absorp-tion processes, both of which have a strong spectraldependence. The details on the development of themodel for each band were previously listed in Sun etal. (2007).

The global solar radiation (F ↓b ) at the surface for

each band was obtained using the following expression(Sun et al., 2007):

F ↓b = μS0Tb(1 − α↑)/(1 − α0α↓) , (1)

where Tb represents band transmittance due to absorp-tion, α ↑ is Rayleigh scattering albedo to downward-travelling irradiance, α↓ is Rayleigh scattering albedoto upward-travelling radiation, α0 is surface albedo,(1−α↑) represents reflection due to Rayleigh scatter-ing, and (1−α0α↓) accounts for the multiple reflectionbetween the surface and the atmosphere. The net so-lar irradiance (Fb,net) at the surface for each band isthen given by

Fb,net = F ↓b (1 − α0) . (2)

The solar irradiances for the three bands determinedby SUNFLUX model agreed well with those deter-mined by SES2 model (Sun et al., 2007; Li et al., 2007).The mean relative errors for both global and net ir-radiances determined by the SUNFLUX model were

NO. 4 LIANG ET AL. 679

< 1% and root mean square (rms) error was < 0.1W m−2. Therefore, the solar radiation determined bySUNFLUX for the three bands may have high accu-racy.

In this study, we used the following three parame-ters to measure the accuracy of the SUNFLUX modelon the Plateau. They are the correlation coefficient(r), mean relative error, and the rms of the error. Themean relative error is defined by

em =

i=1

|εi|∑

i=1

Fi,obs% , (3)

where εi = Fi,fit−Fi,obs is the difference between mod-eled solar irradiances (Ffit) and field measurements(Fobs). The rms of the error is defined by

σ =

√1n

i=1

[εi − E(εi)]2 , (4)

where E(εi) is the mean of εi. This parameter pro-vides a measure of the range of errors.

3. Results

3.1 Seasonal variation of surface albedo

The surface albedo has a significant impact onthe solar irradiances at the surface. It is influencedby many factors, such as soil type, vegetation cover-age, and soil moisture, and it varies with space andtime. The seasonal variations in the daily mean surfacealbedo of Gaize, Naqu, and Lhasa sites are shown inFig. 1. The surface albedo of the three sites is larger inwinter than in summer. Due to the effect of the snowcoverage, some extreme values of the surface albedoare present in winter. The surface albedo is mainlyaffected by the soil moisture and vegetation coveragein summer (Wang et al., 2004). Because the soil mois-ture and vegetation coverage increase in summer, thesurface albedo decreases. Because the land surface fea-tures of the three locations differ from each other, thevalues of the surface albedo of the three sites are dis-tinct. The annual mean surface albedos of Gaize, Naquand Lhasa are ∼0.25, 0.22, and 0.20, respectively.

3.2 Hourly solar irradiance estimations

Due to the significant effect of the solar zenith an-gle on the solar irradiance at the surface, we set thecalculation time interval to 1 min when using the SUN-FLUX model to determine the solar irradiances. Thehourly results were obtained by averaging the 60 cal-culations within 1 h to compare with that of field mea-surements. PW intervals of 30 min and 1-h for surface

pressure and albedo were linearly interpolated to 1 minintervals for datasets that were used in the solar radi-ation calculations. Daily total column ozone amountand annual mean carbon dioxide mixing ratio were alsoapplied to the solar radiation determination.

Anton et al. (2010) found that diurnal variabilityrange of total column ozone amount is usually within10%. This diurnal variation is likely caused by the di-urnal photochemical process in the lower troposphererelated to the formation of tropospheric ozone nearthe Earth’s surface at populated urban locations. Thechanges of global radiation irradiances were within 1.8W m−2 at Gaize if the ozone changed by 10% at thesite during 2003. Therefore, diurnal variation of totalcolumn ozone amount has a minimal impact on theradiation at the surface.

Figure 2 shows the global, direct and net solar ir-radiances determined by the model under clear sky atGaize, Naqu, and Lhasa. The seasonal variability ofsolar radiation is simulated well. The magnitudes ofglobal, direct, net and diffuse solar irradiances at thesame site are clearly differentiated from each other.The solar radiation at the three sites exhibits slight dif-ferences. The diffuse solar irradiance, whose values aremuch smaller than those of global, direct, and net so-lar radiation, shows no significant seasonal variabilityat the three sites. The annual maximums of global, di-rect, net and diffuse solar radiation are ∼1100 W m−2,1000 W m−2, 900 W m−2, and 60 W m−2, respec-tively. Due to the significant effect of surface albedoon the net solar radiation, the net solar irradiance isextremely low when the surface albedo is extremelyhigh during the winter months.

Fig. 1. Seasonal variations in the daily mean surfacealbedo of Gaize (solid line) in 2003, Naqu (broken line)in 2003, and Lhasa (dot-dash line) in 2007. The surfacealbedos of the Gaize and Lhasa sites were determined byfield measurements and that of Naqu was retrieved fromthe MODIS dataset.

680 ESTIMATION OF HOURLY SOLAR RADIATION ON THE TIBETAN PLATEAU VOL. 29

Fig. 2. Global, direct, net, and diffuse solar irradiancedetermined by the parameterization under clear sky con-ditions at 0600 UTC at Gazie and Naqu in 2003 andLhasa in 2007.

To validate the SUNFLUX model, a comparisonbetween model simulated hourly solar radiation andthe field measurements under the cloudless sky at the

Gaize, Naqu, and Lhasa is shown in Fig. 3. The sta-tistical indicators of the agreement between the modelsimulations and observations are provided in Table 3.These indicators include correlation coefficient, meanrelative error from Eq. (3), and the rms error from Eq.(4). From Fig. 3 and Table 3, the modeled solar ir-radiations for the three sites are in reasonably goodagreement with the observations, and the correlationcoefficients between these estimates and correspond-ing ground observations are all > 0.99. Therefore, it isappropriate to use the SUNFLUX model to determinethe solar radiation under clear sky conditions in thesub-arid and sub-moist areas on the Plateau.

However, the modeled errors for the three siteswere different from each other. As Fig. 3 shows, sys-tematic biases clearly exist at Gaize and Lhasa withglobal solar irradiance determined by the model beingslightly overestimated compared with observations,while the results at Naqu do not show systematic bias.The reason for the overestimate of solar radiation atGaize and Lhasa are discussed in the later part of thissection. The rms errors for global solar radiation atGaize and Lhasa are smaller than for Naqu. Thismay be due to the different data sets of the surfacealbedo used in the calculations. The surface albedoof Gaize and Lhasa were determined using ground ob-servations, while that of Naqu was retreived from aMODIS dataset. Wang et al. (2004) have validatedthe accuracy of the MODIS global land surface albedoproduct using ground measurements at Gaize. Theyindicated that the ground surface at the site is ratherflat and homogenous on the scale of several satellitepixels. However, Naqu has hilly terrain and undulatedtopography, which make the surface ground more com-plex and inhomogenous than at Gaize. The MODIS-derived surface albedo averaged on an area of 1 km ×1km may be different from the ground measurements atthe Naqu meteorological station. The surface albedoat Naqu is underestimated by MODIS albedo prod-uct compared with the results shown by Li and Hu(2006). Due to the multiple scattering between thesurface and the atmosphere, the global solar radia-tion at the surface is affected by the surface albedo(Sun et al., 2007). From Eq. (1), we can deduce thatglobal solar irradiances at Naqu were underestimatedbecause of the underestimated surface albedo retrievedby MODIS measurements. In addition, the error in themodel may be also due to the low temporal resolution(8-day intervals) of the MODIS-derived albedo.

To further validate the model to simulate thehourly solar irradiances, the global, direct, net so-lar, and diffuse radiation are modeled and comparedwith ground observations for 8 years at Lhasa. Fig-ure 4 shows that the seasonal variations of solar ir-

NO. 4 LIANG ET AL. 681

Fig. 3. Comparison of modeled solar irradiances with field observations at Gaize andNaqu in 2003 and at Lhasa in 2007.

Table 3. Statistical indicators of the agreement between model simulations and observations at Gaize, Naqu and Lhasa.

SW Site r em (%) σ (W m−2) Year

Global flux Gaiz 0.998 5.9 21.4 2003Naqu 0.995 5.3 31.9 2003Lhasa 0.997 8.6 20.6 2007

Net flux Gaiz 0.997 5.9 17.0 2003Naqu — — — —Lhasa 0.997 8.7 16.5 2007

Direct flux Gaiz — — — —Naqu — — — —Lhasa 0.996 8.0 22.7 2007

682 ESTIMATION OF HOURLY SOLAR RADIATION ON THE TIBETAN PLATEAU VOL. 29

Fig. 4. Comparison of modeled diffuse irradiances with field observations at Lhasa.

Table 4. Statistical indicators of the agreement between model simulations and observations at Lhasa.

Global flux Net flux Direct flux

Year r em (%) σ (W m−2) r em (%) σ (W m−2) r em (%) σ (W m−2)

2001 0.997 8.3 19.5 0.996 8.8 18.7 0.995 7.5 23.42002 0.997 5.1 20.7 0.997 5.6 18.3 0.996 4.9 23.92003 0.998 5.7 17.4 0.997 5.7 16.3 0.996 5.6 22.22004 0.994 4.9 32.0 0.995 4.4 24.1 0.994 5.4 30.32005 0.994 4.6 27.5 0.997 3.4 16.2 0.991 5.1 30.42006 0.996 6.4 20.9 0.995 6.1 17.1 0.995 7.1 22.22007 0.997 8.6 20.6 0.997 8.7 16.5 0.996 8.0 22.72008 0.996 6.2 22.4 0.995 5.7 17.3 0.994 6.4 25.9all 0.996 6.4 24.0 0.995 6.3 19.6 0.994 6.3 26.4

radiances at Lhasa are determined well. The magni-tudes of global, direct, net, and diffuse solar irradi-ance are clearly differentiated from each other. Fordiffuse solar irradiance, values are much smaller thanthose of global, direct, and net solar radiation, whichhad no significant seasonal variability. The variationsof global, direct, and net solar radiation are more re-markable during summer months than during wintermonths. This may be due to the high variability ofPW during summer.

The statistical indicators of the agreement betweenthe model simulations and observations at Lhasa areprovided in Table 4. Global, direct, and net solarirradiances determined using the model are in rea-sonably good agreement with the observations. Thecorrelation coefficients between these estimates andcorresponding field measurements are all > 0.99. Themean relative errors for the global, direct, and netsolar irradiance are 6.4%, 6.3% and 6.3%, and the rmserrors are 24.0 W m−2, 26.4 W m−2, and 19.6 W m−2,respectively. From Table 4, the rms error for directsolar radiation is slightly larger than that for globalsolar irradiance. This may be due to the errors in thediffuse solar radiation measurements. The direct solarradiation was obtained by subtracting the diffuse solarirradiance from the global solar radiation. This maygenerate some uncertainties in the ground measure-ments of the direct solar radiation because the obser-

vation error of the pyranometer is different from thatof the diffusometer. The diffusometer is constructedwith a pyranometer plus a shading disk that removesnot only the direct solar radiation but also part of thediffuse solar irradiance. Because of the uncertaintiesgenerated by the shading disk location, the obser-vation errors of the diffuse solar irradiance are diffi-cult to calibrate (Wang et al., 2008). Figure 5 shows

Fig. 5. Comparison of modeled diffuse irradiances withfield observations at Lhasa.

NO. 4 LIANG ET AL. 683

−100 0 1000

0.01

0.02

0.03

Difference (W m−2)

Pro

babi

lity

dens

ity

(a) SW global flux at Gaize

μ = 23.69

σ = 21.29

−100 0 1000

0.01

0.02

0.03

Difference (W m−2)

Pro

babi

lity

dens

ity

(b) SW net flux at Gaize

μ = 17.58

σ = 19.10

−100 0 1000

0.01

0.02

0.03

Difference (W m−2)

Pro

babi

lity

dens

ity

(c) SW global flux at Naqu

μ = −1.68

σ = 31.93

−100 0 1000

0.01

0.02

0.03

Difference (W m−2)

Pro

babi

lity

dens

ity

(d) SW net flux at Lhasa

μ = 22.32

σ = 19.10

−100 0 1000

0.01

0.02

0.03

Difference (W m−2)

Pro

babi

lity

dens

ity

(e) SW global flux at Lhasa

μ = 30.89

σ = 23.40

−100 0 1000

0.01

0.02

0.03

Difference (W m−2)

Pro

babi

lity

dens

ity

(f) SW direct flux at Lhasa

μ = 26.52

σ = 25.01

Fig. 6. Distribution of probability density for differences of modeled minus observedsolar radiation at Gaize, Naqu, and Lhasa. The solid line is the fitting curve usingthe Gaussian distribution function N(μ, σ).

the comparison of diffuse irradiances determined bythe model with field observations from 2001 to 2008at Lhasa. The ground observations of diffuse solar ir-radiance do not change in time, which may be dueto the low sensitivity of the diffusometers deployed atLhasa. Fortunately, the diffuse solar radiation underclear sky conditions is usually <60 W m−2, and its an-nual mean value is ∼35 W m−2, while the maximumsof the global solar radiation may be > 1000 W m−2.Therefore, we conclude that the direct solar irradiance

determined by subtracting diffuse solar radiation fromglobal solar irradiance did not have serious errors un-der cloudless conditions at Lhasa.

Figure 6 demonstrates the distributions of prob-ability density for differences of modeled minus ob-served solar irradiances at Gaize, Naqu, and Lhasa.The probability distribution functions for the differ-ences are close to Gaussian. The mean differencesbetween modeled and observed solar irradiances arepositive at Gaize and Lhasa, which also means that the

684 ESTIMATION OF HOURLY SOLAR RADIATION ON THE TIBETAN PLATEAU VOL. 29

Fig. 7. The thermal offset of thermopile pyranometerduring nighttime in 2003 at Gaize.

solar irradiances determined by the model at thesesites are overestimated compared with ground obser-vations. These positive biases clearly indicate a ne-cessity to include the aerosol radiative effect in themodel. Though the aerosol optical depth in the visi-ble spectrum is much smaller on the Plateau than onplain areas in eastern China, the annual mean aerosolradiative forcing may be between −10 W m−2 and 0W m−2 (Li et al., 2010).

However, the systematic biases of the solar irradi-ances determined by the model may be also due tothermal offset error of the shortwave solar pyranome-ters, which consist of thermopile plus a black detec-tor. The thermal offset of thermopile pyranometersis a result of the temperature gradient between thepyranometer dome and its thermopile (Dutton et al.,2001; Haeffelin et al., 2001; Philipona, 2002). Due tothe thermal offset, the solar irradiances field measure-ments were underestimated to a certain degree. Thevalues of thermal offset during nighttime were approx-imately −2 W m−2 at Gaize (Fig. 7). The thermaloffset of the thermopile pyranometers may be largerduring daytime than that during nighttime (Philipona,2002). It is therefore necessary to have the instrumentcarefully tested to determine the reasons for the ther-mal offset errors and apply an appropriate correctionfactor, as was done for the Eppley Laboratory preci-sion spectral pyranometer by Reda et al. (2005). Thistask, however, is beyond the scope of this study.

3.3 Estimations of diurnal solar irradiancevariation

Figure 8 shows the comparison of the mean diurnalvariation of modeled solar irradiances with field ob-servations at Gaize, Naqu, and Lhasa. The modeled

diurnal variations were comparable with those fromsolar irradiance field measurements, and the mean er-rors (modeled minus observed) were near zero at thesesites. Several earlier studies (e.g. Masuda et al., 1995;Shazly, 1996; Batlles et al., 2000) have shown thatmodels of solar radiation are sensitive to solar zenithangle and that it is generally difficult to obtain accu-rate results for a solar zenith angle greater than 85◦.

The results of this study show that solar irradiancescan be accurately determined without using additionalconditions, even at zenith angles of 89◦. The modelused in this study does not have the weakness relatedto the size of the solar zenith angle. The modeled solarirradiances were slightly larger than the ground mea-surements at Gaize and Lhasa. The result at Naqu,however, was opposite those at Gaize and Lhasa. Thismay be due to the negative bias of the MODIS-derivedsurface albedo as shown in the previous analysis.

3.4 Solar irradiances absorbed by ozone

Because the Tibetan Plateau has a highland con-tinental climate and a very complex topography withgreat variations, the spatial distributions and temporalvariability of the major absorbing gases (H2O and O3)are different from that of other regions on Earth (Liu etal., 2003; Xu et al., 2008; Zhang and Zhou, 2009). Theradiative effect of these gases on the Plateau is of greatinterest. Figure 9 (left panel) demonstrates that theseasonal variations of total column ozone amounts atthe three sites are similar. The maximal and minimalozone content of the atmosphere in spring and winterwere ∼ 300 DU and 260 DU, respectively. To deter-mine the shortwave radiation absorbed by the ozoneon the Plateau, the global solar irradiances were cal-culated twice using the model. The first calculationdid not include the radiative effect of the ozone, andthe second one did include the effect. The radiativeeffect of the atmospheric ozone was obtained by sub-tracting the global solar radiation determined by thesecond calculation from that derived from the first cal-culation. The monthly mean evolutions of solar radia-tion absorbed by atmospheric ozone at the three sitesare shown in Fig. 9 (right panel). The radiative effectof the atmospheric ozone on the Plateau was largestin spring and smallest in winter. The monthly meanvalues of the effect at the three sites were ∼ 8–12 Wm−2, namely ∼ 1.51%–1.78% of the global solar radi-ation. The values of the effect are comparable withthe results reported by other authors. For example,Ramanathan and Dickinson (1979) showed that theseasonal zonal mean solar absorption by stratosphericozone at 30◦N is ∼ 8–13 W m−2. Therefore, the ozonehas a small impact on the solar radiation at the sur-face on the Plateau. This, however, does not mean

NO. 4 LIANG ET AL. 685

Fig. 8. Comparison of the mean diurnal variation of modeled solar irradiances withfield observations at Gaize, Naqu, and Lhasa. Red solid line and blue broken lineexpress the modeled and the observed, respectively. Green dot-dashed line representsthe simulation error (modeled minus observed). The error bars indicate estimatedstandard deviation of average.

that the atmospheric ozone radiative effect is not im-portant for the solar radiation at the surface. The at-mospheric ozone layer filters out photons with shorterwavelengths (< 0.32 micron) of the ultraviolet raysfrom the Sun that would be harmful to most formsof life on Earth.

3.5 Solar irradiance absorbed by water vapor

Monthly mean evolution of PW and its impact onsolar radiation are shown in Fig. 10. One can see that

the peak PW during the rainy season (June to Septem-ber) is ∼14 mm at Gaize, 15 mm at Naqu, and 20 mmat Lhasa, and during the dry season (8 months peryear); the lowest PW is ∼2 mm at Gaize, Naqu, andLhasa. To determine the solar radiation absorbed bywater vapor on the Plateau, the global solar irradi-ances were also calculated twice using the model. Thefirst calculation did not include the radiative effect ofwater vapor and the second one did include the effect.The radiative effect of the atmospheric water vapor

686 ESTIMATION OF HOURLY SOLAR RADIATION ON THE TIBETAN PLATEAU VOL. 29

Fig. 9. (a) Monthly mean evolution of total column ozone amount, and (b) monthlymean evolution of short-wave radiation flux absorbed by ozone at Gazie, Naqu, andLhasa.

Fig. 10. (a) Monthly mean evolution of PW, and (b) monthly mean evolution ofshort-wave radiation absorbed by water vapor at Gaize, Naqu, and Lhasa.

was obtained by subtracting the global solar radiationdetermined by the second calculation from that de-rived from the first calculation. Monthly mean evolu-tions of solar radiation absorbed by water vapor at thethree sites are shown in Fig. 10 (right panel). Watervapor has a significant impact on the solar irradiancesat the surface on the Plateau, especially during therainy season. The monthly mean values of the effectwere between 14.0 W m−2 and 70.0 W m−2, namelyfrom 3.0% to 11.0% of the global solar radiation atGaize; between 9.0 W m−2 and 71.0 W m−2 (from2.0% to 12.0%) at Naqu, and between 14.0 W m−2 and95.0 W m−2 (from 3.0% to 13.0%) at Lhasa. Tarasovaand Fomin (2000) showed that solar radiation absorp-tion by water vapor for the midlatitude winter atmo-sphere at the 30◦ solar zenith angle was 191 W m−2.The PW on the plateau in winter was ∼7% of that forthe midlatitude winter atmosphere (Gao et al., 2003).Therefore, we conclude that the solar radiation ab-sorption by water vapor on the Plateau in winter isbetween 9 W m−2 and 14 W m−2. Liu et al. (2005)

suggests that the negative bias of PW determined fromECMWF reanalysis data may be overestimated by 7.0mm on the Plateau in summer. Such a PW error canmake the global solar radiation determination error asmuch as 30 W m−2, which is almost half of that ab-sorbed solar radiation by water vapor. In addition,monthly mean dry bias of PW by radiosonde may be> 3 mm during rainy season on the Plateau. Due tothe dry bias, the global solar irradiance determinationerror is > 10 W m−2. Therefore, accurately and con-tinuously measurement of PW is very important forprecise determination of solar irradiances at the sur-face on the Plateau.

4. Summary and discussion

A simple radiation model (SUNFLUX) based ondetailed radiative transfer was used to calculate hourlyglobal, direct, net, and diffuse solar irradiances atthe surface under cloudless conditions on the TibetanPlateau in this study. Carbon dioxide ground mea-

NO. 4 LIANG ET AL. 687

surements, GPS-derived PW, ozone data from TOMsatellites, and MODIS-derived surface albedo wereused in the calculations. Field observations from threesites (Gaize, Naqu, and Lhasa) corresponding to threedifferent climatic regions on the Plateau were chosento validate the solar irradiances determined by themodel. The results show that the model can be usedto produce relatively accurate hourly solar radiationestimates under clear sky conditions. The correlationcoefficients between determinations for global, net anddirect solar radiation and corresponding ground obser-vations were all in excess of 0.99. The mean relativeerrors for global, net, and direct solar radiation were< 6.4%, < 6.3%, and < 6.3%, respectively, and rms er-ror was < 24.0 W m−2, 24.7 W m−2, and 26.4 W m−2,respectively. The solar irradiance can be accuratelydetermined by the model when the solar zenith angle is> 85◦. Moreover, the solar irradiances absorbed by theozone and water vapor were estimated by the model onthe Plateau. The results show that the monthly meansolar radiation absorbed by the ozone is < 2% of theglobal solar radiation (< 14 W m−2). Solar irradianceabsorbed by water vapor was stronger in summer thanin winter. The largest value of monthly mean solar ra-diation absorbed by water vapor during rainy seasonis ∼ 13% of the global solar radiation (95 W m−2).This indicates that PW measured accurately and con-tinuously is very important for precise determinationof solar irradiances at the surface on the Plateau.

The results of this study suggest that the SUN-FLUX model provides an effective way to estimatethe solar energy resource and solar radiation budgetat the surface on the Plateau. However, the solar ir-radiance estimated by the model was slightly overes-timated compared with field observations, indicatinga need to include the atmospheric aerosols radiativeeffects in the model. In addition, solar radiation ob-servations include a thermal offset error, which maycause solar irradiance to be underestimated between 8W m−2 and 20 W m−2 (Dutton et al., 2001; Philipona,2002; Lester and Myers, 2006; Cheng et al., 2009).The pyranometer calibration errors were between 2%and 5%, depending on instrument quality (Mcarthur,2005). So the accuracy of the SUNFLUX model was1%–2% above calibration errors. Nevertheless, furtherstudy is required to include the radiative effects ofclouds and aerosols in the model and to calibrate thethermal offset errors of pyranometers.

Acknowledgements. The authors are grateful to

Prof. Shikui LI and two anonymous reviewers for their

insightful comments, which led to significant improvement

in the manuscript. This work was financially supported by

the National Natural Science Foundation of China (Grant

Nos. 40905038, 40921003, 40775020, and 40905071).

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