Applied Energy 88 (2011) 2480–2489

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Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Estimation of monthly-mean daily global solar radiation based on MODISand TRMM products

Jun Qin a,⇑, Zhuoqi Chen b, Kun Yang a, Shunlin Liang c, Wenjun Tang a

a Laboratory of Tibetan Environment Changes and Land Surface Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, P.O. Box 2871, Beijing 100085, Chinab College of Global Change and Earth System Science, Beijing Normal University, Beijing 1000875, Chinac Department of Geography, University of Maryland, 2181 LeFrak Hall, College Park, MD 20742, USA

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

Article history:Received 27 September 2010Received in revised form 24 November 2010Accepted 6 January 2011Available online 5 February 2011

Keywords:Global solar radiationArtificial neural networkRemote sensingMODISTRMM

0306-2619/$ - see front matter � 2011 Elsevier Ltd Adoi:10.1016/j.apenergy.2011.01.018

⇑ Corresponding author.E-mail address: shuairenqin@gmail.com (J. Qin).

Global solar radiation (GSR) is required in a large number of fields. Many parameterization schemes aredeveloped to estimate it using routinely measured meteorological variables, since GSR is directly mea-sured at a limited number of stations. Even so, meteorological stations are sparse, especially, in remoteareas. Satellite signals (radiance at the top of atmosphere in most cases) can be used to estimate contin-uous GSR in space. However, many existing remote sensing products have a relatively coarse spatial res-olution and these inversion algorithms are too complicated to be mastered by experts in other researchfields. In this study, the artificial neural network (ANN) is utilized to build the mathematical relationshipbetween measured monthly-mean daily GSR and several high-level remote sensing products available forthe public, including Moderate Resolution Imaging Spectroradiometer (MODIS) monthly averaged landsurface temperature (LST), the number of days in which the LST retrieval is performed in 1 month, MODISenhanced vegetation index, Tropical Rainfall Measuring Mission satellite (TRMM) monthly precipitation.After training, GSR estimates from this ANN are verified against ground measurements at 12 radiationstations. Then, comparisons are performed among three GSR estimates, including the one presented inthis study, a surface data-based estimate, and a remote sensing product by Japan Aerospace ExplorationAgency (JAXA). Validation results indicate that the ANN-based method presented in this study can esti-mate monthly-mean daily GSR at a spatial resolution of about 5 km with high accuracy.

� 2011 Elsevier Ltd All rights reserved.

1. Introduction

The sun provides energy for almost all land surface processes onthe earth’s surface. GSR data are required in a large number ofapplications. In ecological modeling, the photosynthetically activepart of GSR is used in the photosynthesis and stored as the chem-ical energy for allocation to different living organs of plants such asroot, stem, and foliage. GSR is an indispensable component in landsurface models and hydrological models, which controls bothwater and heat exchanges. The knowledge of GSR distribution isalso important for the design of the photovoltaic power and solarheating systems in the clean energy area. Especially, GSR playsan irreplaceable part in crop growth modeling due to its tightrelation to photosynthesis. For many crop growth models such asWOFOST (Model for WOrld FOod STudies) and DSSAT (DecisionSupport System for Agrotechnology Transfer), monthly-mean GSRvalues plus other meteorological parameters, such as air tempera-ture and rainfall, are used to generate daily corresponding ones andthen imported into the model through the weather generator [1,2].

ll rights reserved.

Monthly-mean GSR values are also important input for plant distri-bution models [3].

Despite the great importance of GSR, the number of radiationstations is limited, compared to the number of stations where rou-tine meteorological variables are collected, such as air tempera-ture, humidity, sunshine duration, and cloud coverage [4–7].Thus, many empirical parameterization schemes are designed toindirectly estimate GSR from these routine variables [8]. Thesemethods could be roughly divided into three classes in accordancewith inputs: sunshine-based, temperature-based, and cloud-based.Based on mathematical forms, they could be classified as paramet-ric (such as Ångström–Prescott type methods) [9,10] and non-parametric (such as ANN-based methods) [11–14]. If calibratedwell, they (parametric and non-parametric) can estimate GSR witha high accuracy. However, since no explicit physics are consideredin these estimation schemes, calibrated parameters often varyfrom one site to the other, limiting their generalization and leadingto large uncertainties in GSR estimates at sites where no measuredGSR data are available to calibrate these schemes [15].

Remote sensing (RS) provides an alternative method to radia-tion estimation [16–19]. One advantage of RS is its ability to collectcontinuous signals in space and time at the top of atmosphere. This

Nomenclature

ANN artificial neural networkASL above sea levelCMA China meteorology administrationDSSAT decision support system for agrotechnology transferDTR diurnal temperature rangeEVI enhanced vegetation indexGSR global solar radiationJAXA Japan aerospace exploration agencyLST land surface temperatureMLP multilayer perceptron networkMODIS Moderate Resolution Imaging SpectroradiometerNOD number of daysR correlation coefficientRMSE root mean square errorRRMSE relative root mean square errorRS remote sensingRT radiative transferTP Tibetan PlateauTRMM Tropical Rainfall Measuring MissionWOFOST Model for WOrld FOod STudies

SymbolsH global solar radiation at the ground surfaceHo extraterrestrial global solar radiationJ value of cost functionJt value of cost function based upon observationsJw regularization term

M number of weightsN number of input/output pairsT matrix transposeW all the connection weights between network neuron

unitsX input vectorY output vectorYi simulated output vectorYo

i observed output vectorf(�) mathematical form for ANNg(�) transfer functioni running indexn number of weights for transfer functionp precipitationtd daytime land surface temperaturetm mean land surface temperaturetn nighttime land surface temperaturevi enhanced vegetation indexwi weight of input for transfer functionxi input for transfer functiony output of a transfer functionz altitude above sea levelc adjusted parameterdt difference between daytime and nighttime land surface

temperatureg number of daysj clearness indexs ratio of the local air pressure and the one at sea level

J. Qin et al. / Applied Energy 88 (2011) 2480–2489 2481

makes it possible to estimate radiation in remote regions whereradiation stations are sparse. RS can also provide many types ofhigh-level retrieval products for the public, such as surface albedo,LST, enhanced vegetation index (EVI), precipitation, and so on. Aremote sensing algorithm for GSR retrieval is generically basedon the radiative transfer model and the inversion procedure fromthe satellite-observed radiance to the surface GRS is rather compli-cated. Moreover, current RS products of GSR [19] have rathercoarse spatial resolutions such as 1.0� or more although their tem-poral resolutions can be as high as 3 h.

In an effort to develop a relatively simple and effective methodto estimate GSR with a high spatial resolution (0.05�), this studypresents an ANN-based method to directly build the functionalrelationship between available RS products and monthly-meandaily GSR observations. Then, this relationship is validated throughthe comparison of GSR estimates with observations at many radi-ation stations. Its performance is further evaluated against a JAXAGSR satellite product and the estimated GSR by a hybrid method[20]. The latter combines the physical mechanism of radiativetransfer (RT) processes and simplicity of Ångström-typerelationship.

2. Method and data

2.1. Method

ANN can be used to fit a function, recognize patterns, and clus-ter data [21]. It is typically composed of interconnected neuronunits organized in layers. In this study, a multilayer perceptronnetwork (MLP) is used to realize the fitting ability of ANN, whichcould be illustrated in Fig. 1. On the left panel of this figure, theschematic diagram of a neuron unit is displayed and its functioncan be mathematically abstracted as:

y ¼ gXn

i�1

wixi

!ð1Þ

where i denotes the index, xi one component of the input vector, wi

the weight for each xi, g(�) the transfer function which can takemany function forms such as linear, sigmoid, and hyperbolic tan-gent. On the right panel of Fig. 1, a MLP with three layers is illus-trated and its mathematical formula can be written in a compactform as:

Y ¼ f ðX;WÞ ð2Þ

where X represents the input vector, Y the simulated output vectorby ANN, W all the connection weights between network neuronunits, and f(�) denotes functional relationship between the inputvector and the output vector.

Its weights W need to be determined before ANN can be used toestimate or predict. The process of determining the weightsaccording to observations is called training or learning. This pro-cess is realized by adjusting the weights in order to minimize thefollowing cost function:

J ¼ 1N

XN

i¼1

ðYi � Y�

i ÞTðYi � Y

�

i Þ ð3Þ

where i denotes the index, Yi the simulated output vector (simu-lated observations) by ANN, Yo

i the observed output vector, N isthe number of input/output pairs, and J the sum of differences be-tween these pairs. There are many optimization algorithms to real-ize the minimization of J. The whole training process can beillustrated in Fig. 2. However, the over-fitting problem may be in-curred and the ANN generalization quality will weaken if thecost-function form like in Eq. (3) is taken during the learningprocess.

Fig. 1. Schematic diagram of the neuron unit (left panel) and artificial neural network (right panel). The ANN consists of a multitude of neuron units. The ANN could be usedafter its weights are determined.

Fig. 2. Schematic diagram for training process of ANN.

2482 J. Qin et al. / Applied Energy 88 (2011) 2480–2489

In the current process of training, the following cost-functionform is taken [22]:

J ¼ cJt þ ð1� cÞJw

J ¼ 1N

XN

i¼1

ðYi � Y�i ÞTðYi � Y�i Þ

Jw ¼1M

WT W

ð4Þ

where Jw is a regularization term used to make the response of ANNsmoother and less likely to overfit, c is an adjusted parameter,and M denotes the number of weights. In this study, theLevenberg–Marquardt back-propagation optimization algorithmcoupled with Bayesian regularization is used to train the ANN basedon the cost function Eq. (4). This scheme can adjust the value of cautomatically. In order to indicate the advantage of this trainingprocedure, another optimization algorithm, the scaled conjugategradient method, is also utilized to train the same ANN accordingto the cost function Eq. (3).

It is proven that a multilayer feed-forward network with a sin-gle hidden layer has the capability to approximate a function toany accuracy [23]. Thus, this ANN architecture is chosen here.However, both the optimal number of neurons and the type oftransfer function in the hidden layer need to be determinedthrough the trial-and-error procedure. In this work, two types oftransfer function (i.e., hyperbolic tangent sigmoid function and ra-dial basis function) and different numbers of neurons in the hiddenlayer are tested. Moreover, the training results are sensitive to theinitial weights, which are usually assigned randomly. In this study,the training course is performed twenty times to avoid this effect.All of these ANN tasks are performed using MATLAB neural net-work toolbox.

There is one thing worthy of being noticed. It depends on twopoints whether or not ANN performs satisfactorily when beingused to estimate or predict. On the one hand, the physical relation-ship must exist between input parameters and corresponding out-put ones; on the other hand, the chosen structure of ANN musthave the ability to reflect the physical relationship between inputsand outputs. If these two requirements are not met, ANN cannotwork well.

2.2. Study area and data

The Tibetan Plateau (TP) and its surroundings are chosen as thestudy area. The TP is the highest and largest plateau in the world,with an average elevation of 4000 m above sea level (ASL) and anarea of about 2.5 million square kilometers. As shown in Fig. 3,the study area extends from 25�N to 45�N and 70�E to 105�E. There,the elevation range is drastic and the terrain is complex. Moreover,the amounts of cloud and precipitation vary significantly from theeast to the west and from the south to the north. All of above fac-tors have great impacts on GSR. The possibility of generalizing it toother areas, therefore, is high, if some GSR estimation scheme canwork well in this region [24].

Fig. 3. Spatial distribution of meteorological stations where GSR is routinely measured. There are a total of 34 sites. 22 of them (white dot) are used to train ANN and the rest(black triangle) is used to validate retrieved GSR results.

J. Qin et al. / Applied Energy 88 (2011) 2480–2489 2483

Due to the harsh climate in this region, merely 34 radiation sta-tions are deployed by China Meteorological Administration (CMA)to directly measure GSR, which are illustrated in Fig. 3. The GSRmeasuring activity at Chengdu station was moved to Wenjiang sta-tion in 2004 and the one at Lanzhou station was moved to Yuzhongstation in 2005. As Shi et al. [25] pointed out, the errors in radiationmeasuring instruments used at CMA weather stations do not ex-ceed 5% after the year of 1990. However, GSR measurementsmay contain uncertainties larger than 5% due to many problemsother than instruments such as inappropriate measuring manipu-lations and occasional voltage instability. Thus, quality control ofthese measurement data has been made according to steps pre-sented by Tang et al. [26]. These steps could be roughly dividedinto two main procedures. In the first place, daily GSR measure-ments, which do not meet some hard physical conditions such asexceeding the theoretical clear-sky GSR values, need removing. Inthe second place, at each radiation site, the functional relationshipis constructed by ANN between measured GSR values and six rou-tinely measured meteorological parameters, which include dailyair temperature range, daily mean temperature, relative humidity,sunshine duration, precipitation, and relative optical air mass.After this, three sub-steps are performed: first, the scatter-plot ofthe estimated versus the observed is created; second, the fittingline and the 95% confidence interval lines are calculated; third,the GSR data is considered as the suspected data and then is ex-cluded if its value is outside of the 95% confidence interval line.More details on GSR data quality control can be found in Tang’sarticle.

In this study, monthly-mean daily GSR data from 2001 to 2007at 22 stations are used in the training process as input vectors and5 years of GSR data from 2003 to 2007 at the remaining 12 stationsare applied in the process of validation. Both the training and val-idation stations distribute over wide ranges of latitude, longitude,

and altitude in order to ensure the representativeness of the esti-mation algorithm presented in this study.

As mentioned above, RS products are used as inputs to train theANN for building their mathematical relationship with measuredGSR. Thus, these RS products must directly or indirectly containinformation that may affect GSR. Since both diurnal temperaturerange (DTR) and precipitation at weather stations are correlatedwith the amount of cloud and thus have a fairly large impact onGSR at the earth’s surface, they are often chosen as independentvariables in order to estimate GSR in many previous studies[6,27,28]. Thus, MODIS monthly averaged daytime/nighttime LSTs[29] and TRMM monthly accumulated precipitation [30] are cho-sen as one part of inputs to train ANN. However, the spatial reso-lutions of MODIS and TRMM products are 0.05� and 0.25�,respectively. Thus, TRMM data are spatially interpolated to 0.05�in order to match with MODIS products. In this study, MODIS day-time and nighttime LSTs need to be transformed as:

@t ¼ td � tn

and

Tm ¼td þ tn

2

ð5Þ

where td [K] denotes the daytime LST, tn [K] the nighttime LST, dt [K]the difference between the daytime and nighttime LSTs, tm [K] themean LST.

As well known, the ground surface conditions have an effect onGSR through the multiple-scattering between surface and theatmosphere, so MODIS monthly EVI [31] is selected as one inputto ANN since the high value of EVI normally corresponds to smallsurface albedo and then decreases the magnitude of multiple-scattering between the ground and the atmosphere, and vice versa.Besides, the number of days (NOD), in which the LST retrieval is

Table 1Training results for different configurations in the hidden layer.

Number of neurons in hidden layer Bayesian regularization Scaled conjugate gradient

Tansiga Radbasb Tansig Radbas

Best Worst Best Worst Best Worst Best Worst

2 neurons 1.30 1.35 1.30 1.36 1.34 1.75 1.37 3.324 neurons 1.13 1.20 1.13 1.29 1.23 1.47 1.27 1.636 neurons 1.09 1.14 1.08 1.22 1.19 1.44 1.23 1.548 neurons 1.08 1.12 1.07 1.11 1.14 1.42 1.18 1.4210 neurons 1.03 1.09 1.05 1.10 1.14 1.30 1.17 1.4112 neurons 1.04 1.15 1.01 1.08 1.13 1.30 1.12 1.3914 neurons 0.99 1.10 1.03 1.06 1.12 1.24 1.13 1.5316 neurons 1.01 1.14 1.01 1.13 1.07 1.28 1.09 1.2718 neurons 1.01 1.14 1.00 1.14 1.07 1.27 1.08 1.4420 neurons 1.01 1.12 1.01 1.12 1.07 1.17 1.06 1.34

a Tansig denotes hyperbolic tangent sigmoid function.b Radbas denotes radial basis function.

Fig. 4. Comparison between observed GSR and their simulated values after trainingat the training sites.

2484 J. Qin et al. / Applied Energy 88 (2011) 2480–2489

performed in 1 month, is normalized by the number of days in thecorresponding month and then taken as one input. This quantitycan reflect information on the mean amount of cloud cover in 1month because MODIS LST is not retrieved at a cloudy pixel. More-over, the relative optical air mass has a great influence on GSR at

Fig. 5. Holistic validation results at the 12 validation results. (a) Comparison between obsestimates by JAXA algorithm.

the ground surface. Where the altitude is higher and thus the rel-ative optical air mass is smaller, the radiation from sun is lessattenuated, and vice versa. This effect has to be taken into accountby using the relation between the atmospheric pressure and thealtitude and can be represented as:

s ¼ 10

�z18400

� tm

273

� �ð6Þ

where s denotes the ratio of the local air pressure and the one at sealevel, z [m] the altitude ASL, and tm [K] the mean LST. The entire in-put vector to ANN can be represented as X = [dt, tm, p, vi, g, s]T inwhich p [mm] denotes precipitation, vi the EVI, and g the NOD.

The ground GSR depends not only on the extraterrestrial GSR,but also on the atmospheric status. Since the extraterrestrial GSRcan be analytically calculated with high accuracy, the groundGSR could be completely determined once the atmospheric condi-tion is known. Therefore, the clearness index, which represents theatmospheric status, is selected as the output vector and defined as:

j ¼ HH0

ð7Þ

where H[MJ day�1] denotes GSR at the ground surface andH[MJ day�1] is the extraterrestrial GSR. So, the output vector canbe represented as Y = [j]T. Once j is determined, GSR can be ob-tained easily according to Eq. (7).

ervations and retrievals by ANN method. (b) Comparison between observations and

Fig. 6. Individual validation results for all 12 validation sites. They are Yining, Kashi, Ruoqiang, Hami, Dunhuang, Golmud, Shiquanhe, Yushu, Mianyang, Lijiang, Panzhihua,and Kunming from (a) to (l).

J. Qin et al. / Applied Energy 88 (2011) 2480–2489 2485

Table 2Performance of three estimation methods at the validation sites.

Site ANN Yang JAXA

RMSE R RMSE R RMSE R

Yining 1.24 0.98 1.87 0.99 1.86 0.96Kashi 1.24 0.98 2.55 0.98 1.85 0.98Ruoqiang 1.61 0.98 1.63 0.99 1.55 0.99Hami 1.34 0.99 0.83 0.99 1.55 0.99Dunhung 0.86 0.99 0.89 0.99 0.76 0.99Shiquanhe 1.85 0.97 0.90 0.99 0.73 0.99Yushu 1.39 0.96 0.91 0.98 1.74 0.94Mianyang 1.21 0.96 1.01 0.99 1.48 0.97Lijiang 1.37 0.91 1.24 0.94 2.89 0.77Panzhihua 1.73 0.90 2.50 0.97 1.47 0.94Kuming 1.28 0.91 1.26 0.97 0.82 0.96Hotan 1.11 0.98 1.51 0.99 2.41 0.98Emeishan 1.33 0.89 1.39 0.90 4.95 0.83Garze 1.54 0.94 1.60 0.97 5.94 0.79

2486 J. Qin et al. / Applied Energy 88 (2011) 2480–2489

The elevation range over the TP region and its surroundings israther large as shown in Fig. 3. Since the highest radiation station(Nagqu) is located at about 4500 m ASL, the altitudinal extension ofthe trained ANN may be questionable even though Nagqu site is in-cluded into the training dataset, as there is a large fraction of thePlateau where elevation is more than 4500 m ASL. So, some virtualinput/output pairs are generated in order to increase the applica-bility of the ANN-based method in the vertical dimension. First,pixel points, which have high elevations (above 6800 m ASL), littleprecipitation (less than 10 mm month�1), and high NOD (greaterthan 28 days per month), are extracted from remote sensingimages. These pixels correspond to clear skies and thus large clear-ness index values. Second, GSR values are generated at these pixelsby running Yang’s hybrid model for clear-skies. Finally, RS data andthe corresponding simulated clear-sky GSR values at these pixelsare added into the training dataset.

Lhasa 1.14 0.97 0.74 0.98 3.88 0.88

3. Results and discussion

There are a total of 1678 input/output pairs at 22 stations from2001 to 2007. These pairs are used to train ANN to build the relation-ship between the clearness index (the output vector with only onecomponent) T = [j]T and the input vector X = [dt, tm, p, vi, g, s]T. Aftertraining, a comparison is performed between simulated GSR andobserved ones at the training stations in order to examine thetraining performance. Correlation coefficient (R), root mean squarederror (RMSE) and relative root mean square error (RRMSE) are usedas error metrics for comparison. As mentioned in Section 2.1, thedifferent configurations and learning algorithms are tested in orderto select the relatively optimal neural network architecture. Both thebest and the worst performances in the twenty training runs, whichare measured according to RMSE, are shown for each ANN configu-ration in Table 1. As can be seen, the Bayesian regularization trainingalgorithm, in which the Levenberg–Marquardt method is used, isalways superior to the scaled conjugate gradient algorithm in allconfigurations. It is also indicated that the ANN configurationsbehave similarly no matter which transfer function is used. More-over, the training results are hardly improved further when thenumber of neurons in the hidden layer is greater than ten. Basedon the previous discussion, the ANN configuration with 12 neurons

Fig. 7. Comparisons among observed GSR, estimates by ANN method, and JAXA productsresults.

and hyperbolic tangent sigmoid function in the hidden layer isapplied in the following discussion.

As shown in Fig. 4, error metrics show that ANN can grasp thefunctional relationship between GSR and its independent variables.The above examination does not guarantee that the built ANN canbe applied to estimate GSR on the regional scale. In order toachieve this goal, the ANN needs to be evaluated at sites whereGSR observations are not used in the training process. Moreover,the ANN-based GSR estimate also needs comparing with thosefrom the existing satellite products and other estimation methodsto indicate that this ANN-based method can estimate GSR botheffectively and efficiently. So JAXA monthly-mean daily GSR prod-ucts with a spatial resolution of 0.25� based on MODIS sensor andGSR estimates derived from Yang’s hybrid method are chosen inthis study. A total of 12 validation sites, where GSR observationsare left for validation, are illustrated in Fig. 3. As shown in Fig. 5,the ANN-based method presented in this study and Yang’s methodboth performs better than the retrieval algorithm by JAXA. It is alsoshown in Fig. 5 that Yang’s hybrid model estimates GSR better thanthe ANN-based method does at small GSR values, but the reversesituation occurs at large GSR values. Moreover, the hybrid modelcan only work at stations where sunshine data are available.

at four sites (Hotan, Emeishan, Garze, and Lhasa), where JAXA algorithm obtains bad

Fig. 8. GSW estimates for 12 months in 2004 over the entire TP and its surroundings. The water bodies and pixels without remote sensing data are masked.

J. Qin et al. / Applied Energy 88 (2011) 2480–2489 2487

In Fig. 6, GSR time series for each validation site are plotted anderror metrics are provided in order to investigate the retrieval abil-ity of ANN method presented in this study. As seen in Fig. 6, theperformance of the three estimation methods is different at these12 validation sites, although ANN-based method exhibits overallstronger retrieval ability than JAXA GSR algorithms does (Fig. 5).At seven sites (Yining, Kashi, Hami Shiquanhe, Yushu, Mianyangand Lijiang), ANN-based method retrieves GSR more accurately.At other sites (Rouqiang, Dunhuang, Golmud, Panzhihua andKunming), JAXA products perform better. As mentioned above,

Yang’s method generally performs better than both the ANN-basedmethod and JAXA algorithm. However, its retrievals at Kashi andPanzhihua have relatively large errors.

In addition, measured GSR data at the 22 training sites are alsoused to validate JAXA GSR products. It is found that the retrievalerrors are large at four sites (Hotan, Emeishan, Garze, and Lhasa)and RMSEs even reach roughly 5 MJ day�1 at Emeishan and Garzesites. So it is speculated that there perhaps exist some special con-ditions at these sites, which makes JAXA GSR estimates havinglarge errors and the similar situations may happen to ANN-based

2488 J. Qin et al. / Applied Energy 88 (2011) 2480–2489

method presented in this study. However, GSR observations atthese four sites are used to train ANN as aforementioned. There-fore, an experiment has to be made to check whether the ANN-based method can obtain satisfactory GSR estimates at these foursites. In the following, these four sites are excluded from the train-ing sites, measurements only at the left 18 sites are used to trainANN, and then this ANN is applied to retrieve GSR estimates atthese four stations. Fig. 7 indicates that ANN-based algorithm, afterexcluding the four sites, performs much better than JAXA retrievalscheme at these sites. This proves that the bad performance of theJAXA algorithm at these four sites is due to its own failure; ANNscheme has the fairly good robustness. Yang’s method also per-forms well at these four sites as shown in Fig. 7. The error statisticsin Figs. 6 and 7 are also summarized in Table 2.

As shown above, ground-data-based methods such as Yang’smethod may retrieve GSR with high accuracy. However, it isimpossible to estimate GSR on a regional scale since the areal in-puts required by them are not available. So the trained ANN is ap-plied to retrieve GSR over the TP and its surroundings in order toshow the advantage of the method presented in this study. Theestimated monthly-mean daily GSR images for 12 months in2004 are illustrated in Fig. 8. As seen, these 12 images thoroughlyexhibit the spatial–temporal patterns of GSR over the TP region.GSR values in western TP are much larger than ones in easternTP since the western TP is dry and the eastern TP is relativelywet. Following the northwesterly propagation of the Plateau sum-mer monsoon in the summer, the dividing line between high andlow GSR values moves westward, as shown in the June–Augustpanels in Fig. 8. It is also seen that GSR estimates exceed30 MJ day�1 at many points in the western TP since the elevationis high there, the optical air mass is rather small, and the amountof cloud is low due to lack of water vapor.

4. Concluding remarks

Many algorithms have been developed to estimate solar radi-ation either based on surface meteorological observations orbased on satellite data. In many regions over the world, thereare no dense meteorological stations. Therefore, no spatially con-tinuous GSR values can be estimated from routinely observedmeteorological parameters. In this study, an efficient and effectiveANN-based algorithm is presented to estimate monthly-meandaily GSR at a high spatial resolution in order to overcome someweaknesses, especially low spatial resolution, in existing meth-ods. ANN is trained to build the functional relationship betweenobserved GSR and exiting RS products such as LST and EVI. It isdemonstrated that this ANN-based method can retrievemonthly-mean GSR with high accuracy and has a good stabilityin comparison with JAXA GSR products. Moreover, the ANN-basedmethod is used to map the GSR distribution in space and timeover the TP and its surroundings. Resultant images illustrate thatthe reasonable spatial and temporal patterns of GSR could be ob-tained by the method presented in this study, although this re-gion has the very complex terrain and climate, suggesting thatthe estimation scheme presented in this study should be appliedin other places.

In summary, the following findings are acquired in this work.First, ANN can be used to explore the mathematical relationshipbetween GSR and satellite products. Second, this type of relation-ship is stable since it can be validated well at the different sites. Fi-nally, this ANN-based method can be applied to map the regionalGSR distribution with both high efficiency and effectiveness. Inthe future, the estimation method presented in this study can beused to obtain the GSR in China and coupled with other datasets

to provide the distribution of solar energy potential with a highspatial resolution.

Acknowledgements

This work was supported by National Basic Research Program ofChina under contract 2009CB723901, the ‘‘100-Talent’’ Program ofthe Chinese Academy of Sciences, the Natural Science Foundationof China under contract 40701129, 41071220, and China ‘‘863’’project under Contract 2006AA01A120 and 2009AA122100. Thesample GLI data was produced and supplied by the Earth Observa-tion Research and application Center, Japan Aerospace ExplorationAgency.

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