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PUBLICATIONS Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE 10.1002/2015JD023097 Key Points: • Develop an efficient parameterization for surface solar radiation • Estimate surface solar radiation with MODIS atmospheric products • Validate the estimates based on in situ measurements

Correspondence to: J. Qin, [email protected]

Citation: Qin, J., W. Tang, K. Yang, N. Lu, X. Niu, and S. Liang (2015), An efficient physically based parameterization to derive surface solar irradiance based on satellite atmospheric products, J. Geophys. Res. Atmos., 120, 4975–4988, doi:10.1002/2015JD023097. Received 28 JAN 2015 Accepted 18 APR 2015 Accepted article online 23 APR 2015 Published online 18 MAY 2015

An efficient physically based parameterization to derive surface solar irradiance based on satellite atmospheric products Jun Qin1, Wenjun Tang1,2, Kun Yang1,2, Ning Lu3, Xiaolei Niu1, and Shunlin Liang4,5 1 Laboratory of Tibetan Environment Changes and Land Surface Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China, 2CAS Center for Excellence in Tibetan Plateau Earth Sciences, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China, 3State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Science, Beijing, China, 4College of Global Change and Earth System Science, Beijing Normal University, Beijing, China, 5Department of Geography, University of Maryland, College Park, Maryland, USA

Abstract Surface solar irradiance (SSI) is required in a wide range of scientific researches and practical applications. Many parameterization schemes are developed to estimate it using routinely measured meteorological variables, since SSI is directly measured at a very limited number of stations. Even so, meteorological stations are still sparse, especially in remote areas. Remote sensing can be used to map spatiotemporally continuous SSI. Considering the huge amount of satellite data, coarse-resolution SSI has been estimated for reducing the computational burden when the estimation is based on a complex radiative transfer model. On the other hand, many empirical relationships are used to enhance the retrieval efficiency, but the accuracy cannot be guaranteed out of regions where they are locally calibrated. In this study, an efficient physically based parameterization is proposed to balance computational efficiency and retrieval accuracy for SSI estimation. In this parameterization, the transmittances for gases, aerosols, and clouds are all handled in full band form and the multiple reflections between the atmosphere and surface are explicitly taken into account. The newly proposed parameterization is applied to estimate SSI with both Moderate Resolution Imaging Spectroradiometer (MODIS) atmospheric and land products as inputs. These retrievals are validated against in situ measurements at the Surface Radiation Budget Network and at the North China Plain on an instantaneous basis, and moreover, they are validated and compared with Global Energy and Water Exchanges–Surface Radiation Budget and International Satellite Cloud Climatology Project–flux data SSI estimates at radiation stations of China Meteorological Administration on a daily mean basis. The estimation results indicates that the newly proposed SSI estimation scheme can effectively retrieve SSI based on MODIS products with mean root-mean-square errors of about 100 Wm 1 and 35 Wm 1 on an instantaneous and daily mean basis, respectively. 1. Introduction The Sun provides energy for almost all land surface processes on the Earth’s surface. Surface solar irradiance (SSI) is required in a wide range of scientific and engineering applications. In ecological and crop growth models, the photosynthetically active part of SSI is used in the photosynthesis and stored as the chemical energy for allocation to different living organs of plants such as root, stem, and foliage [Brock, 1981]. In land surface and hydrological modeling, SSI is one of indispensable driving factors controlling both water and heat exchanges between the land and the atmosphere [Shook and Pomeroy, 2011]. At the same time, SSI is exploited to evaluate the performance of climate models [Kothe et al., 2011]. Knowledge of SSI distribution also plays a significant part in the design of the photovoltaic power and solar heating systems in the clean energy industry [Coskun et al., 2011].

©2015. American Geophysical Union. All Rights Reserved.

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For all of the above purposes, spatiotemporally continuous fields of surface solar radiation are urgently desired. Despite the great importance of SSI, the number of radiation stations is rather sparse, compared to that of weather stations where routine meteorological variables are collected, such as air temperature, humidity, sunshine duration, and cloud coverage. The reason for this is that the measuring instrument (pyranometer) is elaborate and needs frequent calibration, leading to the high cost of maintenance. Thus, many empirical parameterization schemes are designed to indirectly estimate SSI from routine meteorological

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variables [Wong and Chow, 2001]. These methods could be roughly divided into three classes in accordance with inputs: sunshine based [Ertekin and Evrendilek, 2007], temperature based [Meza and Varas, 2000], and cloud based [Ehnberg and Bollen, 2005]. Based on mathematical forms, they could be classified as parametric (such as Ångström-Prescott-type methods) [Wu et al., 2012] and nonparametric (such as artificial neural network-based methods) [Fadare, 2009]. If calibrated well, these models can estimate SSI with high accuracy. However, since no explicit physics are considered in these estimation schemes, calibrated parameters often vary from one site to the other, limiting their generalization and leading to large uncertainties in SSI estimates at those sites without calibration. Remote sensing provides an alternative method to retrieve spatiotemporally continuous SSI values, because electromagnetic signals received by sensors aboard satellites carry a large amount of information on the atmosphere and the underlying land surface, which are useful for estimation of surface solar radiation. In the early 1960s, Fritz et al. [1964] already found that the reflected solar radiation measured by the sensor on TIROS III is highly correlated with the ground pyranometer measurement. Since then, numerous algorithms, which can be generally categorized into two different types, have been designed and constructed to estimate SSI from satellite signals. One is to directly construct an empirically mathematical relationship between satellite signals and in situ SSI observations [Lu et al., 2011; Qin et al., 2011]. The advantage of this type lies in its high efficiency, but the cost is its limited generalization. The relationship has to be recalibrated when applied in other regions. The other is to use satellite-based atmospheric parameters to drive a complex radiative transfer model (or a look-up table based on such a model) for obtaining surface solar radiation estimates at multiple spectral bands and then integrating them to obtain SSI [Greuell et al., 2013; Huang et al., 2011; Li et al., 1993; Liang et al., 2006; Lu et al., 2010; Pinker and Laszlo, 1992; Zhang et al., 2014]. The benefit of such a type is its explicit account of all physics relevant to SSI and thus has a high generalization capability. But its weakness is the heavy computational burden. So SSI estimates based on this type of retrieval methods generally have a coarse spatial resolution. The examples of this type include the SSI algorithms of the Global Energy and Water Exchanges–Surface Radiation Budget (GEWEX-SRB) [Raschke et al., 2006] and the International Satellite Cloud Climatology Project–flux data (ISCCP-FD) [Zhang et al., 2004], whose spatial resolutions are greater than 100 km. It is well known that the vertical profiles of many atmospheric parameters are needed to drive a radiative transfer model. As a matter of fact, it is very difficult (if possible) for remote sensing to accurately obtain these profiles (such as aerosol and cloud concentrations). At present, most satellite-based atmospheric products merely give the integrated properties of the entire atmospheric layer (such as aerosol and cloud optical depths). So the vertical profiles of these atmospheric products have to be assumed when inputted into a radiative transfer model to estimate SSI [Wang and Pinker, 2009]. That being the case, it can be more efficient to develop a physically based parameterization scheme to directly utilize these satellite-based atmospheric products without any assumptions on their vertical structures. This implies that the atmosphere must be regarded as one layer when constructing such a scheme. As a matter of fact, this line of thought has been taken by some satellite-based SSI estimation schemes such as the Heliosat method [Marie-Joseph et al., 2013] and the Langley parameterized shortwave algorithm [Gupta et al., 2004]. These algorithms use physically based parameterizations to obtain SSI under clear-sky conditions but roughly treat the impact of clouds by using a simple cloud index. As well known, clouds are the most important factor impacting SSI, so such a simple parameterization of clouds could degrade the accuracy in estimating SSI. A parameterization scheme is proposed in this study to alleviate the weaknesses of the aforementioned algorithms by balancing retrieval accuracy and computational efficiency. In this scheme, all its components are physically based, and no empirical relationships are used in order to improve the generalization ability and thus the accuracy. As far as the efficiency is concerned, the atmosphere is regarded as one layer and its vertical structure is ignored. Moreover, the entire shortwave band (300–4000 nm) is not split into multiple bands and separately parameterized, but the full band form is taken, which treat the whole shortwave band as one band. The rest of the article is organized as follows. The parameterization scheme is detailed in section 2; the satellite data used to drive the SSI algorithm and the observed radiation data used to validate the estimated SSI are described in section 3; the estimation results and discussions are presented in section 4; and finally a summary is given in section 5. QIN ET AL.


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2. Parameterization Scheme The newly proposed scheme can be divided into three subschemes whose degrees of complexity gradually increase for clear-sky, cloudy, and all-sky conditions. In the following, their details are described. 2.1. Clear-Sky Conditions SSI under clear-sky conditions (Rclr) can be calculated as follows: Rclr

clr R0 τ clr b þ τd ¼ ; 1 ρa;clr ρg

(1a)

with R0 ¼ S⊙

2 d μ0 ; d0

(1b)

clr where τ clr b denotes the full band beam transmittance, τ d the diffuse transmittance, ρa,clr the atmospheric spherical albedo, ρg the ground surface albedo, S⊙ the solar constant, d the distance between the Sun and Earth, d0 the mean distance between the Sun and Earth, and μ0 the cosine of the solar zenith angle. The clr detailed description of τ clr b and τ d are presented in equations (A1)–(A3) of Appendix A.

2.2. Cloudy Conditions SSI under cloudy conditions (Rcld) is calculated as Rcld ¼

cld R0 τ cld b þ τd ; 1 ρa;cld ρg

(2)

cld where τ cld b denotes the beam transmittance, τ d the diffuse transmittance, and ρa,cld the atmospheric spherical clr albedo under cloudy conditions. The details of τ clr b and τ d are given in equations (A4)–(A6) of Appendix A.

2.3. All-Sky Conditions When the sky is partly cloudy, the cloud fraction (cf) is introduced to calculate SSI as follows: Rall ¼

ð1 cf Þ · R′clr þ cf · R′cld 1 ρa;all ρg

;

(3a)

with ρa;all ¼ ð1 cf Þ · ρa;clr þ cf · ρa;cld ;

(3b)

where R′clr and R′cld denote SSI values under clear and cloudy skies without considering the multiple scattering between the atmosphere and ground surface. Figure 1 summarizes the main steps of the above algorithm for estimating SSI based on atmospheric and land parameters and provides the related key variables at the same time.

3. Input and Validation Data The proposed parameterization scheme in the above section can be driven to estimate SSI once the required atmospheric parameters are available, which include ozone thickness, precipitable water, aerosol loading, water/ice cloud water path, effective particle radius of water/ice clouds, cloud fraction, and ground surface albedo. To validate the scheme, SSI estimates are derived with the 5 km Moderate Resolution Imaging Spectroradiometer (MODIS) atmospheric and land products (collection version 5) as inputs and then their accuracy is examined against in situ observations. In this study, the postlaunch MODIS Atmosphere Level 2 Joint Product is used, which can provide all of the required atmospheric parameters except ground surface albedo [King et al., 2003]. As for albedo, the MODIS 16 day albedo product (MCD43C3) is used [Schaaf et al., 2002]. There are two kinds of the MODIS Atmosphere Joint data products. One is MODATML2 containing data collected from the Terra platform and the other is MYDATML2 from the Aqua platform. So there are four observations provided by these two satellites every day, but only two daytime observations (morning and afternoon) can be used to retrieve SSI values.

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Figure 1. Flowchart of the proposed parameterization for estimating surface solar irradiance.

The retrievals are validated at nine radiation stations on an instantaneous basis, seven of which belong to the Surface Radiation Budget Network (SURFRAD) distributed widely in the United States and two of which are located in the North China Plain (NCP). The seven SURFAD stations are Sioux Falls, Fort Peek, Penn State, Bondville, Table Mountain, Desert Rock, and Goodwin Greek. The two NCP stations are Miyun and Xianghe. Three years (2006–2008) of SSI observations are used at the seven SURFRAD stations, and their sampling frequency is 3 min. For the two NCP radiation stations, 2 years (2008–2009) of in situ observations are taken. Xianghe station belongs to the Baseline Surface Radiation Network, and its sampling frequency is 1 min [Xia et al., 2007, 2008]. Miyun station is maintained by Beijing Normal University, and their sampling interval is 10 min [Jia et al., 2012; Liu et al., 2013]. Because the station observation time is not exactly commensurate with the satellite overpass time, the instantaneous SSI observations closest to the overpass times are selected for validation at the nine stations. In addition, 4 years (2006–2009) of the estimated SSI values are also validated at 91 China Meteorological Administration (CMA) radiation stations on a daily mean basis. The spatial distribution of all the radiation stations is illustrated in Figure 2. As pointed out by Tang et al. [2010], the CMA radiation data often include erroneous and questionable values. Therefore, we only use the data that pass the quality control tests proposed by Tang et al. [2010] to validate the SSI retrievals. As mentioned above, there are only two Figure 2. Spatial distribution of radiation stations used in this study. The daytime SSI estimates available. So the red cross marks illustrate the nine radiation stations on an instantaneous upscaling algorithm proposed by basis, seven of which belong to the Surface Radiation Budget Network Wang and Pinker [2009] is used to (SURFRAD) distributed widely in the United States and two of which are convert these two SSI estimates to a located in the North China Plain (NCP). The blue dot marks represent the daily averaged value for comparison 91 China Meteorological Administration (CMA) radiation stations on a with CMA SSI measurements. daily mean basis.

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Figure 3. Validation results for the clear-sky surface solar irradiance estimated by the scheme proposed in this study at seven SURFRAD stations for Terra and Aqua platforms. These stations are (a) Sioux Falls, (b) Fort Peek, (c) Penn State, (d) Bondville, (e) Table Mountain, (f) Desert Rock, and (g) Goodwin Greek.

It should be noted that many MODIS atmospheric parameters, such as aerosol, ozone, precipitable water, are not available when clouds occur. In this case, the aerosol and ozone climatologies are used. For aerosol, its climatology is produced based on the Level-3 MODIS Atmosphere Monthly Global Product. For ozone, the climatology is made according to the Total Ozone Mapping Spectrometer (TOMS) Level-3 gridded data. As for precipitable water, the National Centers for Environmental Prediction (NCEP) reanalysis is used when the corresponding MODIS data is unavailable.

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Figure 4. Validation results for the all-sky surface solar irradiance estimated by the scheme proposed in this study at seven SURFRAD stations for Terra and Aqua platforms. These stations are (a) Sioux Falls, (b) Fort Peek, (c) Penn State, (d) Bondville, (e) Table Mountain, (f) Desert Rock, and (g) Goodwin Greek.

4. Results and Discussion As described in section 3, the SSI estimates are compared with in situ instantaneous observations at the nine sites and daily measurements at the 91 CMA radiation stations. Figure 3 indicates the validation results at the seven SURFRAD stations under clear-sky conditions, respectively. For Terra, the largest root-mean-square error (RMSE) of 57.8 Wm 2 occurs at Penn State (Figure 3c1), the largest positive bias of 27.0 Wm 2 also happens at this station, and the largest negative bias of 11.3 Wm 2 occurs at Desert Rock (Figure 3f1). For Aqua, the largest RMSE of 59.7 Wm 2 occurs at Penn State (Figure 3c2), and the positive bias of

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2

Table 1. Validation Results at the SURFRAD Stations for the Two Different SSI Estimation Algorithms (Wm Wang’s [2007] Algorithm

Fort Peek Penn State Bondville Table Mountain Desert Rock Goodwin Greek

)

This Study

RMSE

Bias

RMSE

Bias

108 98 75 111 60 121

8 15 3 26 20 9

85.7 91.1 73.3 91.2 45.8 62.1

2.6 18.4 5.5 8.0 12.0 13.1

29.9 Wm 2 both happen at Fort Peek (Figure 3b2). Figure 4 shows the validation results at the seven SURFRAD stations under all-sky conditions. For the Terra and Aqua satellites, the largest RMSE values of 113.6 Wm 2 and 123.0 Wm 2 both occur at Table Mountain station (see Figures 4e1 and 4e2). For Terra, the largest positive bias of 21.8 Wm 2 occurs at Penn State station (see Figure 4c1), and the largest negative bias of 17.7 Wm 2 occurs at Table Mountain station (see Figure 4e1). For Aqua, the largest positive bias of 22.0 Wm 2 occurs at Goodwin Greek station, and the largest negative bias of 1.9 Wm 2 happens at Table Mountain station. Wang [2007] developed an algorithm for estimating SSI based upon MODIS atmospheric products and then validated the estimates for the Terra platform at the SURFRAD

Figure 5. Validation results for the clear-sky surface solar irradiance estimated by the scheme proposed in this study at three radiation stations deployed in the North China Plain. The stations are (a) Miyun and (b) Xianghe.

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Figure 6. Validation results for the all-sky surface solar irradiance estimated by the scheme proposed in this study at three radiation stations deployed in the North China Plain. The stations are (a) Miyun and (b) Xianghe.

stations except at Sioux Falls station. Compared to our method, the distinct characteristic of Wang’s algorithm is to approximate the atmosphere as multiple plane-parallel layers and calculate solar irradiance in different spectral bands. Table 1 lists the validation results provided in Wang’s study and also gives the validation results by our algorithm. As can be seen, the accuracy of our SSI retrievals is better than that of Wang’s estimates as far as RMSE is concerned. At Goodwin Greek, the RMSE even reduces by half. For bias, the maximum absolute values of the biases for our algorithm is less than 20 Wm 2, but for Wang’s algorithm, the maximum absolute value reaches as far as 26 Wm 2. It is noted that for fair comparison, we take the same procedure to handle the estimated SSI values as Pinker et al. [2009] did in their study. So the cases are eliminated when the difference between the SSI estimates and observations is larger than 3 times the standard deviation of the differences. Figure 5 illustrates the validation results at the two NCP stations under clear-sky conditions. The largest RMSE of 49.6 Wm 2 happens to Aqua at Xianghe (Figure 5b2), and the largest positive bias of 16.2 Wm 2 occurs at Miyun but for Terra (Figure 5a1). As we can see in Figure 6, RMSE under all-sky conditions at these two stations is less than 100 Wm 2 for both Terra and Aqua. But the bias values at these two stations are all positive, and the largest bias of 33.9 Wm 2 happens to Terra at Xianghe station. One might doubt that the underestimation of aerosol optical depth (AOD) may take responsibility for the SSI overestimation in the NCP, where the air pollution has been greatly heavy with economic development. However, many studies indicate that the MODIS aerosol AOD retrievals are in agreement with the observations by Sun photometers in the NCP [Li et al., 2007], and it seems that other factors should be accountable for the SSI

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Figure 7. Validation results for the estimated surface solar irradiance by (a) the newly proposed scheme, (b) GEWEX-SRB, and (c) ISCCP-FD at all CMA radiation stations on a daily mean basis.

underestimation. Nevertheless, as well known, the retrieval of AOD is just available only when the sky is judged as clear by the MODIS cloud detection algorithm. In fact, a situation often occurs in the NCP that the haze is so severe that it is judged as the cloud, and thus the aerosol retrieval is not conducted [Li et al., 2013]. So the MODIS-derived AOD climatology is likely to underestimate the true AOD climatology in the NCP. As mentioned in section 3, the SSI estimation algorithm presented in this study uses the MODIS AOD climatology as the input when the cloud occurs. As a consequence, the SSI overestimation happens at the two NCP stations. Both GEWEX-SRB (with 3 h temporal and 1° spatial resolutions) [Stackhouse et al., 2004] and ISCCP-FD (with 3 h temporal and 2.5° spatial resolutions) [Zhang et al., 2004] are two popular SSI products. They are compared with the retrievals in this study. Because the spatial resolutions of these two SSI products are rather coarse, it may incur large errors to validate them by using instantaneous in situ measurements. However, as pointed out by Li et al. [2005], the spatial sampling uncertainties decrease rapidly as the time-averaging interval increases up to 24 h. Thus, GEWEX-SRB and ISCCP-FD SSI products are compared with our SSI estimates at all 91 CMA radiation stations on a daily mean basis. As shown in Figure 7, the ISCCP-FD SSI estimates are slightly inferior to our and GEWEX-SRB SSI estimates. Because it is pointed out in some studies that it is not an easy task to retrieve SSI over the Tibetan Plateau due to its extreme climatic conditions [Yang et al., 2008], we compare our estimates with GEWEX-SRB and ISCCP-FD SSI retrievals at the CMA stations located there. As shown in Figure 8, the performance of ISCCP-FD is worst among these three SSI estimates, and GEWEX-SRB and our SSI estimates are almost identical as far as RMSE is concerned. For bias, the SSI estimated produced by this study is positively biased by 14.5 Wm 2. Figure 9 indicates the spatial distribution of RMSE at each CMA radiation station for these three types of SSI estimates. As we can see, the relatively large RMSE values mainly distribute in the southern part of China for the SSI retrievals in this study, where precipitable water vapor is abundant and the frequency of cloud occurrence is high. Since the daily mean SSI is computed only in terms of morning and afternoon MODIS atmospheric products, the aforementioned temporal upscaling scheme cannot capture the impact of cloud variation on SSI between the two satellite overpass times and thus leads to relatively large errors in

Figure 8. Validation results for the estimated surface solar irradiance on the Tibetan Plateau by (a) the newly proposed scheme, (b) GEWEX-SRB, and (c) ISCCP-FD at all CMA radiation stations on a daily mean.

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the SSI estimates. By contrast, GEWEXSRB provides the surface radiation balance products with a time resolution of 3 h, and thus roughly four daytime SSI estimates can be used to compute the daily mean SSI. So it is unsurprising that the GEWEX-SRB SSI retrievals perform better than our SSI estimates in this study in the south of China as shown in Figures 9a and 9b. The same explanation applies to the better performance of GEWEX-SRB over the Tibetan Plateau, where the diurnal variation of clouds is very dramatic due to the strong heating of the atmosphere there. But in the north of China, the accuracy of our SSI estimates is higher than that of the GEWEX-SRB retrievals. As far as the ISCCP-FD SSI is concerned, its accuracy is generally inferior to our estimates in the north of China and to the GEWEXSRB retrievals in the south of China (see Figure 9c). So its RMSE is larger by roughly 1.5 Wm 2 than the other two estimates (see Figure 7). It is notable that the spatial resolution of our estimates (about 5 km) is much finer than that of GEWEX-SRB (about 1°), although the accuracy of our SSI estimates in the south of China is slightly inferior to that of GEWEX-SRB on a daily mean basis. In order to evaluate the efficiency, the proposed scheme is compared against a standard look-up table method [Ma and Pinker, 2012] on a personal computer with a 3.4 GHz Intel i7 CPU and a 4 Gb double data rate type three random-access memory. These two schemes are implemented to retrieve 1 year of SSI values at 5 km spatial Figure 9. Spatial distribution of root-mean-square errors (RMSEs) when resolution in East Asia, with 1400 × 900 validating the estimated surface solar irradiance by (a) this study, (b) satellite pixels. The new scheme takes GEWEX-SRB, and (c) ISCCP-FD at 91 CMA radiation stations on a daily mean. about 24 h, but the look-up table method does about 120 h. As well known, the look-up table method is much faster than the radiative transfer models in estimating SSI and thus widely used to operationally map SSI. Even so, the newly proposed method still has five times the speed of the look-up table method.

5. Summary A simple physically based parameterization scheme is proposed to compute SSI. In this scheme, the impact of gases, aerosols, and clouds on SSI through the scattering and absorption are explicitly considered in the full

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band form. In addition, the multiple scattering between the atmosphere and land surface is also explicitly treated in this scheme. The MODIS atmospheric and land products are used to drive the newly proposed scheme to obtain SSI estimates. In order to evaluate the performance of these estimates, the validation is performed based on station observations measured at the SURFRAD and the NCP on an instantaneous basis. The daily mean SSI estimates based on two daytime estimates (Terra and Aqua) are validated against observations at 91 CMA radiation stations. At the same time, the instantaneous SSI estimates based on the newly proposed scheme is compared with the retrieved through the algorithm designed by some other researchers at the SURFRAD. Moreover, the derived daily SSI is compared with the GEWEX-SRB and ISCCP-FD estimates at CMA radiation stations. The results indicate that the newly proposed SSI estimate scheme can effectively retrieve SSI based upon MODIS products with average root-mean-square errors of less than 100 Wm 2 and 35 Wm 2 on an instantaneous and daily mean basis, respectively. It is planned that the newly proposed SSI estimation scheme will be used to retrieve SSI globally based on MODIS atmospheric and land products due to its effectiveness and efficiency.

Appendix A clr The full band beam transmittance (τ clr b ) and the diffuse transmittances (τ d ) are parameterized as follows:

τ clr b ¼ τ o τ w τ g τ aa τ as τ r ;

(A1a)

clr clr τ clr d ¼ τ d;r þ τ d;a ;

(A1b)

τ clr d;r ¼ 0:5τ o τ g τ w τ aa ð1 τ r Þ;

(A1c)

τ clr d;a ¼ f aer ðμ0 Þτ o τ g τ w τ aa τ r ð1 τ as Þ;

(A1d)

and

with

and

clr where τ clr d;r and τ d;a denote the diffuse transmittances caused by Rayleigh and aerosol scattering, respectively, and τ o, τ w, τ g, and τ aa denote the transmittances for ozone, water vapor, uniformly mixed gas, and aerosol absorption, respectively; τ as and τ r denote the transmittance for aerosol and Rayleigh scattering, respectively; and faer(·) denotes the forward scattering fraction caused by aerosols. In this study, the atmospheric spherical albedo ρa,clr in equation (1a) is parameterized as follows: n o h pffiffiffii ρa;clr ¼ τ o′ τ w′ τ g′ τ aa (A2) ′ 0:5ð1 τ r′Þ þ 1 f aer 1= 3 τ r′ð1 τ as ′Þ ;

where τ o′; τ w′ ; τ g′ ; τ r′ ; τ aa ′ ; and τ as ′ are the values of τ o, τ w, τ g, τ r, τ aa, and τ as when the relative mass m is equal to pffiffiffi 3. The forward scattering fraction is adopted from the scheme by Raisanen [2002] and expressed as f aer ð·Þ ¼ 0:4482 þ 5:3664 22:1608t þ 28:699t 2 11:1348t3 · ga′ ;

(A3a)

t ¼ ðμ0 þ 0:1Þ0:25 ;

(A3b)

with

and ga′ ¼

ga ; ga þ 1

(A3c)

where ga denotes the asymmetric factor for aerosol that is set to 0.7 in this study. The beam and diffuse transmittances under cloudy conditions can be expressed as τ cld b ¼ τ o τ w τ g τ aa τ wca τ as τ ica τ wcs τ ics τ r ;

(A4a)

cld cld cld cld τ cld d ¼ τ d;r þ τ d;a þ τ d;wc þ τ d;ic ;

(A4b)

and

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with τ cld d;r ¼ 0:5τ o τ w τ g τ aa τ wca τ ica ð1 τ r Þ;

(A4c)

τ cld d;a ¼ f aer ðμ0 Þτ o τ w τ g τ aa τ wca τ ica τ r ð1 τ as Þ;

(A4d)

τ cld d;wc

¼ f liq ðμ0 Þτ o τ w τ g τ aa τ wca τ ica τ r τ as ð1 τ wcs Þ;

(A4e)

and τ cld d;ic ¼ f ice ðμ0 Þτ o τ w τ g τ aa τ wca τ ica τ r τ as τ wcs ð1 τ ics Þ;

(A4f)

cld cld cld where τ cld d;r , τ d;a, τ d;wc, and τ d;ic denote the diffuse transmittances caused by Rayleigh, aerosol, water cloud, and ice cloud, respectively; τ wca and τ wcs denote the transmittances for water cloud absorption and scattering, respectively; and τ ica and τ wca denote the transmittances for ice cloud absorption and scattering, respectively; fliq(·) and fice(·) denote the forward scattering fractions caused by water and ice clouds, respectively. The atmospheric spherical albedo ρa,cld in equation (2) under cloudy conditions is parameterized as pffiffiffi

ρa;cld ¼ τ o′ τ w′ τ g′ τ aa ′ 0:5ð1 τ ′rÞ þ 1 f aer 1= 3 τ ′r ð1 τ as ′ τ wca ′ τ ica ′Þ (A5) pffiffiffi

pffiffiffi

þ 1 f liq 1= 3 τ r′ τ as′ ð1 τ wcs ′ Þ ; ′ Þ þ 1 f ice 1= 3 τ r′ τ as′ τ wcs ′ ð1 τ ics pffiffiffi where τ wca ′ , τ wcs ′ denote the values of τ wca, τ ica, τ wcs, and τ ics when the relative air mass is equal to 3. ′ , τ ica ′ , and τ ics The forward scattering fractions for water and ice clouds are expressed as (A6a) f liq ¼ 0:3312 þ 1:1285 μ0:7469 gwc ′ ; 0

with gwc ′ ¼ and

gwc ; gwc þ 1

(A6b)

gic′ ; f ice ¼ 0:4250 þ 0:9595 μ0:8484 0

(A6c)

with gic′ ¼

gic ; gic þ 1

(A6d)

where gwc and gic denote the asymmetric factors for water and ice clouds.The above transmittances for gases and aerosols are primarily adopted from Yang et al. [2001], but the original transmittance for aerosol only considers the scattering process. Thus, the refinement is performed to explicitly allow for both scattering and absorption (cf. equations (A7d) and (A7e)). They are expressed as h i τ o ¼ exp 0:0365ðml Þ0:7136 ; (A7a) h i (A7b) τ g ¼ exp 0:0117ðmc Þ0:3139 ; τ w ¼ min½1:0; 0:909 0:036lnðmw Þ; h 4:08 i τ r ¼ exp 0:008735mc 0:547 þ 0:014mc 0:00038m2c þ 4:6106 m3c ; n o h i τ aa ¼ exp mβ 0:6777 þ 0:1464ðmβÞ 0:00626ðmβÞ2 ð1 ωa Þ ; and

n h i o τ as ¼ exp mβ 0:6777 þ 0:1464ðmβÞ 0:00626ðmβÞ2 ωa ;

with m¼1

h

= sinh þ 0:15ð57:296h þ 3:885Þ

1:253

i

;

(A7c) (A7d) (A7e)

(A7f)

(A7g)

and mc ¼ mps =p0 ;

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(A7h)

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where l is the ozone layer thickness; w is the precipitable water vapor; β is the Ångström turbidity coefficient; ωa is the single scattering albedo; m is the relative air mass depending on the solar elevation angle; h is the solar elevation angle; mc is the pressure-corrected relative air mass; ps is the site air pressure; and p0 is the standard atmospheric pressure. The full band transmittances for cloud absorption and scattering are developed based upon the wideband scheme by Chou and Suarez [1999]. In this scheme, the entire shortwave range is divided into 11 wide bands and the optical properties for each band are given as follows: di ¼ CWP a0;i þ a1;i =r e ; (A8a) 1 ωi ¼ b0;i þ b1;i r e þ b2;i r 2e ;

(A8b)

gi ¼ c0;i þ c1;i r e þ c2;i r 2e ;

(A8c)

and

where the subscript i denotes the index for the 11 wide bands, di is the water/ice cloud optical depth; re is the effective particle radius of clouds, ωi the single scattering albedo; gi is the asymmetric factor; CWP is the water/ice cloud water path; and a0,i, a1,i b0,i, b1,i, b2,i, c0,i, c1,i, and c2,i are the given coefficients whose values can be found in Chou and Suarez [1999]. In our scheme, the full band effective values of the above three properties are parameterized as follows: 0X 1 Ii edi B i C C (A9a) d ¼ logB @ X I A; i i

0X B ω ¼ logB @

Ii edi ωi C C X Ii A

i

i

and

0X B g ¼ logB @

i

1 Ii edi ωi gi C C X Ii A i

Acknowledgments MODIS data for this work are available via the website (http://reverb.echo.nasa. gov/reverb/). SURFRAD radiation data are available via the website (http:// www.esrl.noaa.gov/gmd/grad/surfrad). CMA radiation data are available via the website (http://cdc.cma.gov.cn). GEWEX-SRB radiation data are available via the website (http://www.gewex.org/ srbdata.htm). ISCCP-FD radiation data are available via the website (http:// isccp.giss.nasa.gov). TOMS ozone data are available via the website (http://disc. sci.gsfc.nasa.gov/). NCEP reanalysis data are available via the website (http:// www.esrl.noaa.gov/psd/data/gridded/ data.ncep.reanalysis.derived.surface. html). The in situ radiation data at Xianghe station are available via the website (http://www.bsrn.awi.de), and the data at Miyun station are available by contacting Shaomin Liu at Beijing Normal University via his e-mail ([email protected]). This work was supported by the Natural Science Foundation of China (grant 41171268 and 41371016) and China “863” project under contract 2013AA122801.

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= =

1

0X

1 Ii edi B i C C logB @ X I A; i

(A9b)

i

0X

B logB @

i

1 Ii edi ωi C C; X Ii A

(A9c)

i

where d, ω, and g denote the effective water/cloud optical depth, the effective single scattering albedo, and the effective asymmetric factor, respectively; and Ii denotes the solar irradiance at the top of the atmosphere at wide band i. Thus, the transmittances for cloud absorption and scattering can be expressed as

τ wca ¼ exp dwc ð1 ωwc Þ ; (A10a) (A10b) τ wcs ¼ exp d wc ωwc ;

(A10c) τ ics ¼ exp d ic ð1 ωic Þ ; and

τ ica ¼ exp d ic ωic ;

(A10d)

where dwc and ωwc denote the effective optical depth and single scattering albedo for water cloud, respectively; and dic and ωic denote the effective optical depth and single scattering albedo for ice cloud, respectively.

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