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Data-driven Estimation of Cloud Effects on Surface Irradiance at Xianghe, a Suburban Site on the North China Plain


doi: 10.1007/s00376-022-1414-x

  • Clouds are a dominant modulator of the energy budget. The cloud shortwave radiative effect at the surface (CRE) is closely related to the cloud macro- and micro-physical properties. Systematic observation of surface irradiance and cloud properties are needed to narrow uncertainties in CRE. In this study, 1-min irradiance and Total Sky Imager measurements from 2005 to 2009 at Xianghe in North China Plain are used to estimate cloud types, evaluate cloud fraction (CF), and quantify the sensitivities of surface irradiance with respect to changes in CF whether clouds obscure the sun or not. The annual mean CF is 0.50, further noting that CF exhibits a distinct seasonal variation, with a minimum in winter (0.37) and maximum in summer (0.68). Cumulus occurs more frequently in summer (32%), which is close to the sum of the occurrence of stratus and cirrus. The annual CRE is –54.4 W m–2, with seasonal values ranging from –29.5 W m–2 in winter and –78.2 W m–2 in summer. When clouds do not obscure the sun, CF is a dominant factor affecting diffuse irradiance, which in turn affects global irradiance. There is a positive linear relationship between CF and CRE under sun-unobscured conditions, the mean sensitivity of CRE for each CF 0.1 increase is about 1.2 W m–2 [79.5° < SZA (Solar Zenith Angle) < 80.5°] to 7.0 W m–2 (29.5° < SZA < 30.5°). When clouds obscure the sun, CF affects both direct and diffuse irradiance, resulting in a non-linear relationship between CF and CRE, and the slope decreases with increasing CF. It should be noted that, although only data at Xianghe is used in this study, our results are representative of neighboring areas, including most parts of the North China Plain.
    摘要: 云是影响地表辐射能量收支的重要参数,云辐射效应与云的宏、微观特性参数密切相关,亟需系统的观测研究。本文利用华北平原香河站高时间分辨率辐射测量数据,结合全天空成像仪观测数据,进行云类型识别,评估云量,并重点探讨了云遮蔽和未遮蔽太阳两种情形下云量和地表太阳辐射的参数关系。结果表明香河站云量年均值为0.50,冬季和夏季云量均值分别为0.37和0.68,其中夏季以积云为主(32%),出现频率约等于层云和卷云出现频率之和。香河站云辐射效应的年均值为–54.4 W m-2,冬季和夏季云辐射效应分别为–29.5 W m-2和–78.2 W m-2。太阳未被遮蔽情况下,云量变化主要影响散射辐射,继而影响总辐射。云量与CRE呈线性关系,CF增加0.1,CRE平均增加1.2(79.5°<SZA<80.5°)–7.0(29.5°<SZA<30.5°)W m-2。在太阳被遮蔽情况下,云量变化同时影响直接辐射和散射辐射,导致云量与云辐射效应呈非线性关系,且斜率随云量的增加而降低。太阳未被遮蔽时云主要起正辐射强迫作用,太阳被遮蔽时主要起负辐射强迫作用,且负辐射强迫的量级是正辐射强迫的3倍。
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  • Figure 1.  Criteria for estimating cloud type based on the standard deviation of scaled observed irradiance (Std21) and the ratio of scaled observed irradiance to scaled clear-sky irradiance (Rc). Cumulus, stratus, and cirrus samples are extracted from 1200–1300 LST on 16 May 2007, 1300–1400 LST on 30 March 2007, and 1030–1100 LST on 6 March 2007, respectively. LST represents Local Standard Time (UTC + 8 hours).

    Figure 2.  (a) Frequency of cloud fraction (CF). (b) The boxplot shows median, quartiles, minimums, and maximums for the shortwave cloud radiative effect of GHI (CREGHI) as a function of SZA from 2005 to 2009 at Xianghe. Circles and triangles represent outliers and means, respectively.

    Figure 3.  Median, quartiles, minimums, and maximums of the annual and seasonal means of (a) CF, (b) CREGHI, (c) CREDNI, and (d) CREDHI from 2005 to 2009 at Xianghe. Circles represent outliers.

    Figure 4.  Seasonal occurrence frequency of the indeterminate samples and three major cloud types using the Duchon and O'Malley (1999) method.

    Figure 5.  (a) Daily course of measured CF and GHIobs at Xianghe for 30 June 2009, CF and irradiance components during (b) 1300–1400 LST, (c) 1400–1500 LST, and (d) CREGHI during 1400–1500 LST.

    Figure 6.  Boxplots (median, quartiles, minimums, and maximums) of CREDHI as a function of CF for seven SZAs under sun-unobscured conditions. The red triangles represent the mean CREDHI, asterisks represent outliers, and the solid red lines represent the fitting results.

    Figure 7.  Boxplots (median, quartiles, minimums, and maximums) of CREGHI as a function of CF for seven SZAs under sun-unobscured conditions. The blue triangles represent the mean CREGHI, asterisks represent outliers, and the solid blue lines represent the fitting results

    Figure 8.  Boxplots (median, quartiles, minimums, and maximums) of CREGHI as a function of CF for seven SZAs under sun-obscured conditions. The blue triangles represent the mean CREGHI, asterisks represent outliers, and the solid blue lines represent the fitting results

    Table 1.  Determination of cloud type by using the Duchon and O'Mallley (1999) method.

    Frequency (%)
    Indeterminate32.67
    Cumulus27.48
    Stratus18.68
    Cirrus21.17
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Manuscript received: 16 November 2021
Manuscript revised: 09 March 2022
Manuscript accepted: 10 March 2022
通讯作者: 陈斌, bchen63@163.com
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Data-driven Estimation of Cloud Effects on Surface Irradiance at Xianghe, a Suburban Site on the North China Plain

    Corresponding author: Xiang'ao XIA, xxa@mail.iap.ac.cn
  • 1. Key Laboratory of Atmospheric Sounding, Chengdu University of Information Technology, Chengdu 610225, China
  • 2. Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
  • 3. Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science & Technology, Nanjing 210044, China

Abstract: Clouds are a dominant modulator of the energy budget. The cloud shortwave radiative effect at the surface (CRE) is closely related to the cloud macro- and micro-physical properties. Systematic observation of surface irradiance and cloud properties are needed to narrow uncertainties in CRE. In this study, 1-min irradiance and Total Sky Imager measurements from 2005 to 2009 at Xianghe in North China Plain are used to estimate cloud types, evaluate cloud fraction (CF), and quantify the sensitivities of surface irradiance with respect to changes in CF whether clouds obscure the sun or not. The annual mean CF is 0.50, further noting that CF exhibits a distinct seasonal variation, with a minimum in winter (0.37) and maximum in summer (0.68). Cumulus occurs more frequently in summer (32%), which is close to the sum of the occurrence of stratus and cirrus. The annual CRE is –54.4 W m–2, with seasonal values ranging from –29.5 W m–2 in winter and –78.2 W m–2 in summer. When clouds do not obscure the sun, CF is a dominant factor affecting diffuse irradiance, which in turn affects global irradiance. There is a positive linear relationship between CF and CRE under sun-unobscured conditions, the mean sensitivity of CRE for each CF 0.1 increase is about 1.2 W m–2 [79.5° < SZA (Solar Zenith Angle) < 80.5°] to 7.0 W m–2 (29.5° < SZA < 30.5°). When clouds obscure the sun, CF affects both direct and diffuse irradiance, resulting in a non-linear relationship between CF and CRE, and the slope decreases with increasing CF. It should be noted that, although only data at Xianghe is used in this study, our results are representative of neighboring areas, including most parts of the North China Plain.

摘要: 云是影响地表辐射能量收支的重要参数,云辐射效应与云的宏、微观特性参数密切相关,亟需系统的观测研究。本文利用华北平原香河站高时间分辨率辐射测量数据,结合全天空成像仪观测数据,进行云类型识别,评估云量,并重点探讨了云遮蔽和未遮蔽太阳两种情形下云量和地表太阳辐射的参数关系。结果表明香河站云量年均值为0.50,冬季和夏季云量均值分别为0.37和0.68,其中夏季以积云为主(32%),出现频率约等于层云和卷云出现频率之和。香河站云辐射效应的年均值为–54.4 W m-2,冬季和夏季云辐射效应分别为–29.5 W m-2和–78.2 W m-2。太阳未被遮蔽情况下,云量变化主要影响散射辐射,继而影响总辐射。云量与CRE呈线性关系,CF增加0.1,CRE平均增加1.2(79.5°<SZA<80.5°)–7.0(29.5°<SZA<30.5°)W m-2。在太阳被遮蔽情况下,云量变化同时影响直接辐射和散射辐射,导致云量与云辐射效应呈非线性关系,且斜率随云量的增加而降低。太阳未被遮蔽时云主要起正辐射强迫作用,太阳被遮蔽时主要起负辐射强迫作用,且负辐射强迫的量级是正辐射强迫的3倍。

    • Clouds play a vital role in the energy cycle and climate of the earth-atmosphere system (Stephens, 2005; Van Tricht et al., 2016). The cloud radiative effect (CRE) depends on cloud macrophysical (cloud fraction, cloud base height, etc.) and microphysical (cloud phase, cloud particle size, etc.) properties. Understanding and quantifying the influence of cloud properties on the radiation budget is important for accurately simulating the Earth's current energy and water cycles and predicting cloud radiative forcing in future climate simulations (IPCC, 2007). Estimating CRE from satellite data is feasible (Chen et al., 2000; IPCC, 2013). However, most satellite data cannot effectively show the variability of cloud properties due to their limited temporal and/or spatial resolution. In addition, the passive remote sensing instruments used by most satellites have certain assumptions in cloud vertical structure (i.e., single or multi-layers), which introduces additional uncertainties in the retrieval of surface CRE (Wild et al., 2013). For instance, observation of low clouds by the satellite may be blocked by optically thick high clouds, leading to substantial CRE underestimation (Lau and Crane, 1997).

      The Atmospheric Radiation Measurement Program (ARM) and CloudNet operate a network of long-term sites with measurements of both cloud properties and surface radiation in the United States and Europe (Atmospheric Radiation Measurement Program Plan, 1990; Illingworth et al., 2007). Data are widely used to study CRE and response to cloud properties in tropical, mid-latitude, and Arctic sites (Dong et al., 2006, 2010; Berg et al., 2011; McFarlane et al., 2013). These studies showed that the magnitude of CRE is highly variable and depends on regional and temporal variations (Kim and Ramanathan, 2008). Since the climate in China is different from the sites in the abovementioned studies, understanding and quantifying the relationship between cloud properties and CRE in China is in high demand.

      Xianghe is located on the North China Plain, characterized by a temperate continental climate with apparent seasonal variability of cloud properties. This paper aims to quantify the influence of clouds on surface irradiance and explore the different relationships between various cloud properties and CRE. The multi-year measurements of surface irradiance from broadband radiometers are combined with measurements of cloud fraction (CF) from the Total Sky Imager (TSI) to characterize the variability of CF, cloud type, and CRE, afterward, detailed analysis of CRE as a function of CF under sun-obscured and sun-unobscured conditions is performed. The results should be significant for understanding cloud-radiation interactions and further evaluating climate model simulations over the North China Plain.

      The remainder of this paper is structured as follows. Section 2 briefly describes the data, clear-sky irradiance estimation methodology and cloud classification algorithm, and section 3 uses the data and methods to characterize CRE at Xianghe. Section 4 summarizes and discusses these results and comments on future prospects.

    2.   Site, data, and methods
    • Xianghe (39°45'N, 116°57'E) is a suburban station located ~70 km southeast of Beijing. Surface irradiance measurements used in the study include global horizontal irradiance (GHI), direct normal irradiance (DNI), and diffuse horizontal irradiance (DHI). The GHI, DNI, and DHI are observed by Kipp & Zonen CM-21 pyranometer, Eppley Laboratory, Inc., Normal Incidence Pyheliometer (NIP), and Model 8−48 black and white pyranometer (Black & White), respectively. The CM-21 is a high-performance pyranometer measuring the irradiance on a plane surface, which results from the direct and diffuse solar radiation incident from the hemisphere above. The NIP is mounted on a solar tracker to provide a sighting arrangement for aiming directly at the sun. The field measurement uncertainties of GHI, DNI, and DHI are less than 5 W m–2, 2 W m–2, and 5 W m–2, respectively. In this study, we applied the quality control methods of the Baseline Surface Radiation Network (BSRN) to surface irradiance data between 2005 and 2009 (Ohmura et al., 1998). The GHI is related to DNI and DHI as follows.

      where SZA is Solar Zenith Angle.

      The instrument used to observe CF is Yankee Environmental Systems, Inc., Model 440 Total Sky Imager (TSI-440). The basic design for the TSI-440 includes a camera and a hemispheric mirror. To prevent flare in adjacent pixels, the TSI-440 uses a shadow band to block the sun's reflection. When processing a cloud image, an empirically derived red-to-blue threshold is used to distinguish between clear and cloudy pixels (Morris, 2005). The estimated CF (0–1) is calculated as the number of cloudy pixels divided by the total number of pixels within the field of view (FOV) of the imager (FOV = 160°). The algorithm often interprets high aerosol loading cases as cloudy because of the forward scattering from aerosol loading. In contrast, cirrus or thin broken clouds are often mistaken as clear skies. To overcome these shortcomings, the cloud detection results by the algorithm are further manually checked for quality assurance (Liu et al., 2021a).

      A CIMEL Sun/sky radiometer was installed in September 2004, and since then, Xianghe has become one of the Aerosol Robotic NETwork (AERONET, https://aeronet.gsfc.nasa.gov/) sites (Holben et al., 1998). The Aerosol Optical Depth (AOD), Angstrom Exponent (AE), Precipitable Water Vapor (PWV), etc., are used in this study.

      The shortwave cloud radiative effect of GHI (CREGHI), cloud radiative effect of DNI (CREDNI), and cloud radiative effect of DHI (CREDHI) are computed as follows:

      where GHIobs, DNIobs, and DHIobs represent observed GHI, DNI, and DHI, while GHIcs, DNIcs, and DHIcs represent expected clear-sky GHI, DNI, and DHI by REST2 solar radiation model (Gueymard, 2008). Previous studies have suggested that REST2 is one of the most widely used models producing reliable results (Badescu et al., 2013). The inputs to the REST2 model include AOD (550 nm), AE, PWV, surface albedo (SA), ozone amount, nitrogen dioxide amount, and site pressure. The first three inputs are from AERONET products (Liu et al., 2021b), while the last four inputs are from MERRA-2 reanalysis (https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/). We have compared the measured and REST2 calculated GHI, DNI, and DHI using clear-sky samples in Liu et al. (2021b). The biases of GHI, DNI, and DHI are 0.83 W m–2, 17.75 W m–2, and –9.97 W m–2, respectively. While the relative mean squared error of GHI, DNI, and DHI is 13.17 W m–2, 54.09 W m–2, and 26.73 W m–2, respectively. Such errors may result in underestimating CREDNI and overestimating CREDHI at Xianghe; however, these errors should influence the magnitude rather than the tendency of their sensitivity to CF.

      A cloud type estimation method based on GHI measurements is used, in which the running standard deviation of the scaled measured surface shortwave irradiance (Std21) and the mean ratio of the scaled irradiance to the scaled clear-sky irradiance (Rc) in a 21-min moving window are used as the classifiers to distinguish cloud types (Duchon and O'Malley, 1999). The determination of cloud-type boundaries is based primarily on a comparison of human-observed cloud types coincident with the measured irradiance parameters at the ARM site and secondarily on nominal values of the two parameters intuitively expected for the different categories according to the standard cloud-type descriptions. As shown by a cases study in Fig. 1, cumulus is characterized by relatively large Rc (> 0.5) and large Std21 (exceeding 120). Meanwhile, observations with an Std21 < 100 and Rc < 0.4 are attributed to stratus. Cirrus occupies an area with Rc varying from 0.8 to 1.05 and an Std21 less than 70. The area outside specific cloud types represents clouds of indeterminate types.

      Figure 1.  Criteria for estimating cloud type based on the standard deviation of scaled observed irradiance (Std21) and the ratio of scaled observed irradiance to scaled clear-sky irradiance (Rc). Cumulus, stratus, and cirrus samples are extracted from 1200–1300 LST on 16 May 2007, 1300–1400 LST on 30 March 2007, and 1030–1100 LST on 6 March 2007, respectively. LST represents Local Standard Time (UTC + 8 hours).

      The algorithm recommended by Roesch et al. (2011) is used to calculate the annual mean of CRE and CF. A 15-min average is first computed from the 1-min data for each month. The monthly mean is then computed by averaging the 96 bins (96 × 15 min = 24 h) that have been produced for each month. The annual means are calculated by averaging the 12 months that have been produced for each year. This method minimizes the impact of missing values, especially when applied to clear and cloudy skies separately.

    3.   Results
    • The frequency distribution of CF at Xianghe during 2005–09 is shown in Fig. 2. (a). Of all cases that were investigated, 34.68% fall into the overcast cases (CF > 0.95), and 12.09% fall into the thin cirrus (CF ≤ 0.05) cases, while other CF cases occur with a frequency of less than 10%. The CREGHI exhibits the strongest variability ([–900, 300] W m–2) for small SZA (about 20°). The variability of CREGHI decreases as SZA increases, with a minimum CREGHI variability of [–150, 100] W m–2 for SZA at 80° (Fig. 2b). The evolution of CREGHI agrees with that found by Mateos et al. (2013); however, the absolute value of CREGHI at Xianghe is much higher than that at South-Western Europe, which is likely due to different climates. In general, the occurrence frequency for samples satisfying –125 ≤ CREGHI ≤ 0 exceeds 25% in all SZA bins. Dong et al. (2006) and Berg et al. (2011) estimated the diurnal variation of CREGHI for high-cloud and shallow-cumulus conditions of [–150, 0] W m–2 in the Southern Great Plains (36.6°N, 97.5°W), the United States. In contrast, this study implies that high clouds or broken clouds contribute a quarter of CREGHI.

      Figure 2.  (a) Frequency of cloud fraction (CF). (b) The boxplot shows median, quartiles, minimums, and maximums for the shortwave cloud radiative effect of GHI (CREGHI) as a function of SZA from 2005 to 2009 at Xianghe. Circles and triangles represent outliers and means, respectively.

      Figure 3 shows the distribution of the annual and seasonal CF, CREGHI, CREDNI, and CREDHI. The annually averaged CF is approximately 0.50 (0.40–0.55) from 2005 to 2009 at Xianghe (Fig. 3a), which is close to the annual CF in North China Plain (0.5 to 0.6) and lower than the annual CF all over China (around 0.61) (Zhang et al., 2018; Zhao et al., 2019). The seasonal mean CF is 0.37 (0.32–0.42, December–February: DJF), 0.59 (0.50–0.67, March–May: MAM), 0.68 (0.58–0.75, June–August: JJA) and 0.47 (0.37–0.55, September–November: SON), respectively. The high CF in JJA is consistent with the expected increases in convection by enhanced solar radiation and sufficient water supply from Pacific Subtropical High, and the low CF in DJF is likely associated with the cooling effect and water vapor deficiency, as the result of Mongolian-Siberia High (Zhao et al., 2019). The annual mean CREGHI is –54.42 (–57.08 to –53.24) W m–2, which is very close to the global annual mean CREGHI (–54 W m–2 and –53.5 W m–2 by observations and CMIP5 multi-model mean, respectively) (Wild et al., 2019). The annual CREGHI obtained here is higher (in absolute value) than the estimation at an Arctic site (–26.2 W m–2) and lower (in absolute value) than those estimated at tropical sites (from –97.8 W m–2 to –67.5 W m–2) (Dong et al., 2010; McFarlane et al., 2013). The seasonal mean CREGHI in DJF, MAM, JJA, and SON is –29.47 (–42.89 to –19.11) W m–2, –71.39 (–80.36 to –64.13) W m–2, –78.24 (–94.21 to –64.76) W m–2 and –51.33 (–61.06 to –41.54) W m–2, respectively. The CREGHI in Fig. 3b shows a weaker seasonal variability (about 49 W m–2) at Xianghe than at tropical (about 64 W m–2) and Arctic (about 80 W m–2) sites (Dong et al., 2010; McFarlane et al., 2013). The annual mean CREDNI is –90 W m–2 to –80 W m–2, and the mean CREDNI in DJF (–62.70 W m–2) shows a large difference relative to the other three seasons (–107.50 W m–2 to –91.14 W m–2) (Fig. 3c). The annual and seasonal distribution of CREDNI is close to that of CREGHI, whose absolute value is higher at MAM and JJA, indicating that the direct beam is the primary modulator of CREGHI or even surface irradiance. The annual mean CREDHI is similar to the seasonal mean of CREDHI, with a magnitude of 0–6 W m–2 (Fig. 3d). It is clearly indicated that the diffuse flux increases for most cloudy conditions instead of clear skies. Seasonal changes in the cloud properties primarily determine these patterns.

      Figure 3.  Median, quartiles, minimums, and maximums of the annual and seasonal means of (a) CF, (b) CREGHI, (c) CREDNI, and (d) CREDHI from 2005 to 2009 at Xianghe. Circles represent outliers.

      Table 1 provides cloud-type classification from 2005 to 2009 at Xianghe, and Fig. 4 further shows the frequency of the three major cloud types. Note that 32.7% of cloudy samples cannot be assigned to a distinct cloud type by this simple cloud classification method. For the remaining samples, 27.5%, 18.7%, and 21.2% are identified as cumulus, stratus, and cirrus, respectively (Table 1). That is, cumulus occurs more frequently than the other two cloud types, which is very close to the results in North China Plain based on satellite datasets (Wang et al., 2021). The frequency of indeterminate samples is similar in all seasons at about 32% (Fig. 4). The frequency of cumulus in JJA (32.8%) is larger than those in the other three seasons by ~8%. This is because the temperature and water content is higher in JJA than in the other three seasons. Thus, the conditional instability required for convective clouds formation is more easily reached (Gao et al., 2019). The occurrence of stratus increases gradually from DJF to SON (13.8% to 23.6%). The cirrus is more frequent in DJF (27.4%) and MAM (26.4%) as compared to the other two seasons. The months of DJF and MAM show less convective movements and reduced water vapor, resulting in situ-origin cirrus, which easily forms during these two seasons and are mostly thin (Huo et al., 2020).

      Frequency (%)
      Indeterminate32.67
      Cumulus27.48
      Stratus18.68
      Cirrus21.17

      Table 1.  Determination of cloud type by using the Duchon and O'Mallley (1999) method.

      Figure 4.  Seasonal occurrence frequency of the indeterminate samples and three major cloud types using the Duchon and O'Malley (1999) method.

    • Figure 5 shows an example of diurnal CF and irradiance evolution when sky conditions change from cloudless in the morning to mostly cloudy in the afternoon on 30 June 2009. The CF observed by TSI is less than 0.1 (clear) before 1300 Local Standard Time, and the corresponding GHIobs variation was relatively smooth (Fig. 5a). Shallow cumulus appeared beginning 1300 LST when CF increased from 0.1 to about 0.4. The sun was obscured by shallow cumulus intermittently, during which GHIobs varied significantly. After 1400 LST, CF increased from 0.1 to 0.9, and the corresponding GHIobs continued to fluctuate greatly. Figure 5b shows the measured and calculated clear-sky irradiance for the shallow cumulus period (1300–1400 LST). When the sun was partially or completely obscured by shallow cumulus (1310–1330 LST), there was a significant reduction in DNIobs compared to DNIcs, by over 700 W m–2, while DHIobs increased slightly by about 50 W m–2, ultimately resulting in negative radiative forcing in GHIobs (about –600 W m–2). When shallow cumulus exists but does not block the sun (1330–1354 LST), DNIobs was almost equal to DNIcs, and DHIobs is enhanced by scattering, which results in positive radiative forcing in GHIobs (about 50 W m–2). The sun is obscured more frequently due to increased CF during 1400–1500 LST (Fig. 5c). There was a "clear line of sight to the sun" during 1404–1413 and 1430–1442 LST. As CF increases from 0.1 to 0.3, the discrepancy between DNIobs and DNIcs was small (about 15 W m–2). However, due to the increase of DHIobs by nearly 45 W m–2, CREGHI has doubled (from about 50 to 100 W m–2), as shown in Fig. 5d. The sun was obscured during 1415–1430 and 1442-1456 LST, and both DNIobs and DHIobs are different from their concomitant clear-sky value. The general picture is that DNI decreased significantly because of cloud reflection and absorption, some part of which was offset by a moderate increase in DHI. The overall effect of clouds under sun-obscured conditions is to induce a notable reduction in GHI. That is, the radiative forcing of CF on DNI and DHI, which in turn affects GHI, depends on the position of the cloud relative to the sun. Therefore, we discuss the radiative forcing by CF under sun-free and sun-obscured conditions separately.

      Figure 5.  (a) Daily course of measured CF and GHIobs at Xianghe for 30 June 2009, CF and irradiance components during (b) 1300–1400 LST, (c) 1400–1500 LST, and (d) CREGHI during 1400–1500 LST.

      The Clearness Index (CI) is used to identify periods with "clear sun" in this study, which is calculated by Eq. (5) (Zhao et al., 2018).

      When CI ≤ 0.25, it is considered as a "clear sun" value (Zhao et al., 2018). In this study, a more restrictive threshold value for the determinant of 0.2 is considered. On the one hand, the bias and relative mean squared error of calculated DNIcs are only about 3.27% and 10% (validated by clear-sky samples in Liu et al. (2021a)), more restrictive threshold value (0.2) would be enough to cover most errors in DNIcs calculation. On the other hand, a more restrictive threshold can, at least to an extent, avoid misclassifying “sun partly obscured” or “sun obscured by thin cirrus” conditions as sun-unobscured conditions. That is, a CI higher than 0.2 is considered as a sun-obscured case here.

      Boxplots of CREDHI as a function of CF for seven SZA ranges are shown in Fig. 6, with at least 439 samples in each SZA range. The mean CREDHI generally changes linearly with CF in all SZA ranges (with p-values for Kendall tau correlation coefficients lower than 0.02 in most SZA ranges). According to the polynomial regression fits in Fig. 6, on average, an increase in CF of 0.1 induces an increase in CREDHI of 0.6 (79.5° < SZA < 80.5°) –7.4 (19.5° < SZA < 20.5°) W m–2 at Xianghe, and the correlation coefficient (R2) between mean CREDHI and the regression results is over 0.8 in most SZA ranges. The slope of CREGHI to CF is very similar to its diffuse counterpart, with p-values for Kendall tau correlation coefficients lower than 0.04 in all SZA ranges, as shown in Fig. 7. As illustrated by the fitting lines in Fig. 7, a small increase in CF (0.1), accompanied by an average of 1.2 (79.5° < SZA < 80.5°) –7.0 (29.5°< SZA < 30.5°) W m–2 increase in CREGHI, and an R2 between mean CREGHI and the regression results is over 0.75 in all SZA ranges. As illustrated in Fig. 7, CREGHI increases with increasing CF under sun-unobscured conditions, with variations from [–100, 50] W m–2 (CF ≈ 0) to [–100, 200] W m–2 (CF ≈ 1) (~20°) and from [–30, 30] W m–2 (CF ≈ 0) to [–10, 40] W m–2 (CF ≈ 1) (~80°). Notably, the calculated clear-sky irradiance has certain errors, which is a potential source of negative CREDHI and CREGHI under sun-unobscured conditions. Moreover, the method used in Zhao et al. (2018) is potentially prone to misclassification, which is another possible source of samples below 0 in Figs. 6-7.

      Figure 6.  Boxplots (median, quartiles, minimums, and maximums) of CREDHI as a function of CF for seven SZAs under sun-unobscured conditions. The red triangles represent the mean CREDHI, asterisks represent outliers, and the solid red lines represent the fitting results.

      Figure 7.  Boxplots (median, quartiles, minimums, and maximums) of CREGHI as a function of CF for seven SZAs under sun-unobscured conditions. The blue triangles represent the mean CREGHI, asterisks represent outliers, and the solid blue lines represent the fitting results

      The following power function is used to fit CREGHI to CF under sun-obscured conditions (Dong et al., 2006):

      where a and b are regression coefficients. Figure 8 shows that CREGHI decreases with increasing CF with a much greater magnitude under sun-obscured conditions, as the variability from [–100, 250] W m–2 (CF ≈ 0) to [–800, 300] W m–2 (CF ≈ 1) (~20°) and from [–100, 50] W m–2 (CF ≈ 0) to [–125, 50] W m–2 (CF ≈ 1) (~80°). In this way, CREGHI changes are asymptotic with respect to changes in CF because, overall, the cloud optical depth tends to increase with increasing CF. The regression function indicates that CREGHI decreases with increasing CF by an average of –22.2 W m–2 (19.5°< SZA < 20.5°) to –2.3 W m–2 (79.5° < SZA < 80.5°) for CF each 0.1 increase (with at least 2871 samples in each SZA range).

      Figure 8.  Boxplots (median, quartiles, minimums, and maximums) of CREGHI as a function of CF for seven SZAs under sun-obscured conditions. The blue triangles represent the mean CREGHI, asterisks represent outliers, and the solid blue lines represent the fitting results

      The above analysis can be briefly summarized follows. A rising CF positively affects CREGHI at Xianghe when the sun is unobscured but negatively affects CREGHI when the sun is obscured. Moreover, the magnitude of the mean negative radiative forcing under sun-obscured conditions is about three times that of the mean positive radiative forcing under sun-unobscured conditions.

    4.   Conclusion and Discussion
    • In this study, we use 5-year ground-based observation of irradiance and clouds at Xianghe to evaluate the influence of CF on CRE, especially under sun-obscured and sun-unobscured conditions. We find strong seasonal variations in CF, cloud type, and CRE. The annual mean CF at Xianghe is 0.50. The seasonal mean CF in DJF and JJA is 0.37 and 0.68, and the major cloud types in these two seasons are cirrus and cumulus, respectively. This, in turn, affects CRE: the annual, DJF, and JJA mean CREGHI is –54.42, –29.47, and –78.24 W m–2, respectively. In addition, in all SZA bins, the proportion of samples with –125 ≤ CREGHI ≤ 0 exceeds 25%, indicating that clouds generate modest negative radiative forcing at Xianghe.

      The impact of a change in CF on CRE is discussed under sun-unobscured and sun-obscured conditions. For those cases in which clouds do not obscure the sun, only DHI is affected by the variation in CF. However, both DNI and DHI are affected by the CF for the sun-obscured cases. On average, a CF increase of 0.1 would induce 0.6 (79.5° < SZA < 80.5°) –7.4 (19.5° < SZA < 20.5°) W m–2 increase under sun-unobscured conditions, and 2.3 (79.5° < SZA < 80.5°) –22.2 (19.5° < SZA < 20.5°) W m–2 decrease under sun-obscured conditions. The CREGHI at Xianghe exhibits a positive linear trend with a rising CF when the sun is unobscured and exhibits a negative trend with a rising CF when the sun is obscured. For the same increase in CF (0.1), the magnitude of negative radiative forcing under sun-obscured conditions is about three times that of positive radiative forcing under sun-unobscured conditions.

      By using long-term ground-based irradiance and cloud observations at Xianghe, the present work provides reliable variations of CF and corresponding radiative forcing at the site for the first time. Furthermore, the study at Xianghe is representative of neighboring areas (i.e., Beijing and Tianjin), and most parts of the North China Plain, since cloud and radiative properties show strong regional characteristics. The results should be of value for advancing our understanding of cloud–radiation interactions, verifying satellite retrievals, and enabling climate/radiation modelers to evaluate their simulations more fully over the North China Plain. It should also be noted that due to the TSI algorithm and the heavy aerosol loading at Xianghe, the CF data used in this study is prone to certain errors, such as the relatively low sensitivity of TSI to thin cirrus and the difficulty of distinguishing polluted cloudless pixels from cloudy pixels by TSI. As a next step, it is necessary to obtain improved ground-truth cloud measurements. Unfortunately, because of the lack of long-term simultaneous measurements of the other cloud properties, only the relationship between CF and CRE is discussed in this study. Therefore, collecting additional cloud properties, such as cloud base height and cloud optical thickness, would allow for the study of cloud radiative forcing at a more detailed level. We expect similar analyses to be conducted using datasets from other regions to improve our understanding of the geographical variability of surface cloud radiative forcing.

      Acknowledgements. This work was supported by the National Natural Science Foundation of China (Grant Nos. 41875183, 41805021) and the National Key R&D Program of China (Grant No. 2017YFA0603504).

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