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 (%) Indeterminate 32.67 Cumulus 27.48 Stratus 18.68 Cirrus 21.17
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.