1. Introduction

Clouds are very important elements in the earth–atmosphere radiative balance because of their role in the interaction with shortwave (SW) (or solar) and longwave (LW) (or thermal) radiation. On one hand, they reflect and absorb part of the incoming SW radiation; on the other hand, they absorb LW radiation emitted from the earth’s surface and, in turn, reemit LW radiation back to the earth and to space. Thus, clouds are the dominant modulators of radiation, both at the surface and at the top of the atmosphere (TOA) (Dong et al. 2006). A way of quantifying the cloud radiation effects at the surface and at the TOA is the cloud radiative forcing (CRF), which is defined as an instantaneous change in net total radiation (SW plus LW; in W m⁻²) obtained under cloudy conditions and its clear-sky counterpart; CRF can produce a cooling (negative CRF) or a warming (positive CRF) effect on the earth–atmosphere system.

CRF has been a research topic over the last decades because of its importance in understanding the effects of clouds on the radiative balance, which controls the earth–atmosphere temperature; Ramanathan et al. (1989) and Harrison et al. (1990) were the first to estimate the global CRF and the seasonal effects of clouds on the radiation budget from Earth Radiation Budget Experiment (ERBE) data. Since then, with the improvement of satellites, ground-based instruments, and radiative transfer and climate models, many other studies dedicated to the radiative effects of clouds were developed (Mace et al. 2006; Dong et al. 2006; Kassianov et al. 2011; Berg et al. 2011; Liu et al. 2011), both at the surface and at the TOA. The calculation of CRF at the surface can be done through ground-based observations, and the information gathered at different sites all over the globe constitutes valuable information for validation purposes. The description of the cloud effects on the surface radiation budget is a critical component for understanding the current climate and an important step toward simulating potential climate change (Dong et al. 2006).

In this work, the shortwave cloud radiative forcing (CRF_SW), defined as the difference between the SW net fluxes (downward minus upward SW fluxes) obtained under both all-sky and clear-sky conditions, is calculated from irradiance measurements taken at the surface in the Geophysics Centre of Évora, which is located in the south of Portugal, about 100 km east from the Atlantic coast. Studies on the shortwave radiative forcing in this region, both at the TOA and surface levels, have already been made but mostly using atmospheric modeling and concentrating on the radiative effect of aerosols and of contaminated clouds by desert dust aerosols (Santos et al. 2008, 2013). However, no investigation of the cloud radiative effects in the shortwave spectral range has been done at the site using the long time series of surface SW irradiance measurements taken during the period 2003–10.

These studies can be extremely useful to validate satellite assessments of radiative forcing or model calculations, particularly over a region of potential interest that is affected by contrasting air masses (Raes et al. 2000), and thus offers opportunities for studying not only clouds, but also their interaction with aerosols from different origins. During the winter season, the large-scale atmospheric circulation in Portugal is primarily determined by the location and intensity of the Icelandic Low. The area is on the track of front systems typical of midlatitude regions, brought from the Atlantic Ocean by the westerly circulation and carrying moist air. These fronts affect the region more often in winter and spring, before the polar front moves northward. When this happens, the synoptic circulation becomes constrained by the Azores anticyclone (during late spring and summer), which transports dry warm air from north or northeast into the region and is associated with clear-sky conditions. Besides, in the warm season, the intense surface heating of inland regions results frequently in the development of a thermal low pressure system at the Iberia scale, with shallow convection originating mostly in the afternoon (Costa et al. 2010).

In this study, the CRF estimates are relative only to the SW spectral range and involve global SW irradiance measurements in two different spectral bands obtained for all cloudy-sky conditions, in terms of cloud type and cloud fraction (from partially cloudy to overcast), taken from ground-based instruments. Other authors have studied the variations of CRF for several sky conditions and for specific types of clouds (Dong et al. 2006; Berg et al. 2011; Liu et al. 2011). Berg et al. (2011) found a shortwave CRF average value of −45.5 W m⁻² for shallow cumuli; Dong et al. (2006) studied the seasonal and monthly variations of CRF for a midlatitude site and showed that CRF_SW at the surface exhibited minimum values in spring and had a spring seasonal average of −61.3 W m⁻² for all-sky conditions. This study also analyzes the seasonal and monthly variability of the surface CRF_SW for all-sky conditions over a midlatitude site in southwestern Europe, aiming to contribute to the understanding of the cloud impact on Earth’s radiation balance, which is important for climate and climate change studies (Ramanathan et al. 1989).

The next section describes the methodology as well as the data used to estimate the shortwave cloud radiative forcing at the ground surface. Section 3 presents the results of this study, and section 4 summarizes the work and the main results.

2. Data and methodology

a. Instruments and data

The measurements used here are recorded with two field instruments, a multifilter rotating shadowband radiometer (MFRSR) (Harrison et al. 1994) and an Eppley black and white pyranometer, both operating since 2003 at the Atmospheric Physics Observatory of Geophysics Center of Évora (CGE; 38°34’N, 7°54’W, 300 m above mean sea level). The MFRSR is an instrument that provides automatic measurements of global and diffuse components of the spectral and broadband hemispherical shortwave irradiances with a temporal sampling of 1 min. It has seven channels, covering the visible and partly the near-infrared spectral regions (415, 500, 615, 673, 870, and 940 nm), with 10 nm of bandwidth and a broadband channel (300–1100 nm), used in this study. The Eppley black and white pyranometer provides measurements of hemispherical shortwave global irradiances, corresponding to the spectral region between 285 and 2800 nm, with a temporal sampling of 1 min and providing 10-min averages. The instruments are regularly calibrated, and their uncertainties are estimated at 5%.

MFRSR broadband irradiance measurements taken from August 2003 to August 2010 have considerable gaps within the period, as listed in Table 1. Only the periods where coincident shortwave irradiance measurements from both instruments occur are used in the study. These measurements cover all-sky situations in terms of cloud type and cloud fraction. The two sets of data from the MFRSR and Eppley instruments are used because the spectral bands of the instruments cover different fractions of the solar radiation spectrum at the surface (the MFRSR broadband channel covers approximately 73.5%, and the Eppley pyranometer covers roughly 95%). This allows comparison of the SW cloud radiative forcing at the surface obtained with two different sets of observed data for the same time period, geographic location, and atmospheric conditions and allows us to estimate the relative contribution of the MFRSR forcing to the total forcing (Eppley).

Table 1.

MFRSR data available in Évora (cells with X) for the period 2003–10.

Aerosol optical thickness (AOT) and precipitable water vapor (PWV) data obtained from direct sun measurements continuously taken at the observatory of the Évora Geophysics Centre as part of the Aerosol Robotic Network (AERONET) (Holben et al. 2001) are also used in the study, as explained in the next subsection.

b. Clear-sky irradiance

The calculation of the SW cloud radiative forcing, which is described in the next subsection, requires irradiance values for clear-sky conditions; these values are not possible to obtain from measurements during cloudy periods. Long and Ackerman (2000) proposed a method to identify and produce continuous estimates of clear-sky irradiance values at the surface based on the empirical fit of clear-sky irradiance functions using the cosine of the solar zenith angle as the independent variable. While this method provides very good estimates of clear-sky irradiance at the surface for the day of the fitting, it ignores changes in atmospheric variables, such as PWV and AOT, between clear-sky days and therefore may introduce errors in the clear-sky irradiance estimates. A different approach is proposed here, based on radiative transfer (RT) calculations. The clear-sky irradiances corresponding to each measurement are calculated using the Library for Radiative transfer (LibRadtran) package (Mayer and Kylling 2005), taking into account both the MFRSR and Eppley spectral response functions. The surface is considered as a Lambertian reflector, with an albedo value of 0.22 for Eppley simulations (http://speclib.jpl.nasa.gov/) and 0.27 for MFRSR broadband channel simulations obtained from spectral reflectance ground-based measurements with a portable spectroradiometer (described by Potes et al. 2012). A midlatitude type of atmospheric vertical profile for winter or summer (McClatchey et al. 1971) was considered, according to the season. PWV and AOT values of 15 kg m⁻² and 0.1 were used, respectively, corresponding to the average of AERONET measurements for the 7-yr period and therefore considered representative of the conditions over Évora. Aerosols are assumed to be described by the Shettle (1989) default properties, with rural-type aerosols in the boundary layer, background aerosols above 2 km, spring–summer or fall–winter conditions (according to the season), and 50-km visibility. The radiative transfer equation is numerically solved using the discrete ordinate method (Stamnes et al. 2000) with 16 quadrature angles.

As mentioned before, day-to-day variations of atmospheric variables, such as PWV and AOT, may induce considerable changes in the radiation field; thus, fixed amounts of these variables may represent a poor approximation to accurately model the clear-sky irradiance. The method proposed here introduces two conversion functions that account for these variations and constitute a fast and accurate correction to the clear-sky irradiances calculated with the radiative transfer model. The conversion functions are defined as:

where is the downwelling shortwave irradiance at the surface, θ is the solar zenith angle, is either the AOT or the PWV value, and takes the value of 0.1 (for the AOT) or 15 kg m⁻² (for the PWV). Tables of the conversion functions are calculated with LibRadtran, considering the above described conditions and varying the solar zenith angle (ranging from 0° to 90° with steps of 1°) and the AOT or the PWV within limits deemed adequate for the site based on AERONET measurements. The values of AOT were varied between 0.01 and 1.5, with a step of 0.1 between 0.1 and 1.5. The PWV was varied between 1 and 50 kg m⁻², with a step of 5 kg m⁻² between 5 and 50. These conversion functions are normalized to unity for an AOT of 0.1 and a PWV of 15 kg m⁻², respectively. Figure 1 shows the contour plots obtained for both instruments and atmospheric variables considered. It can be noted that the conversion functions take values greater than one when the AOT is lower than 0.1 or when the PWV is lower than 15 kg m⁻² (values considered for the normalization of the conversion functions). Above these limits, the conversion functions decrease with the increase of both quantities. It is also worth mentioning that the variation of the conversion functions is more pronounced at higher values of the solar zenith angle, when irradiances are already quite low and differences in the atmospheric variables become increasingly important because of the longer path that radiation must travel in the atmosphere to reach the surface.

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Conversion functions accounting for (a) AOT variations on MFRSR irradiances, (b) PWV variations on MFRSR irradiances, (c) AOT variations on Eppley irradiances, and (d) PWV variations on Eppley irradiances.

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

The clear-sky irradiance corrected to reflect the actual mean daily values of AOT and PWV [] is obtained from Eq. (2) using the conversion functions defined in Eq. (1). The conversion functions are obtained by linear interpolation of the calculated tables using AERONET daily-mean values of AOT and PWV for the Évora site:

The irradiances obtained from Eq. (2) are compared to exact RT calculations considering the values of AOT and PWV represented by the conversion functions and spanning the values mentioned above in order to quantify the error involved in this approximation. Figure 2 shows the relative error as a function of the solar zenith angle, which is, in general, rather small and quite similar for MFRSR and Eppley spectral intervals. MFRSR presents slightly higher/lower extreme relative errors for lower zenith angles (gray dots in Fig. 2), which are obtained because absolute differences for MFRSR and Eppley simulations are roughly of the same order of magnitude, yet the clear-sky irradiance is higher for Eppley than for MFRSR (connected with the spectral range of each), yielding slightly higher relative errors in the latter case. For solar zenith angles lower than 70°, the relative error values are enclosed between −1.5% and 0.5%, increasing then with solar zenith angle to values between −3.5% and 3.0%. Note that the error distribution is biased toward negative values, indicating a slight tendency of the approximated clear-sky irradiance to underestimate the exact calculations. The overall mean bias errors (BIAS), root-mean-square error (RMSE), normalized BIAS (NBIAS), and normalized RMSE (NRMSE), as well as the number of data points used (N) and the correlation coefficient (R) are presented in Table 2. The values obtained for the statistical parameters, with NBIAS of −0.05% and NRMSE of 0.1% in both cases, demonstrate the validity of the approximation expressed by Eq. (2).

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Relative error (%) associated with the solar irradiance calculation using the conversion factors, as a function of solar zenith angle.

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

Table 2.

Statistics of the comparisons between exact radiative transfer calculations of clear-sky irradiance and the corresponding approximation using the conversion factors.

The clear-sky irradiances obtained applying the described methodology are checked against clear-sky observations and are also compared to those obtained applying the method proposed by Long and Ackerman (2000). Figure 3 shows an example of the performance of the method for a case of moderately high values of AOT and PWV (0.47 and 24.6 kg m⁻², respectively) on 10 August 2010 for MFRSR and Eppley measurements. The clear-sky irradiance obtained from RT considering an AOT of 0.1 and PWV of 15 kg m⁻² clearly overestimates the measurements; however, when the conversion factors are applied [Eq. (2)] accounting for the actual AOT and PWV values, a very good match between RT calculations and measurements is obtained in both cases, especially from around 1000 UTC until the end of the day. Small differences between observations and RT calculations may also be due to variations in the AOT and PWV during the day, since daily averages are used to get the conversion factors for a certain solar zenith angle. The fit line obtained from the Long and Ackerman (2000) method also adjusts very well to the experimental points. However, this method requires a minimum number of clear-sky measurements over a considerable range of solar zenith angles to guarantee a statistically accurate calculation (Long and Ackerman 2000), which is not always available. Under cloudy conditions, the fits obtained with this method must be interpolated, introducing additional uncertainties in the clear-sky irradiance. To compare the uncertainties introduced by the different methods, periods of at least four successive clear-sky days were selected from the complete dataset (2003–10), in order to test the effect of the interpolation of the fit coefficients in a similar way to that followed by Long and Ackerman (2000), as well as to test the effect of the RT-based methods. A total number of 64 days were found fulfilling the conditions mentioned before. Figure 4 shows the corresponding frequency histogram of relative differences between Eppley measured and estimated clear-sky irradiance using actually fitted coefficients (diagonal striped bars), interpolated coefficients (solid gray bars), RT calculations (solid black bars), and RT calculations combined with the conversion factors (checkered bars). Of the data obtained with the fitting method (Long and Ackerman 2000), 83% are within 3% of the clear-sky measurements, whereas, when the fitting coefficients are interpolated, only 58% of the data are within the same threshold (about the same percentage for the uncorrected RT method). The value increases to 70% when considering the method proposed here (RTM corrected). Similar results were obtained for the MFRSR data (plot not shown here), with 84% of the fitted clear-sky irradiances within 3% of the observations and 70% of the RT-corrected irradiances within the same limit.

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Global solar irradiance measurements (dots) and corresponding calculations using the Long and Ackerman (2000) method (line), the RT approach for fixed AOT and PWV values (triangles), and the RT approach combined with the conversion functions (squares) for 10 August 2010: (a) MFRSR and (b) Eppley.

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

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Frequency histogram of relative differences between Eppley 1-min measured and estimated clear-sky irradiance using actually fitted coefficients (diagonal striped bars), interpolated coefficients (solid gray bars), RT calculations (solid black bars), and RT calculations combined with the conversion factors (checkered bars).

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

Although the fitting method presents the best performance (NRMSE of 2%), the proposed method constitutes a valid alternative (NRMSE of 3%), especially useful while clear-sky measurements are not available (preventing the use of the fitting method), as frequently happens during relatively long periods (more than 4 successive days) in autumn, winter, and even springtime, when day-to-day changes in columnar aerosols and water vapor are also frequent. Since the main scope of this study is the analysis of the cloud radiative forcing at the surface, the clear-sky irradiance is estimated using the RT-corrected method, which introduces an uncertainty of 3% (NRMSE), comparable to the uncertainty of the measurements (~5%).

c. Cloud radiative forcing

The shortwave cloud radiative forcing at the surface is defined as the instantaneous change in net [downwelling (↓) minus upwelling (↑)] shortwave irradiance (F) at the surface, due to changes in cloud conditions (type and/or cover). Negative values of CRF imply that less solar energy reaches the surface during cloudy conditions relative to the clear-sky ones, causing a cooling effect on the surface energy budget, and vice versa for positive cloud radiative forcing (Kassianov et al. 2011). The CRF_SW, in units of W m⁻², may be expressed by Eq. (3), where the superscripts “cld” and “cs” indicate cloudy and clear-sky, respectively. Considering that upward irradiance may be approximated by , both for cloudy and clear-sky conditions, with the albedo of the surface, the cloud radiative forcing may be rewritten as in Eq. (4):

It is necessary to know the surface albedo, as well as the downwelling surface irradiances in cloudy- and clear-sky conditions, with the latter taken as the reference to evaluate the irradiance change due to clouds. Surface albedo is probably slightly different for cloudy and clear-sky situations, but since this variation is not known precisely, the approximation adopted here is to consider the same surface albedo value, assuming that, to a first order, the variation of the surface albedo with cloud fraction has a minimal impact (Intrieri and Shupe 2004). This approach was also recently adopted by Mateos et al. (2013). A surface albedo of 0.22 is considered for Eppley simulations and 0.27 for MFRSR broadband channel simulations, as mentioned in the previous subsection. The cloudy downwelling surface irradiances are obtained from the MFRSR broadband measurements and from the Eppley measurements; the clear-sky irradiances are calculated with LibRadtran, as described in the above subsection.

It is sometimes useful to normalize the cloud radiative forcing, using the net irradiance for clear-sky conditions at surface (Sengupta et al. 2004) and thus eliminating the solar zenith angle and surface albedo dependence. As a result, the term (1 − α) in Eq. (4), is eliminated, and the radiative forcing is only a function of the downwelling irradiances at the surface, as expressed in Eq. (5). The negative sign in Eq. (5) is introduced to reflect the cooling effect of the SW cloud radiative forcing:

The normalized shortwave cloud radiative forcing (NCRF_SW) expresses the fraction of SW radiation that is attenuated by clouds through absorption or reflection and does not reach the surface. If, in the limit, the NCRF_SW assumes a value of zero, it means that clouds do not exert any effect on SW radiation (clear-sky conditions) and that the irradiance reaching the surface is the same with or without the presence of clouds ; the opposite situation (NCRF_SW = 1) indicates that clouds would attenuate all the SW radiation , which then would not reach the surface.

The (normalized) cloud radiative forcing calculated using the MFRSR broadband data and the Eppley pyranometer data are referred to hereinafter as MFRSR (N)CRF_SW and Eppley (N)CRF_SW, respectively.

3. Results and discussion

The CRF_SW as well as the NCRF_SW are calculated using data from the MFRSR broadband channel and from the Eppley pyranometer measurements [Eq. (4)], both corresponding to 10-min averages. The results correspond to the whole period of measurements indicated in Table 1 for all-sky conditions. Discarding the clear-sky periods, the data corresponds to a total of 28 061 cloud occurrences (10-min bins) in 963 days (240 in winter, 238 in spring, 251 in summer, and 234 in autumn), considering all cloud situations in terms of type and fraction. The daily-mean values of the CRF_SW and NCRF_SW are calculated by integrating the 10-min averaged values of CRF_SW and NCRF_SW over the day (24 h) and dividing by this period, obtaining the all-sky CRF_SW. The cloudy periods, in hours per day, are also estimated from the 10-min averaged data bins; those containing clouds (CRF_SW < 0), in each day, are summed up to yield the cloudy period (in min), then converted to hours per day and averaged for all years of the study (2003–10; Table 1), for each season, and for each month. The use of this threshold to detect clouds constitutes a limitation with respect to enhancement events associated with broken cloud conditions (Piedehierro et al. 2014). These episodes exhibit CRF_SW > 0, and thus, according to the classification adopted here, they are not considered cloudy, which may introduce additional uncertainty in the lower limits of the CRF statistics. Nevertheless, as the calculations are done using the 10-min averages, the number of these enhancement events is expected to be small and the effect in the daily averages even smaller.

Overall CRF_SW results are represented in the probability distribution function (pdf) and cumulative distribution function (cdf) of Fig. 5 and correspond to the 963 days. MFRSR results are represented by the solid line and Eppley pyranometer values by the dashed line. The distribution is clearly skewed to the left, with a long tail, reflecting in a few values with low daily-mean CRF_SW, with the minimum MFRSR (Eppley) CRF_SW of −139.5 W m⁻² (−198.4 W m⁻²) and the median −18.9 W m⁻² (−13.0 W m⁻²). Yet, the interquartile range that contains 50% of the values is only 42.2 W m⁻² (47.6 W m⁻²), and the 10th and 90th percentiles are −73.1 and −2.0 W m⁻² (−84.3 and −0.8 W m⁻²), respectively, indicating a relatively low spread of the majority of the values in the sample. About 25% of the clouds exert a CRF_SW lower than −50 W m⁻², and only 3% (7%) present CRF_SW values lower than −100 W m⁻². Comparing the overall results obtained from MFRSR and Eppley data, only a minor change is observed in the central values; nevertheless, a great difference is obtained in the lower extreme, with a decrease from −139.5 W m⁻² (MFRSR) to −198.4 W m⁻² (Eppley).

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Pdf and cdf of MFRSR (solid line) and Eppley (dashed line) daily averaged CRF at Évora site during the 7-yr period.

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

The monthly-mean cloud periods, as well as the all-sky CRF_SW variability on a daily basis are shown in Fig. 6. Note that only days with at least one cloud occurrence (cloudy days) are represented (963 days in the 7-yr period). A considerable spread of the daily-mean CRF_SW and cloudy periods can be noted in March, April, and May. This indicates a large variability in springtime because of the large dispersion that occurs for all months of this season, with interquartile ranges of the MFRSR (Eppley) CRF_SW between 58.3 and 73.5 W m⁻² (55.6 and 82.2 W m⁻²) and relative errors of the daily-mean cloudy periods ranging between 43% and 47%, hinting at a greater variability in the sky conditions with respect to the other months. Autumn and winter months present very similar distributions, and the cloudy periods present little variation. The summer season (June, July, and August) presents the lowest interquartile distance (MFRSR CRF_SW: 24.4 W m⁻²; Eppley CRF_SW: 17.0 W m⁻²), and the minima are −129.8 W m⁻² (MFRSR CRF_SW) and −177.1 W m⁻² (Eppley CRF_SW), which occur in the month of June. The cloudy periods represented in Fig. 6a show higher variability (higher interquartile ranges) for the spring and autumn months than for winter and summer, when it scarcely varies, suggesting that these are transition months with highly variable conditions in terms of cloud occurrences. In fact, during the spring (autumn) season, the synoptic conditions are determined by the northerly (southerly) migration of the polar front, which determines the passage of Atlantic frontal systems over the area. On the other hand, in these seasons the region is sometimes affected also by northward drifts of the Azores anticyclone, which brings warm dry air into the region and is associated with clear-sky periods. The variability in the cloud occurrences originates from the occurrence of these synoptic patterns, as is typical of the transition seasons.

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Box plots showing the monthly variation of the (a) mean cloudy periods and (b) daily-mean MFRSR CRF_SW (black) and Eppley CRF_SW (dotted gray filled).

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

The all-sky daily CRF_SW is seasonally and annually averaged (considering also clear-sky days), and the results obtained using the Eppley measurements are compared with those reported by Dong et al. (2006) for another midlatitude site. Seasonal and annual CRF averages are also obtained under the conditions of total cloud, as described by Dong et al. (2006). The comparisons are summarized in Table 3 and show, in general, similar CRF_SW annual cycles. The all-sky CRF_SW presents lower absolute values for this study, and the lowest CRF values (more negative) are obtained for spring in both studies. Dong et al. (2006) estimate a springtime average CRF_SW for all-sky conditions of −61.3 W m⁻², whereas in this study, the estimated mean value for the CRF_SW is −45.5 W m⁻². The annual average obtained here of −29.8 W m⁻² is also lower (absolute value) than that estimated by Dong et al. (2006), who present a value of −41.5 W m⁻². As for the CRF for total cloud conditions (also shown in Table 3), it presents very similar results for both studies, with slightly more negative CRF_SW obtained here for winter and summer and slightly less negative values for spring and autumn, with respect to Dong et al. (2006). Overall total CRF_SW is very similar in both sites. The dissimilarities of all-sky CRF and similarities of total CRF also hint at the occurrence of more clear-sky days in Évora. Berg et al. (2011) reported a value of −45.5 W m⁻² for summertime shallow cumuli, which is thus not directly comparable with the CRF_SW obtained here. Mateos et al. (2013) also estimated the CRF_SW for another south Iberian site, obtaining average values of −78 W m⁻² and −50.0 W m⁻², for solar zenith angles of 30° and 60°, respectively.

Table 3.

Seasonal and annual averages of CRF (all-sky and total cloud; W m⁻²), where S denotes this study and D denotes Dong et al. (2006).

Figure 7 presents the pdf and cdf of the daily-mean MFRSR NCRF_SW and Eppley NCRF_SW. The median present moderately low values of 7.8% for the MFRSR NCRF_SW and 4.2% for the Eppley NCRF_SW. The interquartile range of the MFRSR (Eppley) NCRF_SW is 15.9% (13%), and the 10th and 90th percentiles are 0.8% and 26.5% (0.0% and 23.1%), respectively, indicating once again a relatively low variability of the majority of the values in the sample. The distance between the 75th percentile and the maximum is quite large (MFRSR NCRF_SW: 22.8%; Eppley NCRF_SW: 26.8%), significantly higher than the interquartile range (MFRSR NCRF_SW: 15.9%; Eppley NCRF_SW: 13.0%); yet, according to the pdfs, the high extreme values presented in the sample are only a small number. In fact, barely 3% of the data presents a daily-mean MFRSR NCRF_SW above 30% and even less for the Eppley NCRF_SW. Eppley broad band decreases the variability of the central values by about 3% relative to MFRSR data; nevertheless, in terms of total variability, there is practically no change, with the maximum in both cases around 40%, as in the findings of Liu et al. (2011).

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As in Fig. 5, but for the daily-mean NCRF_SW.

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

The monthly variability of the daily-mean MFRSR NCRF_SW and Eppley NCRF_SW is presented in Fig. 8. The season with the largest interquartile range of MFRSR (Eppley) NCRF_SW is again spring with 19.7% (16.5%), contrasting with summer with only 7.6% (5.5%), which is probably related to the longest cloudy periods in spring (6.9 h day⁻¹) and the shortest in summer (3.6 h day⁻¹) (Fig. 6a). Nevertheless, in summer, the low variability in the central values oppose to the rather large upper extremes, which are as high as about 39.5% (originated in June). Autumn and winter present very similar distributions, skewed to the right, with moderately high upper whiskers (maxima of roughly 36% and 35%, respectively).

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As in Fig. 6a, but for the monthly variation of the daily-mean MFRSR NCRF_SW (black) and Eppley NCRF_SW (dotted gray filled).

Citation: Journal of Climate 27, 20; 10.1175/JCLI-D-13-00696.1

The daily-mean surface CRF_SW results obtained from the MFRSR and Eppley measurements are different, basically because of the different spectral regions covered by each instrument (see section 2a). These quantities are compared in order to determine a quantitative relationship relating to both CRFs, which may be applied to other locations where only one of the instruments is present or to modeled data. The minima Eppley CRF_SW values obtained each month (lower ends of the whiskers in the box plots of Fig. 6) exhibit a clear linear dependence on the minima MFRSR CRF_SW, with (R² = 0.97; NBIAS = 0.7%; NRMSE = 5%). Conversely, when all daily-mean surface CRF_SW are considered (963 days), this dependence is no longer linear, being well described by a second degree polynomial equation with a determination coefficient (R²) of 0.87:

When comparing the measured Eppley CRF with that calculated with Eq. (6), the NBIAS is–0.3%, indicating only a very slight tendency to underestimate the Eppley CRF_SW, and the NRMSE is 6%, showing a low dispersion of the data. The reason for the nonlinearity in the previous relationship is related to the different response of the two spectral bands to different atmospheric conditions, increasing the dissimilarity between both as the cloud effect augments (lower CRF corresponding to higher cloud optical depth). As for the minima monthly CRF_SW relationship, these are likely representative of extreme cloudy conditions (highest cloud optical depth each month), when most of the solar radiation at the surface is diffuse and isotropic; therefore, the cloud attenuation behavior in both spectral regions (MFRSR and Eppley) is linearly related. The relationship proposed in Eq. (6) introduces only a low uncertainty (6%) and may constitute a useful tool to relate the CRF_SW in these spectral bands under any cloud conditions.

4. Summary

The main purpose of this work was the calculation of the SW cloud radiative forcing at the surface, using surface irradiance measurements taken at a midlatitude site (Évora), with a multifilter rotating shadowband radiometer (MFRSR CRF_SW) and an Eppley black and white pyranometer (Eppley CRF_SW), for all-sky situations in terms of cloud type and fraction. A new methodology to estimate the clear-sky irradiance is also proposed, based on the correction of the values obtained from radiative transfer calculations, using conversion functions to account for day-to-day atmospheric changes (aerosols and water vapor). It is shown that the clear-sky irradiances obtained in this way present a small uncertainty (~3%), constituting a fast tool to estimate this variable.

Overall results of CRF_SW show a large variability of the springtime values with respect to the other seasons and the lowest variability in summer for both absolute and normalized values; it is also in spring that the cloud occurrence presents the highest values and variability. Minimum values of −139.5 and −198.4 W m⁻² for MFRSR CRF_SW and Eppley CRF_SW, respectively, were obtained considering the complete dataset (Table 1). Yet for this dataset, it was found that the interquartile range (containing 50% of the values) is only 42.2 and 47.6 W m⁻² for MFRSR CRF_SW and Eppley CRF_SW, respectively.

The NCRF_SW presents an amplitude range of approximately 40%, considering the complete dataset (Table 1). This implies that, in this study, clouds may attenuate (by absorption or scattering) up to about 40% of the solar radiation on a daily basis, or in other words, 40% less solar radiation reaches the surface because of the cloud effects. Considering the NCRF_SW results, the spring is the season with the largest variability, contrasted with summer, which presents the lowest variability, and probably this is related to the cloudy periods occurred in spring (6.9 h day⁻¹) and in summer (3.6 h day⁻¹). The same relation, between cloudy periods and CRF_SW, was verified showing that the variability of the cloudy periods is proportional to the variability of the cloud radiative forcing with its maximum value in springtime.

The use of two different instruments (MFRSR and Eppley) that cover different fractions of the solar radiation spectrum reveals some differences, with respect to the distributions of the daily-mean CRF_SW and NCRF_SW. Curiously, there is only a minor change in the central values of the CRF_SW distributions, both from MFRSR and Eppley instruments; nevertheless, there is a strong decrease of the minimum value for the case where most of the solar radiation is included (Eppley). On the other hand, the total variability of the NCRF_SW remains practically unchanged, both for MFRSR and Eppley instruments, although the variability of central values decreases by about 3% in the Eppley case. A mathematical equation is derived, expressing the relationship between the CRF_SW obtained in the two spectral bands, which may constitute a useful tool under any cloud conditions for different locations where only one of the instruments is present, or may even be applicable to modeled data.