SRCF (also called “effective cloud albedo”) was first proposed by Betts and Viterbo to quantify the impact of the cloud field on the surface radiative budget over a southwest basin of the Amazon. It is a non-dimensional measure of surface SW cloud forcing (SWcld = SWdnall − SWdnclear, an upward flux), defined as
 Here, a positive value of the SW fluxes indicates a downward flux. Based on equation (5), we can calculate SRCF if all-sky and clear-sky surface downwelling SW fluxes are available.
 Furthermore, equation (5)indicates that SRCF represents the fraction of clear-sky incoming downward SW flux which is reflected and absorbed by clouds. This non-dimensional quantity offers an effective measure of surface SW cloud forcing and minimizes the influence from solar zenith angle and other non-cloud factors. More discussions and applications of SRCF can be found in previous studies [Betts et al., 2006, Betts, 2009; Betts et al., 2009; Betts and Chiu, 2010; Liu et al., 2011].
2.3.2. Cloud Albedo
 Liu et al.  derived an analytical expression that quantifies the relationship between SRCF, cloud fraction, and cloud albedo,
Where f and αr denote cloud fraction, and cloud albedo, respectively. Liu et al. demonstrated that the estimated cloud albedo by using the surface-based radiation and cloud fraction shows reasonable agreement (correlation coefficient 0.69) with that from satellite measurements. In this study, cloud albedo is estimated using the same procedure, and the same surface-based observations as inLiu et al. . Note that αr implicitly includes cloud absorptance when cloud absorption cannot be ignored, esp., for strongly absorbing clouds.
2.3.3. Procedures of Evaluation
 Detailed procedures of the evaluation are described below. First, the 15-min all-sky/clear-sky surface downwelling SW flux and cloud fraction observations are averaged into hourly data. Here, only those with 4 valid 15-min data points within one hour are used. The valid 15-min data points refer to those with 15-min all-sky/clear-sky surface downwelling SW flux greater than zero and 15-min cloud fraction between 0 and 1. We use the hourly data (for example,xi(d, m, y), i, d, m, yrepresent hour, day, month, and year respectively) to calculate the mean variations of hourly all-sky/clear-sky surface downwelling SW flux and cloud fraction. Considering that the valid hourly observational data points are not evenly distributed temporally, we first calculate each-year seasonal mean values of each-hour variables ( , srepresents season, the line on the top of the function represents mean, and the line with “s” represents seasonal mean), and then average into the overall mean values of each-hour variables. Those valid hourly all-sky/clear-sky surface downwelling SW flux and cloud fraction between 6 am and 6 pm (local standard time: LST) are further averaged into daytime-mean data. Daytime-mean (6 am–6 pm LST) SRCF is calculated using daytime-mean all-sky and clear-sky surface downwelling SW flux. Those daytime-mean SRCF (>−0.05) and cloud fraction are further averaged into monthly data.
 The mean value of overall hourly cloud albedo is calculated using the mean values of overall hourly SRCF and cloud fraction. The daytime-mean cloud albedo is calculated using daytime-mean SRCF and cloud fraction for those with daytime-mean cloud fraction greater than 0.05. We use this filter because cloud albedo is not well described byequation (6) when cloud fraction is small [Liu et al., 2011]. The monthly cloud albedo is calculated by using monthly SRCF and cloud fraction. The mean variations of monthly/yearly cloud properties are the averages of the monthly cloud properties.
 Next, the cloud properties from hourly ERA-Interim and 6-hourly R1 and R2 are used to calculate the mean values of daytime hourly and 6-hourly cloud properties. The calculation procedures are the same as for the observations. Here, only those hourly/6-hourly reanalysis data concurrent to those valid hourly observations are used. The concurrent 6-hourly reanalysis data refer to those: within those concurrent 6 h the hourly observations have valid data. Further, those concurrent hourly/6-hourly reanalyses are averaged into daytime-mean, and then those daytime-mean reanalysis data concurrent to those valid daytime-mean observations are averaged into monthly data. The yearly data are the averages of monthly data. The diurnal/annual/interannual cloud properties from the reanalyses are then evaluated based on the observations.
 After that, for diagnosing the path of model-error propagation, the model biases (model minus observation) in the cloud properties and their relationships are analyzed. Further examined are the relationship between the cloud properties and 2-m temperature/humidity. To do so, we first aggregate the observed 30-min averaged 2-m air temperature, relative humidity and surface pressure into hourly data, and then use hourly temperature, relative humidity and surface pressure to calculate hourly specific humidity byequations (2) and (3). After that, using the same method as for the cloud properties, we use concurrent valid hourly data to generate daytime-mean, monthly, yearly temperature/humidity. And, the three reanalyses' hourly/6-hourly cloud properties and the meteorological variables with concurrency to the valid hourly observations are averaged into daytime-mean and then monthly data. The relationship between the daytime-mean/monthly cloud properties and temperature/humidity from all the data sets are first examined. Then, we compare the multiscale mean variations of 2-m temperature/humidity and corresponding model biases. After that, the relationship between relative humidity (or cloud fraction) biases and the temperature/humidity is examined.
 It is noted that R1 and R2 6-hourly 2-m temperature and relative/specific humidity have three daytime data points at 6 A.M., 12 P.M. and 6 P.M. (LST). Thus, the calculation of the daytime mean is not as straight-forward as the hourly/6-hourly averaged data or the hourly interval data (considering that variations within one hour are small). We examine three common ways to obtain the daytime mean from the three data points using the hourly ERA-Interim data: [(6 am + 12 pm)/2 + (12 pm + 6 pm)/2]/2, [(6 am + 12 pm + 6 pm)/3], and [6 am + 4 × (12 pm) + 6 pm]/6. The last formula is from the Simpson's rule for parabolas. The daytime mean from the three methods are compared to that from the mean of the 13 daytime hourly points. The results are shown inFigure 2, indicating that the first method has the smallest difference (standard deviation) from the 13-point averaged value. Based on this analysis, we chose the first method to calculate R1 and R2 daytime-mean temperature/humidity.
Figure 2. Comparison of the differences between the daytime-mean values from 3 daytime 6-hourly data points using the three methods (red, green, and blue) and those from 13 daytime hourly data points (from 6 am to 6 pm), based on the hourly ERA-Interim data. Red: [(6 am + 12 pm)/2 + (12 pm + 6 pm)/2]/2, green: [6 am + 4 × (12 pm) + 6 pm]/6, and blue: [(6 am + 12 pm + 6 pm)/3]. T, RH, and SH represent 2-m temperature, relative humidity, and specific humidity.
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 Finally, for evaluating the overall performance of the reanalyses in modeling the cloud properties and the meteorological variables, we employ the widely used technique of the Taylor diagram [Taylor, 2001], and also develop a new metric “Relative Euclidean Distance” as a supplement to the Taylor diagram. The Taylor diagram reveals concise and easy-to-visualize second-order statistical differences between two (or more) different time series. It is especially useful for evaluating a model's performance in phase and amplitude of variations (as measured by the correlation coefficientr and standard deviation σ, respectively), and a model's “centered root-mean-square error”E (“RMS error” hereafter). This technique has been widely used in climate researches and IPCC assessment [e.g., IPCC, 2001; Anderson et al., 2004; Martin et al., 2006; Miller et al., 2006; Bosilovich et al., 2008; Gleckler et al., 2008; Pincus et al., 2008]. Briefly, the expressions for calculating r, σ, and E are shown below [Taylor, 2001],
where “Mn” or “On” denote a modeled or observed variable, defined at N discrete temporal (or spatial) points; and the subscript “M” or “O” denote “model” or “observation.” Note that, the correlation coefficient r, standard deviation σ and RMS error E are calculated without removing the periodic signals of the time series.
 As a supplement to the Taylor diagram, we develop a new metric “Relative Euclidean Distance” (D), based on Euclidean-Distance technique [e.g.,Elmore and Richman, 2001] and first- and second -order statistics,
 As can be seen from the expression (13), D measures the overall model performance. A perfect agreement corresponds to D = 0, and the overall model performance degrades as D increases.