Effect of water vapour on the determination of Aerosol Direct Radiative Effect based on the AERONET fluxes

The Aerosol Direct Radiative Effect (ADRE) is defined as the change in the solar radiation flux, F, due to aerosol scattering and absorption. The difficulty in determining ADRE stems mainly from the need to estimate F without aerosols, F, with either radiative transfer modelling and knowledge of the atmospheric state, or regression analysis of radiation data down to zero aerosol optical depth (AOD), if only F and AOD are observed. This paper examines the regression analysis method by using modeled surface data products provided by the AErosol RObotic NETwork (AERONET). We extrapolated F by two functions: a straight linear line and an exponential nonlinear decay. The exponential decay regression is expected to give a better estimation of ADRE with a few percents larger extrapolated F than the linear regression. We found that, contrary to the expectation, in most cases the linear 1 2


Introduction
Significant uncertainties exist in the current estimates of aerosol effects on climate (IPCC, 2013). This holds also for the aerosol direct radiative effect (ADRE) and aerosol direct radiative forcing (ADRF).
The ADRE defines the attenuation of the (cloud free sky) surface solar radiation flux (F) due to aerosol scattering and absorption. Herein, we consider the solar radiation flux at the surface, although ADRE applies also for the longwave flux and above the atmosphere. In the definitions of ADRE and ADRF, effects relate to both anthropogenic and natural aerosol particles, while forcing refers to the impact of anthropogenic aerosol particles. Although, e.g., Myhre (2009) recently showed an increment of the consistency between observation based and global aerosol model estimates, with a reduction in the uncertainty of this effect, other studies (e.g., Loeb and Su, 2010) highlight that considerable uncertainties are still associated with ADRE, mainly due to the uncertainties in single scattering albedo (SSA). Satheesh and Ramanathan (2000) employed a method in which ADRE is estimated using the aerosol direct effect efficiency (ADREE), which is the ADRE normalized by the aerosol optical depth (AOD), and it is estimated by fitting a straight line into surface solar flux and AOD observations. A linear dependence between aerosol attenuation and AOD has been commonly assumed when estimating ADRE (e.g., Kaufman et al., 2002;Valero, 2002, 2003;Dumka et al., 2006;Roger et al., 2006;di Sarra et al., 2008;Garcia et al., 2009;Satheesh et al., 2010). Typical attenuation of radiation intensity, however, implies nonlinear decay, as considered by e.g. Conant et al. (2003), Markowicz et al. (2008) and Kudo et al. (2010). Thus, a linear fit to F and AOD data may result in an incorrect extrapolation of F 0 .
The aim of this paper is to examine the uncertainties involved in estimating ADRE, both using the linear fitting method and a nonlinear approach if F and AOD data are available from surface or satellite measurements. For this, we use Aerosol Robotic Network (AERONET) products (http://aeronet.gsfc.nasa.gov/) from all available AERONET stations, which cover different aerosol types and surface reflectance properties and provide modelled surface solar radiation fluxes also. We conducted our analysis using these modeled fluxes since they represent realistically enough the aerosolinduced relative changes in F and furthermore give an estimate for F 0 , which is self-consistent within the selected F (AOD) data set. As AERONET provides an estimation of F 0 , we can compare the estimations immediately with the baseline (AERONET). Special attention is paid to the possible effect of water vapour on estimating ADRE.

Methods and data
AERONET is a ground-based remote-sensing global network of Cimel sun photometers (Holben et al., 1998) including the AERONET inversion code with radiative transfer code implementation. The inversion strategy, described in Dubovik and King (2000), provides a group of parameters, e.g. AOD, Ångström exponent (AE) and water vapour column (WVC) from the sun measurements and e.g. SSA, . More details about the AERONET description from e.g. García et al. (2012 ) . The uncertainty of AOD is 0.01-0.02 depending on the wavelength (Eck et al., 1999), the uncertainty in SSA is approximately 0.03 (Dubovik et al., 2000), and the uncertainty in WVC of 12 % (Holben et al., 1998).AERONET is a ground-based remote-sensing global network of Cimel sun photometers (Holben et al., 1998), retrieving e.g. spectral AOD, SSA and water vapor column (WVC) (Dubovik et al., 2000). In addition to the retrieved aerosol properties, AERONET inversion product provides also modeled radiative fluxes (both at top of atmosphere and at surface) that are based on the AERONET measurements. We used broad-band modeled surface shortwaveSW fluxes from this data set. In this study, level 1.5 sky AERONET data are divided into groups by station, season observations and the data contained AOD 550 nm values above 0.3 and below 0.1. We chose to use level 1.5 data because using level 2.0 would leave out all quality-assured data with AOD 440 nm < 0.4 (including e.g. quality assured SSA and F calculations). The drawback of this choice is that at these low values of AOD, there are significant uncertainties in the optical properties retrieved. This is especially true for SSA, which is an important parameter. Thus, we applied all other level 2 criteria except for AOD (and SZA) limit, in order to enhance the accuracy of the data set selected. Moreover, we have imposed an additional data flagging criterion, removing those SSA points at the AOD 440 nm < 0.4, which are outside the average SSA ± standard deviation, defined for the AOD 440 nm > 0.4. ADRE at the surface is the difference between the solar flux with and without aerosols: ADRE = ΔF = F aer -F 0 ( F aer is flux with aerosols).The major challenge obviously is the determination of F 0 .
The methodology for its estimation employed in this study is illustrated in Fig. 1 normalized for the average earth-sun distance and cosine correction of F aer the SZA was done within SZA ranges to its midpoints). F 0 represents the case AOD = 0, but with measurements only at AOD above ca. 0.15, we have to extrapolate down to 0. In Fig. 1 we show two such extrapolations: a linear fit (dashed line) and an nonlinear decay fit (solid line) with the data.
We chose this data subset since it represent a case in which the F aer and AOD data exhibit the natural nonlinear behavior of radiation intensity decay. Thus the resulting intercepts of the two curves at AOD = 0 are quite different, 317 Wm -2 with linear extrapolation and 349 Wm -2 with nonlinear regression, with a difference of 32 Wm -2 when estimating ADRE. Also, for each F aer we show the corresponding AERONET F 0 (circles), based on the retrieved WVC and surface albedo, and calculated with a radiative transfer model (e.g., Garcia et al., 2008;Derimian et al., 2008). We use the ADRE obtained by averaging these F 0 (circles) values (bar at F = 325 Wm -2 on the y-axis) as the benchmark against which the extrapolation methods are evaluated.
Mathematically, our analysis can be summed up as a comparison between the extrapolated (1) and the AERONET ADRE in where F aer i and F 0 i is F aer and F 0 , respectively, with i varying from one to the number of dataset, n.
Notably, the extrapolated F 0 (F 0 extrapol ) derived with fits represents a single value for a dataset, but in the AERONET, F 0 is determined side-by-side with each F aer . F 0 extrapol is calculated using fits as follows in where F i nonlin and F i lin is estimated F aer derived for each AOD with the nonlinear and linear method, respectively. Constants of fits are x 1 , x 2 , x 3 , x' 1 and x' 2 , and F i 0,nonlin and F i 0,lin , thus F 0 extrapol of the nonlinear and linear fits, are provided with the constants.
Our decision to use the modeled F from AERONET, instead of pyranometer measurements, was based on two different aspects. First, this allowed us to include a multiple number of sites, with very different and varying aerosol conditions. Second, AERONET data provided interesting ancillary measurements to support and better understand our analysis, WVC being the most crucial one. In addition, the AERONET Fs agree with pyranometer measurements with a correlation better than 99% and the relative difference varies from 0.98 to 1.02 (Garcia et al., 2008). Moreover, we tested the analysis in two sites, Alta-Floresta and Goddard Space Flight Center (GSFC), by using pyranometer measured fluxes F and found no significant difference of the results in these two sites, if compared to the corresponding analysis using the AERONET-modeled fluxes instead.

Results
As further examples of determining ADRE using regression analysis, we show F aer and AOD data from four sites in Fig. 2 Increase in the AOD as a function of WVC is presumably partly due to hygroscopic growth (e.g., Kitamori et al., 2009), although probably a major part of the correlation can be attributed to a large variance in atmospheric conditions of aerosol properties and air humidity during seasons. The performance of the two different regression methods and, in particular, the WVC and AOD correlation effect on the performance, is illustrated as scatter plots in Fig. 3. In Fig. 3a all data are presented in ADRE (nonlinear decay method) and ADRE (AERONET ΔF average , Eq. 2) form. The colour of the single points indicates the correlation of the WVC and AOD. In Fig. 3b the same is shown for the linear regression case. Evidently a majority of the cases are such that WVC and AOD have a strong positive correlation (red colored points). In addition, it seems that for most of these cases, the linear regression method (Fig. 3b) results in a better ADRE estimation than the nonlinear decay regression method (Fig. 3a). This means that the inaccuracy inherent in the linear regression cancels out errors in the west Sahara's region and Central-America, probably caused by a strong desert dust domination and low WVC in the Saharan outflow region (Marsham et al., 2008). During those particular cases, the linear method can significantly underestimate ADRE, as indicated by the points of largest negative WVC vs. AOD correlation in Fig. 3b, while the nonlinear decay provides then a better estimate. The blue points, representing a negative correlation (at least for this season) are all in the Saharan outflow region (Marsham et al., 2008), with a strong desert dust domination and low WVC for larger AOD cases.
Finally, the ADRE estimations of all data are grouped together in numerical form in Table 1 Previous studies have shown that the AERONET WVC agrees well with radiosonde sounding data (e.g., Prasad and Singh, 2009;Bokoye et al., 2007). We also compared AERONET WVC measurements against radiosonde data from five sites (Alta-Floresta, Cuiaba-Miranda, Niamey, Thessaloniki and Wallops) and observed similarly high correlations between these two data sources.
However, we wanted to assess in particular whether there exists any systematic dependence between WVC from these two data sources as a function of AOD, which could affect our ADRE analysis based on the modeled F. We found that while the ratio between the AERONET and radiosonde WVC is essentially constant for AODs (at 500nm) larger than about 0.1, in many sites WVC can deviate for the cases of smallest AOD (below 0.1). We estimated how our ADRE values (based on the F and AOD relation) would change if we normalized the AERONET-modeled fluxes to incorporate the WVC from the radiosonde measurements instead of AERONET-measured WVC. We found that the increased WVC uncertainty at the lowest AOD values introduces an insignificant change in our ADRE estimates.

Conclusions
Determining the ADRE at the Earth's surface from radiative flux, F, measurements is not straightforward because it involves the estimation of the flux without aerosols F 0 . This requires either radiative transfer modelling or an extrapolation of F down to AOD = 0.
We have evaluated two such extrapolation methods: i) a linear fit and ii) an nonlinear decay fit to the F and AOD data. As a reference we used the AERONET ADRE data in which F 0 (and F) is in which there is no correlation between WVC and AOD, the nonlinear decay fit is superior.
As the WVC effect was found to be of such importance, we also investigated the geographical correlation of WVC and AOD. The positive correlations clearly dominate, and clear negative correlations occur predominantly in desert dust dominated data series, such as the regions at the Saharan outflow. The strongest positive correlation was found in in stations in Europe and Eastern USA. Our results indicate that the regression method, either linear or nonlinear, can readily produce a significant error due to the correlation of WVC and AOD. Since for a majority of locations, AOD and water vapour column (WVC) have a positive correlation, the linear method gives somewhat better results in general than the nonlinear approach, for the reasons discussed above. However, there are specific regions of strong negative WVC and AOD correlation, most notably in the Saharan dust outflow region, where the opposite takes place and nonlinear approach results in better estimate for ADRE. Therefore, based on our results we recommend that when the surface ADRE is estimated by using pyranometer and AOD measurements, the site-specific correlation between WVC and AOD should be also estimated to deduce whether linear or nonlinear approach is more suitable. We moreover recommend to take a one step forward and additionally attempt to correct for the possible bias due to