Solar radiation reaching the Earth's surface (SSR) plays a key role in our climate and environment. In the last decades, numerous analyses have demonstrated that SSR records have not been constant over time, but have undergone climatologically significant decadal variations (e.g. ). From the 1930s to the early 1950s the few data available suggest an increase of the SSR in the first part of the 20th century, known as early brightening. This period is followed by a widespread period of reduced solar radiation from the 1950s to the end of the 1990s. This effect, extensively reported by the literature at a global scale, is known as dimming, with a general decline between 4 and 6 % decade-1 considering worldwide distributed stations. Recently, a gradual increase of the SSR has been documented, known as brightening, with trends between +1 and +11 % decade-1 from the 1980s onwards .

The causes of these phenomena are not fully understood currently, but it has been pointed out that changes in the transmissivity of the Earth's atmosphere play a significant role. These changes might be due to changes on global cloud cover and atmospheric aerosol concentrations. found that the changes are observed under all cloud-cover conditions, thus probably the most important cause is the aerosol effects . In this context, the study of the spatial and temporal variability of atmospheric aerosols at sites in background conditions can offer crucial insights to account for their key role on the observed SSR trends. For this purpose, reliable long-term series of aerosol content and properties are fundamental. However, these long-term series are only available typically since the middle of the 1970s, due to the poor data quality and changes in measurements methodology before this date. There are few studies treating aerosol long-term series in the literature. The longest available series are those of normal direct irradiance measured at various stations in Russia, Ukraine and Estonia covering together a 102-year period (1906–2007) with which the atmospheric transparency has been estimated . estimated aerosol optical depth (AOD) combining broadband direct and diffuse irradiance measurements performed at Tsukuba, Japan, from 1975 to 2008. and studied long-term series of AOD from sun photometry at Mauna Loa since 1976, and derived AOD from solar irradiance measurements at Izaña Atmospheric Observatory (IZO) since 1976. All of these studies are based on solar spectrometry, but a different approach is needed to obtain longer AOD time series.

One of the most powerful tools used in science in the last decades are the artificial neural networks (ANNs). The ANNs have been employed in diverse applications and fields such as robotics, pattern recognition, forecasting, medicine, power systems, etc. In atmospheric science the use of ANNs is quite recent, for example, ANNs have been successfully used for estimating solar radiation values or cloud properties . However, their use for AOD estimations is quite recent and limited to short periods. For example, estimated AOD values from all-sky images at Granada (Spain) between 2005 and 2006, finding uncertainties of 0.019 and 0.014 for AOD at 440 and 670 nm, respectively, by comparing with AERONET (AErosol RObotic NETwork; http://aeronet.gsfc.nasa.gov) AOD observations. Also, used ANNs to obtained AOD from global, diffuse and direct normal irradiance in Granada between 2006 and 2008. They found uncertainties of ∼13 % with respect to AERONET AOD values.

In this context, the goal of this paper is to estimate the long-term AOD time series of Saharan mineral dust events at IZO and to document its quality and long-term consistency by a comprehensive validation study. This has been done by using ANN techniques and, as input parameters, in situ meteorological observations performed at IZO between 1941 and 2001. The estimated ANN AOD time series has been completed with AOD observations from sun photometry since 2003. Given the strategic location of IZO, very close to the Saharan desert, the reconstructed ANN AOD time series provide interesting clues on the intensity and the interannual and interdecadal variability of Saharan dust outbreaks over the North Atlantic. This might have important implications for climate analysis. To address this study, this paper has been divided as follows. Section  describes the main characteristics of the site where the ANN AOD estimates have been obtained, while Sect.  presents the architecture, training process and input parameters used to select the optimal ANN configuration, as well as an error analysis of ANN AOD estimations. Section  shows the validation of ANN AOD estimates with coincident AOD measurements, whereas the comparison between long-term ANN AOD and meteorological records is addressed in Sect. . Finally, a summary and the main conclusions are given in Sect. .

Izaña Atmospheric Observatory (http://izana.aemet.es) is a high-mountain observatory located in Tenerife (Canary Islands) at 28.3∘ N, 16.5∘ W, 2373 ma.s.l., and situated approximately 300 km west from the African coast (Fig. a). IZO is managed by the Izaña Atmospheric Research Center (IARC) which forms part of the Meteorological State Agency of Spain (AEMET).

The observatory is located above a strong subtropical temperature inversion layer, which acts as a natural barrier for local pollution (Fig. b). In addition, IZO is affected by a quasi-permanent subsidence regime typical of subtropical latitudes, therefore the air surrounding the observatory is representative of the background free troposphere (especially at night-time). The combination of these two features makes IZO excellent for in situ and remote sensing atmospheric measurements and those features highlight the historical importance of the site. The first meteorological observations date from 1916 . In 1984 IZO became a World Meteorological Organization (WMO) Background Atmospheric Pollution Monitoring Network (BAPMon), and afterwards (1989), a Global Atmosphere Watch (GAW) station. IZO has been part of NDACC (Network for the Detection of Atmospheric Composition Change) since 2001, and has actively contributed to international aerosols and radiation networks such as GAW/PFR (Precision Filter Radiometer Network) since 2001, AERONET (Aerosol Robotic Network) since 2004 and BSRN (Baseline Surface Radiation Network) since 2009. In 2014, IZO was appointed by WMO as a CIMO (Commission for Instruments and Methods of Observation) Testbed for Aerosols and Water Vapour Remote Sensing Instruments .

The typical background free troposphere conditions at IZO are only significantly modified in summer, mainly in July and August, when the most intense and relatively frequent Saharan air mass outbreaks in the subtropical free troposphere reach the observatory . During these months, Saharan dust long-range transport over the Atlantic that can reach the Caribbean is driven by incursions of the so-called Saharan air layer (SAL) over the North Atlantic and references therein.

In order to discriminate these two atmospheric conditions at IZO (clean free troposphere and presence of the SAL) we have combined AOD and Ångström exponent (α) information. While AOD provides the overall solar extinction effect of aerosols, α characterizes the AOD spectral variation, which is related to the aerosol median size . High α values indicate fine particle predominance, while low α values are related to coarse particles . Figure  illustrates an example of AOD–α distributions, showing the daily AOD time series at 500 nm labelled with the corresponding daily α values since AERONET records are available at IZO (2004 onwards). Values of AOD ≤ 0.10 and α ≥ 0.75 (zone I, 63 % of days), correspond to background conditions, while values of AOD ≥ 0.20 and ≤ 0.50 (zone II, 9 % of days), are associated with Saharan dust episodes. Finally, the zone III, characterized by 0.10 < AOD < 0.20 and 0.50 < α <0.75 (28 % of days), describes the periods of transition between these two patterns. As observed, the Saharan dust events at IZO are mainly detected in summer months (July, August and September) with a median AOD value of 0.13 ± 0.02 and α of 0.47 ± 0.03, in contrast with the clean conditions observed in other months (median AOD and α of 0.05 ± 0.01 and 1.17 ± 0.02, respectively, for zone I and median AOD and α of 0.07 ± 0.02 and 0.67 ± 0.03, respectively, for zone III). Therefore, in this work, we have limited the ANN AOD estimation to summer months in order to assess the long-term variability of Saharan outbreaks over the subtropical Eastern North Atlantic. Note that, hereafter, we use AOD medians instead of means because the AOD values dramatically change by orders of magnitude from background conditions to dusty conditions. The errors are given as ±1 SEM (standard error of the median).

ANN is a statistical data modelling tool, inspired by the human brain, capable of simulating highly nonlinear and complex relationships between inputs and outputs by a learning process, the so-called training process. This tool mainly consists of three layers of neurons: the input layer groups the input data in the input vector p and connects them with the hidden layer. In this layer the input vector is transformed into a net input vector, a′, by using adaptive weights, Wh, biases, bh, and a transfer function, TFh, such as a′ = TFh(n), where n= (Whp+bh). Then, the hidden layer is connected with the output layer, in which the outputs obtained in the previous step, a′, are transformed into the net input for the output layer, n′ = (Wout a′ + bout). Finally, the output transfer function, TFout, is applied to n′ to obtain the final output of the ANN, a and references therein. The weights and biases used both in the hidden (Wh and bh) and in the output layer (Wout and bout) were previously computed in the training process.

In this work, the ANNs have been implemented by using the Matlab Neural Network Toolbox with the architecture shown in Fig. 3: the input parameters of the input layer are different meteorological observations taken at IZO (Sect.  details the selection of these inputs), and the hidden layer is made up of 30 neurons with a transfer function defined by the hyperbolic tangent function: φ=tanh⁡(n)=e2n-1e2n+1, where n is the corresponding net input. The hyperbolic tangent is one of the most used transfer function in ANN, since it successfully combines a fast learning rate with reliable results . Finally, the output layer has one neuron with the linear transfer function, which is often used in forecasting and approximation tasks .

The ANN AOD estimates have been validated with coincident AERONET CIMEL photometers of Level 2.0 AOD (cloud screened and quality ensured) from 2004 to 2009, and with a long-term AOD at 769.9 nm data series retrieved by from a solar spectrometer Mark-I for the period 1975–2012.

CIMEL photometers retrieve AOD measurements at different wavelengths between 340–1640 nm from direct Sun observations under cloud-free conditions, with an expected uncertainty of 0.01 at 500 nm for field instruments . The validation procedure of Mark-I AOD time series was performed by , showing a root-mean-square error of 0.022 (R= 0.94) and 0.034 (R= 0.92) in comparison with the PFR reference and AERONET master instruments, respectively. In order to compare the Mark-I AOD values at 769.9 nm and the ANN AOD estimates at 500 nm, we have extrapolated the ANN AOD values from 500 to 769.9 nm by using the Ångström law and the α data retrieved from PFR observations. For Mark-I we have used the AOD records since 1984 when the observations start to be seamlessly performed.

The straightforward comparisons between AOD observations and estimates show a good agreement for the daily values with ∼ 94 % (R= 0.97) of the variance in agreement between AERONET AOD and ANN AOD, and 85 % (R= 0.93) between Mark-I AOD and ANN AOD values (Fig. a and b). When considering monthly values the agreement increases, achieving a correlation of 96 and 98 % with Mark-I/ANN and AERONET/ANN, respectively. Although the comparison with the Mark-I AOD records shows a poorer agreement, both inter-comparisons behave similarly. We observe that the ANN AOD estimates have been shown to be dependent on the AOD range (see Table ), confirming the results obtained in the theoretical error estimation (Table ). For low AOD, the ANN AOD values tend to overestimate compared with the observed AOD values (median bias of ∼ 0.01–0.02), but the contrary behaviour is observed for high AOD (underestimation by 0.01–0.03). However, the overall ANN AOD/ Mark-I AOD scatter (0.06) duplicates that observed for the ANN AOD/AERONET AOD comparison (0.03). This agreement is within the AOD uncertainty of Mark-I and within our error estimation (Table ). Notice that the experimental scatter is significantly smaller than the theoretical one, suggesting that our assumed uncertainties could be very conservative. Therefore, in summary, we consider that the ANN AOD values capture well the day-to-day AOD variability and successfully identify Saharan mineral dust events at IZO.

The long-term Mark-I AOD time series also allows us to analyse the temporal consistency of the ANN AOD estimations by examining possible drifts and discontinuities in the monthly time series of the differences between ANN AOD and Mark-I AOD for July, August and September. A drift is defined as the linear trend of monthly median bias (measurements–estimations), while the change points (changes in the median of the bias time series) are analysed by using a robust rank order change-point test . The Lanzante's procedure is an iterative method that applies a (single) change-point test, based on summing the ranks of the values from the beginning to each point in the series, and followed by an adjustment step (the median computed for the segments enclosed by the identified change points is used to adjust the series). In the subsequent iteration the change-point test is applied to the adjusted series and the iterative process finishes when the significance of each new change point is less than an a priori specified level.

By applying this change-point test we identify 1997 as the change point in the monthly median bias time series (see Fig. c), caused by the horizontal visibility records. Although this discontinuity is significant at 99 % confidence level, the difference of median bias is rather small (-0.013 ± 0.001 for the 1984–1997 period and +0.006 ± 0.003 for the 1998–2009 period) and within the ANN AOD and Mark-I AOD expected uncertainties. Furthermore, we observe that there are no significant drifts in the bias time series either before or after this systematic change point at 99 % of confidence level. For the other months, August and September, the monthly median bias time series have shown neither significant systematic change points nor temporal drifts. These findings indicate that the ANN AOD estimates are consistent over time and, thus, valid to reconstruct the AOD time series at IZO.

We have analysed the long-term variability of ANN AOD time series by comparing with long-term meteorological records identifying Saharan dust events at IZO. On the one hand, we have compared the number of days in which estimated ANN AOD values fall within different AOD intervals with the number of days in which the meteorological observers reported presence of dust in suspension (05–06 SYNOP codes, ) at IZO during the dust season (July–September) since 1941 (see Fig. a and b). On the other hand, locally at the observatory, when haze or dust in suspension is reported by the observers, the wind normally blows from the second sector (90–180∘) (Fig. c). Therefore, we have analysed the relation between the monthly AOD medians in July (month with the maximum frequency of Saharan dust events at IZO in the study period) and the monthly percentage of time the wind is blowing from each of the four quadrants for the period 1941–2009. Both analyses provide consistent results. On the one hand, we found that the number of days with 05–06 Synop codes time series agrees with the number of days with ANN AOD ≥ 0.20 time series (R= 0.89). On the other hand, a high correlation (R= 0.86) between the ANN AOD monthly medians and the percentage of time the wind blows in the second quadrant is observed, whilst no correlation at all is found in the other three quadrants (R of 0.24, 0.16 and 0.14, for the first, third and fourth quadrants, respectively) (see Fig. c and d). These results show that the reconstructed ANN AOD series correlates well with other series of independent atmospheric parameters, confirming its consistency in this long period (1941–2009), and probing its capability for tracking inter-annual variations of dust-laden Saharan air mass outbreaks. The ANN AOD series is suitable to be used in climate analysis.

This paper presents, for the first time, the AOD time series of Saharan mineral dust outbreaks over the subtropical North Atlantic between 1941 and 2013. This has been done at the Izaña Atmospheric Observatory, frequently affected by the Saharan Air layer during the summer months, and by combining AOD estimates from artificial neural networks between 1941 and 2001, and AOD measurements during the period 2003–2013.

The ANN method has proved to be a very useful tool for the reconstruction of daily AOD values at 500 nm from meteorological input data, such as the horizontal visibility, fraction of clear sky, and relative humidity, recorded at IZO. ANN AOD estimates adequately capture the day-to-day AOD variations and the long-term trends when compared to coincident AOD measurements from Mark-I solar spectrometer (1984–2009) and AERONET (2004–2009). The results show a good agreement for the daily values, with Pearson coefficients of 0.97 (AERONET/ANN) and 0.93 (Mark-I/ANN). At the longest timescale (1941–2009), we found a good agreement between ANN AOD monthly medians and the percentage of time the wind blows from the Sahara desert (SE) (R= 0.86), and also a good correlation between the number of days with AOD ≥ 0.20 and the number of days in which synoptical observations reported mineral dust events (R= 0.89). These results show the reliability of the reconstructed ANN AOD series, confirming its consistency in this long period (1941–2009), and capability for tracking inter-annual variations of dust-laden Saharan air mass outbreaks.

Finally, this paper also highlights the potential of ANN to estimate AOD values and probe its suitability for long-term AOD series reconstruction. Thereby, the ANN methodology developed here for AOD series reconstruction might be suitable to be applied in Synoptic stations of North Africa, the Middle East and Asia, in which the reduced visibility is primarily due to the presence of mineral dust, and where recent AOD observations are available for validation.