The SEVIRI instrument onboard MSG carries 11 channels in the visible to infrared spectral range with a spatial resolution of 3×3 km2 at the subsatellite point and a temporal repeat frequency of 15 min. Over Italy the spatial resolution is about 3×5 km2. From the SEVIRI measurements, a range of cloud physical properties can be derived with the Cloud Physical Properties (CPP) algorithm. The algorithm first identifies cloudy and cloud-contaminated pixels using a series of thresholds and spatial coherence tests on the measured visible and infrared radiances (Roebeling et al., 2008). Depending on the tests, the sky can be classified as clear, contaminated, or overcast. Subsequently, cloud optical properties (optical thickness) are retrieved by matching observed reflectances at visible (0.6 µm) and near-infrared (1.6 µm) wavelengths to simulated reflectances of homogeneous clouds composed of either liquid or ice particles. A mixture of ice and water is not possible in this framework. The thermodynamic phase (liquid or ice) is determined as part of this procedure, using a cloud-top temperature estimate as additional input (Roebeling et al., 2008; Stengel et al., 2014).

Building on the retrieval of cloud physical properties, the Surface Insolation under Clear and Cloudy Skies (SICCS) was developed to estimate surface downwelling solar radiation using broad-band radiative transfer simulations (Deneke et al., 2008; Greuell et al., 2013). Both global irradiance as well as the direct and diffuse components are retrieved. While the cloud properties are the main input for cloudy and cloud-contaminated pixels, information about atmospheric aerosol from the Monitoring Atmospheric Composition and Climate (MACC) project is used for cloud-free scenes. Other inputs include surface elevation from the ETOPO2v2-2006 database, monthly varying integrated atmospheric water vapour from the European Centre for Medium-Range Weather Forecast (ECMWF) ERA-Interim reanalysis, and 8-day varying surface albedo derived from Moderate-Resolution Imaging Spectroradiometer (MODIS) data.

The retrieval of cloud properties can be associated with large uncertainties, in particular due to horizontal inhomogeneity (e.g. Coakley et al., 2005). However, subsequently derived irradiances (such as SICCS GHI) have relatively much smaller uncertainty due to compensation of errors in forward and inverse radiative transfer calculations (Greuell et al., 2013; see also Kato et al., 2006). Uncertainties in MACC reanalysed aerosol properties contribute to errors in retrieved clear-sky GHI, but these errors are considerably smaller than those for cloudy skies (Greuell et al., 2013).

Greuell et al. (2013) performed an extensive validation of the MSG-SICCS retrievals with Baseline Surface Radiation Network ground-based observations in Europe for the year 2006. They found median values of the station GHI biases of +7 W m-2 (+2 %) and hourly GHI RMSEs (root mean square errors) of 65 W m-2 (18 %).

The CPP and SICCS products are publicly available at msgcpp.knmi.nl.

In this paper, we evaluate the performance of the RAMS-GHI 1-day forecast. RAMS is a general purpose limited area model designed to be used at the mesoscale (horizontal grid spacing ≈ 1–100 km) or higher horizontal resolutions. It is based on a full set of non-hydrostatic, compressible equations of the atmospheric dynamics and thermodynamics, plus conservation equations for scalar quantities such as water vapour and liquid and ice hydrometeor mixing ratios. The model is widely used for research as well as for weather forecast (Cotton et al., 2003).

The model is run with two one-way nested grids (Table 1, Fig. 1). The coarser domain has 12 km horizontal resolution and covers Central Europe, while the second domain has 4 km horizontal resolution and covers the Italian peninsula. Thirty-six vertical levels, extending up to the lower stratosphere, are used in the terrain-following coordinate system of RAMS.

The exchange between the atmosphere, the surface, and the soil is computed by the LEAF (Land Ecosystem–Atmosphere Feedback) submodel. The LEAF submodel considers the interactions among several features as well as their influence on the atmosphere: vegetation, soil, lakes and oceans, and snow cover.

RAMS parameterises the unresolved transport using K-theory, in which the covariance is evaluated as the product of an eddy mixing coefficient and the gradient of the transported quantity. The turbulent mixing in the horizontal directions relates the mixing coefficients to the fluid strain rate (Smagorinsky, 1963) and includes corrections for the influence of the Brunt–Väisälä frequency and the Richardson number (Pielke, 2002).

Convective precipitation is parameterized following Molinari and Corsetti (1985), who modified the Kuo scheme (Kuo, 1974) to account for downdrafts. The convective scheme is applied to the coarser RAMS domain, while convection is assumed explicitly resolved for the inner domain.

Explicitly resolved precipitation is computed by the WRF (Weather Research and Forecasting Model) single-moment 6-class microphysics scheme (WSM6) (Hong and Lim, 2006), which was recently adapted to RAMS (Federico, 2016).

Short wave and long wave radiation is computed by the Chen and Cotton scheme (Chen and Cotton, 1983); the radiative scheme accounts for the total condensate in the atmosphere but not for the specific hydrometeor type. In particular, the scheme uses an “effective emissivity” for cloud layers, where the cloud emissivity is parameterized empirically from observations (Stephens, 1978). The effective emissivity is a function of the total condensate water path, computed summing all hydrometeor mixing ratios for each model level (liquid, i.e. cloud and rain; solid, i.e. ice and snow; and mixed phase, i.e. graupel) and integrating over the cloud layer (Chen and Cotton, 1983).

Initial and boundary conditions are interpolated from the operational analysis–forecast cycle issued at 12:00 UTC by the ECMWF. Initial and boundary conditions are available at 0.5∘ horizontal resolution and on nine pressure levels, from 1000 to 30 hPa. No additional data are assimilated into the RAMS model.

The model was run for a whole year (1 June 2013–31 May 2014) with the above configuration and with no hydrometeors at the initial time, with the exception of water vapour (cold start). Previous unpublished studies with RAMS showed that 12 h are enough for the model to reach a dynamical equilibrium between the dynamic, thermodynamic, and cloud-precipitation fields starting from a cold start. For this reason, each simulation lasts 36 h, starts at 12:00 UTC of the day before the day of interest, and the first 12 h are used as spin-up time and discarded. The model output is available hourly.

In this work, we consider 12 pyranometers over Italy (Fig. 2). Their coordinates, height above the sea level, the Institution responsible for their management, and abbreviations used in this paper are shown in Table 2. The pyranometers span a wide range of climatic conditions: Trapani, Cozzo Spadaro, Santa Maria di Leuca, Capo Palinuro, Pratica di Mare, Cervia, Pisa and Trieste are located by the sea and show a typical Mediterranean climate; Vigna di Valle is characterized by a mild Mediterranean climate, but it is located in more complex hilly terrain; Paganella, Monte Cimone, and Aosta are mountainous stations, and this has an important impact on the RAMS and MSG performance at the sites. More specifically, Paganella is on the Alps, Monte Cimone is on the Apennines, while Aosta, which is at lower altitude, is embedded in the rough Alpine terrain.

The pyranometers are managed by two different institutions. The Aosta pyranometer is managed by Arpa Valle d'Aosta, while all other pyranometers are managed by the Italian Air Force (Aeronautica Militare). Each institution is responsible for its own measurements.

For pyranometers managed by the Italian Air Force, in addition to basic maintenance and installing procedures recommended by WMO – guide no. 8 (WMO, 2014), data quality is controlled following an internal control procedure described in Vergari et al. (2010).

In particular, to improve quality control checks for global solar radiation and sunshine duration data (available simultaneously for all stations of this paper managed by Aeronautica Militare), two procedures have been implemented. A range limit check, applied to both variables separately, concerns the respect of variables' physical limits. This check has been improved varying physical limits in agreement to the latitude and the season. Furthermore, the monthly atmospheric clearness index has been calculated from the climatic history of each site, by applying the linear form of the Ångström–Prescott model. Then, an upper and a lower bound for the solar radiation are defined as linear functions of clearness index and the sunshine duration value. These bounds delimit the range of the daily solar radiation.

Analysing the distance of daily values from their bounds, it is also possible to prevent instrumental electronic drifts. In fact, if this distance changes in an appreciable way, a recalibration procedure is activated and the device is recalibrated by comparison with a standard pyranometer using the sun as a source, under natural conditions of exposure (ISO, 1993). The reference standard used in this case is a CM11 Kipp&Zonen, calibrated every 2 years by the WMO Regional Instrument Radiation Centre of Carpentras (France), by comparison with a pyrheliometer PMO6 and a pyranometer CMP21.

For the Aosta pyranometer, in addition to the manual maintenance related to the periodical cleaning of the dome, irradiance measurements are daily checked through comparison with clear-sky simulations by a radiative transfer model (libRadtran, Emde et al., 2016) to check for electric wiring faults. In particular, measurements higher than 200 % of the daily maximum expected from libRadtran in clear-sky conditions are removed. The CMP21 radiometer is calibrated every 2 years at the Physikalisch-Meteorologisches Observatorium Davos–World Radiation Center against a member of the World Standard Group for the direct component and a shaded standard pyranometer of the World Radiation Center (WRC) for the diffuse component. The radiometric stability was better than 0.2 % over the period of the 6 years of measurements.

Table 3 shows, for each station and season, as well as for the whole year, the percentage of data in clear, contaminated, and overcast conditions, classified by the satellite method of Sect. 2.1.

There is a considerable variability of the sky conditions with the season for each station. For Trapani, for example, the percentage of clear sky in summer is 82 %, while it reduces to 38 % in fall and 48 % in winter. Additionally, for each season, the variability of the sky conditions among the stations is high. For maritime stations, for example, the percentage of clear skies in summer is above 70 % with few exceptions, while it reduces to 45, 34, 32 % for Paganella, Monte Cimone, and Aosta, respectively.

The RAMS-GHI forecast is available hourly, while the frequency of pyranometer observations and the MSG-GHI estimate is every half an hour. Pyranometer observations and MSG-GHI estimates were considered hourly, at the same time of the RAMS forecast output. Starting from these data, the MBE and the RMSE were computed: MBE=1N∑i=1Nxfi-xoi,RMSE=1N∑i=1N(xfi-xoi)2, where xf is the RAMS forecast or the MSG-GHI estimate, xo is the pyranometer observation, and N is the total number of data available for the statistic.

In addition to the MBE and RMSE computed from hourly data, the statistics are computed starting from daily data. In this case, the integral of the GHI for the whole day is first computed for each dataset, and then the MBE and RMSE are computed from the daily data.

Relative MBE and relative RMSE error measures (rMBE, rRMSE) are also used. The normalization is done with the pyranometer observation for the station and period considered, i.e. rMBE=100∑i=1Nxfi-xoi∑i=1Nxoi,rRMSE=1001N∑i=1N(xfi-xoi)21N∑i=1Nxoi. In order to improve the RAMS 1-day hourly forecast and the MSG-GHI estimate, a post-processing technique, namely the model output statistics (MOS), is used. The MOS technique improves the forecast/estimate of the GHI by reducing the MBE. The MBE is caused by several factors related to both modelling and observations. In the context of this paper the most important causes of MBE are (a) the approximations in the meteorological model and in the methodology used to estimate GHI from MSG data and (b) the horizontal grid used to represent the real world, which smoothens the surface features causing systematic errors. Other contributions arise from small and undetected systematic errors in the observations as well as from the not exact simultaneity of the three datasets (pyranometers, MSG-GHI, RAMS-GHI forecast).

The MOS used here consists of a linear regression computed between the GHI forecast (or estimate) and observation for a training period: y=a+bx, where x is the RAMS-GHI 1-day hourly forecast (or MSG hourly estimate) and y is the pyranometer observation. The application of the MOS is described in Sect. 3.4.

Figure 3a shows the scatter-plot of hourly GHI estimates of MSG and the corresponding pyranometer observations for Vigna di Valle. The black dots refer to clear sky, while the red dots are for contaminated and overcast conditions (after also referred to as cloudy conditions) for the entire yearly dataset. Three regression curves are shown: the black one is for clear conditions, the red one is for cloudy conditions (both contaminated and overcast), and the blue one is for the whole dataset. Linear regression is computed using the pyranometer values as x and MSG-GHI forecast as y. The parameters of the linear regressions are shown in the respective colours: a is the slope, b is the intercept, r is the correlation coefficient, and N is the number of data. The probability to have a correlation coefficient larger than that found by chance is also shown (p>r). A small value of this probability shows a high significance of the regression. The data for cloudy conditions of Fig. 3a show larger deviations from their regression line compared to clear-sky data. This is confirmed by the correlation coefficient, which is 0.96 for clear sky and 0.89 for contaminated and overcast conditions. Additionally, the slope (intercept) of the linear regression is closer to 1.0 (closer to 0.0) for clear sky, which is in better agreement with the perfect regression.

Considering Fig. 3a, two types of error are evident: (a) there are cases when the cloud classification by MSG-GHI is wrong, as, for example, for the black dots in the upper-left part of Fig. 3a. For these points, the MSG-GHI is high (larger than 600 W m-2), while the pyranometer observation is below 300 W m-2. This error becomes particularly important for mountainous stations because, when the soil is covered by snow, it is more difficult for the MSG-GHI algorithm to correctly identify the clouds; (b) the correlation coefficient for cloudy conditions is lower compared to clear-sky data and shows the difficulty in correctly estimating the cloud optical depth, which can result in both overestimation of the MSG-GHI, i.e. the cloud optical depth is underestimated, or underestimation of the MSG-GHI, i.e. the cloud optical depth is overestimated. It is important to note that red points may also contain cases of wrong cloud classification. Nevertheless, the larger spread of the red points compared to the black ones shows, indirectly, the overall good classification of the sky conditions by MSG because the estimation of the GHI is more difficult for cloudy skies.

Figure 3b shows the scatter plot for the same station for the RAMS-GHI 1-day hourly forecast. Linear regression is computed using the pyranometer hourly values as x and corresponding RAMS-GHI forecast as y.The RAMS-GHI forecast data show larger deviations from their regression line compared to MSG-GHI. The correlation coefficient of the linear fit is 0.91 for clear conditions, while it is 0.60 for contaminated and overcast sky, showing a rather poor performance of the RAMS-GHI 1-day hourly forecast in cloudy conditions. Both values are lower than the corresponding values of the MSG-GHI estimate.

Figure 3b for clear sky shows cases when RAMS predicts clouds that are not observed, i.e. the black dots in the lower-right part of the figure, and cases when RAMS does not predict clouds that are observed, i.e. the red dots in the upper-left part of the figure. Additionally, the large deviations of the red dots from their regression line show either cases of incorrectly predicted sky conditions or errors in the representation of the cloud optical depth.

From Fig. 3 it follows that (a) the performance in clear conditions is better compared to cloudy sky and (b) the hourly estimate of the GHI by MSG outperforms the RAMS forecast. For the latter point, however, it is emphasized that the MSG and RAMS performance cannot be directly compared because RAMS is a forecast, while MSG is an estimate of the GHI from radiance observations.

The results of Fig. 3, even if shown for Vigna di Valle, are found for all stations considered in this paper and are similar to the findings of several studies (Kosmopoulos et al., 2015; Lara-Fanego et al., 2012; Gómez et al., 2016).

To show this point for other stations, Fig. 4 shows the RMSE as a function of the cloud coverage for MSG-GHI (Fig. 4a) and for RAMS-GHI forecast (Fig. 4b). In Fig. 4a, the coloured bars for each sky condition (1 = clear, 2 = contaminated, and 3 = overcast) show the GHI average computed from the pyranometer hourly data, while the grey bars in the background show the RMSE of the MSG-GHI estimate for the different sky conditions for hourly data.

Figure 4a shows that the GHI decreases for the sky changing from clear to cloudy conditions, while the RMSE is higher when sky conditions become cloudier. More specifically, the RMSE is between 50 and 150 W m-2, depending on the station, for clear sky; between 50 and 200 W m-2 for contaminated conditions; and between 80 and 200 W m-2 for overcast conditions.

Figure 4b shows the performance of the RAMS-GHI forecast as a function of the sky conditions. The values of the pyranometers are the same as in Fig. 4a and are shown to help comparison. The RAMS-GHI 1-day forecast RMSE increases from clear to overcast conditions and the error is higher compared to MSG-GHI. More specifically, excluding mountainous stations, which have larger errors, the RMSE is 100 W m-2 for clear sky; 150–250 W m-2, depending on the station, for contaminated sky; and around 250 W m-2 for overcast conditions. In the latter case the RMSE is larger than the GHI for most stations, i.e. the relative error is larger than 100 %.

Because of the dependence of the MSG-GHI estimation and RAMS-GHI forecast on the sky condition, a large variability of the performance is expected with the seasons and with the stations, because the cloud coverage at each site varies with the season and, for each season, from site to site. This point is investigated in the following sections.

Figure 5a shows the MBE of the MSG-GHI hourly estimate in all sky conditions for the different seasons, for the whole year, and for all stations. Focusing on the whole year, there are five stations where the GHI is overestimated (maximum value at Monte Cimone; 18 W m-2) and seven stations where the GHI is underestimated (minimum value at Pratica Di Mare; -12 W m-2). The MBE is, however, small in absolute value and it is lower than 10 W m-2 for seven pyranometers. Considering the variability of the results with the station in all seasons, we note the larger absolute values for mountainous stations. This is expected because there are a larger number of cloudy data for those stations (Table 3) and the performance of the GHI estimate by MSG is worse for cloudy conditions (Fig. 3a). This result is general and applies also to the RAMS forecast. Figure 5b shows the MBE for the RAMS-GHI 1-day hourly forecast. Considering the statistics for the whole year it is noted that the values are, in general, positive and below 30 W m-2, with the exceptions of Paganella and Aosta where the MBE is negative, i.e. the RAMS forecast underestimates the GHI and reaches the huge value of -120 W m-2. The same behaviour is found for all seasons, with few exceptions. Excluding the mountainous stations of Aosta and Paganella, the largest MBE is found in summer, showing the tendency of the RAMS forecast to overestimate the GHI in this season, while the smallest values occur in spring. Considering the dependence of the MBE with the station, it is evident the worse performance for mountainous stations, namely Paganella and Aosta, compared to maritime stations. The inspection of the model output for those stations reveals that the main source of error was the over-forecast of cloudy conditions, as shown by the scatter plots between the RAMS-GHI 1-day hourly forecast and the corresponding pyranometer values for these stations, given as a Supplement to this paper. It is not easy to find the reason for this behaviour, because several factors could be involved as errors in the physical and numerical parameterizations of the model and errors in the initial and boundary conditions. Additionally, the 4 km horizontal resolution is not enough to resolve the fine orographic structures over the Alps (Aosta and Paganella) and over the Apennines (Monte Cimone) as well as their interaction with the atmosphere.

Figure 6a shows the RMSE for the MSG-GHI hourly estimate in all sky conditions for different seasons, for the whole year, and for the 12 stations. Considering the whole year, we note two groups of stations: the first with values around 100 W m-2, containing the maritime and hilly stations, and the second with values larger than 150 W m-2, containing the mountainous stations. The increase of the RMSE for mountainous stations is caused mainly by the following: (a) the 3×5 km2 horizontal resolution of the MSG-GHI can be not enough to represent the local sky conditions at the pyranometer, especially for mountainous stations where the complex orography determines rapid changes of the cloud coverage in short distances; (b) the classification of sky conditions is more difficult where the soil is covered by snow, and, because this condition is more frequent for mountainous stations, it increases the MSG-GHI error for those stations; (c) the estimate of the hourly GHI by the MSG is more difficult in cloudy conditions (Fig. 4), which are more frequent for mountainous stations. The different performance of the two groups of stations is confirmed for all the seasons and highlights the difficulty in clearly distinguishing and classifying clouds for the specific sites.

Considering the behaviour of the RMSE with the season, the lowest values are often found in winter even if the performance does not vary sizably with the season. Winter has also the lowest RMSE averaged over all stations (84 W m-2), followed by fall (98 W m-2), summer (112 W m-2), and spring (119 W m-2). The performance in winter is better compared to other seasons because the RMSE statistic is sensitive to the larger errors (Wilks, 2006), and the departures of the GHI estimate from the observation is lower in winter because the GHI is smaller. The larger variability of the performance in summer compared to other seasons is also noted, which will be discussed later on in this section.

Another interesting statistic to quantify the performance of the MSG-GHI hourly estimate is the rRMSE, which is shown in Table 4. Considering the whole year, this value ranges from 14 % for Cozzo Spadaro to 53 % for Monte Cimone; for maritime and hilly stations the rRMSE is below 30 %, while it is above 40 % for mountainous stations, showing again the difference between the two groups. The rRMSE has the smallest value in summer and the highest value in winter. While this result is in part determined by the larger observed values of the GHI in summer, this analysis shows the impact of the cloud coverage on the MSG-GHI performance more clearly. The percentage of cloudy conditions is larger in winter compared to summer for all stations (Table 3), and the error of the MSG-GHI is higher in cloudy conditions, as shown by the rRMSE. However, the larger differences between the MSG-GHI hourly estimate and the pyranometer observation in summer, even if in fewer occasions, determine larger values of the RMSE compared to winter, as shown in Fig. 6a.

Figure 6b shows the RMSE for the RAMS-GHI 1-day hourly forecast. Considering the whole year, the RMSE is below 200 W m-2 for all stations, with the exception of the mountainous stations, where the error is larger because of the difficulty of the RAMS forecast to correctly predict the cloud coverage. Considering the RMSE behaviour for different seasons, averaged for all stations, the lowest error is found in winter (142 W m-2) followed by fall (171 W m-2), summer (186 W m-2), and spring (245 W m-2). Summer has the largest RMSE spread among the stations. In particular, it shows the lowest error among all stations and seasons (Cozzo Spadaro, 110 W m-2) but also values larger than 300 W m-2 for Paganella and Aosta. This result is caused by the large differences between the RAMS-GHI 1-day hourly forecast and observations. These differences are the largest in summer (the lowest in winter) when the forecast of the cloud coverage is incorrect, causing the largest (lowest) spread of the performance among stations. This applies also to the MSG-GHI hourly estimate.

The RMSE of the RAMS-GHI 1-day hourly forecast is more than twice that of the MSG-GHI considering both the whole year and the seasons. The mountainous stations are an exception also in this case because the performances of MSG and RAMS are closer. A better performance of the MSG-GHI estimate is expected, because it is derived from the observations, while the RAMS is a forecast; however, the results of this section quantify the difference between the two GHI sources in different conditions.

The rRMSE for the RAMS-GHI is shown in Table 5. Considering the yearly statistic, the values range from 31 % for Cozzo Spadaro to 81 % for Aosta. The rRMSE varies considerably between the mountainous stations compared to maritime and hilly stations, jumping from 53 % obtained for Trieste (the worst performance for maritime and hilly stations) to 72 % of Paganella (the best performance for mountainous stations). The variability of the rRMSE with the seasons shows again the important impact of the cloud coverage on the RAMS-GHI 1-day hourly forecast performance. The smallest rRMSE are in summer and the largest in winter for all stations. Moreover, for Trieste, Cimone, and Aosta, the rRMSE is about 100 % or larger in winter.

Before concluding this section, it is interesting to compare the RAMS-GHI 1-day hourly forecast with the 1-day hourly persistence forecast (Table 6). The 1-day hourly persistence forecast was computed using the observed values of the previous day hour by hour.

Considering the yearly statistics, the RAMS-GHI has a lower error compared to the 1-day persistence forecast for all pyranometers but Paganella. The improvement given by RAMS is larger than 10 % of the RMSE, showing a sizable impact. However, for Aosta, the difference between the two forecasts is negligible.

Considering the performance of the RAMS-GHI and 1-day persistence hourly forecasts with the seasons, we note that (a) in winter the performance of the 1-day persistence forecast is better than the RAMS-GHI forecast for seven pyranometers. This result is obtained for six stations in fall, four stations in spring, and one station in summer; (b) for mountainous stations the 1-day persistence hourly forecast is better than the RAMS-GHI 1-day hourly forecast for most-cases. These results show again the important impact of the cloud coverage on the performance of the RAMS-GHI 1-day hourly forecast; nevertheless, the RAMS forecast can give added valued to the GHI forecast in most cases.

In this section, we discuss the impact of the time interval on the RAMS-GHI and MSG-GHI performance.

Figure 7a shows the rRMSE for different stations and seasons for the RAMS-GHI 1-day forecast. This figure is still computed from hourly data, as in the previous section (Fig. 4b), but the RMSE is expressed in percentage to help comparison among statistics presented in this section.

Figure 7b shows the rRMSE for daily integrated GHI. Comparing the result of Fig. 7a and b, the impact of the time interval on the rRMSE is apparent. Considering the yearly result, for example, the rRMSE is reduced by more than 9 % (in percentage units and the percentage is computed respect to the corresponding observations, Eqs. 2 and 3) for all stations when the statistics are computed for daily integrated GHI, and for several stations the improvement is larger than 15 %. This improvement is found for all seasons and stations. In addition to the way used to compute the statistic, which produces smaller values compared to the same statistic for hourly data, the improvement is also caused by a partial compensation of the forecast underestimation and overestimation of the GHI during the day.

Considering the rRMSE for the MSG-GHI, a similar improvement is found, when computed for daily integrated GHI (Table 4). For the yearly statistics, the rRMSE decreases by 10 % or more for all stations and an improvement larger than 5 % is found in all seasons with a considerable variation among the stations.

The last problem considered in this paper is the impact of the model output statistics (MOS) on the 1-day RAMS-GHI forecast and on the MSG-GHI, both for hourly and daily integrated GHI. The MOS was computed for each season and the “leave one” methodology was used to verify the RAMS forecast (MSG estimate) using MOS. This method is a cross-validation method to assess how the MOS prediction will perform in practice. For each hour of a season, the dataset is divided in two parts: (a) the actual data (or actual value), which is the value at the selected hour of the RAMS 1-day hourly forecast (or the MSG hourly estimate of GHI) and the corresponding pyranometer observation, and (b) the training dataset, which is composed by all data in the season with the exception of the actual data. The Eq. (5) is computed for the training dataset (y is the pyranometer value and x is the RAMS 1-day hourly forecast or MSG hourly estimate of GHI), and it is applied to the actual data, which is the x, to give the corrected forecast (y). Because the MOS is computed starting from hourly data, the training period is all the season but 1 h. This procedure was repeated for all the hourly data in the season, obtaining the time series of the corrected RAMS 1-day hourly forecast and of the corrected MSG hourly estimation of the GHI. The RMSE and rRMSE were computed for the corrected forecast/estimate of the GHI. In this way, the data used for computing MOS is statistically independent from the dataset used for the verification.

The statistics computed from hourly data are shown in Table 6 for the RAMS forecast. It is apparent that the MOS improves the RAMS performance especially for Aosta and Paganella, where the bias is high (Fig. 5b). In particular, after the MOS application, the absolute value of the bias is less than 30 W m-2 for Paganella and Aosta for all seasons as well as for the whole year (not shown). With the MOS application, the RAMS-GHI 1-day hourly forecast performs better than the 1-day persistence hourly forecast for all stations considering the whole year, even if there are still occasions when the 1-day persistence hourly forecast has a better performance than the RAMS-GHI 1-day hourly forecast (Paganella in winter and fall; Aosta in winter, spring, and fall; Trapani in winter).

Starting from hourly data after the MOS correction, daily integrated GHI statistics were also computed. The rRMSE of RAMS-GHI 1-day forecast is shown in Fig. 7c and Table 5. The rRMSE decreases by 2–8 % (in percentage units) for most stations compared to the daily integrated GHI without MOS, with exception of Paganella and Aosta, where the improvement is larger. This is expected because the bias is larger for these stations (Fig. 5b) and the MOS is a technique that improves the forecast by reducing the bias. This is confirmed by the inspection of the rMBE (not shown), which is reduced by the application of the MOS.

The application of the MOS to the MSG-GHI gives no improvement on both rRMSE (Table 4) and rMBE (not shown). This is caused by the small values of the bias of the MSG-GHI (Fig. 5a).