Total atmospheric transmission factor

The cloud-cover index for the satellite images

Cloudiness is expressed through the cloud-cover index n^t(i, j) at a given point (i, j) and a given time t by applying the following formula (Cano et al. 1986):

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where α^t_toa(i, j) is the instantaneous planetary albedo; α_toa,min(i, j) corresponds to a clear, clean, and dry sky; and α_toa,max(i, j) corresponds to a heavily overcast sky.

The existence of clouds, from the sensor point of view, is translated into an increase in the planetary albedo. The cloud-cover index varied from 0 to 1 and may be interpreted as the cloud coverage percentage per pixel. In addition, it is an indicator of the atmospheric transmission of a column of air located above the pixel, where low values correspond to a high factor of atmospheric transmission.

Statistical relationship between the atmospheric transmission factor and the cloud-cover index

The regression coefficients can be determined by comparing the transmission factors deduced from the solar radiation data measured at ground level with the corresponding cloud-cover index derived from satellite images. Once these coefficients are known at ground stations, methods of interpolation may be applied to define the complete field of coefficients for the study area.

In agreement with the general knowledge of solar radiation, this relationship is restricted to solar elevations greater than 12° and to satellite elevations greater than 5°. It follows that this method cannot operate optimally for latitudes greater than about 60° (Diabaté et al. 1989).

An expression having the same form as that of Eq. (3) was employed by Cano et al. (1986), Nunez (1987), Diabaté et al. (1989), and Rafiqul et al. (1996). Cano et al. (1986) used images from the Meteosat satellite to determine the cloud-cover index; Nunez (1987) only made use of the planetary reflectivity; Diabaté et al. (1989) used the visible channel of geostationary satellite images to obtain global solar radiation maps employing the Heliosat method, which was verified during 30 consecutive months beginning in January of 1983; Rafiqul et al. (1996) employed a bispectral method with application in the visible and thermal infrared ranges of NOAA images to calculate the sky's cloud cover.

Data collection and filtering from the ground measurement stations

Data were collected from 30 global solar radiation surface measurement stations that belong to the networks of the Spanish National Institute of Meteorology (INM), Institut Català d'Energia (ICAEN), and the Department d'Agricultura Ramaderia i Pesca (DARP), each a part of the agrimeteorological network of the Generalitat of Catalonia, which is distributed throughout Catalonia. The measurements were performed using Kipp & Zonen, Inc., Siap, Inc., and Campbell Scientific, Inc., pyranometers. The dataset consisted of 5-min averages of irradiance, together with the daily cumulative insolation for 1998.

These measurement stations are not homogeneously distributed within the territory because their locations depend on a range of factors. Station density is high along the coast and in the central region of Catalonia but is more sparse as one moves closer to the mountains in the north.

A careful filtering process is applied to the pyramometer data to correct any possible measurement errors, for example, flat sensors, the presence of shade, poor calibration, and so on. This process is particularly relevant to this study because any error in the measurements may lead to enormous spatial variability in the data. The method consists of the analysis of a series of data based on two criteria: temporal and spatial coherence of the data.

Temporal coherence is checked by means of a series of graphs, one for each station. An example of these graphs is shown in Fig. 2, which provides data from the Aldea and Perafita stations. Note that the analytic curve has been drawn together with the data series on this figure. This curve was analytically generated by taking into account only the astronomical evolution of daily radiation (for a given latitude and air transmittance) and provides an estimate of the solar radiation at sea level under clear-sky conditions. This curve is employed as a reference to check the evolution of clear days throughout the year. Considerable deviation of the measurements with respect to this curve (not justified by the characteristics of the measurement station site: located on top of a mountain or in misty atmospheric conditions, for example) indicates possible measurements errors. For example, a seasonal deviation could be an indication of the presence of shade at the measurement station site. If the measurements are consistently above or below the curve, then the sensor could be out of calibration.

The spatial coherence of the data is studied simultaneously using a series of radiation isoline maps with global solar radiation maps for Catalonia reported by Santabárbara et al. (1996) and Baldasano et al. (1999), taking into account the fact that stations that are close together should not provide very different records. Some of the sensors were calibrated to obtain various points of control that were used as references during this process.

After combining the two coherence criteria, some of the data periods were eliminated. In some cases, the total data for a particular station were eliminated. This led to the elimination of 9 of the initial 30 stations. The locations of the stations that passed the filtering process are shown in Fig. 1.

Satellite data

This study makes use of data obtained from the polar-orbiting satellite NOAA AVHRR. The spatial resolution of these images is 1.1 km at nadir. The spectral bands (wavelengths in micrometers) of the AVHRR sensor, from channel 1 to channel 5, are, respectively, 0.58–0.68, 0.72–1.10, 3.55–3.93, 10.3–11.3, and 11.5–12.5.

Work was carried out with 189 images for 1998 (see Table 1), which were captured by the receiving station belonging to the Environment Department of the Generalitat of Catalonia, using a Dartcom, Ltd., high-resolution picture transmission system receiver. These images come in an 8-bit format that is geometrically corrected and duly georeferenced.

For temporal resolution, two images may be obtained daily at approximately 0730 and 1430 LST, which correspond to the pass of the morning satellite (NOAA-15) and the afternoon satellite (NOAA-14) respectively. However, for technical reasons, in this study only the images corresponding to 1430 LST (NOAA-14) were available. The image header provides information about the satellite, date and time of acquisition, receiver channel (band), and the calibration coefficients. Image calibration is linear. When it belongs to the visible channel, it provides the albedo; if it is within the thermal infrared band, it provides information about the temperature.

Cloud detection

In general terms, cloud detection using satellite images depends on the contrast between the clouds and the background. In the visible band, this contrast is examined in terms of reflection levels. In infrared, we observe brightness temperature difference, which includes both the effects of reflection levels and thermal emission.

A simple, fast technique for cloud detection consist of the evaluation of radiance, together with the application of predetermined thresholds between various channels of the AVHRR sensor, which enables the various types of surface (land, sea, snow, etc.) and cloud to be discriminated. Allen et al. (1990) and Laine et al. (1999) developed and evaluated algorithms for discriminating among clouds, snow, and land surfaces employing a multispectral technique on channels 1, 3, and 4 of the NOAA AVHRR sensor.

In this work, cloud detection was carried out using the algorithm developed by Laine et al. (1999), which uses the mean reflection level of channel 1 (R₁) together with the brightness temperature from channels 3 and 4 (T₃ and T₄, respectively) to enable the separation of clouds, snow, and land, with the procedure basically consisting of four tests. The first test assumes that clouds are usually cooler than the land, except under conditions of atmospheric thermal inversion. By taking advantage of this condition, the cold clouds located in the high atmospheric layers may be identified by applying a minimum value of brightness temperature (T_min) for channel 4. The second test consists of a general procedure for cloud detection, by means of the application of an empirical threshold of 8 K for T₃ − T₄, which permits clouds to be separated with respect to the land and the sea. The third test enables the high reflection level of clouds and snow to be separated from areas that are snow-free land by the application of a minimum reflection level of 0.15 for channel 1. The final test separates the clouds from snow and ice, using the same principle as test 2 but with an empirical threshold of 4 K.

Determining the hourly global solar radiation from satellite data

From the 21 available measurement stations described in section 3a, only 11 were selected for determining the a and b coefficients (calibration stations) of the atmospheric transmission factor equation. The remaining 10 measurement stations were used for model validation (see Table 2). For each one of the calibration stations, the atmospheric transmission factor is calculated by application of Eq. (1).

For satellite images, the procedure consists of working with a set of images: in this case, all daytime images for a month. The visible and infrared image channels are used to detect the clouds, and the visible channel is used to determine the albedo of both the surface and the clouds.

Each visible image is normalized by dividing by the cosine of the local solar zenith angle. The cloud-cover index is determined by applying a statistical procedure that takes into account the possibility of a pixel being contaminated with clouds or not being contaminated. All daytime images for the month under analysis are taken, and the minimum value for each pixel is taken, giving information on the clear-sky planetary albedo for every pixel (α_toa,min). In a similar way, the maximum value for each pixel in the series is also determined, which corresponds to the planetary albedo of the overcast cloudy sky including cloud top and the atmosphere above the cloud (α_toa,max). Then the cloud index is determined for each pixel by application of Eq. (2).

Coefficients a and b are determined from field data, defining a linear regression [Eq. (3)] between the transmission factor deduced from the solar radiation data measured at ground and the cloud-cover index at the same location determined from satellite. For example, in Fig. 3 a scatterplot of atmospheric transmission factor versus cloud-cover index is shown for 1998 for stations Aldea and Perafita. The yearly regression equation is also included.

Table 3 shows the monthly value obtained for the a and b coefficients, together with the determination coefficient r², for the Aldea and Perafita stations. Note that a determination coefficient r² ≈ 0.80 was obtained for the mean values for all the stations, so that the obtained values of the model coefficients by regression represent a good fit.

After determining the model coefficients, the variation over time and space can be clearly observed (including seasonal variations) so that it is sufficient to calculate them on a monthly basis and assume they are constant throughout the considered month (Rafiqul et al. 1996). This point of the method is different from Cano et al. (1986), who considered the coefficients to be constant with time, with only a slight seasonal variation, or Diabaté et al. (1989), who considered that the model coefficients were constant for a given hour of the day, both in time and space, throughout the year.

Once these coefficients were known at the ground stations, an interpolation process (kriging method) was performed to obtain the a and b field of the area under study. Hourly global solar radiation was then determined for the whole study area using the procedure shown in Fig. 4.

Cloud detection algorithm

Figure 5 shows the application of the cloud detection algorithm for a NOAA image acquired on 11 August 1998. In this figure, bands 1, 3, and 4 of the AVHRR sensor are represented, which correspond to albedo (%) and the brightness temperature (K) for bands 3 and 4, respectively.

When test 1 is applied, high clouds (cirrus, cirrocumulus, etc.) are more evident and appear at the Pyrenean Mountain range and the upper part of the image. When test 2 is applied, some middle clouds appear (altocumulus, altostratus, etc.) both in the Gulf of Vizcaya and the Gulf of Lyon and over the Mediterranean Sea. When test 3 is applied, high and middle clouds appear again together with low clouds (cumulus, stratus, etc.). These clouds are located over a great continental extension toward the lower-left corner of the image. Test 4 detects a series of low clouds located at Gulf of Lyon, at the Mediterranean Sea, and the Balearic Islands, which were not detected in the previous tests. In the last image, all clouds types are represented. To obtain a detailed cloud classification, the procedure described by Karlsson (1989) can be applied.

According to a visual check of the efficiency for the separation of clouds and snow, values close to 100% were obtained under snow-free conditions, just like the values reported by Laine et al. (1999) under similar circumstances.

The employed cloud detection algorithm was good at effectively discriminating the clouds from the land, snow, and ice. Note that, in the study area, the northern-central Catalonia (during certain short periods of time in winter) and the Pyrenean Mountain range (during the whole winter period) may reveal wide areas covered in snow, so that most of the test-3 cases described in section 3c are sufficient for adequate cloud detection.

Comparison of satellite-estimated, surface pyranometer-interpolated, and pyranometer-measured hourly global solar radiation

To validate the satellite estimates of hourly global solar radiation, two comparisons were carried out. First, comparisons were made of satellite estimates with ground pyranometer data. A second comparison was conducted among satellite estimates, surface pyranometer-interpolated data, and ground pyranometer measurements. Both for satellite-estimated and for surface pyranometer-interpolated data, measurements from the calibration stations were used. The result obtained were later compared with another set of independent stations (validation stations).

Figure 6 shows a comparison between the hourly global solar radiation as estimated by satellite and that obtained by measurement stations on the ground for the period of January–December 1998. The diagonal line of slope 1 shows a perfect fit between the estimate by satellite and the measurements, whereas the dotted line represents the curve adjusted by regression of the values. Equations in each plot represent the regression coefficients of the best-fitted line adjusted for each dataset. The determination coefficient for each case is also included. Table 4 shows the values of the comparison between the hourly global solar radiation as estimated by satellite and that measured by the pyranometers, showing the mean, the rmse, and the bias for each of the model validation stations. The results show a determination coefficient of r² > 0.98 in all cases, together with a minimum rmse of 9.6% and a bias of −0.8% for the Deltebre station, whereas a maximum bias of −9.5% with an rmse of 15.7% is obtained for the Lleida station, so that the fit is very good. Only in a few stations, such as Ametlla, Lleida, and Girona, can it be seen that the model slightly underestimates the radiation value given by the pyranometers. For the remaining stations, it can be said that the model correctly estimates the measurements, providing estimated values that are very close to the measured value. Only in the Manresa station is a positive bias value of 1.3% obtained, with an rmse of 10.0%.

The ultimate test for satellite estimates of hourly global solar radiation is to compare them with the surface pyranometer-interpolated data obtained from the calibration stations. From the 10 available validation stations, only 5 were chosen to perform this comparison. The criterion used was that they are evenly distributed in space and allow the division of Catalonia into three areas: north area (Girona station), central area (Montseny and Veciana stations), and south area (Benissanet and Deltebre stations).

The hourly global solar radiation from the calibration stations was interpolated into a grid with squares of dimension equal to that of the pixel provided by satellite images, using the kriging interpolation method, and applying the methodology described by Santabárbara et al. (1996) and Baldasano et al. (1999) for the elaboration of the Solar Radiation Atlas of Catalonia from the interpolation of surface pyranometer data.

The statistics of the comparison between satellite-estimated and surface-interpolated hourly global solar radiation at five validation stations in February and July of 1998 are shown in Table 5. The corresponding time series of the hourly global solar radiation is shown in Fig. 7.

Zelenka et al. (1999) considers that for any application requiring time/site-specific data, the user should rely on the satellite rather than on a neighboring ground station if the latter operates farther away than 20–30 km from the site. For the case of Catalonia, only in the north area (Girona station) are the ground measurement stations separated by more than 30 km. In that area, then, satellite-estimated values were more accurate (correlation of 0.90–0.96 and rmse of 6.9%) than were the surface-interpolated estimates (correlation of 0.75–0.79 and rmse of 11.4%–15.5%).

In the central area of Catalonia (Montseny and Veciana stations), the distance between the stations is almost that given in Zelenka's paper (1999). That is why satellite results (correlation of 0.91–0.97 and rmse of 3.2%–9.4%) are comparable to those obtained by surface interpolation (correlation of 0.74–0.87 and rmse of 4.1%–20.3%). However, it is evident that satellite-retrieved data are better because of the fact that the satellite takes into account spatial variations of the global radiation over the land whereas surface interpolation does not.

For the south area of Catalonia (Benissanet and Deltebre stations), results obtained from satellite (correlation of 0.93–0.97 and rmse of 5.3%–10.2%) and those from surface interpolation are of equal quality (correlation of 0.93–0.97 and rmse of 3.0%–14.6%).

Laine et al. (1999) undertook a similar analysis to check the accuracy of satellite and surface-interpolated estimates. The satellite-based daily global radiation spatial distributions were compared in the region of Finland with those obtained by interpolating the station-based pyranometer data. In southern Finland, the estimates of daily global radiation based on interpolated station data and based on satellite data were of equal quality (standard error of about 10%–15%). In northern Finland, where the stations are farther apart, the satellite-based values were much more accurate (standard error of 11%–16%) than were the interpolated estimates from the stations (standard error of 43%–74%).

Note that Laine et al. (1999) obtained larger differences between satellite estimates and surface-interpolated data in the north of Finland. This result is probably due to the low number of surface pyranometer stations and the nonhomogeneous distribution, with very low presence in the north. Catalonia, however has a very dense network of stations, although a little reduced in the north.

Solar radiation map

Figure 8 shows the hourly global radiation as estimated by satellite between 1400 and 1500 LST for the period of February–December of 1998, and whenever possible the 15th of each month is represented. This day has been taken as the characteristic value for the specific month. All months were represented with the same value scale, so that they could be directly compared.

The map sequence of Fig. 8 clearly shows the seasonal variation of the surface global solar radiation, with minimum values occurring in December in agreement with the winter solstice. These values vary between 0.5 and 1.4 MJ m⁻² h⁻¹, and in space the minimum values are located in the Lleida plain, in the west of Catalonia, possibly because of the persistence of fog during the winter months. Other relative minima are located in the western area and the prelittoral mountain chain and in north Catalonia by the Pyrenean Mountains. The maximum values are found in June, coinciding with the absolute annual maxima and associated with the summer solstice, with values around 3.4 MJ m⁻² h⁻¹. For the spatial distribution, maximum values are registered at the coast and in the western central area of Catalonia, with a slight reduction in the precoastal strip and certain minima in the Girona Pyrenean Mountains to the northeast of Catalonia. Values for the Pyrenees are very variable in a small region, but this variability is due to the characteristics of the measurement points. It is clear that mountain stations, with a good exposure to the sun and less optical mass, record high average values, whereas the low-level stations show lower average values.