A clear sky irradiation assessment using the European Solar Radiation Atlas model and Shuttle Radar Topography Mission database: A case study for Romanian territory

In the last time, some studies have been developed in order to evaluate the potential of solar energy over several countries or regions of the Earth. A literature survey indicates different techniques developed to predict the solar potential, based on recorded solar database^1,2 or geophysical calculations with the solar constant and attenuation effect of the Earth's atmosphere.^3,4 Thus, various parts of the Earth have been covered by these kinds of studies, such as for South-America,⁵ New Zealand,⁶ Africa,⁷ and so forth.

Accurate knowledge of the amount of the solar radiation has a fundamental importance for studying, planning, and designing of these solar energy systems. The best information about the solar radiation is obtained from the real measurements on the system's place, but, unfortunately, the solar radiation measurements are not yet available for many locations. Therefore, modeling is a proper solution for estimation of solar radiation at locations where measurements are not available, taking into account the amount of solar radiation received in clear-sky condition and applying a factor that parameterizes attenuation caused by cloudiness.

In this paper, a software application based on a clear-sky model and on a digital elevation model is developed in order to evaluate the amount of clear-sky solar radiation over the Romanian territory. The clear-sky model is based on the latest mathematical equations published in the European Solar Radiation Atlas (ESRA),^8,9 whereas the digital elevation model (DEM) is developed using the digital topographic database provided by Shuttle Radar Topography Mission (SRTM).¹⁰ In order to evaluate the amount of solar radiation, a matlab^® software application is developed to perform all these calculations, the details of the mathematical model used in the software application are given in Sec. II. The main goal of this section is the simple parameterization of the incoming solar radiation in terms of site elevation, including the shading effect through those factors which take into account the horizon obstructions. The fundamental equations used below are based on ESRA model^8,9 and some standard textbooks on solar engineering.^11–14 The topographic information of Romanian territory is achieved from a DEM, which is developed and adapted in Sec. III in order to provide information about the elevation and horizon obstructions for each point of DEM. This DEM provides the opportunity to take into account the effect of topographic characteristics in spatial distribution of solar radiation over large areas based on the shading effect in zones with a complex topography. In order to create a solar radiation database over Romanian territory (in Sec. IV), the DEM database is joined with the software application, so as the irradiance and irradiation values are calculated for each point of the DEM. The accuracy of solar radiation database certainty depends on DEM resolution. Estimated solar radiation values are tested against values drawn out from others radiation database, namely, with those values drawn out from SoDa^15,17 and Photovoltaic Geographic Information System (PVGIS)¹⁸ database, with the aim of evaluating the level of accuracy of this software application. Generally, for the whole area, the software application has a good performance in terms of standard errors. In Sec. V, the software application is used to build the maps of monthly average of daily irradiation, which in turn are involved in some spatial and temporal statistical analyses. Finally, the main conclusions of this paper are given in Sec. V.

The energy received by the Earth from the Sun rays can be defined as an instantaneous size (irradiance, G (W/m²)), as well as a cumulative size (irradiation, H (Wh/m²)) estimated over a given period of time. The irradiance value reached on a given location of the Earth surface depends on two main factors; namely, the irradiance values outside of atmosphere taking also into account the position of the Sun relative to the site location under evaluation, and also the attenuation effects of the Earth's atmosphere.

Outside the Earth's atmosphere, at any given point in the space, the irradiance received from the Sun is nearly constant. The average of the irradiance at the highest level of the atmosphere is defined as the solar constant, G_S0 (W/m²), and it is adopted to be equal with 1367 W/m². While the astronomical position of the Earth is known, the extraterrestrial irradiance value for a given day of the year can be evaluated based on the ESRA model.^8,9 In order to take into account the position of the Sun relative to the site location, for any moment of day, the relative position of the Sun can be described in terms of its azimuth and altitude angles.^8,9,11–14 The altitude angle is related to the angle of latitude, the Earth's declination, and also the hour angle. The solar declination angle is gradually changed from +23.45° (or North) on June 21, to −23.45° (or South) on December 21. The hour angle represents the number of degrees that the Earth must rotate before the Sun will be directly over the local meridian, being calculated as the difference between the noon and the local solar time, expressed in 2π rotation on the 24 h. The solar time is a correction applied to the local zone time, considering the rotation of the Earth about its axis and, also, the Earth's revolution around the Sun. This correction of local zone time has two components. The first one is a correction for the difference between the local time meridian of the local zone time and the observer's longitude, and, the second one takes into account the perturbations in the Earth revolution around the Sun, during which the Earth does not sweep equal areas.

The second factor that affects the irradiance value at the ground level is the attenuation effect of the Earth's atmosphere. In clear sky conditions, when the solar radiation passes through the Earth's atmosphere, it is reduced only due to scattering and absorption, thus, the irradiance that reaches the Earth's surface is reduced in intensity. Thus, under cloudless conditions, the radiation that is not scattered or absorbed will directly reaches on the Earth's surface as a direct (beam) radiation, while the scatter radiation that reaches the ground is called diffuse radiation. In accordance with ESRA model,^8,9 the clear sky direct irradiance on a horizontal surface, G_D (W/m²), is calculated as follows:

where T_LK is the Linke atmospheric turbidity factor for air mass 2, m is the optical air mass, δ_R(m) is the Rayleigh optical depth, and α is the solar altitude angle.

The Linke turbidity factor is a convenient measure of the atmospheric absorption and scattering of the solar radiation under clear skies, ranging from T_LK = 2 for extremely clear cold air in winter and 3 for clear warm air, to T_LK greater than 6, for the polluted atmosphere.^19,20 The air mass ratio, m, is the path length of the Sun's rays when pass through atmosphere, divided by the minimum path length, which occurs when the Sun is to noon time. The optical air mass is affected by two main factors, the direction of the Sun's rays and the site's atmospheric pressure, which in turn is influenced by the site's elevation above the sea level and can be expressed by the following formula:²¹ 

where α^c (in degrees) is a correction of solar altitude angle

and

is the pressure correction with the site's elevation of the observer location, z (in meters), relative to the sea level, and H_R is the height of the Rayleigh atmosphere, equal to 8435.2 m.

The Rayleigh optical depth, δ_R(m), depends on the optical air mass's value, a widely used empirical equation is given by following expression²⁰:

Returning to the ESRA model, the clear sky diffuse irradiance on a horizontal surface, G_d (W/m²), is the product between the normal extraterrestrial irradiance, the diffuse transmission function Tn, and the diffuse solar altitude function F_d, as follows:

The diffuse transmission function is a function of Linke turbidity factor based on the following expression:^8,9

The solar altitude function is a function of the solar altitude, evaluated using the following expression:

where the values of the coefficients A₀, A₁ and A₂, depending on the Linke turbidity,¹² are defined by the following expressions:

Consequently, all these sets of equations are used to evaluate the values of irradiance on horizontal surface, for a given location on the Earth. The clear sky global irradiation, for a given time interval, is calculated as a cumulative sum of the instantaneous irradiance in time. Therefore, in order to find the daily irradiation values, the global irradiance falling on a horizontal surface have to be integrated between sunrise and sunset, the sunrise and sunset times^11,23 being given by the following formula:

Thus, the daily values of clear sky irradiation could be integrated in order to provide monthly or yearly values of the clear sky irradiation on horizontal surface.

In order to create a solar radiation database for Romanian territory, a DEM based on digital topographic database has been developed. A DEM is a digital three-dimensional model of the Earth's surface, containing the data concerning the terrain elevation for each geographical coordinates of ground position, sampled with a regularly spaced horizontal interval. For a DEM with a medium resolution, the SRTM database has been chosen to assure proper information about the terrain elevation. The SRTM is a joint international project developed by National Aeronautics and Space Administration and the National Imagery and Mapping Agency, whose main objective is to generate a near-global digital elevation model of the Earth using radar interferometry.¹⁰ The SRTM database is a non-commercial product and is freely available for download through the USGS Earth Resources Observation and Science (EROS) Data Centre.²⁴ These data are intended for use with a geographic information system or other special application software, and are not directly viewable in a browser. The original data have a resolution of 3 arc sec (approximately 90 m), a higher resolution of SRTM database (1 arc sec, about 30 m) being available only for the United States and other few countries.^10,24

Romania is located between 43°37′ and 48°15′ North latitude parallels and between 20°15′ and 29°41′ East longitude meridians, covering a geographical area of 238 391 km². For these coordinates, there were downloaded 70 hgt.zip files from USGS website,²⁴ covering different areas by files with the name that includes an extension of 1° latitude and 1° longitude situated between 43° and 48° North latitude parallels, respectively, 19° and 30° East longitude meridians, those files indicating the latitude and the longitude of the area. For instance, the N46E027.hgt.zip includes the area between 46° and 47° North latitudes, respectively, 27° and 28° East longitudes.

A matlab^® routine has been used to draw out from the SRTM files (with 3 arc sec resolution) the data in the DEM format. The routine needs as input arguments the decimal degree coordinates, and it has as output argument the elevation assigned to longitude and latitude coordinates. Although the resolution of SRTM files is approximately 90 m, the resolution of developed DEM has been chosen to be in a step of 0.01° of longitudes and latitudes, between 20° and 29.99° meridians, respectively 43° and 48.99° parallels, meaning a number of 1000 × 600 cells. The resolution of developed Romanian DEM is about 1 km × 1 km (shown in Fig. 1), being enough for purposes of this paper, even if a DEM with a higher resolution can be obtained but it is actually detrimental to the computing time.

Giving the geographical coordinates and elevation for a given cell of the DEM, the direct and diffuse components of solar irradiance at a given time could be estimated. Nevertheless, the Sun obstructions and shading effects caused by the topographic features have to be taken into account for an accurate prediction of solar radiation. In zones with a complex topography, variability in elevation causes the Sun obstructions and shading effects, which leads to a local gradient of isolation. In this order, an angular distribution of Sun obstruction is computed at each moment for every cell of the DEM. It should be noted that the DEM's cells present different relative positions to the Sun during the day. Based on an analysis of the surrounding topography of the DEM's cell, the angular obstruction is evaluated by searching around the cell of interest the maximum angle of Sun obstruction for each moment, having in view the Sun direction (through solar azimuth angle). Fig. 2 depicts an intuitive view of the searching process.

In order to evaluate the shading effect of a given cell from DEM at a moment h, the elevations of the cells that surround the cell under evaluation, corresponding to solar azimuth ψ_h, are compared with the elevation of given cell, in order to find maximum angle of Sun obstruction. If the Sun obstruction angle is greater than the solar altitude angle α_h, then the cell under evaluation is shaded at moment h. An example of shading effect in DEM is shown in Fig. 3.

When the Sun is unobstructed, the global irradiance results from sum of both components, direct and diffuse components, whereas when the Sun is obstructed by terrain features, the global irradiance comprise only diffuse component. Daily solar irradiation is then computed by integrating the instantaneous global irradiance values between sunrise and sunset.

The previous mathematical model has been implemented into a matlab^® software application and used together with the DEM, in order to calculate the irradiance as well as the daily, monthly and yearly irradiation. In order to obtain the direct and diffuse solar radiation, the model needs the geographical coordinates and elevation above the sea level for every cell of DEM and based on the shading information, the global irradiance take in account only diffuse or both components. In addition, the model requires information related to the sky condition, through the turbidity factor value.²⁴ This parameter has been assumed through its monthly average values available on SoDa database. Therefore, using a cumulative sum of irradiance over the whole Romanian territory, the daily, monthly average, and yearly average of daily irradiation have been calculated, the results for yearly average daily global irradiation without shading effect being graphically represented in Fig. 4 and with shading effect in Fig. 5, respectively.

In order to validate the results of the application, some comparisons with data from others solar radiation database have been conducted. Numerous solar database and estimation tools are available worldwide, a significant progress being made in this direction in last time.^25,26 Among of these should be mentioned PVGIS, SoDa, HelioClim, NASA-SSE (Surface Meteorology and Solar Energy programme), Meteonorm, Satel-light, etc, where, in order to account the spatial distributions of solar radiation, the solar radiation models have been integrated within geographical information systems, obtaining so very powerful solar radiation analysis tools and database. The SoDa project is based on the information acquired by processing the satellite images, most of the database resources being available in the graphical and tabular format, the database being available through SoDa services.^15,16 Some information from this database have been drawn out and used in this paper to validate the results of the developed application. Another solar database used in this paper is from PVGIS, project developed by the Joint Research Centre of Europe Commission.¹⁷ This database includes, among other information, the monthly and yearly average values of the clear-sky global irradiation on horizontal surface. Its web interface is developed to provide interactive access to the maps and data solar radiation over European geographical regions.

Thus, for a numerical comparison of performance of the software application, the monthly average daily irradiation values have been computed for six cities of Romania, during the whole year, the cities being chosen in order to cover the all areas of Romanian territory, namely, Brasov, Bucuresti, Cluj, Constanta, Iasi, and Timisoara. The numerical values of monthly average daily irradiation obtained from matlab^® software application (MSA) and also from SoDa and PVGIS database are numerical reported in Table I.

The degree of accuracy of the software application is evaluated by two statistical tests, mean bias error (MBE) and root mean square error (RMSE), these statistical tests being widely used tests in assessing the performance of the analytical models.^22,27,28 The MBE provides information about the model's performance, a lower MBE value being desirable. Positive values indicate overestimated values, while negative values indicate underestimated values. The RMSE is always positive, a lower value being desirable, too. RMSE test provides also the information on the performance of the model considering the deviation between the calculated values and the desired values. To obtain dimensionless statistical indicators, the MBE and RMSE have been normalized to average of database values, the relative errors being calculated with following expressions:

where $xi$ and $x̂i$ are the ith values of software application and from database, respectively, all values used in previous equations referring to monthly average daily irradiation.

The relative mean bias and root mean square errors have been computed for an entire year, from January to December, and for all cities under consideration, based on the numerical values obtained from software application and monthly average daily irradiation draw out from SoDa and PVGIS database, the relative errors being reported in Table II.

Comparisons of the application results with those given by the SoDa and PVGIS database show that the software application gives fairly close results for a preliminary evaluation of the solar irradiation, the percentage of MBE for all under evaluated cases varies between 0.42% to 2.53% relative to SoDa database and between 0.46% to 2.36% relative to PVGIS database, while RMSE varies between 1.35% and 3.92% for SoDa database, and between 1.64% and 3.75% for PVGIS database, respectively. The underlined values indicate the maximal values of percentage of errors and, as can be seen, the relative errors are lower than 5% for all months of the year and for both SoDa and PVGIS database.

Furthermore, the errors indicate that the application results are underestimated relative to database values during the winter period (from October to March), whereas in the in summer period (from April to September) the calculated values are slightly overestimated. The analysis of the errors shows that the results of developed software application are in agreement with those from SoDa and PVGIS database values, giving enough confidence on the values provided by the developed software application. Concerning the fact that during the winter, the application results are underestimated relative to database values, whereas in summer the results are overestimated, it can be explained considering the relationships between direct and diffuse radiations and solar altitude. As is presented in Eq. (1), the direct radiation is related to solar altitude through the sinus function, whereas the diffuse radiation is related to solar altitude through a quadratic polynomial sinus function (Eq. (8)). It means that a higher value of solar radiation has a higher effect on the diffuse radiation in comparison with effect on direct radiation.

The developed software application has been used to evaluate and analyze the amount of clear-sky solar radiation over Romanian territory. Therefore, the solar radiation has been estimated as the monthly maps of average values of daily clear-sky irradiation, evaluated in horizontal surface, without and with consideration of shading effect. The monthly maps have been plotted by calculating the spatial distribution of average values of daily irradiation obtained for each month. Figure 6 shows an example of such maps, which have been drawn in 1 × 1 km² spatial resolution, for four representative months (March, June, September, and December).

These maps allow as the spatial and temporal analyses of monthly average daily irradiation to be conducted. As can be seen, the clear-sky solar radiation values show a north-south variation as well as the influence of the high-elevation zones. As can be seen, the amount of irradiation over Romanian territory increases from the low-elevation zones and northern sides, to high-elevation zones and to that located in southern sides of country. This variation of spatial irradiation is observed for all months of the year, the southern sides obviously receiving more irradiation than northern ones. If the shading effect is taken into account, the high-elevation zones, especially the mountains zones, are affected by the neighboring topographic features that surround the area, especially in the morning and evening, at lower solar altitude angles. These effects can be observed from the fact that the same areas are shaded for every month of the year.

In order to evaluate the temporally variation of solar radiation, the distribution of monthly average daily irradiations has been evaluated over whole Romanian territory, without and with consideration of shading effect. In order to avoid overestimations, all the cells outside Romanian borders have been removed from the DEM. Simultaneous comparisons of distributions of monthly average daily irradiation are shown in Fig. 7; thus, for each month spatial distributions of monthly average daily irradiation have been statistical analyzed using the box-plot representation, for both analyzed cases, with and without shading effect.

Monthly average daily irradiations vary during the year and are very low during the winter season. In the summer season values are the highest, while in the fall and spring seasons values are intermediate. Table III indicates the numerical values of monthly values of mean (M, kWh/m²/day), standard deviation (SD, kWh/m²/day), relative standard deviation (RSD, %) (i.e., absolute value of coefficient of variation) as well as the minimum (Min, kWh/m²/day) and maximum (Max, kWh/m²/day) values of daily irradiation.

Statistical analysis indicates that the amount of monthly average daily irradiation over whole Romanian territory, on horizontal surface and in the clear-sky conditions, varies between 2.04 kWh/m²/day and 9.25 kWh/m²/day if the shading effect is neglected and between 1.99 kWh/m²/day and 9.23 kWh/m²/day with consideration of shading effect. On the other hand, the standard deviations of monthly average daily irradiation have the same tendency, with higher values in winter, around to 10.92% (without shading effect) and 13.15% (with shading effect), and lower values in summer, around to 0.93% and 1.2%, respectively. It is observed that in winter months the standard deviation of clear-sky irradiation is larger that in the summer months, this being obviously the effect of the difference between solar altitudes angles during the year.

In Sec. IV, Figs. 4 and 5 show the maps of yearly average daily clear-sky irradiation over Romanian territory evaluated using data without and with consideration of shading effect, respectively. The yearly average daily clear-sky irradiation for Romanian territory without the shading effect is around 5.6345 kWh/m²/day, with the minimum value to 5.3163 kWh/m²/day and the maximum value to 6.1788 kWh/m²/day. If the shading effect is considered in analysis, the average daily irradiation is around 5.6002 kWh/m²/day, with the minimum value to 0.968 kWh/m²/day and with the same maximum value.

The amount of monthly losses caused by the shading effect, relative to whole Romanian territory, varies from maximum value of 45.66 Wh/m²/day in January to minimum value of 25.62 Wh/m²/day in July. Although absolute values appear comparable, the values relative to monthly average daily irradiation have a variation between 1.95% and 0.28%, respectively. The average value over the whole Romanian territory is around 34.22 Wh/m²/day, but unfortunately this value is not uniformly distributed over the whole territory, the higher amount of losses being located in the zones with a complex topography of terrain, especially the mountains zones.

In this paper, a software application based on the ESRA model and using a DEM database has been developed in order to calculate the irradiance as well as to build the maps of irradiation over different time intervals, in the assumption of the clear-sky conditions and in horizontal surface, for a case study of Romanian territory.

The software results have been validated against the monthly average daily irradiation from SoDa and PVGIS databases, obtaining relative RBE and RMSE under 5%, the relative errors indicating that the software application has a good performance. This application has been involved in order to build and analyze the maps of monthly average of daily clear-sky irradiation in horizontal surface, over whole Romanian territory. This application represents an opportunity to estimate clear-sky solar radiation for any location inside the study area, considering also the shading effect, especially in zones with a complex topography features.

The application presented in the paper uses a simple solar radiation model, which can be easily integrated with a DEM for a relative accurate and fast estimation of solar irradiance over an analyzed territory, taking also in account the shading effect of topographic features. The main advantage of the application, compared with other solar radiation estimation tools, is the estimation of database in a three-dimensional format, for any moment time, being easily analyzed in both graphical and numerical formats.

This paper was supported by the project PERFORM-ERA “Postdoctoral Performance for Integration in the European Research Area” (ID-57649), financed by the European Social Fund and the Romanian Government.