For latitude-longitude coordinates it requires that the elevation map is in meters. The rules are:
The solar geometry of the model is based on the works of Krcho (1990), later improved by Jenco (1992). The equations describing Sun – Earth position as well as an interaction of the solar radiation with atmosphere were originally based on the formulas suggested by Kitler and Mikler (1986). This component was considerably updated by the results and suggestions of the working group co-ordinated by Scharmer and Greif (2000) (this algorithm might be replaced by SOLPOS algorithm-library included in GRASS within r.sunmask command). The model computes all three components of global radiation (beam, diffuse and reflected) for the clear sky conditions, i.e. not taking into consideration the spatial and temporal variation of clouds. The extent and spatial resolution of the modelled area, as well as integration over time, are limited only by the memory and data storage resources. The model is built to fulfil user needs in various fields of science (hydrology, climatology, ecology and environmental sciences, photovoltaics, engineering, etc.) for continental, regional up to the landscape scales.
As an option the model considers a shadowing effect of the local topography. The r.sun program works in two modes. In the first mode it calculates for the set local time a solar incidence angle [degrees] and solar irradiance values [W.m-2]. In the second mode daily sums of solar radiation [Wh.m-2.day-1] are computed within a set day. By a scripting the two modes can be used separately or in a combination to provide estimates for any desired time interval. The model accounts for sky obstruction by local relief features. Several solar parameters are saved in the resultant maps' history files, which may be viewed with the r.info command.
The solar incidence angle raster map incidout is computed specifying
elevation raster map elevin, aspect raster map aspin, slope
steepness raster map slopin, given the day day and local time
time. There is no need to define latitude for locations with known
and defined projection/coordinate system (check it with the
command). If you have undefined projection, (x,y) system, etc. then the latitude
can be defined explicitely for large areas by input raster map latin
with interpolated latitude values or, for smaller areas, a single region
latitude value lat can be used instead. All input raster maps must
be floating point (FCELL) raster maps. Null data in maps are excluded from
the computation (and also speeding-up the computation), so each output raster
map will contain null data in cells according to all input raster maps. The
user can use r.null
command to create/reset null file for your input raster maps.
The specified day day is the number of the day of the general year where January 1 is day no.1 and December 31 is 365. Time time must be a local (solar) time (i.e. NOT a zone time, e.g. GMT, CET) in decimal system, e.g. 7.5 (= 7h 30m A.M.), 16.1 = 4h 6m P.M..
Setting the solar declination declin by user is an option to override the value computed by the internal routine for the day of the year. The value of geographical latitude can be set as a constant for the whole computed region or, as an option, a grid representing spatially distributed values over a large region. The geographical latitude must be also in decimal system with positive values for northern hemisphere and negative for southern one. In similar principle the Linke turbidity factor (linkein, lin ) and ground albedo (albedo, alb) can be set.
Besides clear-sky radiations, user can compute a real-sky radiation (beam, diffuse) using coefbh and coefdh input raster maps defining the fraction of the respective clear-sky radiations reduced by atmospheric factors (e.g. cloudiness). The value is between 0-1. Usually these coefficients can be obtained from a long-terms meteorological measurements.
The solar irradiation or irradiance raster maps beam_rad, diff_rad , refl_rad are computed for a given day day, latitude lat (latin), elevation elevin, slope slopein and aspect aspin raster maps. The program uses the Linke atmosphere turbidity factor and ground albedo coefficient. A default, single value of Linke factor is lin=3.0 and is near the annual average for rural-city areas. The Linke factor for an absolutely clear atmosphere is lin=1.0. See notes below to learn more about this factor. The incidence solar angle is the angle between horizon and solar beam vector. The solar radiation maps for given day are computed integrating the relevant irradiance between sunrise and sunset times for given day. The user can set finer or coarser time step step used for all-day radiation calculations. A default value of step is 0.5 hour. Larger steps (e.g. 1.0-2.0) can speed-up calculations but produce less reliable results. The output units are in Wh per squared meter per given day [Wh/(m*m)/day]. The incidence angle and irradiance/irradiation maps can be computed without shadowing influence of relief by default or they can be computed with this influence using the flag -s. In mountainous areas this can lead to very different results! The user should be aware that taken into account the shadowing effect of relief can slow down the speed of computing especially when the sun altitude is low. When considering shadowing effect (flag -s) speed and precision computing can be controlled by a parameter dist which defines the sampling density at which the visibility of a grid cell is computed in the direction of a path of the solar flow. It also defines the method by which the obstacle's altitude is computed. When choosing dist less than 1.0 (i.e. sampling points will be computed at dist * cellsize distance), r.sun takes altitude from the nearest grid point. Values above 1.0 will use the maximum altitude value found in the nearest 4 surrounding grid points. The default value dist=1.0 should give reasonable results for most cases (e.g. on DEM). Dist value defines a multiplying coefficient for sampling distance. This basic sampling distance equals to the arithmetic average of both cell sizes. The reasonable values are in the range 0.5-1.5. The values below 0.5 will decrease and values above 1.0 will increase the computing speed. Values greater than 2.0 may produce estimates with lower accuracy in highly dissected relief. The fully shadowed areas are written to the ouput maps as zero values. Areas with NULL data are considered as no barrier with shadowing effect .
The maps' history files are generated containing the following listed
parameters used in the computation:
- Solar constant 1367 W.m-2
- Extraterrestrial irradiance on a plane perpendicular to the solar beam [W.m-2]
- Day of the year
- Declination [radians]
- Decimal hour (Alternative 1 only)
- Sunrise and sunset (min-max) over a horizontal plane
- Daylight lengths
- Geographical latitude (min-max)
- Linke turbidity factor (min-max)
- Ground albedo (min-max)
The user can use a nice shellcript with variable day to compute radiation for some time interval within the year (e.g. vegetation or winter period). Elevation, aspect and slope input values should not be reclassified into coarser categories. This could lead to incorrect results.
Currently, there are two modes of r.sun. In the first mode it calculates solar incidence angle and solar irradiance raster maps using the set local time. In the second mode daily sums of solar irradiation [Wh.m-2.day-1] are computed for a specified day.
The clear-sky solar radiation model applied in the r.sun is based on the work undertaken for development of European Solar Radiation Atlas (Scharmer and Greif 2000, Page et al. 2001, Rigollier 2001). The clear sky model estimates the global radiation from the sum of its beam, diffuse and reflected components. The main difference between solar radiation models for inclined surfaces in Europe is the treatment of the diffuse component. In the European climate this component is often the largest source of estimation error. Taking into consideration the existing models and their limitation the European Solar Radiation Atlas team selected the Muneer (1990) model as it has a sound theoretical basis and thus more potential for later improvement.
Details of underlying equations used in this program can be found in the reference literature cited below or book published by Neteler and Mitasova: Open Source GIS: A GRASS GIS Approach (published in Kluwer Academic Publishers in 2002).
Average monthly values of the Linke turbidity coefficient for a mild climate (see reference literature for your study area):
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec annual
mountains 1.5 1.6 1.8 1.9 2.0 2.3 2.3 2.3 2.1 1.8 1.6 1.5 1.90
rural 2.1 2.2 2.5 2.9 3.2 3.4 3.5 3.3 2.9 2.6 2.3 2.2 2.75
city 3.1 3.2 3.5 4.0 4.2 4.3 4.4 4.3 4.0 3.6 3.3 3.1 3.75
industrial 4.1 4.3 4.7 5.3 5.5 5.7 5.8 5.7 5.3 4.9 4.5 4.2 5.00
Planned improvements include the use of the SOLPOS algorithm for solar geometry calculations and internal computation of aspect and slope.
g.region rast=elevation.dem r.sun -s elev=elevation.dem slop=slope asp=aspect beam=beam_map day=180 r.colors beam_map col=grey d.his i_map=beam_map h_map=elevation.dem
Hofierka, J. (1997). Direct solar radiation modelling within an open GIS environment. Proceedings of JEC-GI'97 conference in Vienna, Austria, IOS Press Amsterdam, 575-584.
Jenco, M. (1992). Distribution of direct solar radiation on georelief and its modelling by means of complex digital model of terrain (in Slovak). Geograficky casopis, 44, 342-355.
Kasten, F. (1996). The Linke turbidity factor based on improved values of the integral Rayleigh optical thickness. Solar Energy, 56 (3), 239-244.
Kasten, F., Young, A. T. (1989). Revised optical air mass tables and approximation formula. Applied Optics, 28, 4735-4738.
Kittler, R., Mikler, J. (1986): Basis of the utilization of solar radiation (in Slovak). VEDA, Bratislava, p. 150.
Krcho, J. (1990). Morfometrická analza a digitálne modely georeliéfu (Morphometric analysis and digital models of georelief, in Slovak). VEDA, Bratislava.
Muneer, T. (1990). Solar radiation model for Europe. Building services engineering research and technology, 11, 4, 153-163.
Neteler, M., Mitasova, H. (2002): Open Source GIS: A GRASS GIS Approach, Kluwer Academic Publishers.
Page, J. ed. (1986). Prediction of solar radiation on inclined surfaces. Solar energy R&D in the European Community, series F – Solar radiation data, Dordrecht (D. Reidel), 3, 71, 81-83.
Page, J., Albuisson, M., Wald, L. (2001). The European solar radiation atlas: a valuable digital tool. Solar Energy, 71, 81-83.
Rigollier, Ch., Bauer, O., Wald, L. (2000). On the clear sky model of the ESRA - European Solar radiation Atlas - with respect to the Heliosat method. Solar energy, 68, 33-48.
Scharmer, K., Greif, J., eds., (2000). The European solar radiation atlas, Vol. 2: Database and exploitation software. Paris (Les Presses de l’ École des Mines).
Joint Research Centre: GIS solar radiation database for Europe and Solar radiation and GIS
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