Design and Implementation of the Solar Analyst:
an ArcView Extension for Modeling Solar Radiation at Landscape Scales

Abstract   Introduction: Spatial solar radiation models   Theory, Design, & Implementation of the Solar Analyst   Methods   Results and Discussion   Conclusion   Acknowledgements   References   Contact Information

1. Introduction: Spatial Solar Radiation Models

1.1 Importance of Understanding Landscape Patterns of Solar Radiation

1.2 Spatial Solar Radiation Models

1.3 Features of the Solar Analyst

• versatile outputs: creates maps of direct, diffuse, global radiation, and direct radiation duration for any period (instantaneous, daily, monthly, biweekly .); also calculates skyview factors, sunmaps and skymaps, viewsheds, and horizon angles; analyses can be performed for whole DEMs, restricted areas, or specific cells;
• simple input: uses digital elevation models (DEMs) and a few readily available parameters;
• fast and accurate: uses an advanced viewshed algorithm for calculations;
• easy to use & broad accessibility: based in ArcView, which supplies the Solar Analyst with mapping, query, graphing, and statistical analysis functions in a powerful desktop GIS platform.

2. Theory, Design, and Implementation of the Solar Analyst

2.1 Theory: Use of Hemispherical Viewsheds in Solar Radiation Models

Viewshed Calculation: Viewsheds are calculated for each cell of the input DEM. A viewshed is the angular distribution of sky obstruction. This is similar to the view provided by upward-looking hemispherical (fisheye) photographs. A viewshed is calculated by searching in a specified set of directions around a location of interest (Fig. 1A), determining the maximum angle of sky obstruction, also referred to as horizon angle, in each direction (Fig. 1B)(Dozier and Frew 1990). For other unsearched directions, horizon angles are calculated using interpolation (Fig. 1C). Then the horizon angles are converted into a hemispherical coordinate system, in particular utilizing an equiangular hemispherical projection, which represents a three-dimensional hemisphere of directions as a two-dimensional grid (Fig. 1D). The resolution of the viewshed grid must be sufficient to adeduately represent all sky directions, but small enough to enable rapid calculations, e.g., 200 x 200 cells, 512 x 512 cells.  Each grid cell is assigned a value that corresponds with visible versus obstructed sky directions. The grid cell location, row and column, corresponds to a zenith angle q (angle relative to the zenith) and an azimuth angle a (angle relative to north) on the hemisphere of directions.

Sunmap Calculation: The amount of direct solar radiation originating from each sky direction is represented by creating a sunmap in the same hemispherical projection as for the viewshed (Fig. 2).  The skymap specifies suntracks, the apparent position of the sun as it varies through time.  In particular, suntracks are represented by discrete sky sectors, defined by sun position at intervals through the day and season (e.g., half-hour intervals through the day and month intervals through the season). The position of the sun (zenith and azimuth angles) is calculated based on latitude, day of year, and time of day using standard astronomical formulae (modified version of Gates 1980). Zenith and azimuth angles are projected into two-dimensional grids with the same resolution used for viewsheds. Two sunmaps are created, one to represent periods between the winter solstice and the summer solstice (December 22 to June 22)  and the other to represent periods between the summer solstice and the winter solstice (June 22 to December 22). Each sky sector of the sunmap is flood-filled with a unique identification number. For each sector, the time duration, the azimuth and zenith at its centroid are calculated. This calculation also accounts for partial sectors near the horizon.

Fig. 2. Annual sunmaps for 39^o N latitude using 0.5 hour intervals
through the day and month intervals through the year.

Penumbral Effects: For sunmaps that represent one day or less, penumbral effects must be taken into account. The Solar Analyst uses a solar disc semidiameter of 0.00466 radians near the zenith (0.2668^o) and larger values near the horizon (up to 1.6^o) (U.S. Department of Energy 1978) (Fig. 3). The solar disc appears larger near the horizon due to refraction but it does not differ significantly from 0.5^o after the sun has risen above an elevation angle of approximately 10^o.

Fig. 3. Penumbral effects are accounted for by constructing sunmaps with consideration of the solar disc size.
Note that  the sun track becomes wider near the horizon due to refraction.

Skymap Calculation: Unlike direct insolation, which only originates from directions along the suntrack, diffuse solar radiation can originate from any sky direction. Skymaps are constructed by dividing the whole sky into a series of sky sectors defined by zenith and azimuth divisions. Each sector is flood-filled with a unique identification number (Fig. 4). The zenith and azimuth angles of the centroid of each sector are calculated. Sky sectors must be small enough that the centroid zenith and azimuth angles reasonably represent the direction of the sky sector in subsequent calculations (e.g., sky sectors representing 5.625^o zenith intervals [16 zenith divisions] and 22.5^o azimuth intervals [16 azimuth divisions]).

Fig. 4. A skymap with sky sectors defined by 16 zenith divisions and 16 azimuth divisions.

Overlay of Viewsheds with Sunmaps and Skymaps: The skymap and sunmaps are overlaid on the viewshed (Figure 5). Gap fraction, the proportion of unobstructed sky area in each skymap or sunmap sector, is calculated by dividing the number of unobstructed cells by the total number of cells in that sector.

Direct Solar Radiation Calculation: For each sunmap sector that is not completely obstructed, solar radiation is calculated based on gap fraction, sun position, atmospheric attenuation and ground receiving surface orientation. A simple transmission model (Rich 1989, 1990, Pearcy 1989, Monteith and Unsworth 1990, Gates 1980, List 1971), which starts with the solar constant and accounts for atmospheric effects based on transmittivity and air mass depth, is implemented using the following equations.

Dir_tot = SDir _q,a             (1)

Dir_q,a = S_Const * t^m(q) * SunDur_q,a * SunGap_q,a * cos(AngIn _q,a)             (2)

where:

S_Const is the solar flux outside the atmosphere at the mean earth-sun distance, know as solar constant. Estimates of the solar constant range from 1338 to 1368 WM^-2. As a result of more precise measurements, the Commission for Instruments and Methods of Observation in 1981 agreed to adopt the World Radiation Center (WRC) solar constant (1367 WM^-2), as is used in the Solar Analyst.  Solar constant fluctuates slightly, a few tenths of a percentage over periods of years (Iqbal 1983), and this can be accounted for by differences in the distance between the earth and sun from the mean earth-sun distance;

t is transmittivity of the atmosphere (averaged over all wavelengths) for the shortest path (in the direction of the zenith);

m(q) is the relative optical path length (measured relative to the zenith path length). It is determined by the solar zenith angle and elevation above sea level. For zenith angles less than 80^o, it can be calculated using equation 3, below. For zenith angles greater than 80^o refraction is important. Various astronomical tables provide corrections for refraction at zenith angles greater than 80^o (e.g., List 1971, Table 137; Monteith and Unsworth 1990, p. 40).

SunDur_q,a is the time duration represented by the sky sector. For most sectors, it is equal to the day interval multiplied by the hour interval. For partial sectors (near the horizon), the duration is calculated using spherical geometry;

SunGap_q,a is the gap fraction for the sunmap sector;

AngIn _q,a is the angle of incidence between the centroid of the sky sector and the axis normal to the surface. It can be calculated using equation 4, below. The effect of surface orientation is accounted for by multiplying by the cosine of the angle of incidence.

m = EXP(-0. 000118 * Elev - 1. 638 * 10^-9 * Elev²) /cos(q)             (3)

where:

m is relative optical path length;

q is the solar zenith angle;

Elev is elevation above sea level in meters.

AngIn _q,a = acos[Cos(q)*Cos(G_z)+Sin(q)*Sin(G_z)*Cos(a-G_a)]             (4)

AngInSky _q,a is the angle of incidence between the intercepting surface and a given sky sector with a centroid at zenith angle q and azimuth angle a;

G_z is the surface zenith angle;

G_a is the surface azimuth angle.

Dif_q,a = R_glb * P_dif * Dur * SkyGap_q,a * Weight _q,a * cos(AngIn _q,a)             (5)

where:

R_glb is the global normal radiation (see equation 6 below);

P_dif is the proportion of global normal radiation flux that is diffuse. Typically it is approximately 0.2 for clear sky conditions and ranges from 0. 6 to 0. 7 for very cloudy sky conditions;

Dur is the time interval for analysis;

SkyGap_q,a is the gap fraction (proportion of visible sky) for the sky sector;

Weight _q,a is proportion of diffuse radiation originating in a given sky sector relative to all sectors (see equation 7, below);

AngIn _q,a is the angle of incidence between the centroid of the sky sector and the intercepting surface.

R_glb = (S_Const S (t^m(q) ) )/ (1 - P_dif)            (6)

Weight _q,a = (cosq₂ - cosq₁) / Div_azi             (7)

where:

q₁and q₂ are the bounding zenith angles of the sky sector;

Div_azi is the number of azimuthal divisions in the skymap.

Weight_q,a = (2cosq₂ + cos2q₂ - 2cosq₁ - cos2q₁) / 4 * Div_azi             (8)

Global radiation (Global_tot) is calculated as the sum of direct and diffuse radiation of all sectors. The above processes are repeated for each location on the topographic surface, thus producing an insolation map for the whole study area.

Global_tot = Dir_tot + Dif_tot              (10)

2.2 Design and Implementation of the Solar Analyst

Data input and output were implemented using the ArcView GridIO library (Fig 6), which comes with the ArcView Spatial Analyst. The user interface (Fig 7), which permits parameter input and calls the calculation engine, was developed using the ArcView Dialog Designer and Avenue. Because Avenue can not directly call C++ class member functions, another DLL, which calls the C++ member functions using nonmember functions, was developed as the interface between the calculation engine and Avenue. The Solar Analyst is based in ArcView, which supplies the Solar Analyst with its mapping, query, graphing and statistic analysis functions.

Fig. 6. Flow diagram showing the design of the Solar Analyst.
 
 

7A) Buttons and other tools allow calculation for interactively selected locations.

7B) Menus provide access to full capabilities.

7C) The output dialog window permits specification of custom output.

7D) The topographic parameter window permits specification of calculation parameters
relevant to the topographic surface being analyzed.

7E) The sky parameter window permits specification of parameters
relevant to sunmap and skymap calculations.
 
 

Fig 7. User interface of the Solar Analyst.

Program Specifications: While the model algorithm appears somewhat complex, the Solar Analyst is designed to be easy to use. The Solar Analyst only requires a few input parameters and users do not need to have extensive knowledge of atmospheric physics or meteorology.

Output of the Solar Analyst includes the following:

• Direct insolation, diffuse insolation, global insolation, direct radiation duration, and skyview factor in Arc/Info Grid format or ASCII text format;
• Skymaps and sunmaps in Arc/Info Grid format;
• Viewsheds (for specific cells) in Arc/Info Grid format;
• Horizon angles in ASCII text format.

• DEM file name: specifies an Arc/Info Grid file location. User has options to choose the following analysis areas:
 
• Whole DEM.
• Area covered by a mask grid (in Arc/info Grid format). For pixels near the edges of a DEM, the viewshed calculated may not be true because of the edge problems. Better results can be obtained if viewsheds are calculated only for areas away from the edge. This mask function is implemented for such purposes. While the Solar Analyst only calculates viewsheds for the masked area, it can use cells out of the mask grid boundary in calculating horizon angles.
• Locations by rows and columns in ASCII format.
• Locations by x and y coordinates in ASCII format.
• Locations from a point coverage in Arc/Info coverage or shape file format,
• Locations of graphic points in the view. This allows the user to specify points interactively and calculate the insolation or viewshed.
• Object height offset: this is used for location calculation only. For example, weather station sensors and solar powered devices are usually mounted above the ground.
• Slope and aspect information: users can choose from the following options:
 
• Grids: as calculated from DEMs, or in some special cases provided by the user for a unique purpose.
• Constant values: these values can be different from slope and aspect values calculated from the DEM. For example, solar radiation sensors are usually flat and mounted horizontally.
• ASCII files: field surveys often measure slope and aspect for each sample location. These measured values are generally more accurate than DEM derived values. Using measured values can improve the accuracy of analysis.
• None: perform calculations so that radiation values are corrected for angle of incidence. For example, some solar powered devices automatically change orientation to track the sun. In another example, a plant may have leaves in all orientations (random hemispherical distribution of orientations).
• Directions for viewshed calculation: because the viewshed calculation is highly intensive, horizon angles are only traced in the number of directions specified and horizon angles for other directions are calculated by interpolation.
• Elevation unit: in correction for air mass optical depth, the Solar Analyst performs calculations using elevation in meters. However, if the input DEM is in units other than meters, the program will convert the elevation into meters for calculations.

• Site latitude: this is used in such calculations as solar declination and solar position. Because the Solar Analyst is designed for landscape scales and local scales, it is acceptable to use one latitude value for the whole DEM.
• Sky size: this is the resolution for the viewshed, skymap, and sunmap.
• Zenith and azimuth divisions: these define the sky sectors of the skymap.
• Diffuse radiation model: currently users can choose either the uniform diffuse model or the standard overcast diffuse model.
• Diffuse proportion: the proportion of global normal radiation flux that is diffuse.
• Transmittivity: because the program will correct elevation effects, transmittivity should always be given for sea level. Also it is important to note the inverse relation between transmittivity and diffuse proportion when deciding values to use for calculations.
• Time configuration: the time for which insolation is to be calculated can be specified as follows:
• Within one day: user can specify the day of year, starting time, and ending time. When starting time equals the ending time, instantaneous solar radiation is calculated.
• Special days: for summer solstice, equinox, and winter solstice.
• Multi-day: users can specify the start day, end day, year, day interval, and hour interval for calculations. When end day is smaller than start day, the end day is considered to be in the following year of the start day. A day interval of 7 corresponds with weekly intervals, whereas a day interval of 14corresponds with biweekly intervals.
• Whole year with monthly intervals: this is a special multi-day calculation in that the day intervals are not constant.
• For each interval: this check box gives users the flexibility to calculate total insolation or insolation for each session.  For example, for multiple days with a day interval of 7, checking this box will create weekly insolation; otherwise, only the total insolation during the start day and end day are calculated. In another example, for within day with an hour interval of 1, checking this box will create hourly insolation calculations; otherwise, only the total insolation over the day is calculated.

3. Methods

3.1 Study Site

3.2 Weather Stations & Insolation Monitoring

3.3 Digital Elevation Model

3.4 Viewshed Calculation and Hemispherical Photographs

3.5 Insolation Patterns

Annual Insolation Patterns: Monthly insolation was calculated throughout the course of the year for the "research meadow" site assuming transmittivity of 0.5 and diffuse proportion of 0.3. Again slope and aspect were set to zero, the viewshed was calculated along 64 directions, sky size was set at 512 x 512 cells, and the skymap was created using 18 zenith divisions and 16 azimuth divisions. The sunmap was created using half-hour intervals through the day and monthly intervals through the year.

Spatial Patterns of Insolation: The Solar Analyst was used to calculate monthly direct, diffuse, global, and direct duration maps from the RMBL DEM (4 maps x 12 months = 48 maps total). The program was run on a Compaq Armada 7800 (333MHz CPU and 128M RAM). Parameters were set to transmittivity of 0. 5, diffuse proportion of: 0. 3, 32 viewshed calculation directions, a sky size of 200 x 200, a skymap of 8 zenith divisions and 8 azimuth divisions, and a sunmap of half-hour intervals through the day and monthly intervals through the year. The DEM consists of 1,591,590 (1410 x 1113) grid cells. To avoid edge effects, insolation was only calculated for the center area by applying a mask of 703 x 574 (403,522) cells (Fig. 8). When calculating viewshed, the pixels out of the mask were still used to calculate horizon angles.

3.6 Inferring Insolation from Incomplete Data

• Using measurements from nearby monitoring stations to infer insolation for a broader area: A histogram was constructed to permit examination of the extent of spatial variation in annual global insolation, based on the direct and diffuse maps of insolation for the study area.
• Grouping aspect and slope: Summary statistics of insolation for the month of June (minimum, maximum, and mean) were calculated for six categories of slope and aspect in the study area: aspects of north vs. south and slopes of 0-29^o, 30-59^o, and 60-90^o. These statistics permit examination of the validity of using such categories.
• Using sinusoidal curves to simulate daily insolation patterns: Daily insolation curves were calculated for four locations with different aspects (north-, south-, east-, and west-facing) to examine the influence of orientation on the shape of the daily insolation curve.
• Calculating diffuse solar radiation as a proportion of direct or global solar radiation: The same daily insolation curves for locations with different aspects, along with their viewsheds, were used to examine the validity of calculating diffuse radiation as a proportion of direct or global measurments from sensors.
• Using direct duration to estimate direct insolation: We calculated correlation coefficient between direct duration and direct, diffuse, and global radiation for each month based on the insolation maps for the study area.

3.7 Sensitivity Analysis

• Viewshed Calculation Directions: To assess tradeoffs between calculation speed and accuracy, we tested the sensitivity of the Solar Analyst to different numbers of calculation directions using the RMBL DEM (a topographically complex area) and another DEM in Kansas (a low-relief area). For each of the two DEMs, horizon angles for three locations were computed at 8, 16, 24, 32, 40, 64, 128 and 360 directions. Calculated viewsheds were compared with the 360-direction viewshed.
• Sky resolution and skymap divisions:  To assess tradeoffs between calculation speed and accuracy, we tested the sensitivity of the Solar Analyst to two sets of sky resolution and skymap divisions:  400 x 400 sky size with 16 x 16 skymap divisions and 200 x 200 size with 8 x 8 skymap divisions.
• Sunmap divisions: To assess tradeoff between calculation speed and accuracy, we tested the sensitivy of the Solar Analyst to various combinations of sunmap divisions, ranging from 0.2 to 1.0 hour intervals through the day and between one day and one month intervals through the year.
• Elevation effects: We assessed the importance of elevation corrections in the Solar Analyst by examining relations between elevation, optical air mass, and insolation.

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4. Results and Discussion

4.1 Viewsheds

4.2 Insolation Patterns

Fig. 9 Comparison of calculated and observed insolation for typical clear day

Annual Insolation Patterns: The annual pattern of monthly insolation for the "research meadow" site diplays a distinct sinusoidal pattern, with a peak near the summer solstice and a trough near the winter solstice (Fig. 11). This pattern is driven primarily by the shifting angle of the suntrack with respect to the horizontal surface of interception.  In the field considerable variation exists from one day to another and from one year to another, caused mainly by variation in cloud cover. The Solar Analyst is able to calculate insolation for different atmospheric conditions, but information about variation in transmittivity and diffuse proportion parameters are not typically available. The Solar Analyst can only be used to examine short-term non-systematic variation in cases where detailed insolation monitoring is available for the region of interest. More commonly, the Solar Analyst is best suited for comparing daily patterns and seasonal patterns as they vary spatially.

Fig. 10 Annual pattern of direct, diffuse and global insolation for average clear day for the weather station at the research meadow

Spatial Patterns of Insolation: It required three hours to calculate the monthly direct, diffuse, global, and direct duration maps (48 maps total). Maps of direct and diffuse insolation for the whole year are shown in Figs. 11 and 12. Among the distinct patterns that can be observed by inspection of the annual direct radiation map (Fig. 11) are distinctly lower insolation on north-facing slopes as compared with south-facing slopes, as well as lower insolation levels in landscape positions with high sky obstruction along the suntrack (i.e., mountains toward the south, east, or west). By contrast, variation in the annual diffuse insolation map results primarily as a function of slope (higher slope causing lower values) and sky obstruction in any direction (more sky obstruction causing lower values).

4.3 Inferring Insolation from Incomplete Data

Fig 13. Variation of annual insolation (KWH/m²)  over the study area.

Grouping aspect and slope: Commonly locations with similar slopes and aspects are grouped in analysis to infer variation of insolation in the landscape. In the northern hemisphere it is generally assumed that south-facing slopes receive more insolation than north facing slopes, while the converse is is assumed in the southern hemisphere. While south-facing slopes do have mean insolation values higher than north-facing slopes during the month of June (Table 1), the statistic demonstrate that there are many cases where north-facing slopes receive more insolation than south-facing slopes.  This results because of local sky obstruction and the importance of early and late times during the day when the suntrack is far to the north.

Calculating diffuse solar radiation form direct or global solar radiation: Various relations between diffuse and global or direct model has been formulated (Liu and Jordan 1960, Erbs 1980). These models are used to calculate diffuse radiation components when only global radiation striking a horizontal sensor is measured, or when only direct insolation is calculated.  These models assume relations between diffuse and global or direct radiation without considering differences in viewsheds.  Further, these models have been widely used, even in mountainous regions, to derive daily or seasonal insolation patterns. A western slope may have as much as 100% diffuse radiation in the morning while only 15% diffuse radiation in the afternoon (Fig. XX). Similarly, some slopes may have 100% diffuse radiation during the entire winter season, but with a low proportion of diffuse radiation in the summer. High variability in slope orientation and viewsheds mean that this approach is generally not valid.

Using direct duration to estimate direct insolation: In the absence of solar radiation measurements, it is common practice to use direct duration as an estimate of direct insolation.  Correlations between duration and direct measurements ares higher in winter than in summer; while correlations between duration and diffuse measurements are higher in summer than in winter (Table 2). Correlations between duration and global measurements are higher in winter than in summer, but correlations can be as low as 0.41. The primary problem of using direct duration to predict insolation is that it does not account for either the angle of incidence or the length of the atmosphere traversed, both of which vary markedly through the day.

4.4 Sensitivity Analysis

Sky resolution: Similar results were obtained using 400 x 400 and 200 x 200 sky resolution. are highly similar. The correlation between the calculated global insolation is 0. 99994 at winter and 0.99995 at summer. The average value differs by less than 1%. Based on this testing, we concluded that a 200 x 200 sky size is sufficient for most purposes. Increasing sky size beyond this does not significantly improve model accuracy, but greatly increases computation time. For example, doubling the sky resolution from 200 x 200 to 400 x 400 quadruples the computation time. The Solar Analyst is implemented such that sky resolution is user defined. Further research may reveal cases where higher sky resolutions may be required.

Skymap divisions: Increased number of skymap divisions does not affect computation time greatly and does not improve global radiation much as shown in the above test. The results because diffuse radiation is generally a relatively small proportion of global radiation, and because we are using uniform sky or standard overcast models. In most situations 8 x 8 sky divisions is sufficient. In cases where diffuse radiation is of major interest, skymap divisions should be increased to 16 x 16 or even more. Skymaps of 18 zenith divisions (5-degree intervals) and 16 azimuth divisions (22.5-degree intervals) are commonly employed for detailed studies (Rich et al. 1999).

Sunmap divisions: Changing sunmap divisions does not change computational time much, but can improve calculation accuracy. In general, a 0.2 hour interval through the day is sufficient for daily insolation calculations, and a 0.5 hour interval is sufficient for multi-day calculations. The appropriate interval through the year is usually determined based on user needs.  For example, it should be 7 for weekly calculations, 14 for biweekly calculations, and monthly for monthly calculations.

Elevation effects: Generally, higher elevations receive more insolation than lower elevations. This results both because higher elevation have more open viewsheds and because the solar beam travels through less air mass (Fig. 15). For the vicinity of RMBL, the air mass is approximately half at the upper most elevation ( 4,340 m) as compared with the lowermost elevation (2,532 m).  While a change of 10 m has trivial effects on air mass and insolation, a change from sea level to 5,000 m can result in an increase of 52% in global radiation (Table 2). Another effect that partially counterbalances less air mass at higher elevations involves increased cloudiness with increasing elevation.

4.5 DEM Issues

• Elevation: Elevation is used directly in calculation of air optical depth. Though, elevation can deviate significantly from actual values, a 10 to 30 m error will only affect the air optical depth at 0.1%. Thus elevation errors do not produce significant effects on model accuracy.
• Slope and aspect: Poor DEM quality, limitations due to resolution, and edge effects can lead to inaccurate slopes and aspects. This is a potentially serious source of error because insolation values are corrected for angle of incidence, which ultimately depends on surface slope and aspect. The Solar Analyst has the ability to use surveyed slopes and aspects, which can improve accuracy for various applications.
• Viewsheds: Based on our experience, DEM does not generally change viewsheds greatly, however further work is needed to assess cases where viewshed errors may be significant.

DEM Projection Considerations: For viewshed calculations, the Solar Analyst assumes DEMs are in a projection that preserves direction. Most DEMs are available in projections that do not exactly preserve direction. For some commonly used projections (e.g. UTM), slight rotation of the study area to register correctly with true north can be sufficient to improve accuracy.

4.6 Limitations

Reflected Radiation: The Solar Analyst currently neglects the contribution of reflected radiation from the ground. This is valid for most uses. Reflected radiation is important for places where ground surfaces have high albedo, for example, snow-covered surfaces. Reflected radiation is complex because it varies with surface cover properties, surface orientation, and sun position. However, the algorithm utilized in the Solar Analyst permits calculation of simplified estimations of reflected radiation (Rich 1994). In the viewshed, direct and diffuse radiation come from visible sky directions, while ground-reflected radiation comes from obstructed directions. We can assign obstructed sky sectors a reflectance index that estimates the reflectance from ground features. The reflected radiation can then be calculated by summing the reflected radiation from obstructed sectors in a manner similar to the way direct and diffuse radiation calculated. Locations open to lower surfaces can receive reflected radiation from lower elevations. In these cases a hemispherical view downward could be used to account for upwelling radiation. In general,implement this approach is challenging.

Ground Features: Generally, a DEM only describes the topographic terrain and does not represent ground features such as plant canopies and human structures. Such ground features can have a, which can affect ground insolation strongly. If these ground features can be included in DEMs the Solar Analyst can still be used. For example, in urban areas it is possible to construct a high-resolution DEM that including buildings and other structures. Irregular features, such as plant canopies can also be converted into DEMs, but obtaining such data can be challenging (Rich et al. 1993, Price et al. 1995). For detailed characterization of specific locations, hemispherical photography can be a more appropriate technique (Rich 1989, 1990, Rich et al. 1999). With minor modification, the calculation engine of the Solar Analyst can use hemispherical photography to examine solar radiation regimes for specific locations. Further work is needed to fully integrate the Solar Analyst with spatially explicit canopy models such as those of Fournier et al. (1997). 

4. CONCLUSION

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