GIS Based Estimation and Mapping of Local Level Daily Irradiation on Inclined Surfaces

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1 GIS Based Estimation and Mapping of Local Level Daily Irradiation on Inclined Surfaces SUMMARY Nektarios Chrysoulakis, Manolis Diamandakis and Poulicos Prastacos Foundation for Research and Technology Hellas Institute of Applied and Computational Mathematics, Regional Analysis Division, Vassilika Vouton, P.O. Box 1527, GR-71110, Heraklion, Crete, Greece {zedd2; diamanda; In this stud the spatial distribution of total solar irradiance at the surface was estimated taking into account the effect of topography on the surface orientation. The direct irradiance on surfaces normal to the solar beam, as well as the diffuse irradiance on horizontal surfaces were simulated using an atmospheric radiative transfer model and following a spatial model was developed, using GIS capabilities, to calculate the solar irradiance reaching any arbitrary oriented surface. A Digital Elevation Model derived by photogrammetric processing of satellite stereo imagery was used to define surface orientation. Moreover, satellite derived atmospheric parameters such as cloud cover and column water content were also used in radiative transfer model parameterisation. Finall the spatial distribution of daily irradiation was calculated and mapped. The application area was the broader area of Heraklion, Greece. The methodology and the spatial model developed in this study are considered capable of supporting local and regional level climatological, agrometeorological and forestry studies, as well as of providing professionals and decision makers with accurate local level estimations for spatial-temporal irradiance distribution and energy budget related parameters such as the daily irradiation. KEYWORDS: Solar Irradiance, Radiative Transfer, Inclined Surface, DEM, GIS Modelling. INTRODUCTION The detailed and quantitative knowledge of the earth radiation field is crucial for understanding and predicting the evolution of the components of the earth system. When solar radiation enters the atmosphere, a part of the incident energy is removed by scattering and a part by absorption. The scattered radiation is called diffuse radiation. A portion of this radiation goes back to space and a portion reaches the ground. The radiation arriving on the ground directly in line from the solar disk is called direct radiation. The amount of radiant flux incident upon a surface per unit area of that surface is called irradiance (I) and it is measured in watts per square meter. The knowledge of total solar irradiance (direct and diffuse) arriving at the earth s surface is important for the estimation of heating and cooling loads in architecture, as well as for agricultural applications such as the monitoring of the estimation of the photosynthetic activity and the modelling of evapotranspiration. It is also important for the design of certain solar energy applications such as photovoltaics. Radiative transfer models (Berk et al., 1983; Kneizys et al., 1988) have provided an accurate way to compute radiation levels at low and moderate spectral resolution. Ricchiazzi et al. (1998) developed the SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer) model, a software tool that computes plane-parallel radiative transfer in clear and cloudy conditions within the earth s atmosphere and at the surface. This model is a marriage of a sophisticated discrete ordinate radiative transfer module, low resolution atmospheric transmission models and Mie scattering results for light scattering by water droplets and ice crystals. At visible wavelengths clouds produce large variations in transmission over the typical range of cloud optical thickness. It is extremely difficult to constrain models with accurate 7 th AGILE Conference on Geographic Information Science 29 April-1May 2004, Heraklion, Greece Parallel Session 7.1- Remote Sensing II 587

2 estimates of cloud optical depth and microphysics, however the main cloud parameters can be estimated using satellite data. Even under clear skies, the uncertainty of atmospheric state, particularly aerosol turbidity and atmospheric water vapour distribution, produces significant variation in the short-wave simulations. Atmospheric water vapour by interacting with short-wave solar radiation is considered an important parameter for solar radiation models applied either locally or globally (Kiehl and Briegleb, 1992). Water vapour is the predominant absorber of the incoming solar radiation. Calculation of the vertical profile of the water vapour depends on the existence of radiosondes in the area under consideration. Due to this dependenc the spatial resolution of the water vapour profiles is low, a fact which results in considerable difficulties for the calculation of the incoming solar radiation. An alternative way for defining water vapour in the atmosphere is using the Precipitable Water (PW) defined as the total amount of water vapour in the zenith direction between the surface of the earth and the top of the atmosphere. PW can be estimated from radiosonde measurements (Chrysoulakis and Cartalis, 2000), as well as, from satellite observations such as MODIS (Moderate Resolution Imaging Spectrometer) measurements of near infrared solar radiation reflected by the land surface (Kaufman and Gao, 1992; 1998). Solar radiation data are measured at a limited number of climatic ground stations and before being used they need to be processed by climatologists. Instruments that make measurements of direct and diffuse solar irradiance have generally been expensive and require considerable attention (Muneer at al., 2002). At present, low spatial resolution data for Europe are commercially available (Huld et al., 2003; Scharmer and Greif, 2002; Remund et al., 1999). Geographic Information Systems (GIS) have been employed in several radiation models that calculate solar irradiance on a land surface (Kumar et al., 1997, McKenney et al., 1999). However, professional and decision makers need spatially continuous solar radiation data at high spatial and temporal resolutions. To derive spatial datasets from climatic measurements, interpolation techniques are used, e.g. splines, kriging. Empirical relations have been developed in several studies to take into account the effects of surface slope and orientation on the total irradiance, but most of the results are in graphical or tabular form. This may be good for engineers, who require only point specific data, but in forestry and ecological studies the variation of total irradiance over a study area is required (Kumar et al., 1997). To consider the spatial dynamics of radiation fields determined by local topograph solar radiation models based on Digital Elevation Models (DEMs) have to be used. The digital format of a DEM is capable of deriving additional information for various applications, so that elevation modelling has become an important part of the international research and development programs related to geospatial data. However, DEMs of usable details are still not available for much of the Earth, and when they are available they frequently lack sufficient accuracy (Toutin, 2001). In this stud the spatial distribution of total solar irradiance (I Total ) at any arbitrary oriented surface was estimated for the area of the north-central Prefecture of Heraklion, Greece. The direct irradiance (I Direct ) on surfaces normal to the solar beam, as well as the diffuse irradiance (I Diffuse ) on horizontal surfaces was simulated using SBDART. AVHRR (Advanced Very High Resolution Radiometer) and MODIS observations for cloud cover and PW, respectivel were used for SBDART parameterisation. Following, GIS was employed to develop a spatial model for the calculation of total solar irradiance reaching any inclined surface. In this model, a DEM derived from ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) stereo imagery was used in I Total calculations. Finall the spatial distribution of the total solar energy per unit area arriving at the surface during the course of a day (daily irradiation) was computed and mapped. DATA AND METHODOLOGY I Total was estimated by combining a radiative transfer with a DEM. In this wa both atmospheric and topographic effects to solar radiation reaching the ground were taken into account. Moreover, GIS computations were applied for the estimation of the spatial distribution of total solar irradiance at the surface at different time steps during the course of the day (the surface-sun geometry is continuously 588

3 changing), as well as for the computation and mapping of daily irradiation. The study area is shown in figure 1 as a pseudo-coloured composition of ASTER visible and near infrared spectral channels. Vegetated areas are presented in red and green, whereas urban areas are depicted in bluish tones. Thus, the city of Heraklion can be distinguished at the upper part of the image. Mt. Giouchtas Figure 1: The study area. The data used in this study were horizontal visibility observations from Heraklion Meteorological Station (35.33 N, E), AVHRR and MODIS data for May 20, 2003 and a DEM, which was derived by applying photogrammetric processes to overlapping ASTER stereo pairs. A digital stereo correlation approach based on a rigorous parametric model and set of stereo GCPs (Ground Control Points) were used to calculate parallax differences during the DEM creation. The accuracy of the produced DEM was better than 15 (planimetric and elevation). Following, slope and aspect images covering the study area were produced from this DEM. The slope image illustrates changes in elevation over a certain distance. This distance is the size of the DEM pixel. For a pixel at a given location, the elevations around it were used to calculate the slope. In practice, 3x3 pixel window around each pixel was used to calculate the slope. The aspect image illustrates the prevailing direction that the slope faces at each pixel. Aspect is expressed in degrees from north, clockwise, from 0 to 360. Due North is 0 degrees. A value of 90 degrees is due East, 180 degrees is due South and 270 degrees is due West. The value of 361 degrees is used to identify flat surfaces. As with slope calculations, aspect uses a 3 x 3 window around each pixel to calculate the prevailing direction it faces. SBDART model was used for the estimation of the surface irradiance at each elevation level. In order to determine the position of the sun with respect to an arbitrary oriented surface, it is necessary to prescribe the slope of the surface with respect to the horizontal position and its orientation to the local meridian. The total irradiance on the surface is the sum of the direct plus the diffuse irradiance. The total irradiance arriving at an inclined surface is given by the formula (Iqbal, 1983): I ( x, θ, t) = I ( x, t) cosθ + I ( x, β, t) (1) Total Direct where, x, z are the coordinates of the central point of the surface; β is the surface slope, measured from horizontal position, in degrees; θ is the angle of incidence for this surface, that is the angle between normal to the surface and the sun-earth vector, in degrees; Diffuse 589

4 t is the time of observation; I Total is the total solar irradiance at the inclined surface (W/m 2 ); I Direct is the direct irradiance at a surface normal to the sun-earth vector (W/m 2 ); I Diffuse is the diffuse irradiance at the inclined surface (W/m 2 ). For a surface oriented in any direction with respect to the local meridian (Figure 2), the trigonometric relation for the incidence angle has been given in past studies (Kondratyev, 1969; Coffari, 1977). This relation can be written in the following form (Iqbal, 1983): cosθ = cos β cos zs + sin β sinz scos( a as ) (2) where, θ is the angle of incidence, in degrees; β is the slope of the surface, measured from horizontal position, in degrees; a is the surface azimuth angle; that is, the deviation of the normal to the surface with respect to the local meridian, measured from North, in degrees; z s is the solar zenith angle, that is the angle between the local zenith and the sun-earth vector, in degrees; a s is the solar azimuth angle, that is the deviation of the projection of the sun-earth vector on the horizontal plane with respect to the local meridian, measured from North, in degrees. Figure 2: The solar geometry used in this study. The methodology used in this study is presented in Figure 3. The time and the coordinates of each surface determine the solar zenith (z s ) and azimuth angles (a s ) in each SBDART simulation. Typical trace gases concentrations (360 ppm for CO 2, 1.74 ppm for CH 4 and 0.32 ppm for N 2 O) were used. A standard surface type was used for the surface albedo parameterisation. A rural aerosol model (Ricchiazzi et al., 1998) was used for aerosol distribution parameterisation based on in-situ horizontal visibility observations. PW values were produced from integrated MODIS infrared retrievals of atmospheric moisture profiles at 5 5 km spatial resolution. Elevation values derived from DEM were interpolated with SBDART calculations for direct and diffuse irradiance as shown in Figure 3. For each pixel (x,y) at a given elevation (z) the I Direct and I Diffuse components were calculated. As a result, the spatial distributions of I Direct (x,t) and I Diffuse (x,t) were estimated. At this step, I Diffuse (x,t) values were calculated for 590

5 horizontal surfaces and I Direct (x,t) values were calculated for surfaces normal to the solar beam. For the estimation of the actual diffuse solar irradiance at each pixel, I Diffuse (x,t) values should be multiplied by the sky view factor of the surface. Therefore: β I ( x, β, t) = (1 ) I ( x, t) (3) Diffuse 180 where, β is the slope of the surface, measured from horizontal position, in degrees. For the estimation of the actual direct solar irradiance at each pixel, I Direct (x,t) values should be multiplied by cosθ, where θ is the angle of incidence. For each surface corresponded to a pixel of the DEM raster, z s and a s values are provided by SBDART, whereas β and a values are calculated from the DEM. The resulted cosθ values are used for the estimation of the spatial distribution of the direct solar irradiance at the surface I Direct (x,θ,t) and finall for the estimation of the total solar irradiance I Τotal (x,θ,t) using the Equation (1). Diffuse Figure 3: The methodology steps. In practice, for the estimation of I Τotal (x,θ,t), a spatial model based on the flowchart shown in figure 3 was developed using the ArcView 3.2 commercial software. At a first step, the inputs for this model were the satellite derived parameters including the DEM and the in-situ observations in raster format. As shown in figure 4, a pre-processing component was developed, which prepares the SBDART input file (ASCII file). Following, the SBDART is executed (Fortran code which is called by the spatial model using ArcView capabilities) producing an output file (ASCII file). This output file contains z s and a s values, as well as I Direct (x,t) and I Diffuse (x,t) values for the lower tropospheric levels. A postprocessing component was developed, which uses SBDART output files to produce the spatial distribution of z s, a s, I Direct (x,t) and I Diffuse (x,t) in raster format which are used, at a second step, as inputs for the spatial model. Following, the spatial model calculates the cosθ spatial distribution using β, a, z s and a s, values. The output of this model is the total solar irradiance at the surface in W/m 2. Moreover, if a given time period is divided into N time steps (assuming that the solar position is constant for each 591

6 time step), N SBDART simulations and N spatial model runs should be performed in order to estimate the spatial-temporal distribution of the surface irradiance for the study area. Figure 4: File exchange between the GIS-based spatial model and the SBDART. An useful parameter for engineers and decision makers is produced by integrating the aforementioned spatial-temporal irradiance distribution over a day to estimate the total solar energy per unit area arriving at each surface during the course of a day (daily irradiation): E t2 = t1 I Total ( x, θ, t) dt where, E is the daily irradiation (KWh/m 2 ); t is the time; t 1 is the sunrise time; t 2 is the sunset time; I Τotal is the total solar irradiance at the surface at the time t (W/m 2 ); The daily irradiation was estimated in this study as follows: The time period from 03:20 to 17:30 UTC (May 20, 2003) was divided to 85 time steps of 10 min (N = 85). SBDART was run once for each time step to calculate the average solar irradiance at the midpoint of the 10 min time interval, so the midpoint being taken to represent the average of the irradiance over the time interval. Following, the spatial model was employed to estimate I Τotal (x,θ,t) for each pixel using SBDART outputs from each run. Finall the spatial distribution of the daily irradiation was calculated for May 20, 2003 by summing I Τotal (x,θ,t) values: 85 KWh 1 E ( ) = 2 ITotal ( x, θ, t) i (5) m 6 i= 1 (4) RESULTS AND DISCUSSION The spatial model was run for each time step to calculate surface irradiance values during the course of the day. The estimated spatial distribution of total solar irradiance at selected times is presented in figure 5. Irradiance reached its maximum values around the local noon as it was expected, however the strong topography effect is evident in all cases. For example, at 10:30 UTC when the irradiance values for most of the study area are greater than 750 W/m 2, there are a lot of pixels with irradiance values less than 592

7 200 W/m 2. It is therefore observed in figure 5 that the sinusoidal change of surface irradiance with time is substantially modified by the topography in most surfaces of the study area. The location of the mountains (e.g. Giouchtas, shown in figure 1), and their effect to the local irradiance field is clearly depicted in all maps in figure 5. For example, the northwest areas of mountains can be easily detected in maps of 04:30 UTC and 05:30 UTC as low irradiance areas (bluish tones). These areas are obscured during the morning, but they receive larger amounts of solar radiation in the afternoon. The opposite phenomenon is observed for the southeast mountainous areas. They receive larger amounts of solar radiation during the morning, but they are obscured during the afternoon and therefore they receive only the diffuse part of solar irradiance (around 100 W/m 2 ). The location of extended horizontal areas is also evident in figure 5. In these areas, the spatial distribution of total solar irradiance is characterized by a spatial-temporal homogeneity. For example, at the area located northwest parallel to the north coast, the irradiance field is almost unchanged around the local noon (08:30 UTC to 11:30 UTC). In general, for pixels corresponding to horizontal surfaces the sinusoidal change of irradiance during the day is observed. Figure5: Spatial distribution of total solar irradiance at the surface for May 20, As it has already mentioned, the standard vegetation type has been used for surface albedo parameterisation in SBDART simulations. This surface type is representative for more than 90% for the 593

8 study area during the application period. Moreover, since MODIS derived PW and in-situ observed horizontal visibility values have been used, the error in SBDART predictions of total surface irradiance is less than 20 W/m 2, as it has been analysed by Ricchiazzi et al. (1998). Therefore, it can be stated that for what concerns horizontal surfaces, the irradiance estimation error in this study is around ± 20 W/m 2. For inclined surfaces the respective error depends on the uncertainty the spatial model introduces. The accuracy of the spatial model depends on the accuracy of the DEM, because the error introduced when the solar irradiance is estimated for inclined surfaces is dependent on the accuracy in estimation of the surface slope (β) and azimuth (α) values. In any case, the results of this study are not valid for urban surfaces for two reasons: a) the vegetation type is not appropriate for urban surface parameterisation and b) either the planimetric or the elevation accuracy of the DEM used in this study does not allow to take into account the spatial heterogeneity of the urban surface. Figure 6 shows the spatial distribution of the daily irradiation (KWh/m 2 ) for May 20, 2003 as it has been estimated from Equation (5). It is observed that south inclined and horizontal surfaces without obscure receive the highest amounts of solar energy during the course of the day. The higher the surface elevation, the higher the amount of solar radiation it receives. Figure 6: Daily irradiation (KWh/m 2 ) for May 20, A sensitivity analysis of the model is necessary in order to understand how the uncertainties in estimation of surface slope and azimuth angles affect the surface irradiance estimation. Figure 7 shows the dependence of solar irradiance of both surface slope and azimuth angle for five different times. The uncertainty in estimation of surface slope mainly affects the resulted irradiance at steep surfaces. This effect is stronger for the morning and for the afternoon cases. For surfaces with gentle slopes, the uncertainty in estimation of β lightly affects the resulting irradiance. Therefore, at the local noon (10:00UTC), for gentle surfaces an error of 10% in surface slope, results in less than 2.5% error in estimated irradiance value, whereas for steep surfaces it results in less than 5% error, for any combination of solar and surface azimuth angles. Moreover, 20% uncertainty in β, results in less than 3% and less than 12% errors in estimated I Total value, respectively. For the late morning case (08:00 UTC), as well as for the early afternoon case (12:00 UTC) the uncertainties in surface slope may cause higher errors in irradiance values. Thus, for gentle surfaces 10% uncertainty in β, results in around 3% error in estimated 594

9 irradiance, whereas for steep surfaces the resulted error is around 6%, for any combination of solar and surface azimuth angles. Moreover, 20% uncertainty in estimation of β, results in around 5% and 11% errors in I Total estimation, respectively. For the early morning case (06:00 UTC), as well as for the late afternoon case (14:00 UTC) the uncertainties in estimation of surface slope may cause high errors in irradiance as well. Thus, for gentle surfaces 10% uncertainty in β, results in around 5% error in estimated irradiance, whereas for steep surfaces the resulted error is around 5%, for any combination of solar and surface azimuth angles. Moreover, 20% uncertainty in β, results in around 11% and 9% errors in I Total, respectively. In the case when the solar azimuth angle is equal to the surface azimuth angle (α=α s ), the surface irradiance reaches its maximum values, for all surface slope angles, as it can be clearly seen from the solid curves in Figure 7 (α-α s =0). Moreover, for all α=α s cases, the surface irradiance reaches its maximum values when the surface slope angle is equal to the solar zenith angle, as it can be also seen in Figure 7. It practically means that the normal to the inclined surface is parallel to the sun earth vector and therefore all the amount of solar direct radiation reaches the surface. The latter is not valid for all combinations of solar and surface azimuth angles, because as the difference a-a s increases (or decreases), especially around the local noon, I Total reaches its maximum values for surfaces with slopes smaller than the solar zenith angle. Especially for a-a s > 60, I Total is maximum for small surface slopes. This effect is clearly depicted in figure 7 (10:00UTC) for a-a s around 90. In this case the difference in resulted I Total values between gentle and steep surfaces is maximum. For example I Total = 950 W/m 2 for β=5 while I Total = 725 W/m 2 for β=45. Therefore, the difference between the value of solar irradiance at a near horizontal surface and its value at a steep surface is 225 W/m 2 (about 25%). This difference lies around 18%, 11% and 9% for a-a s around 60, 30 and 0, respectively. The latter explains why horizontal surfaces receive the highest amounts of solar energy during the course of the day. 06:00 UTC 08:00 UTC 10:00 UTC 12:00 UTC 14:00 UTC Figure 7: Effect of surface slope change on estimated I Τotal (x,θ,t) values for four a-a s cases. 595

10 Figure 8 shows the effect of a-a s change on the difference in irradiance values between near horizontal (β=5 ) and steep (β=45 ) surfaces. It is observed that at the local noon (10:00 UTC) the absolute value of this difference is minimum for a-a s <30 ; two hours before (or later) it is minimum for 20 <a-a s <50, whereas four hours before (or later) it is minimum for 65 < a-a s <75. Figure 8: Effect of a-a s change on the difference in estimated I Τotal (x,θ,t) values between near horizontal (β=5) and steep (β=45) surfaces. CONCLUSIONS Solar irradiance over heterogeneous surfaces varies in response to the surface elevation, slope and orientation, as well as in response to the surface position in relation to neighbouring surfaces. While the estimation of solar irradiance on a relative flat surface is straightforward, it requires a dense network of stations for complex terrain. Many processes on land surfaces are influenced by the amount of solar energy that is intercepted on the surface. In environmental modelling, incoming radiation is needed as input. More specificall the estimation of direct and diffuse components of solar irradiance at inclined surfaces has many applications: in modelling the interaction of radiation with crop canopies, in studying the surface energy balance, in evapotranpiration modelling, in hydrological and climatologic modelling, in designing of certain solar energy applications such as photovoltaic systems etc. Low spatial resolution databases have been developed, but they do not pose sufficient accuracy and spatial detail needed for local studies, especially when complex terrain is considered. In this stud the spatial distribution of total solar irradiance at the surface was estimated with ± 20 W/m 2 for the north-central Prefecture of Heraklion on 20 May A DEM derived from ASTER stereo imagery was used to take into account the effect of topography on irradiance estimation. Slope and aspect values were calculated for each arbitrary oriented surface and finally the angle of incidence was calculated using the surface slope and aspect values, as well as the solar zenith and azimuth angles. A spatial model was developed to compute the total solar irradiance value at each arbitrary oriented surface. Inputs of this model were the resulted slope and aspect distributions as well as the SBDART simulation outputs. Surface irradiance values were calculated at 85 time steps during the course of the day and finall the spatial distribution of the daily irradiation was estimated for the study area. A model sensitivity analysis was performed to estimate the error in surface irradiance estimation caused by uncertainties in surface slope and aspect. Both the SBDART and DEM accuracies were considered quite satisfactory for large area surface irradiance spatial distribution estimation. Although the developed spatial model is independent of the spatial resolution of the DEM, it can be stated that it underestimates the surface irradiance, because the reflected from the terrain component radiation has not been taken into account. This component is more important in mountainous areas. For this reason, further research aiming at anisotropic reflectance correction is required to account for multi-scale topographic influences, solar and viewing geometr as well as for shadowing effects of neighbouring terrain features. Moreover, model results should be validated by field pyranometer data. 596

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