In order to provide transparancy and the possibility for others to either reproduce our results or to develope our methods 14 further, we have made all non-confidential data sets as well as all our code with documentation available on the Envidat Data 15 Platform, doi:10.16904/envidat.47. The current version is the orinigal code use for this paper, but we will soon publish a 16 second version that is more versitile and easier to use. Data from SwissGrid and MeteoSwiss cannot be openly distributed but 17 can be made available for research upon request. PV production calculated with the SUNWELL model (detailed) 19 The electricity production of any PV panel is determined by the shortwave radiation that vertically impinges onto the panel 20 surface. Other factors such as age of the panel, ambient temperature and panel technology further affect the panel efficiency, 21 but in this study, we use standard values, since the focus is on input variability and not on panel efficiency. The solar input, i.e. 22 plane of array (POA) irradiance can be accurately modeled and varies by far the most with time and space compared to all 23 other factors. The two basic inputs are: Global Surface Incoming Shortwave radiation (SIS) and Direct Incoming Shortwave 24 radiation (SISDIR). The former indicates how much energy reaches a unit horizontal surface in total. It is the sum of direct 25 beam radiation which reaches the earth's surface on a straight trajectory from the sun and of diffuse radiation which has been 26 scattered on its pathway through the earth's atmosphere. Since the ratio of beam and diffuse radiation varies throughout the 27 day and with the presence of clouds, we use SISDIR to compute the diffuse component. Both, SIS and SISDIR are derived from 28 METEOSAT satellite imagery and were provided by MeteoSwiss at hourly resolution on a 1.25 degree minute grid (1). Over Switzerland this roughly corresponds to a pixel size of 1.6 km in East-West direction and 2.3 km in North-South direction. The 30 products used in this study were computed using the Heliomont algorithm (2) which is specifically conceived for mountainous 31 terrain and includes a snow-cloud discrimination that avoids the misqualification of snow cover as clouds, which would lead 32 to an underestimation of surface irradiance and has been shown to bias irradiance estimates (3, 4). More details of the data 33 acquisition and post-processing are described by Stoeckli (2). Quality assessments of this product are presented below in the 34 section 'Evaluation of the SIS radiation product from Meteosat imagery' . 35 Figure S1 visualizes the modeling steps to compute the POA irradiance from incoming shortwave radiation and the installation 36 geometry of the PV panel. After the separation of global into direct and diffuse radiation, we use the isotropic sky model 37 developed by Liu and Jordan (5) given in Equation 1 to transpose each of the components onto the panel surface. For the 38 transposition of the direct beam radiation I b , the angle between instantaneous beam and panel normal needs to be calculated 39 for every time step, as it changes throughout the day and throughout the year. This angle determines the ratio R b of beam 40 irradiance on the tilted surface to the irradiance on the horizontal surface. Panel azimuth determines at which time of the day 41 maximum beam radiation is collected. Depending on the tilt, this effect will be more or less pronounced. The closer the panel 42 is to a horizontal position, the smaller the effect of the azimuth angle. The tilt also decides at which time of the year the panel 43 is most productive. Steeper tilts elevate production in winter, while shallower angles give preference to summer production. 44 Diffuse radiation I d , reaches the panel from the portion of the sky that is within the panel's hemisphere. Hence the steeper the 45 panel tilt β is from the horizontal, the smaller the portion of the sky that contributes to the panel's diffuse radiation budget. 46 The isotropic sky model for the diffuse radiation assumes that all directions contribute the same amount of diffuse radiation. We convert POA into electricity production assuming a constant system efficiency of 15%. Ground reflected shortwave radiation 56 The amount of radiation that is reflected back from the ground is a function of the surface albedo, which varies between 57 different land surface cover types. Water, wet soil and forests reflect between 5%-15% of the incoming radiation, while fresh 58 snow can reach values as high as 95%. To account for this large discrepancy and the variation throughout the year, we use the 59 Meteosat-derived albedo product MSG.ALB. It provides hourly albedo values, which sets it apart from many other albedo 60 products that are commonly available at daily resolution. Due to its high temporal resolution it can account for the significant 61 change in albedo due to evolving solar zenith angle throughout the day. MSG.ALB provides the all-pixel albedo and not the 62 albedo of the snow-covered portion of the pixel. Since we cannot predict where in the pixel the snow is present and whether it is 63 within the view shed of the PV panel, it seems more prudent to work with the lower albedo value of the mixed pixel. However, 64 with expert knowledge of local professionals, one could envision placing PV panels in a location with a ground reflectance that 65 2 of 10 Annelen Kahl, Jerome Dujardin, Michael Lehning is higher than the pixel-wide average value. In order to visualize a simplified representation of temporal and spatial presence of 66 snow cover we compute the snow cover duration (SCD) in number of days for each pixel. A day is classified as snow day if the 67 pixel albedo given by the MSG.ALB product is 0.4 or higher. SCD is a commonly used parameter to characterize the presence 68 of snow and it has been calculated previously by Huesler et al. (8) for the entire Alps. Their analysis was based on AVHRR 69 imagery and yields matching trends for the mountains of Switzerland. Evaluation of the SIS radiation product from Meteosat imagery 71 The HelioMont product has been validated against five different ground measurement networks (2) and three ground measurement 72 stations (3). The largest errors in diffuse and direct radiation on shorter time scales were found on summer cloud-free days 73 during the central hours of the day and were associated to the use of monthly climatological means for areosol characteristics 74 and water vapor column (instantaneous locally measured values yield far superior results). The evaluation of monthly average 75 values shows that the seasonal cycle of all radiation components is well reproduced. In Davos for example (one of the evaluation 76 sites for our model and a typical alpine site with complex terrain) a mean average bias of 12W/m 2 , was found. To compliment 77 the findings from literature we conducted a small evaluation study ourselves to have a closer look at seasonal variations in 78 accuracy of the SIS product. For the years 2014-2016 we compared daily total irradiance values from two station of the Alpine 79 Surface Radiation Budget (ASRB) network (9) with the daily values of the corresponding satellite pixels. The evaluation sites 80 are located at Weisfluhjoch (WFJ, 2693m) and in the town of Davos (SLF, 1560m). The statistics in Table S1 show good 81 agreement at annual scale: total irradiance is underestimated by only 4% and 1% for SLF and WFJ respectively. When we 82 look at the temporal development of this underestimation throughout time ( Figure S2 ), we can see clear seasonal trends. The 83 difference ASRB -SIS is highest in spring and fall and smaller or reversed in summer and winter. Especially at Weisfluhjoch 84 positive and negative deviations almost compensate each other throughout the year, as represented by the small mean difference, 85 but relatively high RMSD. For our study we can assume simultaneous deviations of modeled from actual electricity production. Topographic shading effects in the radiation product 87 Obstruction of solar irradiance can significantly lower the productivity of a PV panel and needs to be taken into account when 88 selecting the installation site. In flat, urban areas the major concerns are surrounding buildings, which vary over very small 89 scales and cannot be accounted for in our model. We have to assume that any individual PV owner would consider this prior 90 to installation. In the mountains the surrounding terrain can cast large shadows that might decrease the time of direct solar 91 irradiance by several hours. This is particularly true lower down in the valleys and during the winter months. The HelioMont 92 algorithm that calculates the irradiance product used in this paper accounts for terrain shading through the use of a digital 93 elevation model (DEM) (10). For each pixel, 100 horizon angles of the surrounding terrain are calculated over a radius of 25km. 94 That corresponds to an azimuthal sector of 3.6 degrees between individual horizons. For any instance of the sun falling below 95 the local horizon, the pixel's direct beam irradiance is set to zero. More details about the DEM and the associated calculations 96 of terrain shading are given in (2) (section 8.6, 9.2 and 9.4) 97 Maximum allowed cover fraction for PV installations 98 Table S2 lists the different maximum cover fractions that we impose for various landsurface cover types throughout Switzerland. They represent a best guess as to how much PV can realistically be placed in the respective types of land. Urban and industrial 100 land receive the highest percentage, since we count all south oriented roofs to be potential installation zones in addition to 101 public places, gardens and housefronts. As panel tilt increases, the foot print of the installed panels decreases drastically until 102 vertical panels simply represent a line on the ground, with all the surface area stacked in the vertical dimension. At this point 103 we have not undertaken a detailed GIS study to assess whether all the selected pixels are accessible by road, but the Alps and 104 especially Switzerland has a well-developed road network reaching high elevations and due to the large amount of hydropower 105 installations, even grid connections are often already in place. We would also like to remind the reader that this paper does 106 not measure up to an exhaustive development plan for PV installations in Switzerland, rather we want to introduce a new 107 approach toward the seasonal energy gap and provide information about the available potential and physical constraints; It is 108 our hope to trigger the interest of researchers from different backgrounds, such that subsequent studies can shine light on the 109 many questions that remain unanswered here. 110 Simplifications in our estimate of electricity production 111 In view of our study's objective -analyzing the relative spatial variability of PV production in different geographic regions -112 we decided to lump together all contributions to the overall system efficiency and work with one universal, constant efficiency 113 of 15%. This entails the following assumptions (and our respective justifications): 114 1. Constant panel DC efficiency -Assuming spatial and temporal invariance of panel efficiency will likely result in an 115 underestimate of production in cold regions and during winter months (11, 12). Hence, we are putting the urban scenario at an 116 advantage with respect to the mountain scenario. 117 2. Constant reflection characteristics of the panel surface and their independence of tilt angle -This effect is indenpendent of 118 geolocation, it depends on material properties and might change or be completely eliminated in the future, hence we do not 119 consider any variability. 3. Constant AC/DC converter efficiency -The efficiency associated to all electric components that treat the panel's DC output 121 varies highly between different systems and also depends on their connection to the grid. The associated loss can be up to 122 30%, but newest maximum power point tracking (MPPT) algorithms can reach an efficiency of up to 99%. Assuming that all 123 potential new installations can reach the same level of performance, we keep it constant. 4. Neglecting degradation of panel 124 performance due to age -this factor is independent of location and will systematically develop at any installation (13) 125 5. Constant loss due to soiling by dirt, dust, pollen and other particles that cover the PV panel -Compared dry and sandy 126 areas this effect is relatively weak in the mid-latitudes of the northern hemisphere ( (14), Figure 2 ). Urban and industrial 127 areas in particular tend to have a higher rate of soiling than high-elevation mountainous regions. It has further been found 128 that accumulation of snow and its sliding off the panel has a better cleaning effect than rain and that steeper panel tilts thus 129 decrease the loss due to soiling (15). Again, accounting for this would improve modeled performance of installations at high 130 elevations and steep tilt angles compared to the urban roof-top installations. Many models that account for the technical 131 details above have been developed (16) (17) and more refined calculations for the transposition from incoming global radiation 132 to panel normal shortwave radiation have been proposed (18). Furthermore, the selection of online PV estimation tools has 133 grown over the past years. A good overview is given by (19). To show that our modeled electricity production captures the temporal behavior of actual production throughout the year we 136 conducted an evaluation study with four different PV installations in Switzerland. Table S3 shows the characteristics of the 137 individual installations. Our method to estimate PV production is conceived to compare the electricity production of a generic panel in various 139 different locations, and we assume the same overall system efficiency everywhere. Consequently, the model is not set up to 140 account for the individual system characteristics of specific panel types. As mentioned in the conclusions and in the 'limitations 141 of our model' section, there are several other aspects that lower the initial DC output efficiency of the PV panel. And indeed, 142 we see a consistent overestimation when we model production based on the factory-assigned panel efficiencies of the PV panels 143 used in this evaluation. To better capture the overall system efficiency of the different installations, we multiply the DC 144 output efficiency with the ratio of measured to modeled annual total production. Overall, the comparison in Figure S3 shows 145 a good agreement between measured and modeled behavior. The production profiles of the vertical installations with their 146 characteristic double peak in spring and fall stand in clear contrast to the production profiles of the shallow installations, which 147 have one large peak in summer. Below the seasonal scale, short term variations are also quite closely captured by SUNWELL. In addition to the modeled production that was calculated from satellite-derived products (blue lines), we also show modeled 149 production where the SIS time series of global incoming shortwave radiation was substituted with measured values of surface 150 incoming global radiation from the exact location of the PV installlations (9), available for Weisfluhjoch and Davos. These 151 latter results, depicted in green, allow us to estimate how much of the difference between modeled and measured electricity 152 production is due to an error in the satellite product and how much of it is due to the combined errors from the transposition of 153 surface-incoming to panel-normal radiation and the consecutive conversion to electricity. The green line lies almost exclusively 154 between the measured and modeled timeseries, splitting the difference in production into a small error contribution from the 155 satellite product and a larger contribution from the remaining model steps. Furthermore, we can observe a small but persistent 156 overestimation of production during the winter months. The fact that this difference is more expressed for the two shallow PV 157 installations at Laret and Lac des Toules suggests temporary accumulation of snow on the panels as possible cause. In the 158 smoothed times series it looks as if this is a continuous difference throughout the winter, but when we compare the two time 159 series at daily resolution it becomes apparent that the differences occur only very punctually. A second period of overestimation 160 during the summer months at SLF and WFJ can most likely be attributed to high temperatures on those vertically facades 161 that temporarily decreased the efficiency of the panel. 162 Those last two effects illustrate the shortcomings of our simplified model, as listed in the previous paragraph, and indicate a 163 clear direction to future improvements. 164 References 165 1. Dürr B, Zelenka A (2009) Deriving surface global irradiance over the Alpine region from METEOSAT Second Generation 166 data by supplementing the HELIOSAT method. International Journal of Remote Sensing 30(September 2013):5821-5841. 167 2. Stoeckli R (2017) The HelioMont surface solar radiation processing 2017 update. Scientific Report MeteoSwiss (93):122 pp. 168 3. Castelli M, et al. (2014) The HelioMont method for assessing solar irradiance over complex terrain: Validation and 169 improvements. Remote Sensing of Environment 152:603-613. 170 4. Dürr B, Zelenka A, Mueller R, Philipona R (2010) Verification of CM-SAF and MeteoSwiss satellite based retrievals of 171 surface shortwave irradiance over the Alpine region. International Journal of Remote Sensing 31(15):4179-4198. 172 5. Liu BYH, Jordan RC (1963) A Rational Procedure for Predicting The Long-Term Average Performance of Flat-Plate 173 Solar-Energy Collectors. Solar Energy 7(2):53-74. 174 6. Odermatt D, et al. (2005) Seasonal study of directional reflectance properties of snow. EARSeL eProceedings 4 (2):203-214. 175 7. Painter TH, Dozier J (2004) Measurements of the hemispherical-directional reflectance of snow at fine spectral and angular 176 A satellite-based snow cover climatology (1985-2011) for the 178 European Alps derived from AVHRR data. Cryosphere 8(1):73-90. 179 4 of 10 Annelen Kahl, Jerome Dujardin, Michael Lehning 9. Philipona R, Marty C (2001) Surface Radiation Budget and Cloud Forcing Over the Alps ed. von Bremen L. (A. Deepak 180 Pub, Hampton, Va.). 12. Singh P, Singh SN, Lal M, Husain M (2008) Temperature dependence of I-V characteristics and performance parameters 184 of silicon solar cell. Solar Energy Materials and Solar Cells 92(12):1611-1616. 185 13. Jordan D, Kurtz S, VanSant K, Newmiller J (2016) Compendium of photovoltaic degradation rates. Progress in photovoltaics 186 24:978-989. 192 95(12):3359-3369. 193 17. Sukamongkol Y, Chungpaibulpatana S, Ongsakul W (2002) A simulation model for predicting the performance of a solar 194 photovoltaic system with alternating current loads. Renewable Energy 27(2):237-258. 195
REF ) quantifies three possibilities for the potential of PV installations to increase PV production in winters when electricity is most needed.
The bright side of PV production in snow-covered mountains
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Environmental Science Medicine