GOLD

The Effect of Weather on Solar Electricity Generation

An investigation on how weather impacts the generation of electricity of solar panels in Calgary.
Aarushi Bhargava
Grade 10

Hypothesis

If solar panels are used on the roof of a home in Calgary, then they can generate at least 7,200 kWh per year (average Alberta home’s annual consumption) and are a sustainable source of energy, considering the city’s varying weather conditions affecting temperature, visibility, precipitation, hours of daylight, solar radiation and cloud cover.

Research

The implementation of renewable energy sources is a strategy that combats climate change by harnessing the energy of natural sources without the release of greenhouse gases or other associated air pollution. Sustainable energy meets the demand for electricity without being depleted; not only is sustainable energy beneficial to the Earth, but clean energy  provides other benefits such as: creating jobs, making electric grids more resilient, expanding energy access, and lowering energy bills (Nunez, 2019). Due to the recent awareness among the public, there has been a recent boom in the solar industry (Rinkesh, 2017). However, in Calgary, due to the reliance on the oil industry, there is a misconception that solar panels are not a viable choice for electricity generation, as they will not work well in the city’s long and dark winters. This experiment explores factors such as daylight hours, solar radiation, cloud cover and precipitation impact the amount of electricity generated by solar panels in Calgary, to refute the assumption that solar panels cannot generate much electricity in Calgary.

Renewable energy is energy produced from natural sources without its depletion. It approximately accounts for 22% of the world’s electricity  and serves as an alternative to traditional energy production methods such as the burning of fossil fuels (Frewin, C., n.d., para. 4). Renewable energy is a growing field of science and has potential as the future of energy production because they use natural sources that do not deplete, and produce a smaller amount of greenhouse gas emissions. When fossil fuels are burned, greenhouse gases such as carbon dioxide, methane and nitrous oxides are released into the atmosphere where they trap heat. These greenhouse gases increase the temperature of the air, contributing to global warming.  Unlike traditional energy sources, renewable energy has minimal impacts on the environment (Frewin, n.d.).

Solar energy is a renewable source of energy created by harnessing the heat and/or light from the Sun to be used for solar heating, photovoltaics, and solar thermal energy usage. Solar technology is one of the fastest-growing and cheapest sources for renewable energy. Solar energy systems do not produce air pollutants or greenhouse gases, with few environmental impacts excluding the manufacturing process.

There are two main systems for capturing solar energy: photovoltaics and solar thermal capture. Photovoltaic (PV) solar energy is often used on small scale projects such as residential solar panel installations. In PV systems, when sunlight strikes a semiconducting material, such as silicon, electrons are knocked loose and set into motion, generating an electric current. The current is converted by an inverter, and electricity can be used or put back toward an electricity grid.  

On the other hand, solar thermal energy is used for industrial projects and utility solar installations. This type of solar energy production captures the heat from solar radiation. There are three types: low-temperature, mid-temperature and high-temperature, which are used for useful heat, heating water and electricity generation, respectively. Low-temperature energy systems use the heating and cooling of air to control the climate. This system is often used in passive solar building design, a building with properties that block light to control heat. Solar water heating systems are an example of mid-temperature solar thermal systems that capture the heat of sunlight that is expended in the heating of water. High-temperature systems are used on a larger scale and use mirrors to focus light on tubes of a specified liquid. This heated liquid then turns water into steam, generating electricity. This system mainly uses the heat of the sun to heat water (NASA, 2008).

Solar panels are composed of modules of photovoltaic cells which are connected electrically and packaged into a frame. Photovoltaic cells are composed of a semiconductor, often silicon. To generate electricity, an electric field is created by separating charges, much like a magnetic field. To create this field, the silicon is “doped” with other materials which give each layer of the photovoltaic system either a positive or a negative electrical charge. Most commonly, phosphorus is seeded into the top layer of silicon, giving it extra electrons, and resulting in a negative charge (N-type Silicon). The bottom layer is seeded with boron, giving it a positive charge (P-type Silicon). This process creates an electric field between the two layers. When a photon knocks an electron free, the electron will be pushed out of the silicon junction. Conductive metal plates on either side of the cell collect the electrons and transfer them to wires as shown in Figure 1 (Toothman & Aldous, n.d., para. 8-12).

Figure 1. Diagram of how photovoltaic technology operates. (Solar Metric, 2020)

Currently, there is limited statistical analysis on the effect of weather on electricity generation of solar panels. Solar panels can generate electricity through clouds, rain, and fog, but the electricity generation will be reduced. It is also suggested that rain and snow are beneficial for washing off any dust from the solar panels. Falling snow seems to have little effect, except when layers of snow settle on the solar panels, impeding electricity generation. However, the angle of the solar panels usually ensures that snow will slide off the panels and the black solar panels will absorb heat to melt the snow (Ficazzola, T., 2018). Finally, extreme temperatures, hot or cold, will reduce electricity production. The ideal weather for solar panels is cool, sunny days. It is also important to consider that solar panels are designed to withstand weather such as high wind speeds, hail and lightning, so such rare weather events have little effect on the solar panels (Padden, D., 2017).

Variables

Independent Variables: Temperature (°C), Visibility (m), Precipitation(mm), Daylight (hours), Solar radiation (kJ/m2), and Cloud cover (oktas).

Dependent Variable: Solar Energy Production in Wh

Controlled Variables: Angle of solar panels (30 degrees), Number of panels (30), 9.6 kW Solar PV system, Types of solar cells (monocrystalline Q.ANTUM solar half-cells)

Data Collection Start Date: August 1, 2019

Data Collection End Date: February 28, 2021

This experiment was conducted for 82 weeks and 4 days at a residential solar PV system in Calgary.

Procedure

First, daily solar energy production data was collected from the SolarEdge App which automatically records how much electricity the solar panels produces, for a duration of 82 weeks and 4 days. Data was then imported into a Master Data Spreadsheet included in Appendix A. 

Historical weather data for the independent variables: Temperature (°C), Visibility (m), Daylight (hours), Solar radiation (kJ/m2) and Cloud cover (oktas) were collected from the Calgary Weather Stats website (https://calgary.weatherstats.ca/download.html) for the same duration of 82 weeks. Data from Calgary Weather Stats was also verified through comparison of the data available from the Government of Canada’s Historical Climate Data Page. The precipitation data (mm) was collected from the Government of Canada’s Historical Climate Data (https://weather.gc.ca/) page, as there were inconsistencies in the data taken from Calgary Weather Stats. All data for the independent variables were sourced from the Calgary International A weather station. The station has a latitude of 51°07'21.000" N, longitude of 114°00'48.000" W and an elevation of 1,099.10 m. For reference, the climate ID is 3031092, the WMO ID is 71877, and the TC ID is YYC. The spreadsheet was set up with each independent weather variable in separate columns, with the data in the leftmost column, and electricity production in the rightmost column. On additional sheets, each individual variable was plotted in comparison to electricity production. This data was used to create scatter plots to compare each independent variable with electricity generation. 

A statistical analysis was also utilized in this experiment, and included calculating the correlation factor. The correlation factor is  in the form of the Pearson Product-Moment Correlation Coefficient, r,  which is a measure “of the strength of linear association between two variables”. The stronger the association between the two variables, the closer r will be to +1 or -1, with a value of 0 meaning this is no correlation. The sign of the correlation coefficient represents whether the relationship between the two variables is positive or negative. The calculation for r is shown below, where n is the number of data points, x is the independent variable and y is the dependent variable.  

Correlation Coefficient Equation

The second method of statistical analysis is, r2, the square of the correlation coefficient, which indicates if a change in one variable results in a change in the second variable. Multiplying this value by 100 provides the percentage of correlation between the two variables. The higher the percentage is, the stronger the connection between the two variables. (Excelchat, 2019, para. 1-3). 

In this experiment the correlation coefficient between each independent variable and the electricity output was calculated as well as the rvalue to determine the relationships between each independent variable and the dependent variable. All calculations were completed in Google Sheets. 

Observations

At mean daily temperatures lower than -20 degrees Celsius, there was little to no electricity generation. At mean daily temperatures higher than 20 degrees Celsius, the solar electricity generation decreases as well. The highest solar electricity generation is when the mean daily temperature is between 10-20 degrees Celsius.

Solar electricity generation increases when the number of daylight hours and solar radiation also increases. The solar radiation increase above 10,000 kJ/m2 does not result in much higher peaks for solar electricity production while the number of daylight hours have a directly proportional effect on solar electricity generation.

No significant relationship was observed between solar electricity generation and other independent variables (visibility, precipitation and cloud cover). 

Analysis

In order to consider the effects of different weather conditions on electricity generation, the correlation between independent variables (temperature, visibility, precipitation, daylight hours, solar radiation, and cloud cover) and electricity generation in Wh was graphed. 

Figure 2. Mean Temperature (°C) and Electricity Generation (Wh) over time.

Figure 3. Correlation between Electricity Generation (Wh) and Temperature (°C).

Figure 2 shows the scatter plot and trend lines of the temperature and electricity generation over time. In Figure 2, there is a lot of variation in the mean temperature data. However, the temperature and electricity generation follow a similar curve that is high during the summer seasons, and low during the winter. This curve can be explained by the rotation of the Earth. In the winter, the Northern Hemisphere faces away from the Sun, resulting in a lower average temperature, and a lower amount of sunlight reaching the Earth (Reasons for Seasons, n.d.). This explains why electricity generation is also lower, as a reduced amount of sunlight reaches the solar panels. In contrast, in the summer, the mean temperature is higher, and a higher amount of sunlight will reach the Earth, explaining why electricity generation is higher. Overall, there is some level of correlation between temperature and electricity generation. 

Figure 3 shows the scatter plot and trendline of the direct correlation between temperature and electricity. The x-axis is an independent variable, temperature, and the y-axis is the dependent variable, electricity generation. The data points for electricity generation show variation, but there are more frequent data points from -10 to 20 degrees Celsius. It is observed that there is a positive slope, where as the temperature increases, the electricity generation of the solar panels also increases. In understanding that there is some level of correlation between the two variables, the graph shows an r2 value of 0.46. This indicates a moderate level of positive correlation.

Figure 4. Visibility (m) and Electricity Generation (Wh) over time.

Figure 5. Correlation between Electricity Generation (Wh) and Visibility (m).

Figure 4 shows the scatter plot and trend lines of the visibility, which is measured in meters and electricity generation over time. In meteorology, visibility is the distance at which it is just possible to see an object or light (National Weather Service, n.d.). This has to do with the transparency of the surrounding air. In Figure 2, there is a lot of variation in the visibility data. The majority of the data is from 30,000 m to 45,000 m. However, there is a small similarity between the trendlines of the visibility and electricity generation. The visibility is a straighter curve than electricity generation, but follows a similar trend to electricity generation. This can be explained as generally the more visibility, the more photons are reaching the solar panels.  

Figure 5 shows the scatter plot and trendline of the direct correlation between visibility and electricity. It is observed that there is variation in the data points for electricity generation, but there is a general trend where the greater visibility, the greater the electricity generation. The r2 value for this graph is 0.229. This means that there is no statistical significance that the dependent variable is explained by the independent variable. This indicates little to no correlation. Solar panels still work without direct sunlight, explaining why there is no apparent relationship between the two variables. 

Figure 6. Precipitation (mm) and Electricity Generation (Wh) over time.

Figure 7. Correlation between Electricity Generation (Wh) and Precipitation (mm).

Figure 6 displays the scatter plot and trend lines of precipitation and electricity generation over time. Visibly, there is more variation in the electricity generation data compared to the precipitation data. Electricity generation follows a more specific polynomial curve that is higher in the summer and lower in the winter, whereas precipitation data is concentrated near 0 mm and is relatively low and consistent, as displayed in the trendline. This can be explained because precipitation has little impact on the solar panels itself, and the solar panels can still generate electricity without direct sunlight. Furthermore, the precipitation that occurs will not last for over a day, meaning that more electricity will be generated one the weather event has occurred. Overall, there is little correlation between precipitation and electricity generation. To get a better understanding of a correlation between precipitation and electricity generation, data would need to be taken over a period of hours during a day, rather than on an overall daily basis. 

Figure 7 shows the scatter plot and trendline of the correlation between precipitation and electricity. The data points for precipitation tend to be closer to 0, representing the little precipitation that is observed. It is observed that the trendline is at a negative slope such that the more precipitation, the less electricity generation. However, the r is 0.019, which is very small. This indicates that there is no significant relationship between the dependent variable and the independent variable. Generally, there is very little correlation between the precipitation and the electricity generated.

Figure 8. Hours of Daylight and Electricity Generation (Wh) over time.

Figure 9. Correlation between Electricity Generation (Wh) and Hours of Daylight.

Figure 8 compares the hours of daylight and electricity generation over time. There is a lot of variation in electricity generation data, whereas hours of daylight data points have very little variation and follow a polynomial curve. The trendlines between both variables over time are similar, which indicates some relationship between the variables. The pattern of the trendlines can be explained by the rotation of the Earth. During the winter, the northern hemisphere faces away from the Sun, resulting in shorter days whereas during the summer, the days are longer. As a result, the number of hours of daylight are higher during the summer, and lower during the winter. Because electricity generation is often related to the amount of sunlight, it would also follow a similar trend as the hours of daylight.

Figure 9 shows the correlation between hours of daylight and electricity generation. The x-axis shows the hours of daylight and the y-axis is the dependent variable, electricity generation. The data points for electricity generation show variation, but follow a trend such that as the greater hours of daylight, the greater amount of electricity generation. This is shown by the positive slope. The graph has an rof 0.45 which is a little less than an r2 value that would be considered significant. Hence, the hours of daylight have some determination on the electricity generated. This indicates a moderate level of positive correlation.

Figure 10. Solar Radiation and Electricity Generation (Wh) over time.

 

Figure 11. Correlation between Electricity Generation (Wh) and Solar Radiation.

Figure 10 shows the scatter plot and trend lines of solar radiation and electricity generation over time. There is a lot of variation in the electricity generation, but it follows a similar trend to that of solar radiation. Both variables peak around July and are lowest in December. Like hours of daylight, this trend can also be explained by the rotation of the Earth. During the summer, there is more solar radiation as the Northern Hemisphere directly faces the Sun. This results in the curve in the trendlines that is seen in Figure 10. From this, it can be determined that there is likely correlation between solar radiation and electricity generation. 

Figure 11 illustrates the correlation between solar radiation and electricity generation. The x-axis is the amount of solar radiation and the y axis shows electricity generation. This graph is similar to that of hours of daylight in that though there is variation in electricity generation, it increases when there is more solar radiation. This can be explained as solar panels work by collecting the energy from solar photons. It is observed that there is a positive slope between the two variables. Essentially, there is a moderate level of correlation between the two variables. The graph has an rvalue of 0.45. This further indicates that there is some correlation between the two variables. It can be noted that this ris the same as the rvalue determined when correlating daylight hours and electricity generation. Both these variables are closely related, which highlights the reliability of data collected. 

Figure 12. Cloud Cover (oktas) and Electricity Generation (Wh) over time.

Figure 13. Correlation between Electricity Generation (Wh) and Cloud Cover (oktas).

Figure 12 shows the scatter plot and trend lines of cloud cover and electricity generation over time. Cloud cover is a measure of the amount of sky that is covered in clouds from a scale of 0 to 8. There is a lot of variation in the cloud cover, but cloud cover averages around 4. Looking at the trendlines of the variables, there seems to be very little correlation as cloud cover has a very straight trendline whereas electricity generation follows a specific polynomial curve. This demonstrates that over time there is no similar pattern between the electricity generated and the cloud cover over time. However, to determine if cloud cover impacts the amount of solar electricity generated, Figure 13 must be analyzed.

Figure 13 shows the scatter plot and trendline of the correlation between cloud cover and electricity production. From the trendlines, it can be seen that there is a negative correlation between the two variables. This indicates that as one increases, the other decreases. This means that the more cloud cover there is, the less electricity will be generated. However, the r2 the value is 0.129 which is very small. This indicates little correlation between the two variables. Though there is indication of a trend between electricity generation and cloud cover, there is no real evidence that cloud cover impacts electricity generation.

Statistical Analysis

The statistical analysis in this experiment discusses the correlation coefficient, R squared, and the correlation percentage. In order for an independent variable to be considered as having a significant impact on the electricity output, the r value must be closer to 1 or -1 and the R squared percentage must be greater than 50%. The statistical analysis was used for temperature, visibility, precipitation, hours of daylight, solar radiation, and cloud cover.

Table 1. Statistical Analysis of Independent Variables in Comparison to the Dependent Variable

Independent Variables

Statistical Measures

r

r2

Correlation Percentage

Precipitation (mm)

-0.13850

0.01918

1.92%

Cloud Cover (oktas)

-0.35945

0.12920

12.92%

Average Visibility (m)

0.47844

0.22891

22.89%

Solar radiation (kJ/m^2)

0.66906

0.44765

44.77%

Daylight hours (hours)

0.67236

0.45206

45.21%

Mean Temperature (°C)

0.68394

0.46778

46.78%

A statistical analysis was used to quantify the correlation between the independent variables and dependent variables to identify which has the greatest impact on the amount of electricity generated by solar panels in Calgary. The independent variables represented different aspects of the weather, including temperature, visibility, precipitation, hours of sunlight, solar radiation, and cloud cover. Table 1 shows the statistical analysis of each variable ordered from least correlation to most. The variable with the least correlation was precipitation, with an r2 value of 1.92%. This shows that precipitation, including rain and snow, had the least effect on solar energy production. This can be explained as precipitation often does not last for an entire day, rather for a few hours at a time. This means that electricity will still be generated in the hours where there is more precipitation. To identify if precipitation has a bigger correlation, an hourly analysis would have to be conducted. Secondly, solar panels can still produce electricity regardless of whether or not there is direct sunlight. This proves that on a daily basis, precipitation has little effect on the electricity produced by solar panels. In comparison, the three variables with the greatest correlation were solar radiation, hours of daylight, and temperature. They each had a correlation above 45%. This indicates that the amount of electricity that is generated by solar panels is related to the availability of photons from the Sun. Furthermore, the graphs for each variable followed the pattern that would be expected of the Earth's rotation in relation to the Sun. In the summer, there is more available daylight due to the angle of the Earth and in the winter, there is less available sunlight. This is reflected in the electricity generation, as the most electricity would be generated during the summer. However, this does not indicate that no electricity was generated in the winter. During the winter, a significant amount of solar electricity was generated, despite the cold temperatures and the large amounts of snow. It should be noted that the temperature had the highest correlation, which was approximately 2% higher than the hours of daylight. This difference can be explained by a higher variation in temperature data compared to the consistent pattern daylight hours follow. In addition, the temperature is often related to the amount of sunlight available in a given location. Hence it can be concluded that the amount of daylight is most influential on solar electricity production in Calgary. However, none of the variables had a correlation over 50%. This indicates that there is no statistically significant correlation between the independent variables and solar electricity production.

The daily generation of electricity from July 2019 and June 2020 was summed to determine that approximately 11,377 kWh were generated from this specific residential PV system. Of this, the net solar electricity sent to the grid was 4,254 kWh. Assuming that the average Albertan household consumes 7,200 kWh (How much Electricity Does the Average Albertan Consume?, 2015) per year, the solar panels could still generate enough excess electricity for 58% of another home’s electricity. The calculations for these results are shown below.

11,377 kWh - 7,200 kWh = 4,177 kWh sent to grid.

(4177 kWh/7200 kWh)(100%) = 58%

To analyze the sustainability of solar panels, a life cycle analysis of emissions was completed. Since the Alberta Electricity Grid Emissions Intensity Factor is 0.57 CO2e/MWh, the number of tonnes of CO2displaced from the grid, per year can be calculated, as shown below (Government of Alberta, 2019). 

113771000MWh * (0.57 CO2e tonnes/MWh) = 6.48 tonnes CO2 per year

Therefore, 6.48 tonnes of CO2 would be released per year if electricity were drawn from the Alberta grid. Assuming that the solar panels will operate for their lifespan of 30 years and considering that the life-cycle carbon emissions of solar panels is 0.052 tonnes CO2/MWh, the total tonnes of COemissions can be calculated (Komoto, K., 2008) as per below.

113771000MWh * 0.57 CO2e tonnes/(MWh year) * 30 years  * 0.052 tonnes CO2/MWh = 17.75 tonnes CO2

The number of years required to cover life cycle emissions is calculated by dividing the total tonnes of COproduced in 30 years by the tonnes of COdisplaced from the grid in a year. 

Number of years to cover life cycle emissions = 17.75 tonnes CO2/6.48 tonnes CO2 = 2.74 years

The COemissions associated with the life cycle cost of this photovoltaic system will be accounted for in approximately 2.74 years.  Thus, after 3 years, solar panels are a clean source of energy, with zero emissions. 

Finally, the reliability of the data can be evaluated by the process of data collection and variation within the data. Most of the weather data was collected from accurate and reputable sources such as the Government of Canada. In addition, electricity generation data was automatically collected directly from the solar panel through the use of a desktop application, reducing human and measurement error, thus increasing reliability. Overall, the data is quite spread out annually, which may suggest lower reliability. However, variation in the daily data recorded is expected, and can be described by natural phenomena such as Earth’s rotation around the Sun. 

Conclusion

There is a common misconception that electricity cannot be generated by solar panels during winter due to the heavy amounts of snow and cold temperatures. In this experiment, different weather factors were compared to the amount of electricity generated by solar panels in Calgary to determine if there was any relationship between these variables. The correlation between electricity generation and weather factors (temperature, visibility, precipitation, daylight hours, solar radiation, and cloud cover) were all less than 0.50, indicating no significant relationship. The variable with the lowest correlation was precipitation. The variables with the highest correlation were solar radiation, hours of daylight, and temperature. This can be explained as the amount of electricity generated is directly dependent on the availability of sunlight. Consequently, the results of this experiment strongly suggest that solar panels can still be effective despite the long winter season and heavy snowfalls in Calgary. In addition, the annual generation of electricity from the solar panels surpassed the average annual consumption of a typical home in Alberta. The hypothesis is proven true, because regardless of weather effects the solar panels were able to generate at least 7, 200 kWh per year. It has also been proven that solar panels have very little impacts on the environment and are sustainable based on the life cycle emissions that are covered in less than 3 years whereas the typical life of solar panels is considered as 30 years.

Application

While this experiment proves the reliability of solar panels as an adequate source of electricity generation with respect to different weather conditions, other factors can also be explored to determine the viability of this technology. For example, more in depth research can be taken place to determine the relationship between snowfall, rainfall, and cloud cover on a daily basis. It may also be pertinent to do an analysis between certain weather factors such as precipitation over an hourly basis to further explore relationships to electricity generation. 

This experiment disproves common misconceptions individuals have about solar technology such as weather and reliability. It proves that individual weather factors do not strongly affect the energy generated by solar panels, and on an annual basis, solar energy is quite reliable. Only in certain instances, such as cold temperature and low daylight hours, solar panels may not be reliable. Furthermore, solar panels were able to produce more energy than consumed by a typical house in Alberta. As a result, this experiment highlights why solar energy would be a good technology for Calgarians to embrace and potentially adopt in the future. Analyzing the life cycle emission of solar panels, and recognizing that the economical footprint of solar panels can be covered in under 3 years shows the sustainability of this technology. The results from this experiment can be used to promote solar energy as both a reliable and sustainable source of energy that can meet the energy demands of present generations without compromising the ability of future generations to meet their own needs. 

 In the future, a more extensive life cycle analysis can be used to analyze the full environmental benefits of using solar energy as opposed to traditional electricity generation methods. Considerations such as the effect on wildlife and water consumption can also be considered. Finally, an economical analysis could also be considered to highlight the benefits or losses of adopting solar technology. Furthermore, investigating the effect of weather on solar electricity production in multiple locations would reveal more evidence on how weather accounts for electricity production. Overall, these extensions would provide insight on different aspects individuals consider when using renewable sources of energy. 

Sources Of Error

Based on the current treatment of weather data, the different variables (temperature, visibility, precipitation, daylight hours, solar radiation, and cloud cover) were treated independently when comparing their effect on solar electricity generation. However, weather is always a combination of these independent variables and this analysis does not consider multivariate dependence. This shows some invalidity in the data as the combination of multiple variables is not considered. To consider the effect of multiple variables on electricity generation, multiple variable linear regression would have to be calculated to find the probability of obtaining such test results. This is useful in determining more accurate trendlines for the variables. However, this is a very advanced statistical procedure. Another potential source of error could be in the measured data for electricity generation and weather due to limitations placed on by the technology being used for measurements and data processing. Finally, a potential source of error may be that there is variation in weather in different regions in Calgary, and the measurements made from the weather station may not reflect the true conditions experienced by the solar panels.

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Acknowledgement

The completion of this study would not have been possible without the mentorship of Dr. Shahin Jabbari. I would also like to thank Dr. Vincent Chan and Mr. Merrick Fanning for providing additional support.  Ms. Sara Haney also helped me submit and share my project in the science fair. 

A debt of gratitude is also owed to Ms. Akanksha Bhargava for providing feedback and support. Lastly, I would like the Renert School for providing the opportunities for me to learn and grow academically. Without the support from the school this project would not be possible.