Weather Prediction Using Historical Data

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1 Weather Prediction Using Historical Data COMP 381 Project Report Michael Smith

2 1. Problem Statement Weather prediction is a useful tool for informing populations of expected weather conditions. Weather prediction is a complex topic and poses significant variation in practice. The student will attempt to understand and implement a weather prediction application in attempts to investigate ways upon which this area could be improved. 2. Background Work The weather prediction application involves two major components: the sliding window algorithm and ID3 algorithm. The sliding window algorithm divides a collection of data into groups. More specifically, the sliding window algorithm is used to segment a two week collection of historical weather data into week long windows [1]. A window can be explained as follows. Consider a table with 14 rows. The sliding window algorithm treats rows 1-7 as a window, 2-8 as a window, 3-9 and so on. The purpose of separating the historical 14 day period into 7 day windows is to align the data trends with the current week s weather. The goal of this segmentation is to find a closely related trend of past data approximate to the same date to predict the upcoming day. An example of how the Sliding Window segments this data can be found below. November 4-17, 216 Weather The above selection of data would be used to predict the weather for November 18, 217. The ID3 algorithm created a decision tree based on a collection of sample data. The ID3 algorithm uses entropy gains to determine which parameter provides the most information in the decision [2]. It then narrows down expected results based on these parameters. In terms of

3 weather prediction, this algorithm uses historical data as a training set to establish connections of each parameter with the resulting outlook. The parameters used are: high temperature, low temperature, humidity, and rainfall (precipitation). The ID3 algorithm uses the same 14 days of historical data as the sliding window and decides which parameters are key in determining the outlook. When the decision tree is created, the ID3 tree is executed using the sliding window algorithm s weather prediction to determine what the outlook will be based on the projected dataset. An example ID3 tree produced on the previously shown historical data can be seen below. The predicted data from the sliding window algorithm would choose a path based on the Sliding Window prediction. This would then yield the expected outlook. As shown in the diagram, Failure is possible. This is due to limited variety of the sample data; the data does not cover all possible scenarios. This means that if the current weather has a large discrepancy from historical data, a prediction of the outlook may not be possible. Darksky.net was used as the historical data repository. The Darksky API provided free weather queries of previous years which is idea for this study. Darksky.net provided its own real-time weather prediction that was adjusted throughout the day. This provided an easy comparator to my own implementation.

4 3. Theoretical Analysis Weather is relatively consistent over the course of a year. It is common knowledge that Ottawa in winter has temperatures of -2 C. In addition, the summer months have temperatures of 2 C. The main idea is that weather has a certain amount of consistency throughout the year. How historical weather trends relate to current weather trends can be observed through the Sliding Window Algorithm. 3.1 The Sliding Window Algorithm & Weather Weekly weather trends may not align perfectly with historical data. There may be varying conditions that could offset a historical trend that is relatively close to current conditions. The Sliding Window Algorithm accounts for this potential offset by sampling from a two week data set. By dividing up this sample data, the algorithm can determine the best fit trend and predict the following day s weather. An advantage of this algorithm is that it uses data observed from the same time period in a previous year. The sample data can also be adjusted; data from multiple years can be observed in addition to increasing the number of historically observed weeks. Increasing the number of observed weeks should be limited to ensure that the predictions are based around the same time of year. A disadvantage of this algorithm is that the historical data that has been sampled may not reference the current trend whatsoever. This could happen due to impactful weather conditions that had not been observed in previous years. Occurrences like this would result in a skewed prediction due to lack of similar data. 3.2 The ID3 Algorithm The weather s outlook cannot be predicted the same way that the temperature, humidity and rainfall parameters can. The motivation behind the ID3 algorithm is that the weather parameters may have a correlation with the outlook. Consider a day with a lot of rain. It is trivial to see that the outlook would be apparently rainy. This logic is similar for significantly warmer days resulting in a sunny outlook. Based on these assumptions, the ID3 algorithm builds a decision tree based on how the weather parameters relate to the outlook using historical data. The advantage of this algorithm is similar to the Sliding Window Algorithm. The ID3 Algorithm also uses historical data to make a prediction. A disadvantage to the ID3 Algorithm is the small sample size of weather data. There are four parameters used and only 14 days worth of data considered. This results in some failure nodes appearing in a resulting tree as there is not enough data (or varying data) to account for some situations. A way to handle this better is to take several years of historical data instead of a

5 single year. In addition, if the historical trends don t relate to the current one, there is a higher risk of hitting a failure node. 4. Experimental Design and Analysis 4.1 The Experiment The experiment relied on day to day data collection and thus provides a small sample size in the result. The experiment involved predicting the following day s weather for a period of two weeks. The predictions were compared to the actual reported weather by darksky.net. Weather networks each provide discrepancies between weather reports. Thus since darksky.net was used for the source of historical data, it is also used for the prediction comparison. A noticed issue with darksky.net is that the some of the reported actual weather after the day had ended was drastically different than the report during the day. Days that had this strange recording were adjusted to reflect the condition recorded throughout the day rather than what was retrieved from the API. 4.2 Analysis The experimentation had a limited time to collect data. Due to this, data from November 4 th 217 to November 17 th 217 is presented in each of the charts. Max Temp Trend Min Temp Trend Degrees Fahrenheit Degrees Fahrenheit Predicted Predicted

6 Humidity Trend Rainfall Trend Percentage Millimeters Predicted Predicted At first glance the trend lines of the predicted and actual weather parameters have relative similarities. However, the main measurement of the data lies in the daily discrepancies. By taking the difference of the predicted from the actual, the following graphs show the differences in the daily predictions. Degrees Fahrenheit Daily Prediction Difference in Max Temp Degrees Fahrenheit Daily Prediction Difference in Min Temp

7 Percent Daily Prediciton Difference in Humidity Millimeters Daily Difference Predicition in Rainfall The graphs show large amounts of variation during some days. This is likely due to the error in relying strictly on the historical observations. The percentage of error can be calculated by using the Mean Absolute Percent Error (MAPE) [3]. MAPE = n Prediction MAPE [Max Temperature] = 2.% MAPE [Min Temperature] = 8.9% MAPE [Humidity] = 12.9% MAPE [Rainfall] = 172% The MAPE implies the Sliding Window Algorithms results predicted the Max Temperature with 79.% accuracy, the Min Temperature with 91.1% accuracy and the Humidity with 87.1% accuracy. The MAPE is sensitive to low-volume data and data that pertains to zeros. In this case, the zeros skew the percentage of the Rainfall so that it does not make much sense. For this, the Mean Absolute Deviation (MAD) can be used instead [3]. MAD = 1 n Prediction MAD [Max Temperature] = 7.7 MAD [Min Temperature] = 3. MAD [Humidity] = 9.9 MAD [Rainfall] =.2 The MAD shows that the Sliding Window Algorithm was off by an average of 7.7 F for the Max Temperature, 3. F for the Min Temperature, % for the Humidity, and.2 millimeters for the Rainfall. An observation made from inquiring multiple weather networks showed a discrepancy of the actual temperatures of within 3- F and similar results for the other parameters. Taking this into consideration, the Sliding Window Algorithms average variation was not significantly different than the discrepancies of weather networks.

8 # of Correct Outlook Predictions 12 # of guesses cloudy sunny rain Correct Incorrect The above figure is the number of successful predictions of the outlook using ID3 Algorithm based on the Sliding Window algorithms results. The statistical analysis doesn t work the same way as these are based on quantitative values. Using the chart above, the ID3 Algorithm was able to correctly predict /14 outlooks giving 71% accuracy.. Conclusions The experimentation had many limitations to it considering the sample size of historical data and the resulting collection of data. This likely had an impact on limiting the accuracy of both the algorithms used. Overall I would consider these algorithms to be reasonable choices in weather prediction if the experimentation is restricted to only using historical data. This experimentation could be improved upon by the earlier mentions of the disadvantages of both of the algorithms. For example, expanding the sample sizes for both the Sliding window and ID3 Algorithms would likely result in less variation in predictions.

9 6. References [1] Kapoor, P., & Bedi, S. S. (213, December ). Weather Forecasting Using Sliding Window Algorithm. Retrieved December 1, 217, from [2] Building Classification Models: ID3 and C4.. (n.d.). Retrieved December 1, 217, from [3] Stellwagen, E. (n.d.). Forecasting 1: A Guide to Forecast Error Measurement Statistics and How to Use Them. Retrieved December 1, 217, from

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