Weather Generator and Hourly Disaggregation Model

Transcription

1 Weather Generator and Hourly Disaggregation Model A Report Describing the Work Done With the Weather Generator Prepared By: Rami Mansour and Donald H. Burn, Ph.D., P.Eng. Department of Civil and Environmental Engineering University of Waterloo Waterloo, ON CANADA N2L 3G1. April 2010

2 Executive Summary Four different versions of the Weather Generator code have been created in an attempt to find an effective way to reproduce accurate precipitation values for the London Weather Station. These include the original version, a version using only three variables in the analysis, a version with pertubation removed, and finally a version with pertubation removed that uses only stations within 50 km from London. The precipitation values outputted by the Weather Generator are sent through a Disaggregation Model that creates hourly values using historical records. The IDF values from the resulting data are then compared to London s historical IDF values; the results from the version of the Weather Generator with pertubation removed and which uses only the closest London stations are found to be the most accurate. The Return Annual Rainfall amounts are also calculated in an attempt to verify that the disaggregation model is working correctly. i

3 Table of Contents Executive Summary... i List of Figures... ii List of Tables... ii 1.0 Introduction Updating The Code Analysis of WG Outputs Regarding the Usage of Different Stations Disaggregation Model IDF Values Problems Encountered Effects of Removing Pertubation Conclusion... 9 List of Figures Figure 1 Map of WG Stations Used... 3 Figure 2 Different Stations WG Outputs... 3 Figure 3 Original Stations WG Output... 4 Figure 4 Comparison of Actual Vs. Estimated Values... 5 Figure 5 Comparison of Historical Vs. Generated Values... 5 List of Tables Table 1 IDF Values for 1 Hour Duration... 1 Table 2 IDF Values for 24 Hour Duration... 2 Table 3 Pertubation Removed with 7 Variables... 7 Table 4 3 Variables... 7 Table 5 7 Variables... 7 Table 6 Stations Used in Close Analysis... 8 Table 7 Closer to London Pertubation Removed Results... 8 Table 8 Percentage of Error Results... 8 ii

4 1.0 Introduction The Weather Generator (WG) takes in historical data (including precipitation levels) and uses these amounts to predict values for the number of years specified by the user. It also creates seven different variables of data including: PRL/MSL (mean sea level pressure), SPFH (near surface specific humidity), UAS (zonal wind component at 10 m height), VAS (meridional wind components at 10 m height), PPT (precipitation), TemMax (max temperature), and TemMin (minimum temperature). However, only the precipitation was taken into account for this specific project. Originally the WG that was updated by Mamun was being used, but the precipitation results were not as expected. A meeting was set with Tarana who was doing work with the Weather Generator in Western University and the latest model of the Weather Generator was given to be used. 2.0 Updating the Code The WG code originally uses seven variables in its analysis. In an attempt to create better results, a version was saved that uses only three of the variables (PPT, TempMax, and TempMin). This was done in an effort to see what the effect of using different variables would be on the precipitation output. However the results from the three variable version of the WG did not differ significantly from the seven variable version. The Table 1 shows the generated IDF values with 1 hour duration for both the 3 and 7 variable versions of the WG. The Table 2 illustrates the same concept but with an interval of 24 hours. It was concluded that using the different sets of variables did not have a large impact on the testing results, as can be confirmed with the similar results in both tables. 1

5 Table 1 - IDF Values for 1 Hour Duration IDF Values Year 3 Var 7 var Table 2- IDF Values for 24 Hour Duration IDF Values Year 3 Var 7 Var

6 2.1 Analysis of WG Outputs Regarding the Usage of Different Stations For the original analysis 22 Weather Stations shown in Table 3 were used. The Figure 1 is a map of the stations that are used be the Weather Generator. The stations include: Blythe, Brantford, Chatham, DelhiCS, Dorchester, Embro, Exeter, Fergus, Folden, GlenAllan, HamiltonA, Illderton, LondonA, Petroliatown, Ridgetown, SarniaA, Stratford, StThomas, Tillsonburg, WaterlooA, Woodstock, and Wroxeter. Table 3 - Stations Used with Weather Generator Stations Latitude Longitude Elevation (metres) Geographical Distance from London in KM (approximate) IDF data Daily Precipitation data Hourly Precipitation data From To From To From To FERGUS SHAND DAM FOLDENS GLEN ALLAN ILLDERTON BLYTH BRANTFORD MOE CHATHAM DELHI CS DORCHESTER EMBRO EXETER HAMILTONA LONDON PETROLIA TOWN RIDGETOWN RCS SARNIAA St. THOMAS WPCP STRATFORD TILLSONBURG MOE WATERLOOWELLINGTONA WOODSTOCK WROXETER Figure 1- Map of WG Stations Used 3

7 The WG was run using a different number of stations to try and find the best combination of factors that would give the most accurate results. Since the London station was being analysed, it was decided that using only the stations closest to it would provide the best estimate for precipitation values. Two different sets of stations were used with the WG to see the effects this would have. The first test involved the stations London, Dorchestor, Ilderton, Foldens, Embro, and St. Thomas (six stations). Figure 2 is the monthly totals for this test, while Figure 3 shows the original output from the WG using all 22 stations. A second test was done on the stations of London, Dorchestor, Ilderton, and St. Thomas. It was found that only using stations near London reduced the variance of the monthly data and reduced extreme outliers; however this difference was not as significant as was predicted. Figure 2 - Different Stations WG Outputs Figure 3 - Original Stations WG Output 3.0 Disaggregation Model The WG outputs the precipitation in daily values for the years 2001 to In order to find the hourly values for each day, a disaggregation model was created. This model takes previous sets of hourly data that were collected in 4

8 the same region as the input data for the WG and uses these as a template for how the hourly values should be calculated. The program is a simplified version of what has been developed by many research papers and Masters Students. This program works by finding a specified number of days (a 50 day windows was used) in which the current daily PPT value will be compared to (will use the same ratio of hourly values). The best match is determined by using the formula: where NDP is the new daily precipitation (Weather Generated data), ODP is the old daily precipitation (historical data), NE is the new event value (Weather Generator event), and OE is the old event value (historical events). An event is defined as a two or more days with rainfall data (the total amount of rainfall in the consecutive days is considered the event precipitation values). The weights (w1 and w2) are used to decide which historical hourly ratio is best for the data. An hourly value that is within the set window of days can be chosen for a similar event (w2) or for the total daily precipitation (w1). The lowest value (Val) found in the window is chosen as the daily ratio of historical hourly values used to make the WG s daily data into hourly values. The ratio of hourly values found within the chosen day is then applied to the daily value; this creates a plausible hourly set-up for the given daily data. This program has been sent daily data that already had known hourly values and the results have been compared in an attempt to verify that the model works correctly. The actual hourly values and the estimated hourly values were then compared to try and see if a correlation existed. The data points between the two periods did not correlate well together due to many precipitation values of zero, so all zero values were removed and the data was sorted. The Figure 4 shows the sorted comparison data. The graph shows a strong correlation between the estimated and generated values; the generated and historical values were found to have a correlation of over 0.9. Figure 4 - Comparison of Actual Vs. Estimated Values 5

9 Further comparisons were done for the observed and generated data. The average precipitation levels for each historical year were compared with those generated by the WG. However, the historical data was for the years and the Weather Generated values were for the years , so it was not a direct comparison. This is illustrated in Figure 5. The values are generally similar in trend and variance; however the outliers in the generated data were observed to be much higher than that of the historical, which skewed the data. This was solved by averaging out different outputs from the Weather Generator. Figure 5 - Comparison of Historical Vs. Generated Values 3.1 IDF Values IDF values were found for different time periods that included 1, 2, 6, 12, and 24 hours. This was done for the entire 27 year analysis for ten different sets of Weather Generator output for both the 3 and 7 variable versions. To test this procedure, the program was used to find the IDF values for the historical values, which was then compared to the known IDF values for that time. There was a close match with the two, which helps justify that the disaggregation model is effective in modeling hourly data. 4.0 Problems Encountered One of the biggest problems with the WG is the large amount of time that it takes to finish running. However it was observed that reducing the overall number of stations and variables being used reduced the amount of time needed to finish running. Another problem was the huge amount of data that needed to be processed. This caused the editing of the Hourly Values Generator to slow down until a smaller data set was used; in effect this reduced the editing time, and only when the model was ready was the full data finally used. When the Weather Generator was first used to create 6

10 precipitation values, it was evident that some extreme outliers were skewing the data. In order to combat this and reduce the number of outliers, the Weather Generator was run three times and the values were all averaged. Although this greatly reduced the number of zero values, it also kept any outliers within reason and helped create more realistic and accurate results. 5.0 Effects of Removing Pertubation The Weather Generator code was updated to remove pertubation from the coding in an attempt to improve the accuracy of the outputs with respect to Return Period Rainfall Amounts. The historical values were compared with the 3var, 7var, and pertubation removed values to see which produced the closest values. The following tables are the results of the analysis, with smaller values being optimal. The analysis involved running each program ten times, using the hourly disaggregation model to find hourly data. To calculate the return period rainfall amounts we use two formulae: P = P + K S T T P where P T is the return period rainfall amount for the return period T (where T = 2, 5, 10, 25, 50 and 100), P is the mean of the rainfall values for the duration selected, S p is the standard deviation of the rainfall values for the duration selected and K T is given in the equation below. K T 6 T = ln ln π T 1 where T is again the return period. The results should be close to (if not exactly) the results from the historical IDF Data. The Return Period Rainfall Amounts for the average of the ten tests is presented in Table 3, 4 and 5. Table 4 - Pertubation Removed with 7 Variables Period Hours

11 Table 5-3 Variables Period Hours Table 6-7 Variables Period Hours The pertubation removed values were found to be the best of the three (by far). In order to further optimize these values however, tests were run using different weights for two parameters in the Hourly Desegregation model, but it was found that the ones being used were giving the best results (w1 = 0.2, w2 = 0.8, window = 50 days). To help improve the values further, only stations within 50 km of London were used with the Weather Generator (pertubation removed). These stations were as follows: Table 7- Stations Used in Close Analysis Stations Latitude Longitude Elevation (m) 8 Geographical Distance from London LONDON DORCHESTER ILLDERTON St. THOMAS WPCP EMBRO FOLDENS WOODSTOCK STRATFORD EXETER

12 The results of this comparison were then put through the same process as stated above, and the results were compared to the pertubation version using all the stations. The return period rainfall amounts for the average of fifty tests for the nine stations closest to London are: Table 8 - Closer to London Pertubation Removed Results Period Hours These values are much better than the version using all stations, so this format will continue to be used. The percentages of error with these results are: Table 9 - Percentage of Error Results % Error Hours % 5.22% 12.13% 6.32% -0.23% % 3.29% 6.90% 3.99% -4.00% % 2.48% 4.65% 2.93% -5.65% % 1.74% 2.58% 1.91% -7.19% % 1.33% 1.41% 1.32% -8.07% % 0.99% 0.45% 0.83% -8.79% 5.1 Box Plots Box plots were made for the Weather Generated Rainfall Return Amounts for each time period (1, 2, 6, 12, and 24 hours), each containing a different plot for the different return periods (2, 5, 10, 25, 50, and 100). As well the historical values have been plotted to serve as a comparison for the two. For each box plot the center mark is the median of the data, the edges of the box are the 25 th and 75 th percentiles, the whiskers extend to the most extreme data points that are not considered outliers, and outliers are shown as small crosses. The outliers are defined using the equation: 9

13 (6) The variable w is the whisker length and q1 and q3 are the 25 th and 75 th percentiles, respectively. Any values larger or smaller than the +/- of this equation are considered to be outliers. Figure 6 shows the return period rainfall amounts for all fifty tests done for the one hour time period. It can be seen that the median for the Weather Generated values is lower than that of the historical values. As well with a larger return amount, the variance of values increases at a steady rate. However the median values are not very far off which shows the effectiveness of the Disaggregation Model being used. Figure 6-1 Hour Box Plot Figure 7 shows the return period rainfall amounts for the 24 hour values for all fifty tests. Similar to the 1 hour box plots, the median values for the Weather Generator are lower than those for the historical values. However the difference is much larger than the 1 hour box plots, which shows that the increase in analysis period causes the Disaggregation Model to work less effectively. Similar to the 1 hour box plot, Figure 7 has an increasing variance in return period rainfall amounts for the larger return periods. Despite this the Weather Generator values are still somewhat similar to the Historical values which confirm the effectiveness of the Disaggregation model. 10

14 Figure 7-24 Hour Box Plot 6.0 Conclusions From this testing it was found that by removing pertubation and using only the stations within 50 km of London the WG can provide a more accurate representation for precipitation values. This was found by testing four different versions of the Weather Generator code and comparing the generated and historical values. By calculating total monthly precipitation values, plotting the different values to find any correlations, finding IDF values, and finding return period rainfall amounts a proper comparison of the different versions generated precipitation to the historical records could be made. The low percentage of error in the comparisons between the historical and generated return rainfall period amounts and IDF values provided a greater insight to the effectiveness of the hourly disaggregation model, and helped conclude that the weights being used in the disaggregation equation are optimal. 11