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Analysis of Trends in Extreme Rainfall

A report prepared for the Canadian Foundation for Climate and Atmospheric Sciences project:

Quantifying the uncertainty in modelled estimates of future extreme precipitation events

Prepared By:

Kan Zhang and Donald H. Burn, Ph.D., P.Eng. Department of Civil and Environmental Engineering

University of Waterloo Waterloo, ON CANADA N2L 3G1.

August 2009

Executive Summary

Trend analysis was performed on extreme precipitation data for stations that were deemed within sufficient distance of the case study area of London for the periods of 1974 to 2003, 1969 to 2003 and 1964 to 2003. The Mann‐Kendall statistical test for trend was used to identify significant positive and negative trends. It was shown that the 40 year period had no significant trends, the 35 year period had a few positive trends and the 30 year period showed a number of negative trends.

A secondary analysis which took into account stations that had less than the required amount of data for the above analysis was conducted to find that many of the stations with less available data show negative trends throughout the available data record.

Temporal changes were shown to be caused by temporal clusters of high and low extreme rainfall values. These were generally occurring around the 1965 to 1975 range, which explains the variation of trend throughout the three analysis periods.

Three other non‐parametric tests were conducted to determine if the data analyzed were homogeneous, random and independent. It was determined that for the most part, the data met these conditions at the five percent significance level. A few stations showed non‐homogenous behaviour which corresponded to a significant trend. Stations that showed other qualities such as not random and dependent did not correspond to a trend.

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Table of Contents Executive Summary....................................................................................................................................... ii

Table of Contents......................................................................................................................................... iii

List of Figures ............................................................................................................................................... iv

List of Tables ................................................................................................................................................. v

1.0. Introduction ...................................................................................................................................... 1

2.0. Methodology..................................................................................................................................... 2

2.1. Station Selection ........................................................................................................................... 2

2.2. Validity of Data.............................................................................................................................. 2

2.3. Trend Test ..................................................................................................................................... 3

2.4. Field Significance........................................................................................................................... 4

2.5. Temporal Analysis ......................................................................................................................... 4

2.6. Other Non‐Parametric Tests ......................................................................................................... 4

3.0. Results ............................................................................................................................................... 5

3.1. Stations and Time Periods Examined............................................................................................ 5

3.2. Analyzing Trend Results ................................................................................................................ 7

3.3. Temporal Patterns in Trends.......................................................................................................13

3.4. Summary of Other Non‐Parametric Tests...................................................................................15

4.0. Conclusions and Recommendations ...............................................................................................18

References ..................................................................................................................................................19

Appendix A..................................................................................................................................................20

Appendix B ..................................................................................................................................................27

Appendix C ..................................................................................................................................................30

Appendix D..................................................................................................................................................37

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List of Figures Figure 1 – Geographical location of initial 38 stations.................................................................................. 6 Figure 2 ‐ Slope values of the 15 minute interval and all stations for the three analysis periods..............11 Figure 3 ‐ Typical type 1 behaviour ............................................................................................................14 Figure 4 ‐ Typical type 2 behaviour.............................................................................................................15 Figure 5 ‐ Rainfall data for Preston WPCP for the 30 minute intervals showing typical non‐homogeneous behaviour ....................................................................................................................................................16 Figure 6 ‐ Rainfall data for Waterloo Wellington Station for the 30 minute intervals showing typical non‐homogeneous behaviour ............................................................................................................................17

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List of Tables

Table 1 – Available stations for the 30, 35 and 40 year analysis periods ..................................................... 6 Table 2 ‐ List of stations utilized for trend analysis based on stations individual time periods ................... 8 Table 3 ‐ Number of stations showing trend as a percentage of total number of stations for 1974 to 2003 (30 Year Analysis Period) – 10% Significance Level ...................................................................................... 9 Table 4 ‐ Number of stations showing trend as a percentage of total number of stations for 1969 to 2003 (35 Year Analysis Period) – 10% Significance Level ...................................................................................... 9 Table 5 ‐ Number of stations showing trend as a percentage of total number of stations for 1964 to 2003 (40 Year Analysis Period) – 10% Significance Level ....................................................................................10 Table 6 ‐ Station trend summary for analysis based on individual analysis periods ..................................12 Table 7 ‐ Types of discrepancies between trend results for the 30, 35 and 40 year analysis periods and the number of occurrences.........................................................................................................................13

1.0. Introduction

It has been suggested that extreme precipitation events that exceed the previously determined design storm are likely to become more frequent in the future. Stemming from this would be the need for procedures and guidelines for risk‐based decision‐making in the presence of the impacts of climate change. To understand the impact of climate change on extreme precipitation events, a good historical base is needed. Trend analysis will be performed on extreme precipitation events of various durations for stations within and near the case study area.

The trend results will provide a general idea of any changes noticeable within the historical data and point out certain concerns for the area regarding extreme precipitation events. It will also serve as a comparison for extreme precipitation events predicted by General Circulation Models (GCMs). One intent of the investigation carried out in this report was to establish whether the current trend as determined by the trend analysis will match the projections of future conditions from the GCM outputs.

Previous research on trend analysis has been performed for different areas and different meteorological variables. Adamowski and Bougadis (2003) did a study on extreme rainfall events similar to that conducted in this report, with similar methodology as well. Their analysis on 44 stations across Ontario on a 20 year time frame showed a total of 23% of the region showed a trend at the 5 % significance level. It was also noted that trends were more prominent for shorter time intervals. Groisman et al. (1999) did a study on the probability of heavy precipitation in eight different countries, one of which was Canada. It was noted that Canada (along with six of the other seven countries) showed at least a 5% increase in mean summer precipitation in the past decade. However, they also concluded that there was no increase in precipitation frequency in the past 50 years. By assuming a 5% increase in mean summer precipitation and applying a statistical model, the probability of daily precipitation event of over 25.4 mm increased by about 20%.

Mirza et al. (1998) did a study on precipitation trends in the Ganges, Brahmaputra and Meghna river basins using much the same methods that will be employed in this report, such as Mann‐Kendall trend test and Student’s t‐test. The analysis showed a generally stable trend, however both the Ganges and Brahmaputra basins had both region(s) with increasing trend as well as region(s) with decreasing trend. Osborn et al. (2000) analyzed the trends in the daily intensity of United Kingdom precipitation. They placed more focus on seasonal variations of the precipitation intensity. They noted that in winter, the number of medium and light events decreased while the number of heavy events increased, while the opposite was observed for summer precipitation. Daithi et al. (1999) reported their findings on the trends present in the intensity of Canadian precipitation. It was found that southern areas of Canada had increasing intensity for all seasons. Zhang et al. (2000) outlined Canadian precipitation trends along with temperature trends. It was seen that from 1900 to 1998, the annual mean temperature increased 0.5 to 1.5 oC in the southern part of Canada. Annual precipitation increased 5% to 35% during the same period. Finally, it was noted that there were significant negative trends in precipitation in southern regions during winter.

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2.0. Methodology

The methodology involved the selection of stations, determining the validity of the data, analyzing the data for a trend using a trend test at individual stations, determining the field significance of the trend results and performing a temporal analysis on the trend results. Each of these methodologies will be explained in further detail within this section.

Trend analysis was conducted using the Mann‐Kendall non‐parametric statistical test for trend, since it has been successfully used in other similar studies that look at trends in meteorological variables. Three other non‐parametric tests were also used to help further understand the data and the reasoning behind the trends. These tests were the Spearman rank order serial correlation coefficient test for independence, the Mann‐Whitney split sample test for homogeneity and the runs above and below the median for general randomness.

2.1. Station Selection

Initially, data for 38 stations near the case study location were obtained for analysis. After further investigation, it was determined that three of these stations were spatially too far away to be considered. The remaining stations were all within approximately 115 km of London, which was the case study area. Next, stations were eliminated based on the types of information that they were able to provide, as some only provided daily data, while others hourly and still others down to five minute intervals. It was decided that daily data was not enough, as the trend for the lower intervals should be explored as well, therefore excluding stations that had only daily data. This left two groups of stations, one with detailed extreme precipitation data, such as data used to create Intensity Duration Frequency (IDF) graphs, and another group with only hourly data. It was decided that the stations that had the IDF data would be examined for 40, 35 and 30 year periods, which further eliminated stations. Most stations with only hourly data had 21 years of data, which meant they did not have sufficient data for any of the previously stated time periods, but were analyzed for trend in a secondary analysis.

There are a total of 19 stations with IDF data and nine stations with only hourly data. Out of the 19 IDF stations, the number of stations used for the 30, 35 and 40 year period were 10, 10 and 8 stations, respectively.

For the secondary analysis, all 28 available stations were used.

2.2. Validity of Data

For 13 of the stations with IDF data, there were also hourly data available. Therefore, comparison of the two sets of data were made to ensure completeness and accuracy of the data used. The IDF data came in the desired table form, with the maximum precipitation event for the stated interval listed for each year. The hourly data only came as a list of how much precipitation occurred during each hour of each day for its record period. The hourly data had to be translated into longer intervals (i.e., two hour, six

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hour, etc.), and then the maximum of each interval had to be found for each year. This was done through the manipulation of spreadsheets.

The results from the hourly data were then compared with the IDF data, with any discrepancies noted. Small discrepancies were not a concern, but reasoning was required for the larger discrepancies. Also, the difference between the data was determined by subtracting the hourly data from the IDF data. Negative discrepancies were examined since the expectation is that the difference will be zero or positive. IDF data should result in larger values for the various durations since the selection of data is not restricted to hourly intervals that start on the hour, as is the case with the hourly data (i.e., for the IDF data, it is possible for the largest hourly value to occur between 6:05 a.m. and 7:05 a.m., whereas the hourly data would only be based on the amount from 6 a.m. to 7 a.m.).

2.3. Trend Test

The statistical trend test selected was the Mann‐Kendall non‐parametric test for trend (Mann, 1945; Kendall, 1975). This trend test has been commonly used in similar applications (Hirsch et al., 1982; Gan and Kwong, 1992) and has been found to be an effective tool for identifying trends in hydrological and other related variables. The test statistic for the Mann‐Kendall test is given in the form

(1)

where xj are the sequential data values, n is the total number of data points in the set, and sgn( ) being the sign functions is defined as

(2)

where is the argument of the sign function.

The null hypothesis is stated as the data series has no trend, and is given by

(3)

and

(4)

where t is the number of data points tied at a given value. The summation of t is therefore over all values for which there are tied data points. For n greater than ten, the statistic closely resembles a normal distribution if a continuity correction is applied, giving

(5)

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where S’ is the corrected test statistic value. Assuming that this corrected test statistic follows a Normal distribution, it becomes possible to calculate a Z statistic as follows

(6)

where Z is the standard variate. Alongside a table or formula, this Z value can be used to determine the probability of the data series containing a trend, either positive or negative.

A non‐parametric estimate of the slope of the trend can also be estimated by the following equation from Hirsch et al. (1982)

(7)

where β is the slope of the trend, which is also a representation of the magnitude of the trend.

2.4. Field Significance

Field significance allows the determination of the percentage of tests that are expected to show a trend, at a given local (nominal) significance level, purely by chance, reflecting the cross‐correlation in the data. A bootstrap, or resampling, approach was used to determine the critical value for the percentage of stations expected to show a trend by chance. Any temporal structure (i.e., a trend or pattern) that exists in the original data set will not be reproduced in the resampled data sets because of the nature of the resampling process, which selects the years to be included at random. However, the cross‐correlations in the original data sets are preserved through including all data values for a given year in the resampled data set. This allows the impact of cross‐correlation to be determined in establishing the critical value for the percentage of stations exhibiting a trend.

2.5. Temporal Analysis

From past experience, it was expected that there would be temporal changes in the trends for differing study periods. An example would be that a trend that was seen for the 30 year study period might not have existed for the 35 year period. Stations that showed this behaviour were identified and classified into types according to the types of changes. It was decided that a smoothed graphical representation of the data series would greatly help identify the reasoning behind these changes. The LOWESS smoothing technique (Cleveland, 1979) was utilized for this purpose.

2.6. Other NonParametric Tests

Three other non‐parametric tests were conducted on the data to gain a better understanding of the reasoning behind the trends (or lack there of) found by the trend analysis. The three additional tests used were the Spearman rank order serial correlation coefficient test for independence, the Mann‐

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Whitney split sample test for homogeneity and the runs above and below the median test for general randomness.

Independence of two events is defined such that the possibility of either event occurring does not affect the possibility of the occurrence of the other. This definition can easily be expanded to a sample size of size n. For a time dependent series, the significance of the correlation within this data series can be translated to the independence of the data set (i.e., if the correlation is close to zero, the data within the set are deemed to be independent. It should be made clear that this does not meet the strict mathematical definition of independence.

Homogeneity of the sample is confirmed by a lack of sudden or large changes that occur during a sampling period. This change can be easily identified by the mean of the subsamples before and after the previously mentioned change. Two subsamples of approximately the same size will be expected to have relatively similar rank sums if they are homogeneous. The Mann‐Whitney U statistic is a function of the size of the subsamples, as well as the sum of the ranks within the subsamples. The U statistic will then be compared to critical values to determine the significance level of the difference of the rank sums, which will identify at what significance level the data are considered homogeneous.

The runs above and below the median test for general randomness is a very straightforward test. The series is arranged in chronological order and the median is determined. The number of “runs” above and equal to, or below the median is then recorded, which each run being consecutive data points sharing the previously stated characteristics. Random data sets will have a certain range of number of runs for a specified significance level, with only data sets with number of runs falling into this range considered to be random at that significance level.

3.0. Results

3.1. Stations and Time Periods Examined

Initially, 38 stations were available for the trend analysis, with Figure 1 providing a general overview of the stations and their location.

The time intervals looked at for the analysis were five minute, ten minute, 15 minute, 30 minute, one hour, two hour, six hour, 12 hour and 24 hour intervals for the IDF data. The one hour, two hour, six hour, 12 hour and 24 hour intervals were used for the hourly data, to mimic the IDF data intervals. The five minute, ten minute, 15 minute and 30 minute intervals were ignored for the hourly data as breaking down the hourly data into smaller intervals would be unrealistic and inaccurate.

The 30 year period made use of a total of ten stations, with the name and location of these sites shown in Table 1. Other relevant data, such as the elevation of these stations and the years of data available for these stations can also be found in Table 1.

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Figure 1 – Geographical location of initial 38 stations

Table 1 – Available stations for the 30, 35 and 40 year analysis periods

IDF Available Station ID Stations Latitude Longitude Elevation (metres) From To

6144475 London 43.03 ‐81.15 278.00 1943 20036131982 Delhi CS 42.87 ‐80.55 232.00 1962 20036149387 Waterloo Wellington

A 43.45 ‐80.38 317.00 1971 2003

6153194 Hamilton A 43.17 ‐79.93 238.00 1971 20036127514 Sarnia A 43.00 ‐82.32 181.00 1962 20026131415 Chatham 42.38 ‐82.20 179.00 1966 20036137362 StThomas WPCP 42.77 ‐81.22 209.00 1926 20036153300 Hamilton BRG 43.28 ‐79.88 102.00 1963 20036148105 Stratford 43.37 ‐81.00 354.00 1966 20036142400 Fergus Shand Dam 43.73 ‐80.33 418.00 1962 2003

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The station selection process was mostly based on data availability constraints. The analysis period was decided to be from 1974 to 2003 to include the largest number of stations. The rejected stations not only consisted of stations whose records ended too early or started too late, but there were also some cases where a number of years were missing from the middle of the record period.

The next study period considered was the 35 year period from 1969 to 2003, which coincidentally included the same stations as the 30 year analysis period. From Table 1, it can be seen that all but two stations have complete data ranging from 1969 to 2003. Although the Waterloo Wellington A station and the Hamilton A station started in 1971, it was decided that there would be a four year maximum on missing year allowance, therefore even though these two stations were missing two years of data, they were still considered valid for this time period.

The next study period was a 40 year study period from 1964 to 2003. From Table 1, it can be seen that Waterloo Wellington A and Hamilton A are no longer acceptable as they do not contain enough years of data. The Chatham and Stratford stations are missing two years of data, but are still considered valid for the purposes of the trend analysis, and all the other stations contain more than sufficient years of data.

Due to the lack of stations with sufficient number of years of data, a more general analysis was done based on the individual periods of each station, such that the trend over the lifetime of the station could be found. Although this makes it harder to compare the stations with each other, it does provide substantially more data. For this secondary analysis, all 28 stations with available data were used. Stations used for this analysis are listed in Table 2

The last nine stations in Table 2, specifically Exeter, Thamesford, Fanshawe Dam, Avon River, Conestogo, Innerkip, Mitchell, St. Marys and Waubuno station did not have IDF data, and only had hourly data meaning the shorter time periods of five minutes, ten minutes, 15 minutes and 30 minutes were not available. Also, the amount of data available is quite limited, with only 21 years available for seven stations, and 17 years for Exeter station.

3.2. Analyzing Trend Results

The Mann‐Kendall test for trend was applied to all stations previously mentioned. The test was done at both the 5% and 10% significance level for the 30, 35 and 40 year analysis periods. The number of stations that show either positive or negative trend were expressed as a percentage of the total number of stations considered for that time period. Table 3 summarizes the results for the 30 year analysis period at the 10% significance level.

The 30 year period shows that most of the longer time intervals had a slight trend, all of them negative. As for non‐significant trends, the ten minute to one hour intervals have more cases of positive non‐significant trend while the other intervals have more negative non‐significant trends. For the most part, the non‐significant trends seem to be evenly distributed.

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Table 2 ‐ List of stations utilized for trend analysis based on stations individual time periods

IDF Available Hourly Available

Station ID

Stations Latitude Longitude Elevation (metres)

From To From To

6144475 London 43.03 ‐81.15 278.00 1943 2003 1965 20006137730 Simcoe 42.85 ‐80.27 241.00 1962 1986 N/A N/A6146714 Preston WPCP 43.38 ‐80.35 273.00 1971 1996 N/A N/A6131982 Delhi CS 42.87 ‐80.55 232.00 1962 2003 1965 20006149387 Waterloo

Wellington A 43.45 ‐80.38 317.00 1971 2003 N/A N/A

6153194 Hamilton A 43.17 ‐79.93 238.00 1971 2003 1965 20006140954 Brantford MOE 43.13 ‐80.23 196.00 1961 2001 1965 20006137147 Ridgetown RCS 42.45 ‐81.88 206.00 1959 2003 N/A N/A6127514 Sarnia A 43.00 ‐82.32 181.00 1962 2002 1965 20006131415 Chatham 42.38 ‐82.20 179.00 1966 2003 1965 20006137362 StThomas WPCP 42.77 ‐81.22 209.00 1926 2003 1965 20006153300 Hamilton BRG 43.28 ‐79.88 102.00 1963 2003 N/A N/A6149625 Woodstock 43.13 ‐80.77 282.00 1962 2003 1965 20006148105 Stratford 43.37 ‐81.00 354.00 1966 2003 1965 20006122847 Goderich 43.77 ‐81.72 214.00 1970 2003 N/A N/A614B2H4 Elora Auto

Station 43.65 ‐80.42 376.00 1970 2002 N/A N/A

6143069 Guelph Turfgrass CS

43.55 ‐80.22 328.00 1954 2003 N/A N/A

6142400 Fergus Shand Dam

43.73 ‐80.33 418.00 1962 2003 1965 2000

6142803 Glen Allan 43.68 ‐80.72 404.00 1960 1970 N/A N/A6122370 Exeter 43.35 ‐81.50 262.10 N/A N/A 1986 20036148233 Thamesford 43.07 ‐81.00 289.60 N/A N/A 1984 2005

N/A Fanshawe dam 43.04 ‐81.18 N/A N/A N/A 1984 2005N/A Avon R N/A N/A N/A N/A N/A 1984 2005N/A Conestogo 43.55 ‐80.50 N/A N/A N/A 1960 2000N/A Innerkip 43.22 ‐80.69 N/A N/A N/A 1984 2005

6145239 Mitchell 43.47 ‐81.18 335.30 N/A N/A 1984 20056147340 St. Marys 43.25 ‐81.18 317.00 N/A N/A 1984 2005

N/A Waubuno 42.98 ‐81.13 N/A N/A N/A 1984 2005

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Table 3 ‐ Number of stations showing trend as a percentage of total number of stations for 1974 to 2003 (30 Year Analysis Period) – 10% Significance Level

Trend 5MIN 10MIN 15MIN 30MIN 1H 2H 6H 12H 24H

Significant Positive 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%Significant Negative 0.00% 0.00% 0.00% 0.00% 10.00% 10.00% 0.00% 10.00% 10.00%Total Significant 0.00% 0.00% 0.00% 0.00% 10.00% 10.00% 0.00% 10.00% 10.00%Non Significant Positive 20.00% 60.00% 60.00% 60.00% 60.00% 40.00% 30.00% 40.00% 30.00%Non Significant Negative 80.00% 40.00% 40.00% 40.00% 30.00% 50.00% 70.00% 50.00% 60.00%Total Non Significant 100.00% 100.00% 100.00% 100.00% 90.00% 90.00% 100.00% 90.00% 90.00%

The 35 year period was analyzed in much the same fashion also at the 10% significance level, with its results displayed in Table 4. However, this time period has an anomaly, because the Fergus Shand Dam station is missing data for the two hour and six hour time intervals in the year 1987, causing this station to only have 30 years of available information for the two hour and six hour time intervals, and therefore not included in the trend analysis for the 35 year analysis period.




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From Table 4, it can be seen that the longer time intervals have no visible trend at all, with the shorter intervals showing slight trends that favour positive trends. The non‐significant trends resemble the 30 year period with the ten minute to one hour intervals having more cases of positive non‐significant trends while the other intervals have more negative non‐significant trends or equal numbers of positive and negative non‐significant trends. For the most part, the non‐significant trends seem to be evenly distributed.

The 40 year period was also analyzed for trends, with the results shown in Table 5.




The 40 year analysis produced no significant trends, which seems very strange. The trend test is usually less sensitive on shorter time periods, therefore having trends for the two shorter time periods and not the longer one is an anomaly. It should be mentioned that this analysis had two stations less than the other two analysis periods, bringing its total stations used to only eight, with two more stations having time intervals with missing data. These stations were Fergus Shand Dam station, which did not have sufficient data for the five minute, ten minute, two hour and six hour intervals, and the Stratford station, which did not have sufficient data for the five minute, ten minute and 15 minute intervals.

Taking a look at the non‐significant trends, it can be noted that for the shorter intervals of ten minutes, 15 minutes, 30 minutes, one hour and two hours, there is a much larger number of positive non‐significant trends, while for the longer intervals of six hours, 12 hours and 24 hours, the opposite is true with mostly negative non‐significant trends.

Comparing Tables 3, 4 and 5, it can be seen that the longer time period of 40 years produced no trend in any station, while as the time period of analysis was reduced, trends started to appear. The analysis

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period of 35 years showed numerous positive trends, but no negative trends, while the analysis period of 30 years showed negative trends, but no positive trends. This will be explored further in the temporal analysis presented in section 3.3.

Slope values of the stations for all time intervals were taken into consideration, and plotted according to analysis period (Figure 2).

Figure 2 ‐ Slope values of the 15 minute interval and all stations for the three analysis periods

It can be seen that for this time interval, the slope values are generally clustered between 0.15 to ‐0.15, with one point outside these bounds. In general for all time intervals, the bounds are approximately 0.4 and ‐0.4. For the 30 year analysis period, the ten minute interval had data clustered around the zero value, while the five minute interval had the majority of its values clustered below the zero value. The other time intervals had the slope values spread out evenly. For the 35 year analysis period, the five minute interval once again had the majority of its values clustered below zero, while for the ten, 15 and 30 minute interval the majority of the values were clustered above zero. The other intervals were considerably more evenly spread out. Finally, for the 40 year analysis period, the ten and 15 minute intervals had the majority of the slope values above zero, while the six, 12 and 24 hour intervals had the majority of their slope values below zero. The remaining plots are located in Appendix A

As previously mentioned, a trend analysis was also done on each station with all existing data for that station used. The results of this analysis could not be summarized the same as the other time frames

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due to the differing nature of each station’s analysis period, therefore the results were summarized simply as whether the station had a positive trend, negative trend or no significant trend. This is shown in Table 6 where an absolute value of 0.5 represents no significant trend, and a positive or negative number representing a positive or negative trend, respectively. A number with absolute value of two means a trend was shown at the 5% significance level, while an absolute value of one shows a trend at the 10% significance level. The last nine stations in the table are the stations that had only hourly data, with most stations only having 21 years of data.

Table 6 ‐ Station trend summary for analysis based on individual analysis periods

Time Interval (hours) Station Name Station ID 1/12 1/6 1/4 1/2 1 2 6 12 24

Elora Auto Climate 614B2H4 0.5 ‐0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Goderich 6122847 2 2 2 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5Sarnia A 6127514 ‐0.5 ‐0.5 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5Chatham WPCP 6131415 0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5Delhi CS 6131982 ‐0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5Ridgetown RCS 6137147 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5StThomas WPCP 6137362 ‐0.5 ‐0.5 ‐0.5 0.5 0.5 0.5 ‐0.5 0.5 0.5Simcoe 6137730 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐2Brantford MOE 6140954 ‐0.5 ‐0.5 ‐0.5 0.5 0.5 0.5 0.5 ‐0.5 0.5Fergus Shand Dam 6142400 ‐0.5 0.5 ‐0.5 ‐0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Geln Allan 6142803 N/A N/A N/A N/A 0.5 0.5 0.5 0.5 0.5Guelph Turfgrass CS 6143069 0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5London CS 6144475 0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 0.5Preston WPCP 6146714 0.5 0.5 0.5 2 0.5 0.5 ‐0.5 0.5 ‐0.5Stratford MOE 6148105 ‐0.5 ‐0.5 ‐0.5 ‐0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Waterloo Wellington A 6149387 ‐0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Woodstock 6149625 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Hamilton A 6153194 ‐0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Hamilton RBF CS 6153300 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Avon N/A N/A N/A N/A N/A ‐0.5 ‐0.5 ‐0.5 ‐1 ‐1Conestogo N/A N/A N/A N/A N/A ‐2 ‐0.5 ‐0.5 ‐0.5 ‐0.5Exeter N/A N/A N/A N/A N/A ‐0.5 ‐1 ‐1 ‐0.5 ‐0.5Fanshawe N/A N/A N/A N/A N/A ‐2 ‐2 ‐2 ‐2 ‐1Innerkip N/A N/A N/A N/A N/A ‐0.5 0.5 ‐0.5 0.5 ‐0.5Mitchell N/A N/A N/A N/A N/A ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5StMary N/A N/A N/A N/A N/A ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Thamesfo N/A N/A N/A N/A N/A ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Waubuno N/A N/A N/A N/A N/A 0.5 0.5 ‐0.5 ‐0.5 ‐0.5

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It can be easily inferred from these results that this area of study showed no significant trend. Only seven out of the 28 stations showed a noticeable trend, with four of these coming from the stations with hourly data only. This also further strengthens the argument that as the study period increases, there is no significant trend, while shorter analysis periods produce more noticeable trends, in this case negative trends. All three stations that showed trend from the stations that had IDF data all only had a small number of years of data and were not considered for the 30 year, 35 year or 40 year analysis. Goderich station had only 18 years of data, Simcoe only 25 years and Preston WPCP only 23 years. More detailed results of the trend analysis are available in Appendix B

Due to the small number of significant trends identified, it was not necessary to use the bootstrap resampling approach to ascertain the field significance of the results. For each analysis period and each rainfall duration, the number of significant trends is not significant.

3.3. Temporal Patterns in Trends

Taking a closer look at the results summarized by Tables 3, 4 and 5 will show that there exist stations that display differing trends depending on the time period analyzed. Stations that showed differing trends were then classified into different types. The types and the descriptions are located in Table 7, while the actual trend analysis results for each time period are located in Appendix B.

Table 7 ‐ Types of discrepancies between trend results for the 30, 35 and 40 year analysis periods and the number of occurrences

Type 30 Year Trend

35 Year Trend

40 year Trend

Number of Occurrences

Type 1 None Increasing None 6 Type 2 Decreasing None None 4

The occurrences for each type listed were counted and the number of occurrences summarized in the table. Although these are not all the permutations possible for the three analysis periods, these were the only two types with non‐zero number of occurrences. Due to the small number of stations, as well as the lack of trends amongst these stations, this type of analysis does not give us a very complete view of the results. To compliment Table 7, a few facts should be mentioned. First, no station exhibited a trend for all analysis periods and no station showed a trend in two analysis periods. Second, all negative trends existed solely in the 30 year analysis period, while all positive trends existed solely in the 35 year analysis period, with no trends in the 40 year analysis period. This is why Table 7 only has values for type 1 and type 2.

To explain why this anomaly exists, it was found useful to review the LOWESS smoothed curves of the stations that displayed these discrepancies.

Figure 3 shows typical type 1 behaviour as represented by the one hour time interval for Chatham WPCP station. As can be seen, the data in the 1974 to 2003 (30 year) analysis period is relatively flat, which

13

explains why there is no trend for a 30 year analysis period. For the 35 year analysis period, there are a lot of years with very low precipitation values around the year 1970, which would translate to an increasing trend for the analysis period 1969 to 2003. Finally, for the 40 year analysis period, we can see that there were many larger extreme precipitation values around 1964, at the beginning of the 40 year period, which would have counterbalanced the lower values of precipitation around the year 1970, therefore once again providing no trend overall. This was the general case for all stations showing type 1 behaviour, with a group of high precipitation followed by a group of low precipitation, followed by the rest of the data, which were usually quite uniform and showed no trend.

Figure 3 ‐ Typical type 1 behaviour

Figure 4 is a plot of both the LOWESS smoothed graph as well as the raw data of the one hour interval for extreme rainfall for the Hamilton RBG station. The type 2 behaviour can be explained by looking first at the 30 year analysis period which starts in the year 1974. As can be seen, there is a large group of high precipitation around and after the year 1975. This means that when looking from year 1974 and beyond, the period will begin with a considerable grouping of high precipitation values that decrease in the rest of the analysis period. However, around 1970 is a small grouping of lower precipitation values, with the years 1964 to 1974 brought back into consideration in the 35 and 40 year analysis periods, there is no significant trend to be seen. All type two behaviour typically has a peak around or after 1974, the beginning of the 30 year analysis period, with lower values around the year 1965 to 1970 to counter‐balance the peak. LOWESS smoothed graphs for all stations that showed either a type 1 or type 2 behaviour are presented in Appendix C.

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Figure 4 ‐ Typical type 2 behaviour

3.4. Summary of Other NonParametric Tests

The remaining three non parametric tests were performed on the 40 year analysis period of 1964 to 2003, however, no stations were eliminated for missing data and the test was simply done with whatever data were available within the specified range. The stations were separated into two groups, with the first group being stations that had IDF data available and the second group being stations that only had hourly data available. All the tests were done at a 5% significance level, including the trend analysis.

Taking a closer look at the results located in Appendix D from the first group, it was noticed that while the majority of stations contained homogeneous, random and independent data, there were a few that were not. The focus will first be on stations that showed a trend and failed one of the other three non‐parametric tests. The three stations where this occurred were Goderich, Preston WPCP and Simcoe station. At these stations, there were both a positive trend and a rejected null hypothesis for the Mann‐Whitney homogeneity test. This was during the five minute and ten minute intervals for Goderich, during the 30 minute interval at Preston WPCP and during 24 hour interval at Simcoe. A non‐homogeneous data set would mean it is very likely that some change occurred during the time period of analysis that would cause a difference between the means of the subsamples before and after said change. Therefore this would be an obvious explanation for the existence of a trend. An example to illustrated this is provided as Figure 5.

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Figure 5 ‐ Rainfall data for Preston WPCP for the 30 minute intervals showing typical non‐homogeneous behaviour

From Figure 5, it can be seen that there is an obvious separation of data at approximately 1985, with data before and after 1985 having distinctly different averages. It can also be seen from the LOWESS smoothed curve, that before 1985, the curve stays between the 15 and 20 mm range, while after 1985, the curve increases to a 20 to 25 mm range. This is very typical non‐homogenous behaviour.

Although the majority of the trends were accompanied by a rejected null hypothesis for the Mann‐Whitney homogeneity test, there was one case where there was a trend but the null hypothesis was accepted in Goderich during the 15 minute interval. This could be explained by a weaker trend for this time interval, as it had a probability level of 95.6%, which was very close to the cut off limit of 95%.

There were also many cases where the data set was deemed to be not homogeneous, but did not show a trend. Preston WPCP and Waterloo Wellington showed such traits. The Preston WPCP showed a rejected null hypothesis for the homogeneity test but no trend for the 15 minute interval. The Waterloo Wellington station showed such behaviour for four time intervals, 15 minute, 30 minute, one hour, and 12 hour intervals. Although the Waterloo Wellington station did not show a trend for the 40 year analysis period, it did show trends for the shorter 30 year analysis period, which could then be used to explain the rejected null hypothesis for the homogeneity test. Figure 6 is provided to illustrate this.

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Figure 6 ‐ Rainfall data for Waterloo Wellington Station for the 30 minute intervals showing typical non‐homogeneous behaviour

Figure 6 shows that there is obvious non‐homogeneous behaviour, with a separation of data behaviour at approximately 1980. The pattern shown in Figure 6 resembles that of Figure 5, except Figure 6 has a much more prominent downward trend after its peak that causes the LOWESS curve to go below the 20 mm range. The average before 1980 is approximately 17, as the LOWESS curve is in the 15 to 20 range. After 1980 however, there is an increase to 20 to 25 mm range. Although there is a dip below 20 mm after the year 2000, this did not seem to affect the Mann Whitney Homogeneity test. It did seem to affect the trend test, however, since there was no trend for the 40 year analysis period. It should be noted that for shorter time periods, this station showed negative trends, while the Preston WPCP station showed a positive trend with a data set much like that of Figure 6 from years 1970 to 1990.

The non‐parametric test for randomness concluded that all stations other than Glenn Allan and Waterloo Wellington stations were completely random (with 5% significance). The Glenn Allan station had less than four pieces of data falling within the 40 year analysis period, making the results not as meaningful. The Waterloo Wellington station had a rejected null hypothesis for the randomness test only for the 12 hour interval.

The results for the Spearman Rank Order Serial Correlation Coefficient test for independence did not correlate very well with whether or not a station showed trend. Brantford MOE, Guelph Turfgrass CS and Stratford stations had their null hypothesis rejected due to an overly large negative correlation, while Hamilton A and Hamilton RBG CS had time intervals where the null hypothesis was rejected due to an overly large positive correlation. Waterloo Wellington was a strange case, with the null hypothesis

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being rejected for negative correlation for the five minute interval, and rejected for positive correlation for the 12 hour and 24 hour intervals.

4.0. Conclusions and Recommendations

The analysis of historical extreme precipitation events around the case study area of London, Ontario showed no trends for the 40 year analysis period. The stations that did not have enough data to be considered for the 40 year analysis did show trend during the available data period. The majority of these were approximately 20 years in length and generally showed negative trend.

Although stations did not show any trend for the 40 year analysis period, some stations did show positive trend in the 35 year analysis period and other stations a negative trend in the 30 year analysis period. These temporal differences were found to be caused by differing temporal clusters of high and low extreme precipitation values. Stations that had no trend in the 40 year analysis period but an increasing trend in the 35 year analysis period, which was named a type 1 behaviour, generally had a “check mark” shape when the data was smoothed into a LOWESS curve. For the stations that had a negative trend in the 30 year period and no trend in the 40 year period, which was named a type 2 behaviour, the LOWESS curve looked generally flat with a “bump” in the middle, typically around the year 1975. Both types of discrepancies were caused by a group of high extreme precipitation values and a group of low extreme precipitation values, with the difference being that type 1 had the group of higher values come before the group of lower values, while type 2 had them in the reverse order.

The secondary analysis that looked at all stations for their corresponding time periods showed nearly no trend. A total of seven stations out of 28 showed trends. However, four of these came from stations that had only hourly data for 21 years, while the other three came from stations with less than 25 years of data

Trend slopes seemed very evenly distributed for all three periods of analysis. While the 35 year analysis had more variation and more extreme values, the slope values were generally bound by the ‐0.4 to 0.4 values. For all three analysis periods, there seemed to be a larger number of negative slope values.

The results of the other non‐parametric tests showed that the data utilized for this analysis was for the most‐part, random, independent and homogeneous. However, stations that were not homogenous were usually related to a trend detected by the trend test. The other non‐parametric tests did not have such tendencies.

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References

Adamowski, K., and Bougadis, J. 2003. Detection of Trends in Annual Extreme Rainfall. Hydrological Processes. 17: 3547-3560.

Cleveland, W.S. 1979. Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74(368): 829-836. Groisman, P.Y., Karl, R.T., Easterling, R.D., Knight, W.R. and Jamason, F.P. 1999. Changes in the Probability of Heavy Precipitation: Important Indicators of Climatic Change. Climatic Change 42: 243 – 283.

Kendall, M.G. (1975) Rank Correlation Measures, Charles Griffin, London.

Mann, H.B. (1945) Non-parametric tests against trend. Econometrica, 13: 245-259.

Mirza, M.Q., Warrick, R.A., Erickson, N.J. and Kenny, G.J. 1998. Trends and Persistence in Precipitation in the Ganges, Brahamaputra and Meghna basins in South Asia. Hydrological Sciences Journal, 43: 845-858.

Orsborn, T.J., Hulme, M., Jones, P.D. and Bassett, T.A. 2000. Observed Trends in the Daily Intensity of United Kingdom Precipitation. International Journal of Climatology. 20:347- 364.

Stone, A.D., Weaver, J. and Zwiers, W.F. 2000. Trends in Canadian Precipitation Intensity. Atmosphere – Ocean. 38(2): 321 – 374. Zhang, X., Lucie, V.A., Ain, N. and Hogg, W. 2000. Temperature and Precipitation trends in Canada during the 20th Century. Atmosphere – Ocean, 38(3): 395 – 429.

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Appendix A

Slope Analysis

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Figure A1 – Slope analysis for the 5 minute interval

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Figure A5 – Slope Analysis for the 1 hour interval

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Figure A6 – Slope analysis for the 2 hour interval


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Figure A9 – Slope Analysis for the 24 hour interval

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Appendix B

Trend Summary

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Table B1 – Trends for the 40 year analysis period

Station Name Station ID 5MIN 10MIN 15MIN 30MIN 1H 2H 6H 12H 24H

Brantford MOE 6140954 3 3 3 3 3 3 3 3 3Chatham WPCP 6131415 0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5Delhi CS 6131982 ‐0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5Elora Auto Climate 614B2H4 3 3 3 3 3 3 3 3 3Fergus Shand Dam 6142400 3 3 ‐0.5 ‐0.5 ‐0.5 3 3 ‐0.5 ‐0.5Geln Allan 6142803 3 3 3 3 3 3 3 3 3Goderich 6122847 3 3 3 3 3 3 3 3 3Guelph Turfgrass CS 6143069 3 3 3 3 3 3 3 3 3Hamilton A 6153194 3 3 3 3 3 3 3 3 3Hamilton RBF CS 6153300 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5London CS 6144475 0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5Preston WPCP 6146714 3 3 3 3 3 3 3 3 3Ridgetown RCS 6137147 3 3 3 3 3 3 3 3 3Sarnia A 6127514 ‐0.5 ‐0.5 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5Simcoe 6137730 3 3 3 3 3 3 3 3 3StThomas WPCP 6137362 ‐0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Stratford MOE 6148105 3 3 3 ‐0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5Waterloo Wellington A 6149387 3 3 3 3 3 3 3 3 3Woodstock 6149625 3 3 3 3 3 3 3 3 3



Brantford MOE 6140954 3 3 3 3 3 3 3 3 3 Chatham WPCP 6131415 1 2 0.5 1 1 0.5 0.5 0.5 0.5 Delhi CS 6131982 ‐0.5 0.5 0.5 0.5 1 1 0.5 0.5 0.5 Elora Auto Climate 614B2H4 3 3 3 3 3 3 3 3 3 Fergus Shand Dam 6142400 ‐0.5 ‐0.5 0.5 0.5 0.5 3 3 ‐0.5 ‐0.5 Geln Allan 6142803 3 3 3 3 3 3 3 3 3 Goderich 6122847 3 3 3 3 3 3 3 3 3 Guelph Turfgrass CS 6143069 3 3 3 3 3 3 3 3 3 Hamilton A 6153194 ‐0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 Hamilton RBF CS 6153300 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 0.5 ‐0.5 London CS 6144475 ‐0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 0.5 Preston WPCP 6146714 3 3 3 3 3 3 3 3 3 Ridgetown RCS 6137147 3 3 3 3 3 3 3 3 3 Sarnia A 6127514 ‐0.5 ‐0.5 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5 Simcoe 6137730 3 3 3 3 3 3 3 3 3 StThomas WPCP 6137362 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 Stratford MOE 6148105 0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5

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Waterloo Wellington A 6149387 ‐0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 Woodstock 6149625 3 3 3 3 3 3 3 3 3



Brantford MOE 6140954 3 3 3 3 3 3 3 3 3 Chatham WPCP 6131415 0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 0.5 ‐0.5 Delhi CS 6131982 ‐0.5 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 Elora Auto Climate 614B2H4 3 3 3 3 3 3 3 3 3 Fergus Shand Dam 6142400 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ‐0.5 Geln Allan 6142803 3 3 3 3 3 3 3 3 3 Goderich 6122847 3 3 3 3 3 3 3 3 3 Guelph Turfgrass CS 6143069 3 3 3 3 3 3 3 3 3 Hamilton A 6153194 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 Hamilton RBF CS 6153300 ‐0.5 0.5 0.5 ‐0.5 ‐2 ‐2 ‐0.5 ‐0.5 ‐0.5 London CS 6144475 ‐0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 0.5 Preston WPCP 6146714 3 3 3 3 3 3 3 3 3 Ridgetown RCS 6137147 3 3 3 3 3 3 3 3 3 Sarnia A 6127514 ‐0.5 ‐0.5 ‐0.5 0.5 0.5 0.5 0.5 0.5 0.5 Simcoe 6137730 3 3 3 3 3 3 3 3 3 StThomas WPCP 6137362 ‐0.5 ‐0.5 ‐0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 Stratford MOE 6148105 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 ‐0.5 Waterloo Wellington A

6149387 ‐0.5 0.5 0.5 0.5 0.5 ‐0.5 ‐0.5 ‐1 ‐2

Woodstock 6149625 3 3 3 3 3 3 3 3 3

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Appendix C

Temporal Analysis – LOWESS plots

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Figure C1 – LOWESS smoothed curve for Chatham WPCP station for the 5 minute interval – Showing Type 1 behaviour

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Figure C2 – LOWESS smoothed curve for Chatham WPCP station for the 10 minute interval – Showing Type 1 behaviour

Figure C3 – LOWESS smoothed curve for Chatham WPCP station for 30 minute interval – Showing Type 1 behaviour

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Figure C4 – LOWESS smoothed curve for Chatham WPCP station for the 1 hour interval – Showing Type 1 behaviour

Figure C5 – LOWESS smoothed curve for Delhi CS station for the 1 hour interval – Showing Type 1 behaviour

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Figure C6 – LOWESS smoothed curve for Hamilton BRG CS station for the 1 hour interval – Showing Type 2 behaviour

Figure C7 – LOWESS smoothed curve for Delhi CS station for the 2 hour interval – Showing Type 1 behaviour

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Figure C8 – LOWESS smoothed curve for Hamilton BRG CS station for the 2 hour interval – Showing Type 2 behaviour

Figure C9 – LOWESS smoothed curve for Waterloo Wellington A station for 12 hour interval – Showing Type 2 behaviour

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Figure C10 – LOWESS smoothed curve for Waterloo Wellington A station for 24 hour interval – Showing Type 2 behaviour

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Appendix D

Other NonParametric Test Results

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Table D1 – Results for the Spearman rank correlation test for independence, runs above and below the median for randomness and Man‐Whitney test for homogeneity for the 5 minute interval at the 5% significance level

Station ID Trend Spearman Rank Correlation

Runs above and below the median

Mann‐Whitney

614B2H4 0 accept accept accept 6122847 1 accept accept reject 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 accept accept accept 6142400 0 accept accept accept 6142803 3 N/A reject reject 6143069 0 accept accept accept 6144475 0 accept accept accept 6146714 0 accept accept accept 6148105 0 accept accept accept 6149387 0 reject accept accept 6149625 0 accept accept accept 6153194 0 accept accept accept 6153300 0 accept accept accept

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Table D2 ‐ Results for the Spearman rank correlation test for independence, runs above and below the median for randomness and Man‐Whitney test for homogeneity for the 10 minute interval at the 5% significance level



Mann‐Whitney

614B2H4 0 accept accept accept 6122847 1 accept accept reject 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 accept accept accept 6142400 0 accept accept accept 6142803 3 N/A reject reject 6143069 0 reject accept accept 6144475 0 accept accept accept 6146714 0 accept accept accept 6148105 0 accept accept accept 6149387 0 accept accept accept 6149625 0 accept accept accept 6153194 0 accept accept accept 6153300 0 accept accept accept

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Table D3 ‐ Results for the Spearman rank correlation test for independence, runs above and below the median for randomness and Mann‐Whitney test for homogeneity for the 15 minute interval at the 5% significance level



Mann‐Whitney

614B2H4 0 accept accept accept 6122847 1 accept accept accept 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 accept accept accept 6142400 0 accept accept accept 6142803 3 N/A reject accept 6143069 0 reject accept accept 6144475 0 accept accept accept 6146714 0 accept accept reject 6148105 0 accept accept accept 6149387 0 accept accept reject 6149625 0 accept accept accept 6153194 0 reject accept accept 6153300 0 accept accept accept

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Table D4 ‐ Results for the Spearman rank correlation test for independence, runs above and below the median for randomness and Mann‐Whitney test for homogeneity for the 30 minute interval at the 5% significance level



Mann‐Whitney

614B2H4 0 accept accept accept 6122847 0 accept accept accept 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 accept accept accept 6142400 0 accept accept accept 6142803 3 N/A reject accept 6143069 0 accept accept accept 6144475 0 accept accept accept 6146714 1 accept accept reject 6148105 0 accept accept accept 6149387 0 accept accept reject 6149625 0 accept accept accept 6153194 0 reject accept accept 6153300 0 accept accept accept

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Table D5 ‐ Results for the Spearman rank correlation test for independence, runs above and below the median for randomness and Man‐Whitney test for homogeneity for the 1 hour interval at the 5% significance level



Mann‐Whitney

614B2H4 0 accept accept accept 6122847 0 accept accept accept 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 reject accept accept 6142400 0 accept accept accept 6142803 0 N/A reject accept 6143069 0 accept accept accept 6144475 0 accept accept accept 6146714 0 accept accept accept 6148105 0 accept accept accept 6149387 0 accept accept reject 6149625 0 accept accept accept 6153194 0 reject accept accept 6153300 0 reject accept accept

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Table D6 ‐ Results for the Spearman rank correlation test for independence, runs above and below the median for randomness and Mann‐Whitney test for homogeneity for the 2 hour interval at the 5% significance level



Mann‐Whitney

614B2H4 0 accept accept accept 6122847 0 accept accept accept 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 reject accept accept 6142400 0 accept accept accept 6142803 0 N/A reject accept 6143069 0 accept accept accept 6144475 0 accept accept accept 6146714 0 accept accept accept 6148105 0 accept accept accept 6149387 0 accept accept accept 6149625 0 accept accept accept 6153194 0 accept accept accept 6153300 0 accept accept accept

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Mann‐Whitney

614B2H4 0 accept accept accept 6122847 0 accept accept accept 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 accept accept accept 6142400 0 accept accept accept 6142803 0 N/A reject accept 6143069 0 accept accept accept 6144475 0 accept accept accept 6146714 0 accept accept accept 6148105 0 accept accept accept 6149387 0 accept accept accept 6149625 0 accept accept accept 6153194 0 accept accept accept 6153300 0 accept accept accept

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Mann‐Whitney

614B2H4 0 accept accept accept 6122847 0 accept accept accept 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 0 accept accept accept 6140954 0 reject accept accept 6142400 0 accept accept accept 6142803 0 N/A reject accept 6143069 0 accept accept accept 6144475 0 accept accept accept 6146714 0 accept accept accept 6148105 0 accept accept accept 6149387 0 reject reject reject 6149625 0 accept accept accept 6153194 0 accept accept accept 6153300 0 accept accept accept

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Mann‐Whitney

614B2H4 0 accept accept accept 6122847 0 accept accept accept 6127514 0 accept accept accept 6131415 0 accept accept accept 6131982 0 accept accept accept 6137147 0 accept accept accept 6137362 0 N/A accept accept 6137730 ‐1 accept accept reject 6140954 0 reject accept accept 6142400 0 accept accept accept 6142803 0 N/A reject accept 6143069 0 accept accept accept 6144475 0 accept accept accept 6146714 0 accept accept accept 6148105 0 reject accept accept 6149387 0 reject accept accept 6149625 0 accept accept accept 6153194 0 accept accept accept 6153300 0 accept accept accept

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