Historical climate data (Precipitation and Temperature) analysis of Ottawa
Farshad Jalili Pirani (251000339)
October 26, 2018
Introduction
Human health, energy demand and many global services such as water, agriculture (crop production) can be affected by climate especially extreme events of two main temperature and Precipitation parameters (Cong and Brady 2012, Tencer, Weaver et al. 2014, Rana, Moradkhani et al. 2017). Under specially and temporally climate change condition, such affects will be worse. Changes in many extreme weather and climate events have been observed since about 1950. The global surface temperature has risen up by 0.6°C since late 19th century and it is projected to increase by over 1.5°C until the end of 21th under all emission scenarios. Moreover, extreme precipitation events will become more intense and frequent in many regions especially in most parts of the multitude areas; however, this change is not uniform throughout the world (Trömel, Schönwiese et al. 2007, Allen, Macalady et al. 2010, Pachauri, Allen et al. 2014). Obviously, such changes have many climatological and hydrological implications. For example, high extremes of temperature along with low extremes of precipitation leads to different degrees of droughts which causes water shortage in many parts of the world mainly dry regions affecting environmental aspects especially crop production, directly(National Drought Policy Commission %J US Department of Agriculture 2000). On the other hand, high extremes of precipitation concurrent with low quantiles of temperature will result in flood having many physical damages like destroying infrastructures and human casualties (Deshmukh, Ho Oh et al. 2011). Regarding such affects for climate parameters, the aim of this study is to quantify and analyze the relationship between Precipitation and Temperature and their changes for Ottawa city using two deterministic algorithms.
Data and study area
With an elevation of 70 m above sea level and a population of 964743, Ottawa as the capital of Canada is locating at northern part of Ontario. From viewpoint of climate, it locates in climate zone of Great Lakes with humid continental climate. While summers are warm and humid in this city, Snow and ice are dominant during the winter season and spring. And fall are variable, prone to extremes in temperature and unpredictable swings in conditions. According to more than 100 years record of climate data for this city, the highest and lowest temperatures till now are 38 °C and -39 °C, respectively.
Daily precipitation (Pcp), temperature (Temp) data used in this study were obtained based on Adjusted and Homogenized Canadian Climate Data (AHCCD; Mekis and Vincent 2011). The time span of both Pcp and Temp data is from 3/1/1890 to 30/12/2017. A summary of the data are in following table.
| Number | Year | Month | Day | Date | Pcp | Temp |
|---|---|---|---|---|---|---|
| 1 | 1890 | 3 | 1 | 1890-03-01 | 11.3 | -6.7 |
| 2 | 1890 | 3 | 2 | 1890-03-01 | 0 | 1.1 |
| 3 | 1890 | 3 | 3 | 1890-03-01 | 0 | -9 |
| 4 | 1890 | 3 | 4 | 1890-03-01 | 1.02 | -19 |
| 5 | 1890 | 3 | 5 | 1890-03-01 | 1.02 | -15 |
| - | - | - | - | - | - | |
| - | - | - | - | - | - | |
| 47554 | 2017 | 12 | 11 | 2017-11-12 | 1.27 | -7 |
Methodology
In this part, we are going to:
To Analyze time series of both Pcp and Temp and understanding any upward or downward trend for these data at different time scales of Daily, Monthly (sum of Pcp for all days of a month and mean of Temp of days within a month), seasonal (sum of Pcp for all days of a season and mean of Temp of days within a season) and Annual (sum of Pcp for all days of a year and mean of Temp of days within a year). Besides, the trend analysis has also been done for daily data at different months and seasons.
Studying the variation in Pcp and Temp at all time-scales mentioned above.
Finding the relationship correlation between Pcp and Temp using two deterministic methods (linear and non-linear methods). Kendall’s Tau criterion has been used to evaluate how strength is their dependency.
In the end, we will come up with the true distribution of data at different time-scales.
Results
1. Time series and Trend analysis
1.1. Daily
The time series (in blue) of Pcp and Temp accompanied with fitted trend line (green line) were plotted. As we can see, most daily precipitation are less than 30 and the mean of temperature is almost zero. The trend for 128 years of daily data for Pcp and Temp along with the p-value of Mann-Kendall test shows both variables are non-stationary and have upward trend although this trend is more sensible for temperature. This trend is negligible for Pcp (Figure 1).
Figure1) Trend of daily Pcp and Temp
1.2. Monthly and seasonal
When we aggregate the data for each month and then see the results of p-values, it can be seen that there is no trend for monthly Pcp with p-value of 0.179; however, monthly Temp with p-value less than 0.05 still has trend in its data. The results of seasonal time scale is the same as monthly time step (No significant trend for Pcp while vice versa for Temp) (Figure 2, 3).
Figure 2) Trend of monthly Pcp and Temp
Figure 3) Trend of seasonal Pcp and Temp
1.3. Annual
Regarding aggregated data for each year, both Pcp and Temp have an increasing trend. While having a mean value of almost 5 in 1890, Temp increased by 6.5 in 2017 on average. Annual Pcp also was less than 1000 mm per year before 1950; however, it increased by more than almost 1100 in 2017 (Figure 4).
Figure 4) Trend of Annual Pcp and Temp
1.4. Results of different months and seasons
No trend is observed for daily data of Pcp for some months; however, for some other months, this trend is a very small increasing or decreasing trend although accretionary trend is more sensible. The condition for Temp is a little bit different. Obviously, there is an upward trend for all months although it’s more for December and February (Figure 5, 6). Like months, no significant trend for Pcp for all seasons except summer having a slight increasing trend; however, Temp experienced accretionary trend in four seasons, especially, Winter (Figure 7, 8).
Figure 5) Trend of Pcp for different months
Figure 6) Trend of Temp for different months
Figure 7) Trend of Pcp for different seasons
Figure 8) Trend of Temp for different seasons
2. Variation of Pcp and Temp
2.1. Boxplots of daily, monthly and seasonal Pcp and Temp
The boxplot of daily data for 128 years indicates a wide variation in the Pcp data. Actually, due to too many zeros (not having precipitation for many days), the median of Pcp data inclines toward zero which is almost 3 or 4mm and therefore, many values especially, extreme values of Pcp will be treated as outliers; however, the boxplot of aggregated monthly data is almost symmetric around median and variation increased in comparison with daily scenario. Again, no Pcp for some months in summer cause a decrease in the quantiles of Pcp leading to many outliers. Seasonal boxplot also is symmetric and it seems it has a normal distribution (Figure 9).
For Temp, the boxplots show no noticeable skewness in the Temp data of three time-scales; however, the variation is less for seasonal scenario in comparison with daily and monthly data.
Figure 9) Boxplot of daily, monthly and seasonal Pcp
Figure 10) Boxplot of daily, monthly and seasonal Temp
2.2. Boxplots of Pcp and Temp for different months and seasons
Regarding Pcp, while most months have median close to each other and they follow a normal distribution, they have some differences in variations. For example, the Pcp variation in March, July and September is more than other months. Regarding Temp, It’s obvious that since January as the coldest month to till july, the monthly mean Temp is increasing and the variation of Temp also is decreasing; however, since July onward, the mean Temp decreases till December. The variation also partly increases till December. The first and last month of the year have the most variation in the data (Figure 11).
Figure 11) Boxplot of Pcp and Temp for different months
The amount of Pcp in winter and summer is more than two other seasons; however, the variation of Pcp in summer (the highest variation) and fall is more than winter and spring. On the other hand, winter Temp and its variation is the lowest while summer Temp and its variation is the most (Figure 12).
Figure 12) Boxplot of Pcp and Temp for different seasons
3. Relationship between Pcp and Temp
3.1. All data (daily)
The daily data of Pcp and Temp have been plotted against each other in order to see the relationship between them. Both linear and non-linear models have been fitted. The results of Kendall’s Tau (Linear model) indicate that in daily time scale, this dependency is week (-0.01) because most values of Pcp are zero. A simple look at the axises, we can see that Pcp has a Positive skewness while Temp has negative skewness. The distribution of none of them is normal. The yellow dashed lines demonstrate the upper (0.95) and lower (0.05) quantiles of these two variables. Joint occurrence of extreme Pcp and Temp have also been shown in dark colors. It seems that higher quantiles of Pcp called extreme Pcp happening with higher quantiles of Temp (higher temperatures) are more than extreme Pcps and Lower Temps (Figure 13).
Figure 13) Correlation of daily Pcp and Temp
3.2. Different months and seasons
Figure 14 and 15 shows the dot plot and fitted nonlinear line to daily data for each month. Again, not a satisfactory relationship exists between Pcp and Temp in each month and each season. This can be observed in figure 15 as well.
Figure 14) Correlation of daily Pcp and Temp for different months
Figure 15) Correlation of daily Pcp and Temp for different seasons
Figure 16) Correlation of daily Pcp and Temp for different months and seasons
3.3. Monthly and seasonal time steps
In monthly and seasonal time steps, also not meaningful relationship exists between Pcp and Temp. The graph for seasonal obviously shows three different patterns which are related to almost different temperatures in different seasons (figure 17).
Figure 17) Correlation of monthly and seasonal Pcp and Temp
4. Histogram and density function of Pcp and Temp
4.1. daily, monthly and seasonal
The histogram and true density of Pcp and Temp have been created. For Pcp, due to many zeros (many days don’t have Pcp), the histogram and its density are like Gamma distribution; however, the aggregated monthly and seasonal data are almost normal (Figure 17). Regarding Temp, both daily and monthly are not that much like normal distribution; however, in seasonal time step, the condition is different (more similarity to normal distribution) (Figure 18).
Figure 18) Histogram and density figure of Pcp at different time steps
Figure 19) Histogram and density figure of Temp at different time steps
4.2. Different months and seasons
The histograms of Pcp for different months indicate that none of them are like normal distribution but like Gamma distribution; however, for Temp, based on obtained histogram, data follows normal distribution except for months June, July and August which their data are a little bit skewed towards right-hand side (negative skewness) (Figure 19). Regarding seasonal time scale, Pcp and Temp almost have normal distribution in all seasons (Figure 20).
Figure 19) Histogram of Temp at different Pcp and at different months
Figure 19) Histogram of Pcp and Temp at different seasons
Discussion and conclusion
Regarding obtained results for trend, it can be said that Ottawa is going to experience an increase in both temperature and precipitation although this increasing trend is more remarkable for Temp rather than Pcp. this highlights the real fact of global warming (climate change) over the world. Winter will be more warmer than past and summer is going to be more wet. Regarding any analysis with the assumption of normality, Temp data almost follows normal distribution while Pcp follows Gamma distribution; however, there are some differences at different time steps. Besides, according to boxplots, the variation of Pcp is more than Temp. This is very important for predicting Ppc and Temp in future. In other words, for Pcp, there is higher uncertainty in predictions than Temp. Overall, there is not significant relationship between Pcp and Temp. While currently, most floods are happening in winter, the effects of climate change seems to trigger flooding in summer in future as higher Pcps are occurring with higher temperatures which are in summer.
References
Cong, R.-G. and M. J. T. S. W. J. Brady (2012). “The interdependence between rainfall and temperature: copula analyses.” 2012. Tencer, B., A. Weaver, F. J. J. o. A. M. Zwiers and Climatology (2014). “Joint occurrence of daily temperature and precipitation extreme events over Canada.” 53(9): 2148-2162. Rana, A., H. Moradkhani, Y. J. T. Qin and A. Climatology (2017). “Understanding the joint behavior of temperature and precipitation for climate change impact studies.” 129(1-2): 321-339. Trömel, S., C.-D. J. T. Schönwiese and A. Climatology (2007). “Probability change of extreme precipitation observed from 1901 to 2000 in Germany.” 87(1-4): 29-39. Allen, C. D., A. K. Macalady, H. Chenchouni, D. Bachelet, N. McDowell, M. Vennetier, T. Kitzberger, A.