1. Climate Trends in America
By: Andrew Bechard and Michael Drebot

4. Global Warming Effects
Increase of greenhouse gas in our atmosphere
Warmer temperatures give rise to changes in weather

5. Carbon Footprint
Earth’s temperature increasing at .8o F per year

6. Is there a Change?
Want to know if there is a trend between the rise of temperature and the rise of rain or snowfall
Use data from the past to mathematically determine if there is a trend

7. Mathematical Solution
Take data from the past 47 years of two cities in America
Interpret the data using mean, standard deviation, and z-scores
Communicate results through graphs by linear regression and Mann-Kendall tests

8. Linear Regression
Finding a similarity between all data points placed on a graph
Will show us if there is a trend between the average temperature data and the average rainfall data
The closer the points are to the best fit line, the better the line models the data

9. Mann-Kendall Test Another way to find trends within data
Bases its results on the variance of the data to the mean
Excludes outliers based on this system

10. Choosing the Cities
Chose two different cities throughout the United States
Vary greatly in average temperature and average rainfall

11. El Paso, Texas Population of over 649,000
Located in the western part of Texas on the border of New Mexico and Mexico
Known as of the driest and hottest places in America

13. Buffalo, New York Population of over 261,000
Elevated at 619 feet above sea level
Surrounded by lakes and rivers, most notably Lake Erie

15. Buffalo Temperature Data
Z=Data Point-Mean
Standard Deviation

16. Buffalo Temperature Graphs

17. Hypothesis Testing Buffalo Temperature
We checked to determine if there was enough evidence to say that temperatures have increased over time
We used the line y=.0408x , and found Z score using data analysis on Excel
Z>1.645, therefore there is enough evidence to suggest a trend

18. Buffalo Precipitation Data

19. Buffalo Precipitation Graphs

20. Hypothesis Testing Buffalo Precipitation
We checked to determine if there was enough evidence to say that precipitation has increased over time
We used the line y=.0842x
We do not have enough evidence to suggest a trend since z<1.65

21. Mann-Kendall Test
Another way to help determine trends, which places less emphasize on possible outliers
This type of test only determines correlation, but has no predictive features

22. Example of Mann-Kendall Test
Given Data Points 1,5,3,9,14,15
1: 1,1,1,1,1
5: -1,1,1,1
3: 1,1,1
9: 1,1
14: 1
Ho: u=0
Ha: u>0
S=1(14)+(-1)1=13
V=(1/18)(n(n-1)(2n+5)-∑tk(tk-1)(2tk+5))
V=(1/18)(6(5)17)=28.33
Z=(13-1)/√28.33=2.25
Enough to accept correlation exists, z>1.645

23. Mann-Kendall Buffalo Temperature
Ho: μ=0
Ha: μ>0
S=(-1)369+(1)703=334
V=(1/18) (47(46)99)=11891
Z=(334-1)/((11891)^(1/2))=3.05
p= =.0011
Shows trend since Z>1.645

24. Mann-Kendall Buffalo Precipitation
Ho: μ=0
Ha: μ>0
S=(-1)416+(0)1+(1)656=240
V=(1/18)(47(46)99-2(1)9)=11890
Z=(240-1)/ ((11890)^(1/2))=2.19
P= =.0143
Shows Trend since Z>1.645

25. El Paso Temperature Data

26. El Paso Temperature Graphs

27. Hypothesis Testing El Paso Temperature
We checked to determine if there was enough evidence to say that temperatures have increased over time
We used the line y=.0482x
Z>1.645, therefore there is enough evidence to suggest a trend

28. El Paso Precipitation Data

29. El Paso Precipitation Graphs

30. Hypothesis Testing El Paso Temperature
We checked to determine if there was enough evidence to say that temperatures have increased over time
We used the line y=.0071x
Z<1.645, therefore there is not enough evidence to suggest a trend

31. Mann-Kendall El Paso Temperature
Ho: μ=0
Ha: μ>0
S=(-1)346+(1)734+(0)2=388
V=(1/18)(47(46)99-2(1)9)=11890
Z=(388-1)/((11890)^(1/2))=3.549
p≈0
Shows Trend since the Z>1.645

32. Mann-Kendall El Paso Precipitation
Ho: μ=0
Ha: μ>0
S=(-1)548 +(0)1+(1)561=13
V=(1/18)(47(46)99-2(1)9)=11890
Z=(13-1)/ ((11890)^(1/2))=.11
p=2( )=.9124
Doesn’t show trend since Z<1.645

33. In Conclusion
The linear regressions for temperature in Buffalo and El Paso provide ample evidence to suggest the existence of a trend
For Precipitation, the linear regressions do not provide enough evidence to suggest a trend in either Buffalo or El Paso
In Buffalo, the Mann-Kendall Test shows trend for both temperature and precipitation over time, signifying a trend
In El Paso, the Mann-Kendall Test shows a trend for temperature, but not for precipitaion

34. Reasoning
A possible reason that precipitation shows a trend in Buffalo for Mann-Kendall but not for regression is the variance of precipitation
A possible reason for the lack of a trend in El Paso in regards to precipitation is the low levels of precipitation that exist in general

35. The End