Climate Trends in America By: Andrew Bechard and Michael Drebot

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

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

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

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

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

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

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

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

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

Buffalo Temperature Data Z=Data Point-Mean Standard Deviation

Buffalo Temperature Graphs

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+47.184, and found Z score using data analysis on Excel Z>1.645, therefore there is enough evidence to suggest a trend

Buffalo Precipitation Data

Buffalo Precipitation Graphs

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+37.626 We do not have enough evidence to suggest a trend since z<1.65

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

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

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=.5-.4989=.0011 Shows trend since Z>1.645

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=.5-.4857=.0143 Shows Trend since Z>1.645

El Paso Temperature Data

El Paso Temperature Graphs

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+63.127 Z>1.645, therefore there is enough evidence to suggest a trend

El Paso Precipitation Data

El Paso Precipitation Graphs

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+8.7068 Z<1.645, therefore there is not enough evidence to suggest a trend

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

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(.5-0438)=.9124 Doesn’t show trend since Z<1.645

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

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

The End