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Weather Patterns

Weather Patterns. Michael Levin & Andy Suh. About Weather Predictions. For years, people have been trying to predict weather patterns and to predict oncoming weathers; even the Babylon, Greeks, and the Renaissance people have tried.

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Weather Patterns

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  1. Weather Patterns Michael Levin & Andy Suh

  2. About Weather Predictions • For years, people have been trying to predict weather patterns and to predict oncoming weathers; even the Babylon, Greeks, and the Renaissance people have tried. • Techniques, like barometer, looking to the sky, forecast models, analog techniques, and persistence, have been used to predict weathers (note: persistence stands for relying today’s conditions to predict conditions, while analog techniques is remembering the previous weather patterns and using it). • Figuring out weather patterns are important, esp. to be prepared for natural disasters coming up, for protection of people’s health, agriculture, and environment. • You predict the weather using the sampling method to get the sample of the state of fluid at a certain time and place, and use equations from fluid dynamics and thermodynamics to estimate what kind of fluid will appear and in what state in some time after today.

  3. Objective • The goals for this research is: • To Find Out the Average March 16th Temperature Difference in Each City Between the 2005 and 1945. • Finding the relationship between the difference in temperature and the number of natural disasters. • Finding the relationship between the difference in temperature and the change in population.

  4. The Procedure Note: For the weather websites, some contain “actual mean” (which is what we’ve used) and some contain “average mean.” • 2 Options: • Going to the library and find the records and information (like using the book: Farmers Almanac) for temperature, population, and number of natural disasters. • Or using the websites listed below: • www.almanac.com • http://www.wunderground.com/history/ • http://weather.org/weatherorg_records_and_averages.htm • http://www.infoplease.com/ipa/A0004986.html • http://www.factmonster.com/ipka/A0764220.html • http://en.wikipedia.org/wiki/List_of_natural_disasters_in_the_United_States Below is the websites for Temperature Below is the websites for Population Below is the website for Natural Disasters

  5. Sampling Distribution • Method of picking 30 states: • Splitting up the regions based on their temp. conditions (for instance, cities in deserts and cities in the mountains). • Do a random sampling distribution on each of the regions (hot temp., warm temp., and cold temp. regions). • Note: The northern parts of USA are colder than the southern parts of USA. Also, USA has 1 desert and 2 mountains.

  6. Data

  7. Temperature Difference Shape: Right Skewed Center: Median Spread: IQR The mean for temperature difference is -14.9667. The standard deviation for temperature difference is 15.1668. Its median is -15.5. The interquartile range is 25. The range is 40. It appears that the difference between the two years: 1945 and 2005, are all negative. The fact that the numbers (mean, maximum, minimum, median, third quartile, and first quartile) of temperature difference (from 1945 to 2005) are all negative means that the temperature in the USA has gotten lower than before. Thus, the temperature has decreased form 1945 to 2005.

  8. Paired T-test and interval for temperature difference • Null Hypothesis: Temp. Diff. = 0. • Alternate Hypothesis: Temp. Diff < 0. • Conditions StateCheck 2 Ind. SRS Stated Paired Data The two temp. years are both paired. Pop.d >= 10nd Lists of states >= 300 Normal Pop. Of diff. 30>=30 or nd. >= 30

  9. Cont. • Conditions have met  t distribution  Paired t test. T = (xd - µd)/(sd/√(nd)) = -5.405 P(t<-d.405 │df = 29 ) = < 0.0001 We have rejected the null hypothesis since P-value: <0.0001 < 0.05. We have sufficient evidence that the temp. diff. is less than 0. Thus, the temp. was getting colder over time.

  10. Cont. • Conditions have met  t distribution  Paired t interval. • Xd ± t*(sd/√(nd)) = -15 ± 6.57786 = (-21.57790, -8.42214 ) (95% Confidence Level) • We’re 95% confident that the temp. diff between 1945 and 2005 in USA would be between 8.42 degrees F and 21.58 degrees F. • Since a 0 can’t be included in the interval, the temp. diff can’t be 0 too, and that the temp. diff. can be a negative b/c of the negative interval.

  11. Temp. Diff. vs. # of Natural Disasters ND = Natural Disasters The correlation of temp. diff. vs. # of ND is -0.171. The residual plot has a scattered data, which proves that there is a linear relationship between temp. diff. and # of ND. The negative correlation states that as temperature difference increases with extra degree Fahrenheit, the number of natural disasters decreasesby 0.171 disasters.Thus, having the temp. diff. increasing will make an impact of having less natural disasters occurring.

  12. Test for Independence b/w temp. diff. and # of ND using LinReg t test and interval • Null Hypothesis: β = 0. • Alternate Hypothesis: β ≠ 0 • Conditions: StateCheck SRS Stated Linear Data Scatterplot is almost linear w/ 1 outlier. Independence Each piece of the data can be assumed independent from each other. Normal Residual Normal Prob. Plot of the residuals is linear. Equal Variance The residual plot is scattered, which shows that the linear model is best fit for our data.

  13. Cont. • Conditions have met  t distribution  LinReg t test. • T = b/SEb = -0.0263/ 0.0286 = -0.9196. • 2*P(t < -0.9196 │df = 28) = 0.37. • We fail to reject the null hypothesis b/c the P-value: 0.37 > 0.05. • We have sufficient evidence that the slope of population regression line is equal to 0. • Therefore, an increase in temp. diff. has no effect on # of natural disasters.

  14. Cont. • Conditions have met  t distribution  LinReg t interval. • b ± t*(SEb)  -0.0263 ± 0.0286 = (-0.0549, 0.0023) (95% Confidence Level). • We’re 95% confident that the slope of population regression between # of natural disasters and the temperature difference is (-0.0549,0.0023) . Since there can be a 0 in the interval, it is possible that the temp. diff. has no influence on # of natural disasters.

  15. Temp. Diff vs. Pop. change PC = Population Change. The correlation of temp. change vs. PC is 0.395023. The residual plot has an almost scattered data, which shows that there almost is a linear relationship between temp. diff. and PC (not completely, but roughly a linear relationship). The positive correlation states that as temp. diff. increase with extra degree Fahrenheit, the population change has increased by 0.395023 people. Thus, an increase in temperature can lead to an increase in population.

  16. Test for Independence b/w temp. diff. and PC using LinReg t test and interval • Null Hypothesis: β = 0. • Alternate Hypothesis: β ‹ 0 • Conditions: StateCheck SRS Stated Linear Data Scatterplot is almost linear w/ 4 outliers. Independence Each piece of the data can be assumed independent from each other. Normal Residual Normal Prob. Plot of residuals is linear. Equal Variance The residual plot is scattered, which shows that the linear model is best fit for our data.

  17. Cont. • Conditions have met  t distribution  LinReg t test. • T = b/SEb = 2.275. • P(t < -0.9196 │df = 28) = 0.015. • We reject the null hypothesis b/c the P-value: 0.015 < 0.05. • We have sufficient evidence that the slope of population regression line is greater than 0. • Therefore, an increase in temp. diff. will have an increase in population.

  18. Cont. • Conditions have met  t distribution  LinReg t interval. • b ± t*(SEb)  = 178970 ± 78657.1 = (1003212.9,257627.1) (95% Confidence Level). • We’re 95% confident that the slope of population regression between population change and temp. diff. is between (1003212.9,257627.1). Since there can’t be a 0 in the interval, the population change can be influenced by the temp. change and that it’ll be influenced positively since it’s a positve interval.

  19. Applications to population • Throughout time, the temperature has gotten colder. It’s possible that the production of wintery coats and other clothes for winter has increased along with its purchase b/c of the temp. decrease. It could also be a possible evidence to disprove about global warming being real. Test and interval proves that the mean temp. diff. is less than 0, meaning the temp. actually has gotten colder over time. • The # of natural disasters has decreased as temp. increased. Since temperature difference in most cities are negative, as if temp. have decreased in time, that means that the # of natural disasters has increased in time and that more safety policies and protections were made over time. The data was proven that the # of natural disasters has increased over time, yet the test and the interval proves that there’s no relationship between temp. diff. and # of natural disasters. So, we can’t assume that the # of natural disasters can be influenced by the temp. diff. • The population has increased over time, despite that the temperature difference is low in most cities. The availability of food will decrease b/c of population increase.

  20. Bias and Error • Possible biases and errors are: • Can’t find the exact websites that contains population in Year: 1945 and Year: 2005, but websites that bests approximate them (Year: 1950 and Year: 2006). • The population are measured by states than cities. The only case this isn’t a bias is if each city in a state are evenly distributed. But that can’t be certain. • Since the population website is set on spreadsheet, we can get lost or missed track on our progress. • In the natural disasters’ website, some of marked locations are marked in city(ies), and some of them are marked in regions (like northeastern region of USA).

  21. Personal Opinions/Conclusions • I believe that, since the temp. has gotten colder over time, we can be facing global cooling rather than global warming. • Since the test and the interval of temp. diff. and # of ND says that the temp. diff. and # of ND are independent from each other, we can’t be certain that we have more natural disasters just because the temp. diff. was low. So, there’s no conclusion on a relationship b/w temp. diff. and # of ND just because they’re independent from each other, or that there’s no relationship between those two. • Even though there’s limiting factor on carrying capacity (esp. with populations), our populations kept increasing. Population increase is more related or influenced with ecology and the ecosystem than with meteorology and the climate. The population has increased when the temp. diff. has increased, not b/c the temp. has increased b/w 1945 to 2005.

  22. Questions?

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