WEATHER PATTERNSMichael Levin & Andy Suh

About Weather PredictionsFor 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.

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.

The Procedure

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.ht

m

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 Population

Below is the websites for Temperature

Below is the website for Natural Disasters

Note: For the weather websites, some contain “actual mean” (which is what we’ve used) and some contain “average mean.”

Sampling Distribution

Method of picking 30 states:1. Splitting up the regions based on their temp.

conditions (for instance, cities in deserts and cities in the mountains).

2. 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.

Data

Collection 1

Cities Temp_1... Temp_2... Temp_D... Disaste... Populatio... Populati... Populati... <new>

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28

29

30

Pittsburgh 68 32 -36 5 10498012 12441000 1942988

Sacramento 43 55 12 7 10586223 36458000 25871777

Austin 62 48 -14 6 7711194 23508000 15796806

Orlando 78 73 -5 8 2771305 18090000 15318695

Memphis 75 42 -33 7 3291718 6039000 2747282

Bismarck 30 14 -16 3 128643 670000 541357

Raleigh 51 40 -11 1 638800 636000 2800

Dover 68 39 -29 2 318085 853000 534915

Boston 46 36 -9 2 4690514 6437000 1746486

New York 42 38 -4 5 14830192 19306000 4475808

Washington D.C. 72 42 -30 1 2343001 5616000 3272999

Little Rock 53 42 -11 1 1909511 2811000 901489

Portland 48 46 -2 2 1521341 3701000 2179659

Jefferson City 70 41 -29 4 3954653 5843000 1888347

Reno 30 46 16 1 160083 2496000 2335917

Trenton 65 41 -24 2 4835329 8725000 3889671

Montgomery 78 50 -28 5 3061743 4599000 1537257

Indianapolis 66 36 -30 6 3934224 6314000 2379776

St. Louis 68 42 -26 4 3954653 5843000 1888347

Lincoln 60 41 -19 1 1325510 1768000 442490

Baton Rouge 78 48 -30 7 2683516 4288000 1604484

San Diego 56 62 6 7 10586223 36458000 25871777

Annapolis 65 39 -26 1 2343001 5616000 3272999

Hartford 52 37 -15 2 2007280 3505000 1497720

Salt Lake City 43 46 3 1 688862 2550000 1861138

Concord 38 32 -6 2 533242 1315000 781758

Harrisburg 68 36 -32 5 10498012 12441000 1942988

Providence 39 38 -1 2 428556 1068000 639444

Richmond 72 42 -30 4 3318680 7643000 4524320

Boise 37 47 10 1 588637 1466000 877363

Temperature Difference

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2

3

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Temp_Difference

-40 -30 -20 -10 0 10 20 30

Collection 1 HistogramCollection 1

Temp_Difference

-14.9667

15.1668

-36

-29

-15.5

-4

16

S1 = meanS2 = sS3 = minS4 = Q1S5 = medianS6 = Q3S7 = max

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.

Shape: Right SkewedCenter: MedianSpread: IQR

Paired T-test and interval for temperature difference

Null Hypothesis: Temp. Diff. = 0. Alternate Hypothesis: Temp. Diff < 0. Conditions

State Check2 Ind. SRS StatedPaired Data The two temp. years

are both paired.Pop.d >= 10nd Lists of states >= 300Normal Pop. Of diff. 30>=30

or nd. >= 30

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.

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.

Temp. Diff. vs. # of Natural DisastersCollection 1

DisastersNumbers

Temp_Difference

-0.171215

15.1668

-36

-29

-15.5

-4

16

S1 = correlationS2 = sS3 = minS4 = Q1S5 = medianS6 = Q3S7 = max

0

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Temp_Difference

-40 -30 -20 -10 0 10 20

DisastersNumbers = -0.0263Temp_Difference + 3.1; r2 = 0.029

Collection 1 Scatter Plot

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 decreases by 0.171 disasters. Thus, having the temp. diff. increasing will make an impact of having less natural disasters occurring.

ND = Natural Disasters

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:

State CheckSRS 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.

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.

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.

Temp. Diff vs. Pop. changeCollection 1

PopulationChange

Temp_Difference

0.395023

15.1668

-36

-29

-15.5

-4

16

S1 = correlationS2 = sS3 = minS4 = Q1S5 = medianS6 = Q3S7 = max

0

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Temp_Difference

-40 -30 -20 -10 0 10 20

PopulationChange = 1.79e+05Temp_Difference + 7.1e+06; r2 = 0.16

Collection 1 Scatter Plot

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.

PC = Population Change.

Test for Independence b/w temp. diff. and PC using LinReg t test and interval

Null Hypothesis: β = 0. Alternate Hypothesis: β ‹ 0 Conditions:

State CheckSRS 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.

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.

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.

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.

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).

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.

Questions?