Relationship Between Ozone & Temperature

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Data

The atmos data set resides in the nasaweather package of the R programming language. It contains a collection of atmospheric variables measured between 1995 and 2000 on a grid of 576 coordinates in the western hemisphere. The data set comes from the 2006 ASA Data Expo.

Some of the variables in the atmos data set are:

• temp - The mean monthly air temperature near the surface of the Earth (measured in degrees kelvin (K))
• pressure - The mean monthly air pressure at the surface of the Earth (measured in millibars (mb))
• ozone - The mean monthly abundance of atmospheric ozone (measured in Dobson units (DU))

You can convert the temperature unit from Kelvin to Celsius with the formula

\[ celsius = kelvin - 273.15 \]

And you can convert the result to Fahrenheit with the formula

\[ fahrenheit = celsius \times \frac{9}{5} + 32 \]

Cleaning

To analyze this data, we will use the following R packages:

library(nasaweather)
library(tidyverse)
1:20 + 1:6 

##  [1]  2  4  6  8 10 12  8 10 12 14 16 18 14 16 18 20 22 24 20 22

slide 43 stuff. what is the result of 2+3: 5. and the year we analyzed is 1995.

For the remainder of the report, we will look only at data from the year <!—code chunk 3: Insert inline code to reference year –>1995. We aggregate our data by location, using the R code below.

means <- atmos %>%
  filter(year == year) %>%
  group_by(long, lat) %>%
  summarize(temp = mean(temp, na.rm = TRUE),
            pressure = mean(pressure, na.rm = TRUE),
            ozone = mean(ozone, na.rm = TRUE),
            cloudlow = mean(cloudlow, na.rm = TRUE),
            cloudmid = mean(cloudmid, na.rm = TRUE),
            cloudhigh = mean(cloudhigh, na.rm = TRUE)) %>%
  ungroup()

## `summarise()` has grouped output by 'long'. You can override using the
## `.groups` argument.

summarise() has grouped output by ‘long’. You can override using the .groups argument.

where the year object equals 1995.

Ozone and temperature

Is the relationship between ozone and temperature useful for understanding fluctuations in ozone? A scatterplot of the variables shows a strong, but unusual relationship.

Model

We suggest that ozone is highly correlated with temperature, but that a different relationship exists for each geographic region. We capture this relationship with a second order linear model of the form

\[ ozone = \alpha + \beta_{1} temperature + \sum_{locales} \beta_{i} locale_{i} + \sum_{locales} \beta_{j} interaction_{j} + \epsilon\]

This yields the following coefficients and relationships.

# code chunk 7
means$locale <- "north america"
means$locale[means$lat < 10] <- "south pacific"
means$locale[means$long > -80 & means$lat < 10] <- "south america"
means$locale[means$long > -80 & means$lat > 10] <- "north atlantic"

# code chunk 8
lm(ozone ~ temp + locale + temp:locale, data = means)

## 
## Call:
## lm(formula = ozone ~ temp + locale + temp:locale, data = means)
## 
## Coefficients:
##               (Intercept)                       temp  
##                  1336.508                     -3.559  
##      localenorth atlantic        localesouth america  
##                   548.248                  -1061.452  
##       localesouth pacific  temp:localenorth atlantic  
##                  -549.906                     -1.827  
##  temp:localesouth america   temp:localesouth pacific  
##                     3.496                      1.785

# code chunk 9
ggplot(means, aes(temp, ozone, color = locale)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE) +
  facet_wrap(~ locale)

## `geom_smooth()` using formula = 'y ~ x'

Diagnostics

An anova test suggests that both locale and the interaction effect of locale and temperature are useful for predicting ozone (i.e., the p-value that compares the full model to the reduced models is statistically significant).

# code chunk 10
mod <- lm(ozone ~ temp, data = means)
mod2 <- lm(ozone ~ temp + locale, data = means)
mod3 <- lm(ozone ~ temp + locale + temp:locale, data = means)

anova(mod, mod2, mod3)

## Analysis of Variance Table
## 
## Model 1: ozone ~ temp
## Model 2: ozone ~ temp + locale
## Model 3: ozone ~ temp + locale + temp:locale
##   Res.Df   RSS Df Sum of Sq      F    Pr(>F)    
## 1    574 99335                                  
## 2    571 41425  3     57911 706.17 < 2.2e-16 ***
## 3    568 15527  3     25898 315.81 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1