Lecture 12 — Real Climate Data in R

How fast is your city warming? (regression on time)

Bill Perry

2026-10-05

Where we left off (Lecture 11 — Regression)

• lm(Y ~ X, data = df) fits a straight line through a cloud of points
• summary(model) gives you:
  • the slope — how much Y changes per 1 unit of X
  • its p-value — is that slope real, or could it be chance?
  • R² — how tightly the points follow the line
• geom_smooth(method = "lm") draws the line
• plot(model) checks the residuals

Note

✅ Where today comes in

• Last time X was paper mass and the slope converted grams into cm²
• Today X is time
  • the slope becomes a rate of change — degrees per year
  • and that is exactly what a “warming rate” is

Goals for Today

• Download real weather station data from inside R — no Excel, no copy-paste
• Clean the names with janitor so the code stays easy to type
• Summarize ~28,000 daily records into one mean per year
• Fit lm(temp ~ year) and read the warming rate straight off summary()
• Split by season — is winter warming faster than summer?
• Find a station for a city you choose and run the whole thing again

Tip

🖐 Where this is going

• The analysis is the same four lines every time
• Change the station, and it is a new city
• That is your out-of-class extension

Tools today:

• GSODR — download NOAA station data
• janitor — clean_names()
• tidyverse — summarize and plot
• lm() — the slope is the answer

Reading:

• 📖 R for Data Science 2e
  • Ch. 3 Data transformation
• 📖 Whitlock & Schluter Ch. 17 — Regression

Naming conventions:

• data frames → _df
• plots → _plot
• models → _model

🧩 Chunk 1 of 3 · The Question

We will cover: where the data comes from, why the slope of a regression on time is a warming rate, and why you have to summarize before you can see it. No code in this chunk.

Where Does This Data Come From?

• GSOD = Global Surface Summary of the Day, run by NOAA
  • daily weather from thousands of stations worldwide
  • many records reach back to the 1940s
  • free, and no account needed
• The GSODR package pulls it straight into R
  • you give it a station ID and a range of years
  • it hands back a data frame

Our station to start:

• Duluth International Airport
• Station ID 727450-14913
• Daily records since 1948

• Why this matters:
  • this is the same messy, real-world data you will meet in your own project
  • the workflow — download → summarize → model — is the one you will reuse all term
• And it is yours to reuse:
  • every city with a long station record can be run through the exact same code
  • you will pick one later today

The Slope Is the Warming Rate

Last lecture:

\[\widehat{\text{area}} = a + b \times \text{mass}\]

• b was cm² per gram — a conversion factor

Today:

\[\widehat{\text{temp}} = a + b \times \text{year}\]

• b is °C per year — a rate of change

Nothing about the code changes. Only what X means.

• Reading the slope:
  • b positive → warming
  • b negative → cooling
  • b near 0 → no trend
• Make it human: °C per year is a tiny number
  • multiply it by 10 → °C per decade
  • 0.027 °C/year → about 0.27 °C per decade
• The p-value still does the same job
  • H₀: the slope is 0 — no trend at all
  • small p → the trend is real, not chance

Why You Must Summarize First

• A station reports one row per day
  • 78 years × 365 days ≈ 28,000 rows
• Every one of those days carries the seasonal cycle
  • January is 30 °C colder than July, every single year
  • that swing is enormous compared with a few tenths of a degree of warming
• So the trend you want is buried in the noise you don’t

Summary level	group_by()	Rows left
Daily (raw)	none	~28,000
Yearly	year	78

Important

Summarizing is not throwing data away.

• It is choosing which question you are answering
• Want to study a heat wave? Use daily
• Want to study climate? Use yearly

• One group_by(year) %>% summarize() — the same two lines from Summary Statistics
• That is the whole fix

🧩 Chunk 2 of 3 · Duluth’s Warming Rate

We will cover: downloading the Duluth record, cleaning the names, summarizing to yearly means, and fitting lm(temp ~ year).

🛑 After this chunk: Activity Parts 1–5 (download, summarize, plot, fit, read the slope).

Load Libraries and Download the Data

# Load packages at the top -----------------------------
library(tidyverse) # dplyr + ggplot2
library(janitor)   # clean_names()
library(GSODR)     # NOAA weather station data

# Download daily Duluth weather, 1948-2025 -------------
# clean_names() makes every column lower case
duluth_df <- readRDS("duluth_cached.rds") %>%  # STUB
  clean_names()

• get_GSOD() takes years and a station and goes and gets the data
  • 1948:2025 is a vector — “every year in this range”
  • it takes a minute; 78 years of daily data is a lot
• clean_names() is the important habit here
  • NOAA ships columns as TEMP, YEARMODA, MXSPD
  • R is case-sensitive, so temp would error
  • clean_names() makes everything lower case and snake case, once, at the top

Tip

Clean the names as you load the data, and you never think about capitals again.

What Did We Get?

# How big is it, and what is in it? --------------------
dim(duluth_df)

[1] 25441    47

names(duluth_df)[13:18]

[1] "yearmoda" "year"     "month"    "day"      "yday"    
[6] "temp"    

• ~28,000 rows — one per day
• 47 columns — temperature, dew point, wind, precipitation, flags…
• The handful we care about:
  • yearmoda — the date
  • year, month, day
  • temp — daily mean temperature in °C

Note

names(df) is how you find out what a downloaded data set actually calls things. Always look before you type.

Trim to What We Need

# Keep only the columns we actually use ----------------
dlh_df <- duluth_df %>%
  select(name, yearmoda, year, month, temp)

head(dlh_df, 3)

                           name   yearmoda  year month  temp
                         <char>     <Date> <int> <int> <num>
1: DULUTH INTERNATIONAL AIRPORT 1948-01-01  1948     1  -8.2
2: DULUTH INTERNATIONAL AIRPORT 1948-01-02  1948     1  -4.1
3: DULUTH INTERNATIONAL AIRPORT 1948-01-03  1948     1  -8.4

• 47 columns is more than anyone needs to look at
• select() keeps the five that answer our question
• Same select() from the Wrangling lecture — just on a much wider real file

Tip

Trim early. Every later line is easier to read when the data frame has 5 columns instead of 47.

Look at the Raw Daily Data

# Every single daily temperature -----------------------
raw_temp_plot <- dlh_df %>%
  ggplot(aes(x = yearmoda, y = temp)) +
  geom_point(alpha = 0.2, size = 0.5)
raw_temp_plot

• A solid band about 60 °C tall — that is summer vs winter, repeated 78 times
• ~28,000 points on top of each other
• Any warming trend is in there, but it is a fraction of a degree against a 60 °C swing

So you cannot see it. That is not a plotting problem — it is a summarizing problem.

Summarize to One Mean per Year

# Mean temperature per year ----------------------------
dlh_year_df <- dlh_df %>%
  group_by(year) %>%
  summarize(temp = mean(temp, na.rm = TRUE))

head(dlh_year_df, 3)

# A tibble: 3 × 2
   year  temp
  <int> <dbl>
1  1948  3.76
2  1949  4.10
3  1950  1.60

• group_by(year) — one group per year
• summarize(temp = mean(temp)) — one number per group
• 28,000 rows become 78
• na.rm = TRUE ignores days the station missed

Note

Reusing the name temp on the left means every line below keeps working — the same trick from T-Tests II.

Plot the Yearly Means

# Yearly means with the regression line ----------------
yearly_temp_plot <- dlh_year_df %>%
  ggplot(aes(x = year, y = temp)) +
  geom_point() +
  geom_smooth(method = "lm")
yearly_temp_plot

• Now you can see it. The line clearly rises
• 78 points instead of 28,000 — and the story is clearer, not weaker
• Still plenty of scatter: single years are weather, the line is climate
• Exactly the same geom_smooth(method = "lm") as the Regression lecture

But “it looks like it goes up” is not a result. We need the number.

Fit the Trend

# Temperature predicted by year ------------------------
dlh_year_model <- lm(temp ~ year,
                     data = dlh_year_df)

summary(dlh_year_model)

Call:
lm(formula = temp ~ year, data = dlh_year_df)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.99794 -0.51059  0.00688  0.49950  1.90458 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -49.096842   9.119103  -5.384 9.77e-07 ***
year          0.026872   0.004585   5.860 1.49e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.8774 on 68 degrees of freedom
Multiple R-squared:  0.3356,    Adjusted R-squared:  0.3258 
F-statistic: 34.34 on 1 and 68 DF,  p-value: 1.489e-07

• lm(temp ~ year) reads “temperature is predicted by year”
• Y on the left, X on the right — same as always
• The three numbers you want are all in this output:
  • the slope (year → Estimate)
  • its p-value (year → Pr(>|t|))
  • R² (Multiple R-squared)

Reading the Warming Rate

Look at the year row of the Coefficients table.

• Estimate ≈ 0.027 — that is the slope
  • units: °C per year
  • positive → Duluth is warming
  • ×10 → about 0.27 °C per decade
  • over ~78 years → roughly 2 °C
• Pr(>|t|) is tiny (far below 0.001)
  • the warming is real, not year-to-year luck

• Multiple R-squared ≈ 0.34
  • year explains about a third of the variation in annual temperature
  • the other two thirds is weather — some years are just cold
  • a modest R² next to a rock-solid p is completely normal in climate data

Important

The intercept looks absurd — about −49 °C.

• That is the predicted temperature at “year 0”
• Year 0 is 2,000 years outside the data
• The intercept is bookkeeping; the slope is the science

→ ACTIVITY 12 Parts 1–5 now

🛑 Do Activity Parts 1–5 now

• Download the Duluth record and clean_names() it
• Trim the columns and plot the raw daily data
• Summarize to one mean per year and plot it
• Fit lm(temp ~ year) and read the slope, p, and R² off summary()

🧩 Chunk 3 of 3 · Seasons, and Your Own City

We will cover: labelling each day with a season, fitting a separate model for summer and winter, and finding the station ID for a city you choose.

🛑 After this chunk: Activity Parts 6–10 (seasons, two models, your own city).

A Better Question — Which Season Is Warming?

• The annual mean says Duluth warmed about 0.27 °C per decade
• But an annual mean hides which part of the year moved
• That distinction is the biologically interesting one:
  • ice-out dates and frozen soil depend on winter
  • heat stress and drought depend on summer
  • growing season length depends on the shoulders

The plan — three steps you already know:

1. mutate() + case_when() to label each day
2. group_by(year, season) + summarize()
3. One lm() per season

Important

⚠️ Seasons are not months — they are hemispheres.

• June–August is summer north of the equator
• June–August is winter south of it
• If you pick Melbourne, Santiago or Cape Town later, you must swap the labels

• A station’s latitude column tells you which hemisphere you are in
  • positive → northern
  • negative → southern

Label Each Day with a Season

# Northern hemisphere seasons --------------------------
# SOUTHERN hemisphere: swap summer and winter
dlh_season_df <- dlh_df %>%
  mutate(season = case_when(
    month %in% c(6, 7, 8) ~ "summer",
    month %in% c(12, 1, 2) ~ "winter",
    TRUE ~ "shoulder"
  ))

# Did it work? -----------------------------------------
dlh_season_df %>% count(season)

     season     n
     <char> <int>
1: shoulder 12718
2:   summer  6436
3:   winter  6287

• case_when() reads top to bottom: condition ~ answer
  • the first matching line wins
• month %in% c(6, 7, 8) = “is month 6, 7 or 8?”
• TRUE ~ "shoulder" is the catch-all for everything left over — spring and fall
• count() is the check: roughly a quarter of the days in each of summer and winter, half in the shoulder

📖 R4DS §3.4 — case_when()

Summarize by Year and Season

# Drop the shoulder, then one mean per year per season -
season_year_df <- dlh_season_df %>%
  filter(season != "shoulder") %>%
  group_by(year, season) %>%
  summarize(temp = mean(temp, na.rm = TRUE),
            .groups = "drop")

head(season_year_df, 4)

# A tibble: 4 × 3
   year season  temp
  <int> <chr>  <dbl>
1  1948 summer  17.4
2  1948 winter -12.6
3  1949 summer  18.4
4  1949 winter -11.4

• filter(season != "shoulder") — != means “is not”
  • keeps only the two extremes
• group_by(year, season) — two grouping columns
  • one row per year per season
  • 78 years × 2 seasons ≈ 156 rows
• .groups = "drop" tidies up afterwards

This is the same two-column group_by() from T-Tests II.

Plot Both Seasons

# One line per season ----------------------------------
season_temp_plot <- season_year_df %>%
  ggplot(aes(x = year, y = temp, color = season)) +
  geom_point() +
  geom_smooth(method = "lm")
season_temp_plot

• color = season inside aes() does two jobs at once:
  • colors the points by season
  • makes geom_smooth() fit a separate line per season
• Two bands, far apart — winter near −11 °C, summer near 18 °C
• Don’t compare the heights. Compare the steepness.
  • the height is just “winter is cold”
  • the slope is the warming rate
• Winter’s line looks steeper — but we need the numbers

A Model for Summer

# Summer only ------------------------------------------
summer_df <- season_year_df %>%
  filter(season == "summer")

summer_model <- lm(temp ~ year, data = summer_df)
summary(summer_model)

Call:
lm(formula = temp ~ year, data = summer_df)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.6841 -0.7543  0.1585  0.6622  2.1918 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -24.267149  10.815992  -2.244 0.028116 *  
year          0.021059   0.005439   3.872 0.000245 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.041 on 68 degrees of freedom
Multiple R-squared:  0.1807,    Adjusted R-squared:  0.1686 
F-statistic: 14.99 on 1 and 68 DF,  p-value: 0.0002448

• filter() first, then the same lm() as before
• Two small models are far easier to read than one complicated one

Summer slope ≈ 0.021 °C/year

• ×10 → about 0.21 °C per decade
• p = 0.0002 → real

Now do exactly the same thing for winter.

A Model for Winter

# Winter only ------------------------------------------
winter_df <- season_year_df %>%
  filter(season == "winter")

winter_model <- lm(temp ~ year, data = winter_df)
summary(winter_model)

Call:
lm(formula = temp ~ year, data = winter_df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.5398 -1.3901  0.0164  1.1662  4.0695 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -78.24857   20.10231  -3.893 0.000229 ***
year          0.03417    0.01011   3.380 0.001202 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.934 on 68 degrees of freedom
Multiple R-squared:  0.1439,    Adjusted R-squared:  0.1313 
F-statistic: 11.43 on 1 and 68 DF,  p-value: 0.001202

Winter slope ≈ 0.034 °C/year

• ×10 → about 0.34 °C per decade
• p = 0.001 → real

Winter is warming about 1.6× as fast as summer.

• This is the expected pattern across the northern continents
• Fewer extreme-cold nights, shorter ice seasons, earlier thaw
• The annual mean — 0.27 °C/decade — sat right between the two and told you neither

Reading Two Models Side by Side

Both slopes come straight off the year row of each summary():

Model	Slope (°C/yr)	×10 (°C/decade)	p
Annual	0.027	0.27	<0.001
Summer	0.021	0.21	<0.001
Winter	0.034	0.34	0.001

• Winter’s slope has a bigger standard error too — winters are more variable than summers
• A bigger p with a bigger slope is not a contradiction; it is noisier data

How to write it up:

Mean annual temperature at Duluth rose significantly from 1948 to 2025 (linear regression: slope = 0.027 °C yr⁻¹, equivalent to 0.27 °C per decade; F(1, 68) = 34.3, p < 0.001, R² = 0.34). Winter warmed roughly 1.6 times faster than summer (0.34 vs 0.21 °C per decade).

• Give the slope with units
• Convert to per decade so a reader can feel it
• Report p and R² the same way as any regression

Now Do It for Your City

# Find stations near a place you care about ------------
# Duluth is 46.84 N, -92.19 W
nearest_stations(LAT = 46.84, LON = -92.19,
                 distance = 50) %>%
  clean_names() %>%
  select(stnid, name, begin, end) %>%
  head(3)

          stnid                         name    begin      end
         <char>                       <char>    <int>    <int>
1: 727450-14913 DULUTH INTERNATIONAL AIRPORT 19480101 20250827
2: 999999-14913 DULUTH WILLIAMSN-JOHNSN MUNI 19650101 19721231
3: 997269-99999                       DULUTH 20080101 20081231

• nearest_stations() takes a latitude, a longitude, and a radius in km
• Look up your city’s lat/long in any search engine
  • south of the equator → negative latitude
  • west of Greenwich → negative longitude
• Then read the table:
  • stnid is what you paste into get_GSOD()
  • begin and end tell you the years available

Important

Pick a station with a long record. A trend needs decades — aim for a begin date of 1970 or earlier.

Swap One Line, Get a New City

# The ONLY line that changes ---------------------------
city_df <- get_GSOD(years = 1973:2025,
                    station = "948660-99999") %>%
  clean_names()

# Everything below is identical ------------------------
city_year_df <- city_df %>%
  group_by(year) %>%
  summarize(temp = mean(temp, na.rm = TRUE))

city_model <- lm(temp ~ year, data = city_year_df)
summary(city_model)

• That is the whole point of today
  • one line names the place
  • the rest of the analysis never changes
• Use the years = range your station actually has — don’t ask for years before begin

Important

If your city is in the southern hemisphere, swap the season labels in case_when():

• month %in% c(12, 1, 2) → summer
• month %in% c(6, 7, 8) → winter

→ ACTIVITY 12 Parts 6–10 now

🛑 Do Activity Parts 6–10 now

• Label the seasons with case_when() and summarize by year and season
• Plot both seasons, then fit a model for each
• Write the warming rates in °C per decade
• Find the station for a city you choose — that is your Extension

What We Learned Today

The ideas:

• A regression on time turns a slope into a rate of change — ×10 for per decade
• Raw daily data hides the trend; group_by(year) %>% summarize() is the fix
• An annual mean hides which season moved — Duluth’s winter warms ~1.6× faster
• Seasons are set by hemisphere, not by month number
• A modest R² with a tiny p is normal — real trend, weather scatter

The code:

• get_GSOD(years =, station =) and nearest_stations()
• clean_names() — lower-case names, once, at the top
• group_by() + summarize() — to the right level
• case_when() — build the season
• lm(temp ~ year) + summary() — the rate

Hand in: your finished activity script, plus the warming rate you found for your own city.

References:

• 📖 R4DS Ch. 3 — Data transformation
• 📖 W&S Ch. 17 — Regression
• NOAA GSOD — ncei.noaa.gov

Up next:

• The final project — the same pipeline, on data you choose
• Download → clean → summarize → plot → model → report