Compare climate windows and trend summaries

Ask what a slope summarizes

A climate record can fluctuate from year to year while changing over a longer interval. This lab offers several explicit analysis windows and keeps the full record visible. The window changes which observations enter a summary; it does not erase years outside the selection.

Begin with 1959–2024 and the native temperature reference. Write down the number of annual values, the mean, the endpoint slope and the fitted slope. Before switching to 1998–2012, predict whether the two slope methods must agree. They summarize the same selected series in different ways, so agreement is not guaranteed.

These are real annual estimates from a frozen NASA GISTEMP dataset. They are not a controlled experiment in which only one climate influence changes. Short-term departures from a fitted line should be described before any explanation for them is assigned.

Calculate an endpoint slope carefully

The endpoint slope uses only the first and last values. In the stored data, 1998 is +0.61°C and 2012 is +0.65°C relative to 1951–1980. Their difference is +0.04°C over 2012 − 1998 = 14 elapsed years.

Divide 0.04 by 14 and multiply by ten to express the result per decade: about +0.02857°C/decade. There are fifteen annual observations when both endpoints are included, but only fourteen years between them. Confusing count with elapsed time changes the denominator.

On paper, draw the two endpoints and connect them. Then add a few interior values from the selected record. The connecting line did not use those interior observations. That omission is a property of the method, not evidence that the interior values are unimportant.

Fit a line using all selected years

Ordinary least squares, or OLS, chooses an intercept and slope that minimize the sum of squared vertical residuals between the line and the data. A residual is an observed anomaly minus the fitted value for that year. Squaring prevents positive and negative residuals from cancelling in the objective.

For 1998–2012, the fitted slope is about +0.13393°C/decade, substantially different from the endpoint result. The interior observations affect the fitted line. For 1959–2024 the temperature OLS slope is about +0.17679°C/decade in this snapshot.

The fitted slope is a descriptive linear summary of its selected interval. It does not mean every year increases by that amount, that the underlying response is exactly linear, or that the same slope predicts all future years. Nor does choosing OLS make the selected period automatically representative of every climate question.

Compare windows without hiding the choice

Use 1981–2024, 1998–2012 and 2015–2024. For each, record actual coverage, count and both slopes. Explain differences with reference to the visible values and interval length before offering a physical interpretation. Keep the full timeline beside your table so a short-window claim cannot quietly replace a long-record conclusion.

Change the anomaly reference while holding one window fixed. The fitted and endpoint slopes remain unchanged because a constant vertical shift changes neither differences nor the best-fitting slope. If your hand calculation changes, inspect inconsistent baselines or rounding.

Source uncertainty and trend uncertainty are distinct. The lab’s slope is not accompanied by a regression confidence interval, and a source uncertainty for another variable cannot serve as one. Temperature observations also need not be independent annual draws. NASA’s uncertainty research treats observational uncertainty beyond this descriptive exercise.

Transfer with a short constructed series

A paper series at years 0, 1, 2, 3 and 4 has values 0, 0, 0, 4 and 0. Its endpoint slope is zero. Does that force its OLS slope to be zero? Explain what additional information the fitted line uses.

Check the climate-windows transfer

No. The interior value of 4 at year 3 shifts the fitted slope positive; using mean year 2, the slope is 4/10 = 0.4 units per year. The endpoint method misses that interior structure. Neither summary alone identifies a physical cause.