# Can the Hottest Ten Days Reveal What Averages Hide?

## Answer

No—not in Central Park’s record since 1991. Across the 35 complete calendar years from 1991 through 2025, annual mean temperature rose by **0.31 °C per decade** (95% confidence interval **0.09 to 0.52 °C per decade**; linear-trend R² = **0.20**). The mean temperature of each year’s ten hottest daily maxima showed no warming: its fitted trend was **−0.16 °C per decade** (95% confidence interval **−0.63 to 0.31 °C per decade**; R² = **0.02**). Thus the annual average displays the clearer warming signal in this station and interval.

## Data and method

The analysis uses NOAA’s current GHCN-Daily fixed-width file for station **USW00094728**, identified in the station inventory as **NY City Central Park** (40.7789° N, 73.9692° W; elevation 42.7 m). Data and format documentation were downloaded from NOAA’s [GHCN-Daily archive](https://www.ncei.noaa.gov/pub/data/ghcn/daily/), specifically the [station data file](https://www.ncei.noaa.gov/pub/data/ghcn/daily/all/USW00094728.dly), [station inventory](https://www.ncei.noaa.gov/pub/data/ghcn/daily/ghcnd-stations.txt), and [readme](https://www.ncei.noaa.gov/pub/data/ghcn/daily/readme.txt).

The station file contains TMAX and TMIN, but no TAVG. Following the documentation’s defined fallback, daily average temperature was calculated as **(TMAX + TMIN) / 2**. For each year, the annual average is the mean of all daily averages; the hot-days metric is the mean of the ten largest daily TMAX values. Temperatures were converted from tenths of degrees Celsius to degrees Celsius.

A complete year had exactly 365 or 366 calendar days, nonmissing TMAX and TMIN on every day, and blank NOAA quality flags for both elements. All years from 1991 through 2025 met these criteria. The partial 2026 record was excluded. Ordinary least-squares trends were fitted against calendar year, with two-sided 95% confidence intervals.

## Evidence

The annual-mean trend is positive and its confidence interval excludes zero. Its R² of 0.20 means that a linear time trend explains about one fifth of the year-to-year variation—not a perfect fit, but a detectable signal.

The hottest-ten-days series is much noisier. Its small negative fitted slope is not evidence of cooling: the confidence interval is wide and includes both substantial cooling and moderate warming. Time explains only about 2% of its interannual variation. On the requested criterion of revealing warming “more clearly,” the average wins both statistically and visually.

The contrast is plausible. An annual mean aggregates 365 or 366 observations and therefore suppresses weather noise. A ten-day extreme metric is driven by a small sample of heat events, whose timing and intensity vary strongly with circulation, humidity, soil moisture, and chance. Extremes can change differently from means, but this particular top-ten statistic does not isolate a warming signal over this period.

## Limitations

This is one station and a 35-year interval, so it does not establish a regional or global relationship between mean and extreme-temperature trends. Central Park is an urban site; urbanization, vegetation, instruments, observation practices, station moves, and NOAA homogenization choices can affect long-term behavior. GHCN-Daily is primarily a daily observational archive, and this analysis did not apply an independent homogenization or breakpoint test.

The calculated daily average, (TMAX + TMIN) / 2, is not a true 24-hour mean and may respond differently to asymmetric daytime and nighttime warming. The hottest-ten-days statistic is also definition-sensitive: the tenth-highest threshold, an annual percentile, heat-wave duration, warm-season-only analysis, or nighttime minima could yield different conclusions. The ten selected days need not be consecutive.

Linear regression summarizes a monotonic trend and assumes independent, well-behaved residuals; it does not test nonlinear change, serial correlation, or regime shifts. The confidence intervals should therefore be treated as descriptive inferential summaries, not definitive causal estimates.

## Conclusion

For Central Park from 1991–2025, the ten hottest days do **not** reveal warming more clearly than the annual average. The annual mean shows a modest positive trend, while the hot-ten mean is dominated by year-to-year variability and has no detectable trend. The result answers the station-specific question but should not be generalized without comparing alternative extreme indices, nearby stations, and homogenized regional series.
