Forecasting Extreme Day and Night Heat in Paris

Abstract

As a form of ``small AI'', quantile statistical learning is used to forecast diurnal and nocturnal Q(.90) air temperatures for Paris, France from late spring to late summer months of 2020. The data are provided by the Paris-Montsouris weather station. Rather than trying to directly anticipate the onset and cessation of reported heat waves, Q(.90) values are estimated because the 90th percentile requires that the higher temperatures be relatively rare and extreme. Predictors include eight routinely available indicators of weather conditions, lagged by 14 days; the temperature forecasts are produced two weeks in advance. Conformal prediction regions capture forecasting uncertainty with provably valid properties. For both diurnal and nocturnal temperatures, forecasting accuracy is promising, and sound measures of uncertainty are provided. Benefits for policy and practice follow.

Figures (5)

• Figure 1: Histograms of the Paris daily 2 AM air temperatures in the left panel and 2 PM air temperatures in the right panel, both in celsius, for April through September in 2020. The solid black line in both panels is an overlaid density smoother serving as a visual aid. (N = 183 days)
• Figure 2: Fit quality is displayed for quantile gradient boosting applied to the 2020 daily 2 PM temperatures. The vertical axis represents the observed temperatures in celsius whereas the horizontal axis represents the $Q(.90)$ fitted temperatures in celsius. The black dots are the observations, and the solid black line is a loess smooth provided as a visual aid. (N = 183 days because the data for March are no longer included.)
• Figure 3: A time series plot is shown with the 2 PM temperatures on the vertical axis, date on the horizontal axis, and a loess smooth of the fitted values overlaid to help visualize the temporal path of the fitted values (span = .30). The circles are the observations. The horizontal dotted line is placed at the $Q(0.90)$ value of the June through August data. To help avoid clutter, only the summer months are shown. If there is excessive heat, these are the months when it is most likely.
• Figure 4: The figure shows time series of observed 2 AM temperatures (circles) with an overlaid $\tau = 0.90$ quantile smoothing spline fit based on projected 2 PM temperatures. The horizontal dotted line marks the empirical $Q(0.90)$ threshold computed from June through August observations. To reduce visual clutter, only summer months are shown, when sustained warm nighttime temperatures are most likely to occur.
• Figure 5: For the 2019, 2020, and 2021 datasets, the left panel displays the 2 AM temperatures and the right panel displays the 2 PM temperatures. For both, the counter is used for fitting, starting with early spring and ending with late summer. On the bottom is a legend showing the kind of line plotted for each dataset.