Changes in frost days in simulations of twentyfirst century climate

Abstract

Global coupled climate model simulations of twentieth and twentyfirst century climate are analyzed for changes in frost days (defined as nighttime minima less than freezing). The model simulations agree with the observed pattern for late twentieth century of a greater decrease of frost days in the west and southwest USA compared to the rest of the country, and almost no change in frost days in fall compared to relatively larger decreases in spring. Associated with general increases of nighttime minimum temperatures, in the future climate with increased greenhouse gases (GHGs) the number of frost days is fewer almost everywhere, but there are greatest decreases over the western parts of the continents. The numbers of frost days are most consistently related to sea level pressure, with more frost days occurring when high pressure dominates on the monthly time scale in association with clearer skies and lower nighttime minimum temperatures. Spatial patterns of relative changes of frost days are indicative of regional scale atmospheric circulation changes that affect nighttime minimum temperatures. Increases of soil moisture and clouds also contribute, but play secondary roles. The linkages among soil moisture, clouds, sea level pressure, and diurnal temperature range are quantified by a statistical multiple regression model. Coefficients for present and future climate are similar among the predictors, indicating physical processes that affect frost days in present and future climates do not appreciably change. Only the intercept changes in association with the significant warming of the mean climate state. This study highlights the fact that, though there is a general decrease in the number of frost days with global warming, the processes that affect the pattern of those changes, and thus the regional changes of frost days, are influenced by several interrelated physical processes, with changes in regional atmospheric circulation generally being most important.

Appendix 1

Curves like those shown in Fig. 7 are sometimes defined “probability of detection” (POD) curves, and are an effective way of verifying the performance of a statistical prediction when the outcome is a binary variable, 0 or 1 or, in our case, non-frost day or frost day.

The statistical model in Eq. 1 produces a prediction of the probability p _f of the minimum temperature falling below 0 °C for each day used for verification. An actual prediction of frost-day demands the arbitrary choice of a threshold, a value t between 0 and 1 such that for any day’s predicted value p _f ′, the day will be predicted as a frost-day if p _f ′ ≥ t, otherwise it is a non-frost day.

For any given choice of a threshold, values of (a) the fraction of correctly identified frost days (sometimes called “probability of detection of 1’s, or POD 1”) and (b) the fraction of correctly identified non-frost days (sometimes called “probability of detection of 0’s or POD 0”) can be easily computed by building a two-way table of predicted versus true frost days:

$$\begin{aligned} &\quad {\text{T0 T1}} \cr & {\text{P0 n00 n01}} \end{aligned} $$

$${\text{P1 n10 n11}}$$

In the two way table, n00 is the number of days correctly predicted as non-frost days, n01 is the number of frost days incorrectly predicted as non-frost days, n10 is the number of non-frost days incorrectly predicted as frost days and n11 is the number of frost days correctly predicted. The fraction in (a) is given by n11/(n11+n01); the fraction in (b) is given by n00/(n00+n10).

For any real-life prediction (i.e., for any non-perfect model), the two PODs are constrained by a trade-off. The higher t (the higher we demand p _f ’ to be before labeling a day “frost-day”), the lower will be the number of days in the P1 row, so the lower POD 1 and the higher POD 0 (protecting against false positives). Conversely, the lower t, the higher will be the number of days in the P1 row, so the higher POD1 and the lower POD0.

The better the model, the higher the values of POD0 and POD1 will be at the same time. A perfect model would be able to achieve 100% in both PODs at the same time (n10 = n01 = 0). A bad model could do no better than chance, identifying only 50% of both. All intermediate models will achieve pairs of values for POD0 and POD1 between 0.5 and 1, differently balancing the two as a function of the threshold t chosen.

Any given model’s prediction can be represented by a POD curve, with each point on the curve having coordinates given by the values of POD0 and POD1 corresponding to a value of the threshold t. The better the model, the higher towards the upper right corner the POD curve will be. Perfect predictions would be represented by a curve overlaying the upper and right sides of the plotting region, reaching 100% in both coordinates.

No-skill predictions would be represented by straight lines joining the upper left to the lower right corners (through the 50%–50% point).