A phase-space consideration of changing climate-PDF

Abstract

Based on a single-model 100-member ensemble of climate change simulations performed with the MPI-ESM, this paper investigates how the probability density function (PDF) of atmospheric general circulation (AGC)—a marginal distribution of the full climate PDF—responds to increasing ${\hbox {CO}}_2$ concentration. The investigation provides a first assessment of ${\hbox {CO}}_2$-induced changes in AGC-PDF derived from ensemble statistics (as oppose to time statistics in usual practice) that arise solely from internal variability consistent with the imposed ${\hbox {CO}}_2$-forcing. By focusing on the first two moments of the AGC-PDF related to the Hadley circulation and the subtropical jets, we find that the major ${\hbox {CO}}_2$-induced changes in the PDF are related to structure changes in the mean circulation and in the circulation variability. As ${\hbox {CO}}_2$ concentration increases, different components of the AGC can co-evolve with changing forcing. In particular, the mean Hadley cell co-evolves with the mean subtropical jets. The co-evolution is characterized by the concurrent Hadley cell widening and poleward shifting of the subtropical jets (particularly strong in January), by a strengthening of both the Hadley cell and the subtropical jets in October, and by a weakening of the Hadley cell and a strengthening of the northern and southern jets in January. The changes in circulation variability are more subtle, and reveal only large and spatially coherent changes in places, where the variability is already strong without increasing ${\hbox {CO}}_2$ concentration, such as at the northern and southern flanks of the summer southern subtropical jet, and at the northern flank of the southern polar night jet. There are some significant cross-variabilities between different components of the AGC. Overall, the ${\hbox {CO}}_2$-induced AGC-changes can be described by linear trends in the first and second moments, with the trends in the means being much stronger than those in the variances and co-variances.

Appendix

1.1 Changes in ensemble means and ensemble variances in physical space

The purpose of this appendix is to provide an overview of changes in physical space, regarding both the ensemble mean and the ensemble variability of the AGC and as described by the ensemble mean and ensemble variance of meridional mass stream function and of zonal velocity. Both meridional-height sections of mass stream function and zonal mean zonal wind and horizontal maps of zonal velocity are shown. To describe the changes of the mean and the variability with increasing ${\hbox {CO}}_2$ concentration, the mean and variability at the beginning and the end of the simulation, corresponding to the pre-industrial time and the ${\hbox {4xCO}}_2$-time, are considered. We included also the absolute trends (instead of t values) of ensemble statistics of circulation indices in Tables 6, 7, 8 (Figs. 16, 17, 18, 19, 20, 21).

Table 6 Linear trends in ensemble mean time series of $S_{HC}$ (Tg/s per decade), $S_{Jn}$ and $S_{Js}$ (m/s per decade), $W_{HC}$ , $P_{Jn}$ , and $P_{Js}$ (deg per decade) for January, April, July and October shown in Fig. 9

Table 7 Linear trends in ensemble standard deviation time series of $S_{HC}$ (Tg/s per decade), $S_{Jn}$ and $S_{Js}$ (m/s per decade), $W_{HC}$ , $P_{Jn}$ , and $P_{Js}$ (deg per decade) for January, April, July and October shown in Fig. 10

Table 8 Linear trends (change per 150 years) in ensemble correlation time series

Fig. 16

Ensemble-means of zonal-mean meridional mass stream function at pre-industrial time (color shadings) and at $4 \times \mathrm{CO}_2$-time (black contours) in a January, b April, c July and d October. The scale of black contours corresponds to that of color shadings. The black dotted lines at 500 hPa denote the height, at which Hadley circulation strength $S_{HC}$ and width $W_{HC}$ are determined. Unit is 10 Tg/s

Fig. 17

Ensemble-means of zonal-mean zonal wind at pre-industrial time (color shadings) and at $4 \times \mathrm{CO}_2$-time (black contours) in a January, b April, c July, and d October. The scale of black contours corresponds to that of shaded contours. Unit is m/s

Fig. 18

Same as Fig. 17, but extending to the upper stratosphere at 1 hPa

Fig. 19

Ensemble-means of 2-dimensional zonal wind at 200 hPa at pre-industrial time (color shadings) and at $4 \times \mathrm{CO}_2$-time (black contours) in a January and b July. The scale of black contours corresponds to that of color shadings. Unit is m/s. Stippled zonal bands mark areas of the westerlies at 200 hPa. Zonal anomalies within these bands are considered in Fig. 13

Fig. 20

Difference in ensemble variance of 200-hPa zonal wind between the $4 \times \mathrm{CO}_2$- and the pre-industrial time ($4 \times \mathrm{CO}_2$ minus pre-industrial time, color shadings), and the ensemble mean of 200-hPa zonal wind in pre-industrial time (black contours), for a January, and b July. Contour interval is 12 m/s

Fig. 21

Difference in ensemble variance of 1-hPa zonal wind between the $4 \times \mathrm{CO}_2$- and the pre-industrial time ($4 \times \mathrm{CO}_2$ minus pre-industrial time, color shadings), and the ensemble mean of 200-hPa zonal wind in pre-industrial time (black contours), for a January, and b July. Contour interval is 12 m/s