Nonlinear statistics of daily temperature fluctuations reproduced in a laboratory experiment

The near-global statistics of daily mean temperature changes reveals a robust asymmetry. Warming steps have significantly higher frequency and lower average magnitude than those of cooling steps for most weather stations. This is a markedly nonlinear feature: Fourier surrogate time series exhibit completely symmetric increment statistics. The obtained geographic distribution of asymmetry parameters suggested an experimental test in a classical rotating tank setup. Temperature measurements in the dynamical regime of geostrophic turbulence reproduce quantitatively the strong asymmetry and spatial dependence of field observations. The statistics might be relevant in other systems of nonequilibrium steady states.

Figure 1

(Color online) Statistics of daily mean temperature changes for 13 208 weather stations. (a) Number of warming steps, $N_w$, over the number of cooling steps, $N_c$, as a function of record length $n$ (the horizontal scale is logarithmic). (b) Average warming step $⟨\Delta T_w⟩$ over average cooling step $⟨\Delta T_c⟩$ as a function of the latter for each station. (c) Geographic distribution of the step number ratio shown in (a) (the color scale is nonlinear) [2].

Figure 2

(Color online) (a) Experimental setup. $A$: Plexiglas bottom plate. $B$: outermost glass cylinder of radius $20.3\mathrm{cm}$. $C$: middle copper cylinder of radius $15.0\mathrm{cm}$. $D$: inner copper cylinder of radius $4.5\mathrm{cm}$. (b) Dye visualization of typical flow patterns in the working fluid of height $4.0\mathrm{cm}$ (the two slanted stripes are parts of the bottom plate). (c) Example time series recorded in a nonrotating convection experiment with a sampling rate of $3\mathrm{s}$. The location of the probes is indicated in (a) by colored circles: distance from the sidewall is $8\mathrm{mm}$, height from the bottom is $3\mathrm{mm}$ in both cases. The warm boundary temperature $T_{w0}=35°\mathrm{C}$; black triangles indicate when ice was refilled in the middle cylinder. (d) The same as (c) rotated with $\Omega =2.73{\mathrm{s}}^{-1}$.

Figure 3

(Color online) Correlation plot between step number ratio and average step size ratio for temperature changes. Black dots: terrestrial weather stations. Colored circles: laboratory experiments. Dashed line indicates the perfect stationarity condition.

Figure 4

(Color online) (a) Step number ratio for temperature changes as a function of nondimensional distance from the warm boundary. Black dots: meteorological records. Color symbols: experiments for two control temperatures. Dashed lines indicate the horizontal contraction of the experimental data resulting in approximately the same slope as the meteorological observations. (b) Step number ratio for two fixed locations close to the boundaries as a function of angular velocity $\Omega$, at $T_{w0}=40°\mathrm{C}$. Dashed lines are only a guide for the eye.

Figure 5

(Color online) Average temperature profiles as a function of nondimensional distance from the warm boundary. (a) Zonal average for the meteorological records. Error bars represent one standard deviation; seasonality is included. $x∕L$ is given by the latitude normalized by $\pi ∕2$. (b) Profiles in the rotating tank for two control temperatures.