Jet stream variability in a polar warming scenario - a laboratory perspective

. We report on a set of laboratory experiments to investigate the effect of polar warming on the mid-latitude jet stream. Our results show that a progressive decrease of the meridional temperature difference slows down the eastward propagation of the jet stream and complexiﬁes its structure. Temperature variability decreases in relation to the laboratory ‘Arctic warming’ only at locations representing the Earth’s polar and mid-latitudes, which are inﬂuenced by the jet stream, whilst such trend reverses 5 in the subtropical region south of the simulated jet. The reduced variability results in narrower temperature distributions and hence milder extreme events. However, our experiments also show that the frequency of such events increases at polar and mid-latitudes with decreased meridional temperature difference, whilst it decreases towards the equator (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) subtropics. Despite missing land-sea contrast in the laboratory model, we ﬁnd qualitatively similar trends of temperature variability and extreme events in the experimental data and the National Centers for Environmental Prediction (NCEP) reanalysis data.


Introduction
Since 1980, the polar regions have been warming approximately twice as fast as the mid-latitudes in the Northern Hemisphere, a phenomenon known as Arctic warming amplification. Model simulations (the 40-member CCSM3 ensemble) imply that this trend will continue in the future due to a robust global warming signal (Wallace et al., 2014). The signal-to-noise ratio is relatively small at higher latitudes and more significant in the tropics. Despite its well-established presence, there is still a debate 15 about the leading causes of Arctic warming amplification. Different models suggest that sea-ice loss, lapse-rate feedback, or increasing downwelling radiation at the surface could be the main contributor (Stuecker et al., 2018).
Regardless of the causes, it is unclear whether this faster Arctic warming impacts the large-scale circulation and, if so, the effects of such changes on extreme events. Francis and Vavrus (2015) found that the Arctic amplification enlarges the North-South meandering of the mid-latitude jet-stream and causes a slow down in the eastward progression of Rossby waves.
Over many years, these laboratory experiments have played a prominent role in geophysical fluid dynamics and climate studies. Several examples are given in the review article by Vincze and Jánosi (2016), such as investigating asymmetries of 60 atmospheric temperature fluctuations and experiments on interdecadal climate variability. The emerging scenario reveals that local variability, e.g. in Western Europe or North America, has increased in the past 40 years. Vincze et al. (2017) investigated the nature of connections between external forcing and climate variability conceptually using a laboratory experiment subject to continuously decreasing 'pole-to-equator' temperature contrast ∆T . Finally,  recently demonstrated the potential for using laboratory data to study multiple-scale interactions and explain even mesoscale atmospheric 65 processes. Their study reveals that frequency spectra from the differentially heated annulus experiment are comparable to the power spectra from atmospheric field observations. The paper is structured as follows. In section 2, we briefly describe the experiment, and in section 3, we give insight into typical flow regimes of the annulus experiment. We further study the impact of polar warming on the wave train structure and zonal phase speed. : In ::::::: sections :: 4 ::: and :: 5, ::: we ::::: focus :: on :::::::: statistical ::::::::: properties ::: that ::::::: depend :: on ::: the ::::::::::: temperature. Section 4 is the core 70 of this paper, where we investigate the temperature distributions and the impact of polar warming on extreme event frequency from experimental data. We then inspect and compare some of these features in NCEP reanalysis data in section 5. Finally, in section 6, we offer our concluding remarks.

Experimental apparatus and measurements
The experiments presented in this paper have been run with a differentially heated rotating annulus at the BTU Cottbus-

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Senftenberg laboratories (see von Larcher and Egbers (2005) for more details about the experimental apparatus). The experimental setup, sketched in Fig. 1, consists of a cylindrical tank divided into three concentric rings , which are filled with de-ionised water. The inner cylinder has a radius :: of a = 4.5 cm and is made of anodised aluminium. The water filling the inner cylinder is cooled by an external thermostat connected to the experiment. The tank is made of borosilicate glass, and the outer ring is separated from the middle cavity by a wall placed at radial distance b = 12 cm. Heating wires, supplied with 80 constant power by a control unit, warm up the water in the outer ring. The mid-gap (of width b − a = 7.5 cm) is filled up to the height D = 5 ::::: D = 5 : cm, and the fluid is subjected to a radial temperature difference ∆T imposed at the boundaries by the two thermally conducting walls. The tank is mounted on a turntable, which rotates counterclockwise around its vertical axis of symmetry at a constant rate Ω. The combined effect of the radial temperature difference produced by the two thermal baths and the rotation of the tank results in the set-in of the baroclinic instability in the middle gap giving rise to baroclinic waves.

::
In ::: the ::: rest :: of ::: the :::::: paper, :: we :::: use ::: the :::: more ::::::: general :::: term ::::: 'polar ::::::::: warming' :: for :::: this ::::::: scenario. Sensors are placed in the outer warm 95 and inner cold ring to measure the temperature in the two thermal baths, T cold and T warm , and calculate the radial temperature difference ∆T . Figure 2 and table 1 show the mean temperature measured by these sensors as a function of the temperature set in the cooling basin of the thermostat for each experimental run. Increasing the temperature in the cold bath leads to a higher equilibrium temperature and consequently an increase in the temperature in the warm outer bath, which is supplied with the same power at each experimental run. The rise in temperature in both baths is visible in : It ::: can ::: be :::: seen :: in Fig. 2 . But the  Figure 2. Temperature in the cold inner cylinder (blue) and hot outer ring (red) as a function of the cold thermostat target value. In the experiments discussed here (see table 1 :::: Table :: 1), the temperature of the cooled water was increased 1.75 times more than the temperature of the heated water. The series of experiments form an Arctic amplification scenario with an increase in mean temperature but a decrease of the radial temperature gradient.

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The surface temperature is measured with an Infrared Camera, IR camera in short (Jenoptik camera module IR-TCM 640, with thermal sensitivity of 0.01 K and image resolution 640 × 480 pixels). The IR camera is fixed in the laboratory reference system and mounted at the top of the experiment (see Fig. 1). The IR camera outputs are the time series of the entire annulus 2D surface field measured once at each tank rotation, corresponding to a sampling interval dt = 7.5 s. The advantage of having 115 the 2D field is that some characteristics, such as dominant wave patterns, zonal phase speed (i.e. the speed at which the pattern drifts as a whole anticlockwise around the apparatus in the rotating frame), and changes in the structure, can be detected. The spatial and temporal resolution are 400 × 400 × 3000 (pixels and times, x, y, t).

Flow regimes
This section discusses the dependency of the flow regimes on the radial temperature difference ∆T . Understanding how 120 changes in ∆T impact the spatio-temporal flow features is a necessary first step for examining the effects on the temperature distribution.
T cold and T warm are plotted in Fig. 2 as a function of T C . It can be noticed that T cold (in blue) increases 1.75 times more than T warm (in red in figure 2). This temperature change is well suited to experimentally mimic the polar warming effect observed 145 in the atmosphere.

Wavenumber transitions
It is enlightening to study the effects of lowering Ro t on the flow regimes in the azimuthal wavenumber space.
The column noted with m in table 1 indicates the dominant azimuthal wave number observed during the data acquisition.
into the wave trains, e.g. in the form of exceptional large meanders, will be slowed down, and the events in real atmospheric 215 flows might unfold their local destructive potential over a more extended period.

Temperature distributions and variability
This section investigates how polar amplification affects temperature distributions, mainly focusing on the variability. 'e'. Distributions at all three locations present a visible deviation from Gaussianity, which is more pronounced for larger ∆T .
Noticeably, the polar and middle regions are characterised by broader temperature distributions, whilst the distribution in the outer region is much narrower. This difference tends to be less marked for smaller ∆T ::: ∆T . For the polar and middle regions (left and middle plots), temperature variability consistently decreases for decreasing ∆T ::: ∆T (red lines), with distributions that become narrower and more symmetric :::::::::: distributions. In the equatorial :::::::: subtropical : regions, the tendency is the exact opposite: 225 the distributions broaden for decreasing ∆T . The run "C9", at the highest ∆T , stands out for its double-peaked distributions at all latitudes, which are also much broader than all other runs.
The changes in temperature anomalies variability are quantified in Fig. 8, where standard deviation (left), skewness (middle), and excess of kurtosis (right) are plotted for the distributions at the three latitudes shown in Fig. 7.
The standard deviation decreases with decreasing ∆T in the polar and mid-latitude regions (blue and black lines), whilst it 230 increases in the proximity of the equator :::::::: subtropics : (red line). To establish the statistical significance of the trends, we calculated the p-value with the t-test of the fit linear regression model fitlm, considering the 95% significance level. Hence, we consider trends with p < .05 as statistically significant, meaning that there is a probability higher than 95% that the corresponding coefficient is different from zero.
The negative trends of the standard deviation are statistically significant (p = .01 for the polar region and p = .003 for the 235 middle region), but the positive trend in the subtropical region is nonsignificant (p = .11). Note that the data point corresponding to the highest ∆T has been ignored to calculate the trends in Fig. 8 since it lies far off all the other data points. These points correspond to the double-peaked distributions in Fig. 7. The excess kurtosis in Fig. 8 (right) shows an evolution towards more Gaussian distributions for decreasing ∆T , confirming what can be seen in Fig. 7. The polar and middle regions have a highly significant positive trend (p < .001 in both cases). In 240 the subtropical region, the excess kurtosis has a nonsignificant negative trend (p = .5).
The skewness (Fig. 8 middle) does not show a statistically significant trend for any of the regions investigated. Linz et al.
(2018) studied the effects of decreasing ∆T on temperature distributions in an idealised advection-diffusion model and con-250 cluded that whilst a smaller ∆T reduces the variance, it does not have any direct effect on the skewness and kurtosis. Changes in the kurtosis should be attributed to a response to changes in the flow field instead. Therefore, the lack of a clear trend in skewness in our data agrees with the results by Linz et al. (2018). Our experimental data clearly show a relation between the decrease in meridional temperature difference and temperature variability. These results are consistent with what was found by Dai and Deng (2021) in model simulations and reanalysis data.

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Their analysis indicates that Arctic amplification decreases the temperature variability over the northern mid-high latitudes.
What does the reduction in temperature variability mean in terms of extreme events? Narrower and more symmetric probability distributions imply that cold and warm extreme events become weaker with decreasing ∆T . It follows that extreme events decrease in intensity in polar and middle regions whilst near the equator :::::::: subtropics, they become stronger. However, this does not help predict extreme events' duration or frequency. In the next section, we analyse the impact of changes in ∆T on 260 the frequency of extreme events.

Extreme event frequency
Extreme events are defined using a variety of metrics such as temperature thresholds and indices. The thresholds can be defined in different ways, the most common distinction being between relative thresholds (for example, defined by using specific percentiles of distribution or more straightforward measures like standard deviation) or absolute thresholds (for example, days 265 with temperatures exceeding 35 • ) (Seneviratne et al., 2021). Therefore, the choice of the definition used to calculate extreme events can affect the meaning of extremes and possibly the results.
We have discussed in section 4 that the reduction in meridional temperature difference impacts the temperature variability and results in milder extreme temperatures from the poles to the mid-latitudes, whilst at low latitudes, the extremes might become stronger. To study whether this variability reduction impacts the frequency of extreme events, we define extreme 270 temperature events based on a relative threshold. We chose such threshold as the standard deviation (σ) calculated for each experimental run, corresponding to a fixed ∆T , on ensembles of data measured at fixed latitudes. We then call extreme cold/hot events all temperatures such that |T − T mean | > 2σ.
Note that the σ−threshold is latitude-dependent. The extreme event frequency is defined as the number of times the temperature crosses the set threshold normalised by the total length of the data set (which is, in any case, the same for all the data sets 275 considered). The event duration is neglected, i.e. only the number of measurements ("days") where the temperature exceeds the threshold is counted, without distinguishing whether such days are consecutive or isolated.
The number of extreme events as a function of ∆T is plotted in Fig. 9  This difference in the cold trends can be partially explained by the fact that the baroclinic wave dynamics do not govern the subtropical dynamics, and we have already suggested that the extreme event distribution along the inner regions is tightly linked to the baroclinic waves. The decrease in cold events is consistent with a possible change in the subtropical extension of the baroclinic wave.

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For a complete understanding, we also study how extreme events are distributed as a function of latitude. For this analysis, temperatures at fixed latitudes are collected into sets, where each set is constituted by 1.2 × 10 6 temperature measurements for different times and longitudes. The standard deviation σ is calculated for each set, and, successively, the extreme event frequency is calculated as a function of the latitude.

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In summary, we suggest that the large-scale baroclinic wave dynamics govern the extreme event spatial frequency distribution in the laboratory experiment.

High-variability events in NCEP data
After analysing the lab data for changes in variability and the distributions of high-variability events as a function of the North-South temperature gradient, it is instructive to see what atmospheric data show concerning changes in variability and variability extremes. We use the National Centers for Environmental Prediction (NCEP) reanalysis data (Kalnay and collaborators, 1996).
In contrast to operational counterparts, the reanalysis data do not suffer from inhomogeneities introduced by changes in the data assimilation system. In this respect, they are a good supplement to data based on individual instrumental records or climatemodel simulations (Uppala et al., 2008). Moreover, reanalysis data cover historical data as well. We use two temperature data sets from the collection "NOAA-CIRES 20th Century Reanalysis, version 2, Daily Averages", covering the period from 320 1871 to 2012. The first set is the daily ensemble mean pressure level data (1000hPa to 10hPa), from which we extracted just the 500hPa level. The second set is the daily ensemble mean tropopause data. We start by considering the gradient and the standard deviation of the 500hPa temperature from 1871 to 2012.
The upper panel of Fig. 11 shows the trend in the North-South temperature difference (∆T ) taken from the NCEP 500hPa data for the Northern Hemisphere (blue line) and the Southern Hemisphere (red line). These temperature gradients are eval- of the Arctic (Arctic amplification) in the Northern Hemispheric data. However, the warming is pronounced particularly in surface data. For the lower stratosphere, the Arctic region is even cooled due to climate change (Stendel et al., 2021) and, as shown in the upper panel of Fig. 11, according to the NCEP data, even for the 500hPa level, the warming is not obvious. This discrepancy between the change of the North-South temperature gradient for low and high levels of the troposphere drives the 335 debate whether climate change leads to more or less wavier jet streams (Stendel et al., 2021). is consistent with other model data (Rind et al., 1989) and therefore it might still be physically significant. These observations are also in qualitative agreement with the results from the laboratory experiment.

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To inspect the frequency of high-variability (extreme) events, we focused on NCEP reanalysis data of the tropopause temperature. These data are less prone to the effects of land-sea contrasts and might be closer to the lab experiment.  have shown that spectra from tropopause data are comparable to the frequency spectra of the baroclinic wave experiment, and we suggest a similar connection concerning extreme values. We highlighted three ten-year periods: 1871 to 1880, 1951 to 1960, and 2003 to 2012. The seasonal cycle has been removed from the data. The frequency of extreme values, 350 defined as values larger or smaller than twice the standard deviation, has been calculated for all longitude circles with an increment of 20 • . Subsequently, for enhancing the robustness of the analysis, we took the mean of the Northern and Southern Hemisphere frequencies and finally we zonally averaged the frequency data. This gives the mean frequency of extreme values as a function of latitude ranging from 90 We see from Fig. 12  Comparing the experimental data ( Fig. 10) with the NCEP data ( Fig. 12) we find a notable qualitative similarity of the curves from 'p' to 'e' and from about 90 • to 20 • , respectively. Cold/warm extreme events occur more at low/high latitudes, in agreement with what was observed by Garfinkel and Harnik (2017). Furthermore, the cold events in NCEP and experimental data with large ∆T are most numerous at low latitudes. The frequency decreases for lessening ∆T . In contrast, cold events are most probable for smaller ∆T for near-polar and equatorial latitudes. It should be noted that the NCEP data ( Fig. 12)

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do not show such distinct extreme event peaks around the near equator region but have a monotonic increase/decrease for cold/hot events instead. This difference can be expected since the appearance of a local peak in the experiment might be due to the mentioned missing tropical dynamics, as previously explained. Note further that the largest ∆T experiment gives a very regular baroclinic wave (see figure 3 a), somewhat unrealistic with respect to atmospheric flows. Caution is, therefore, required when comparing the ∆T = 5.2 experiment with atmospheric temperature data.
We have presented a series of experiments with a differentially heated rotating annulus to model a global warming scenario.
Our study aims to reproduce the Arctic warming and study the possible effects on other atmospheric phenomena. For this simple experimental environment, the impact of a reduced pole-to-equator temperature difference on the mid-latitude largescale dynamics and consequences for the likelihood and distribution of extreme events could be isolated from various processes 380 that, in a more complex way, might play a role also for the Earth's atmosphere.
We found that the jet stream becomes more irregular due to warming the pole, making it challenging to identify a clear dominant azimuthal wavenumber. Moreover, the eastward propagating speed of the meandering baroclinic jet decreases, which, for the experiment, is a consequence of a slow down of the westerly mean flow for reduced ∆T . The decreasing meridional temperature difference also leads to a reduction of the temperature variability in regions of the experiment where the baroclinic 385 waves drive the dynamics. These regions, corresponding to polar and mid-latitudes, are characterised by temperature distributions that become narrower and more symmetric. Towards the outer ring of the annulus, corresponding to subtropical regions, the dynamics is less affected by the baroclinic, and consequently, the variability shows a slight increase. Our experimental findings agree with the recent analysis of coupled model simulations and ERA5 reanalysis by Dai and Deng (2021).
The consequence of a reduced temperature variability is that extreme events tend to become milder. However, our experiment 390 also reveals that extreme cold/warm events tend to become more frequent. Furthermore, these events are larger in number at lower/higher latitudes independently of the time period and temperature differences considered in agreement with NCEP data and with measurements of near-surface tropospheric temperature reanalysis data (Garfinkel and Harnik, 2017).
We think the results of the study underpin the usefulness of the laboratory approach to understanding specific processes of climate change, in particular with a view to temperature variability and extreme events. However, we have only taken a 395 first step and more sophisticated aspects like the use of extreme value theory, long-term memory effects, heavy tails in the amplitude of fluctuations, power-laws, spatial correlations and teleconnections etc., have been neglected in the work presented here. Moreover, a more recent and bigger rotating tank has proven to be closer to the atmospheric case than the smaller system used here . Hence, further experiments using this bigger differentially heated rotating tank and a deeper statistical analysis are planned for the future to add more experimental data to observations and climate simulations.
Data availability. The NCEP reanalysis data are from https://psl.noaa.gov/data/gridded/data.20thC_ReanV2c.pressure.html. We used two temperature data sets from the collection "NOAA-CIRES 20th Century Reanalysis, version2, Daily Averages", covering the period from 415 1871 to 2012. The first set is the daily ensemble mean pressure for the 500hPa level. The second one is the daily ensemble mean tropopause data set.
Author contributions. All authors have contributed to conceiving and designing the experiments. C.R. has run the experiments and analysed the experimental data. U.H. has analysed the NCEP data. C.R. and U.H. have drafted the paper. All authors have reviewed the manuscript and given final approval for publication.