Suppression of Arctic air formation with climate warming: Investigation. with a 2-dimensional cloud-resolving model

Transcription

1 1 Suppression of Arctic air formation with climate warming: Investigation 2 with a 2-dimensional cloud-resolving model 3 Harrison Li 4 Harvard University, Cambridge, Massachusetts Timothy W. Cronin, Department of Earth, Atmospheric, and Planetary Sciences, MIT, Cambridge, Massachusetts Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts Eli Tziperman Department of Earth and Planetary Sciences and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts Corresponding author address: Department of Earth, Atmospheric, and Planetary Sciences, MIT, Cambridge, Massachusetts, USA twcronin@mit.edu Generated using v4.3.2 of the AMS LATEX template 1

2 ABSTRACT Arctic climate change in winter is tightly linked to changes in the strength of surface temperature inversions, which occur frequently in the present climate as Arctic air masses form during polar night. Recent work has proposed that an increase in low clouds in a warmer climate could suppress formation of Arctic air masses, leading to amplified winter warming over continents and sea ice relative to open ocean. But this low-cloud insulation mechanism was proposed based on single-column simulations that did not allow for assessment of how fractional cloud cover might change in warmer climates. This paper examines the potential for suppression of Arctic air formation with climate warming, using a 2-dimensional cloud-resolving model with several different microphysics schemes. The cloud-resolving model supports the results of the single-column model: low cloud optical thickness and duration increase strongly with initial air temperature, slowing the surface cooling rate as the climate is warmed. The cloud-resolving model cools slightly less at the surface than the single-column model and is more sensitive to warmer initial states, because it allows for stronger lower-tropospheric mixing and distributes the cloud-top cooling over a deeper layer with a larger heat capacity. These findings support the hypothesis that increasing insulation of the high-latitude land surface by low clouds in a warmer world could act as a strong positive feedback in future climate change, and suggest studying the process of Arctic air formation in a 3-dimensional climate model as a productive future research direction. 2

3 36 1. Introduction In recent decades, the Arctic has warmed significantly faster than the rest of the globe, particularly during winter (Chylek et al. 2009; Hartmann et al. 2013). This pattern of Arctic-amplified warming is expected to continue through the 21st century according to climate model simulations (Holland and Bitz 2003; Pithan and Mauritsen 2014). Arctic amplification of climate change occurs in models primarily due to positive feedbacks that act at high latitudes, especially those related to decreased surface albedo from melting of ice and snow and to changes in the tropospheric lapse rate (Pithan and Mauritsen 2014), though it can also occur due to increased poleward latent heat transport in the absence of locally amplifying feedbacks (e.g., Alexeev and Jackson 2013). Although changes in tropospheric lapse rate contribute strongly to Arctic amplification, assessment of lapse rate changes in models has often been diagnostic, and a more process-based understanding of the controls on high-latitude lapse rates and surface inversion strength is needed. Recent work by Cronin and Tziperman (2015) found amplified surface warming and weaker surface inversions over high-latitude winter continents due to increasing insulation of the surface by optically thick liquid clouds in a single-column model. The goal of this study is to test the viability and strength of this mechanism increased surface insulation by low clouds in a warmer world in a model that resolves clouds, and to compare cloud-resolving and single-column model results. Arctic air formation is an initial value problem in which an air mass with a prescribed initial temperature and moisture profile is allowed to cool by radiation to space over a low heat capacity surface in the absence of sunlight. This idealized problem represents the advection of maritime air over high latitude land or sea ice during polar night. The concept of Arctic air formation was first introduced by Wexler (1936), who explored the transformation of polar maritime air into Arctic air 3

4 by longwave radiative cooling in the absence of sunlight or clouds. Based on observed soundings during events of high-latitude air mass stagnation over land, Wexler (1936) suggested that the temperature profile of an Arctic air mass could be represented by a relatively cold isothermal layer overlying an even colder surface inversion layer. Both the isothermal layer and the inversion layer cool as time progresses and the isothermal layer deepens; in essence, radiative cooling of the surface to space steadily consumes the heat content of the lower troposphere from beneath. Work since the study of Wexler (1936) has slowly built from his original idea. Curry (1983) used a one-dimensional model with more detailed radiative transfer to examine the role of clouds, subsidence, and turbulence on the formation of Arctic air and found that the process is especially sensitive to the amount of condensate in the atmosphere and its partitioning between liquid and ice. Overland and Guest (1991) conducted longer simulations, and attempted to modify the problem from one of transient air mass cooling to one of winter equilibrium Arctic atmospheric temperature structure. They also examined the rapid adjustment of surface temperature and surface inversion strength to transitions between clear and cloudy skies. Emanuel (2008) performed single-column model calculations of Arctic air mass formation with a warm but very dry initial atmosphere, and showed that, owing to its large static stability, Arctic air has greater saturation potential vorticity relative to the rest of the troposphere, which may allow it to play an important role in development of mid-latitude weather systems. Pithan et al. (2014) motivated study of Arctic air formation with the observation of distinct clear and cloudy modes of the Arctic winter boundary layer (Stramler et al. 2011), and the poor representation of the these two modes in many global models. Pithan et al. (2014) found that distinct clear and cloudy states emerge in a single-column simulation of Arctic air formation, and that a bimodal distribution of surface longwave radiation emerges when the transient cooling process is sampled in time. 4

5 Cronin and Tziperman (2015) examined the climate sensitivity of the process of Arctic air formation by modifying the temperature of the initial sounding (representing maritime air) while holding relative humidity fixed. They found that a warmer initial maritime atmosphere leads to longer-lasting low clouds and a reduced surface cooling rate, potentially suppressing Arctic air formation and amplifying winter continental warming which would help explain continental warmth in past climates (e.g., Greenwood and Wing 1995). Increasing optical thickness of low clouds with warming results from increasing condensate amount and from a change in cloud optical properties that occurs as cloud particles change from solid to liquid. A potential concern that could be raised with these findings, however, is that the single-column model used did not allow for fractional cloud cover. A decrease in cloud fraction with warming would damp the effect of more cloud condensate on reducing the surface cooling rate. To test the suppression of Arctic air formation with climate warming found by Cronin and Tziperman (2015), this paper studies the process of Arctic air formation and its sensitivity to temperature in a 2-dimensional cloud-resolving model. At all but the warmest temperatures, we find that clouds tend to be stratiform and have large fractional area coverage. Thus, results in the single-column and cloud-resolving configurations differ little, and our findings are consistent with Cronin and Tziperman (2015): warming of the initial atmosphere leads to more low clouds and a reduced surface cooling rate. We describe the model setup in section 2, present results in section 3, and discuss our findings in section Model description We use a 2-dimensional idealized configuration of the Weather Research and Forecasting (WRF, version 3.4.1) model to simulate the process of Arctic air formation over a low heat capacity land surface for a 14-day period during polar night. We perform simulations across a range of different 5

6 initial temperature profiles and microphysics schemes. As in Cronin and Tziperman (2015), the surface is set to be a uniform moist slab with the roughness of an ocean surface and heat capacity J m 2 K 1 (the same as an oceanic mixed layer of depth 5 cm; this depth corresponds to the heat capacity of the surface layer of a deep snowpack that communicates with the atmosphere on a 1-day time scale). Initial temperature profiles are defined by a single parameter, the initial 2-meter air temperature T 2 (0) (note that we use the terms 2-meter air temperature and surface air temperature interchangeably in this paper). Above the surface, initial soundings have a tropospheric lapse rate that is either moist-adiabatic or -8 K km 1, whichever is more stable, and an isothermal stratosphere at -60 C. The initial atmospheric relative humidity decreases from 80 percent at the surface to 20 percent at 600 hpa; above 600 hpa the relative humidity is constant at 20 percent up to the tropopause and set to a mixing ratio of g kg 1 in the stratosphere. In this paper we use the phrase climate warming synonymously with warming of the initial atmospheric state. The model domain is periodic in the horizontal dimension with a length of 15 km and a height of approximately 15 km, with a uniform horizontal grid spacing of 100 m and an initial vertical grid spacing of 50 m. The model time step for dynamics is 1.5 seconds. No cumulus parameterization scheme is needed due to the fine horizontal and vertical grid spacing. The spacing of levels in height decreases with time in each simulation because the vertical coordinate in the model is based on hydrostatic pressure, so cooling causes compression. The horizontal domain size was chosen as a compromise between computational cost and resolution. Although the single-column simulations in Cronin and Tziperman (2015) extend up to 35 km, in this work we reduce the vertical extent of the model because modeling the stratosphere is not essential for the problem being addressed. We also run the model with several different grid spacings in both the horizontal and vertical to test the robustness of the main results to model resolution (see section 4d). To 6

7 stimulate turbulent mixing near the surface (both parameterized mixing and resolved eddies) and prevent the development of stationary surface temperature heterogeneities, a uniform initial 5 m s 1 zonal wind is imposed throughout the spatial domain of the model, and the horizontal mean flow is relaxed to this value over a 1-day period. Longwave radiative transfer in the model is parameterized using the RRTMG scheme (Iacono et al. 2008). The RRTMG scheme computes radiative transfer in 16 longwave spectral bands using a correlated-k distribution approach to calculate probability density functions for absorption coefficients of major greenhouse gases, and is called every 2 minutes. Test simulations with 6 seconds between radiation calls lead to minimal difference in the results, but are substantially more computationally costly. We use the Yonsei University (YSU) boundary layer scheme, which diffuses heat and moisture non-locally within a layer of depth diagnosed using a bulk Richardson number (Hong et al. 2006). Because the near-surface stability in our model setup is generally very high, and winds are relatively weak, boundary layer depths are quite small rarely up to a few hundred meters and often less than 50 m in depth. Surface turbulent fluxes are parameterized using Monin- Obukhov similarity with separate look-up functions for different stability classes, and the latent heat flux is not allowed to be negative (i.e., there is no dew or frost). Test simulations allowing for dew and frost show small effects on the surface energy balance and do not substantially alter the results presented here. One of the advantages of using WRF is the ability to easily test different parameterizations of cloud microphysics. The Appendix gives some basic information about each cloud microphysics scheme that we considered, particularly including details on the temperature-dependence of mixed-phase clouds. Microphysics schemes are called at every model time step. As in Cronin and Tziperman (2015), some results are shown only for the Lin-Purdue microphysics scheme, but many plots show mean and spread of the 6 microphysics schemes used. The Lin-Purdue scheme 7

8 is a relatively simple bulk (single-moment) scheme that models six hydrometeors water vapor, cloud water, cloud ice, snow, rain, and graupel assuming exponential size distributions of rain, snow, and graupel particles (Lin et al. 1983). We also perform sensitivity tests labeled no-crf where cloud-radiation interactions are disabled; the Lin-Purdue scheme is still used but cloud water concentrations are set to zero in the radiative transfer scheme (latent heat associated with phase changes is still considered). Comparing no-crf results to the results with radiatively active clouds allows us to quantify the impact of cloud longwave forcing on Arctic air formation. One important caveat of this modeling setup is that, although some of the microphysics schemes predict particle sizes in different categories, this information is not passed to the RRTMG radiation scheme. Rather, in the version of WRF that we use, only the total cloud liquid and ice content in each column and vertical level is passed to RRTMG, and the radiation scheme makes assumptions about the cloud particle sizes. With more complete radiation-microphysics coupling, differences in microphysics schemes would likely affect the results more than indicated here Results An increase in cloudiness with warming of the initial state is evident from snapshots of modeled Arctic air formation after four days of cooling from initial 2-m air temperatures (T 2 (0)) of 0, 10, and 20 C and the Lin-Purdue microphysics scheme (Figure 1, Video S1). When the initial surface temperature is T 2 (0) = 0 C (Figure 1a), a strong surface inversion develops, and the surface cools by more than 25 C in four days under an essentially cloudless sky. With a warmer initial surface temperature of T 2 (0) = 10 C (Figure 1b), an optically thick liquid fog layer develops near the surface, which strongly inhibits cooling; the surface cools only by about 12 C by the end of the fourth day, and the surface inversion is nearly nonexistent. For an even warmer initial surface temperature of T 2 (0) = 20 C (Figure 1c), two distinct optically thick liquid cloud layers insulate 8

9 the surface, one at low levels and one at roughly 700 hpa. This abundant cloud cover displaces radiative cooling upwards from the surface to the top of the upper cloud layer, and as a result there is only about 10 C of surface cooling by the fourth day, with the low-level lapse rate remaining nearly moist adiabatic as in the initial state. Between the two cloud layers for T 2 (0) = 20 C, horizontal variance of vertical velocity is large, and the evolution of the clouds in time suggests that the region between the cloud layers is convective (see Video S1). Snapshots of domain-average soundings and cloud properties every 2 days during the cooling process also show the strong increase in cloudiness with warming of the initial state (Figure 2), again for T 2 (0) in {0,10,20} C and the Lin-Purdue microphysics scheme. It is evident that whenever optically thick low-level liquid clouds are present, they prevent the development of the surface inversion characteristic of Arctic air, instead giving rise to a strong cloud-top inversion with temperatures increasing from the cloud top down to the surface (Figure 2). The result is that the simulation with T 2 (0) = 20 C has a total surface air temperature decrease of 39.7 C over two weeks, compared to 52.2 C for T 2 (0) = 10 C and 57.3 C for T 2 (0) = 0 C. Comparing the evolution of surface longwave fluxes (Figure 3a) with the soundings in Figure 2 shows a clear correspondence between suppressed surface cooling rates and the presence of low-level liquid clouds. This is illustrated more explicitly by Figure 3c, which shows that warmer initial states have a more positive and more persistent surface cloud longwave forcing; for the warmest case, surface cloud longwave forcing increases until after day 10. Turbulent surface heat fluxes are also important for the total cooling rate under clear skies; once the cloud layer dissipates in each simulation, about half of the surface radiative cooling is offset due to sensible heating of the surface by the warmer overlying air in the surface inversion (Figure 3b, negative fluxes indicate warming of the surface). Synchronous spikes in surface longwave cooling (upward) and surface cloud radiative effect and condensate path (downward) appear prominently for the warmest simulation in Figure 3. These 9

10 spikes occur due to quasi-periodic formation and upward propagation of a near-surface fog and stratus cloud layer, which repeatedly transforms into cumulus convection and dissipates, allowing the surface to cool and again form a fog layer (see Video S1; frames near and leading up to a spike at day 4, hour 21 provide a good example). The frequency of these spikes is 1-2 d 1, but the timing, regularity, and amplitude varies substantially across microphysics schemes. Although these spikes are an intriguing feature of the warmer simulations, they do not seem to play a key role in any of the main conclusions, and consequently we do not discuss them further. Looking at the mean and spread of the surface air temperature evolution across the six microphysics schemes shows that warming the initial atmosphere leads to a robust reduction in the surface cooling rate over the two-week cooling period, especially over the first week of the Arctic air formation process (Figure 4a). The greatest spread in surface air temperature across microphysics schemes occurs when there are lower-tropospheric mixed-phase clouds, which occur progressively later for warmer initial states (Figure 4a). Time series of the mean of surface air cooling (T 2 (0) T 2 (t)) across microphysics schemes indicate that, after a brief initial clear-sky cooling period (lasting well under a day), the surface air temperature plateaus for progressively longer for warmer initial states (Figure 4b). For radiatively clear skies, the no-crf simulations show that surface air cooling would be much less sensitive to the initial atmospheric temperature (dash-dotted lines in Figure 4b). To synthesize many cooling time series such as those shown in Figure 4, we define a metric of time-mean surface air cooling, T 2 by T 2 = T 2 (0) T 2 (t), (1) where the overline on T 2 (t) indicates a time-mean over the two week simulation. Time-mean sur- face air cooling decreases nonlinearly with initial temperature, with relatively little spread across 10

11 microphysics schemes (Figure 5a), and is much greater for the no-crf simulations (dash-dotted line in Figure 5a). A least-squares fit of T 2 averaged over all microphysics schemes gives: T 2 = T 2 (0) T 2 (0) 2 (2) 224 and for the no-crf simulations gives: T no CRF 2 = T 2 (0) T 2 (0) 2, (3) with T 2 (0) in C. The slope γ = T 2 T 2 (0) is a dimensionless feedback measure that indicates the extent to which the Arctic air formation process amplifies initial surface air temperature differ- ences. In the mean across microphysics schemes, each degree of warming of the initial state leads to a decrease of time-mean surface air cooling by γ = T 2 (0) degrees. For ex- ample, for the warmest case (T 2 (0) = 20 C), each degree of initial warming implies a γ 1.7 degree decrease in average cooling. In comparison, the no-crf feedback is about 65% smaller: γ no CRF = T 2 (0). Thus, cloud radiative effects alone reduce surface cooling by about a degree for each degree warming of T 2 (0) in the warmest cases that we simulate. The time for the 2-meter temperature to reach freezing, τ 0, remains identically short well under a day for all microphysics schemes when T 2 (0) is less than 8 C. For a two-degree warming above 10 C (8 C for the Goddard microphysics scheme), however, the time to freezing very rapidly jumps to 4-6 days, then increases further to days for T 2 (0) = 20 C. The rapid jump and subsequent continued increase occur because of the shape of the cooling time series, and because the time to freezing is the time to cross a fixed threshold of 0 C (Figure 4a). When T 2 (0) is less than 10 C, the surface drops below freezing during a period of rapid cooling before clouds form; for the warmer cases, clouds form before the surface has the chance to cool to freezing, and the threshold is crossed during a period of slow cooling. The abrupt jump in τ 0 near T 2 (0)=10 C is thus an indicator of the flatness of the cooling time series in Figure 4a. 11

12 Mean statistics averaged over time and across microphysics schemes are given in Table 1, for simulations with T 2 (0) in { 10, 5,0,5,10,15,20} C, and will be discussed in more detail below. One noteworthy aspect of the simulations is that the time-mean surface skin temperature T S is 3 C colder than the time-mean surface air temperature (T 2 ) in the coldest simulations, because the strong surface inversion includes a near-discontinuity between the surface and near-surface air. Evolution of the surface temperature jump T S T 2 closely follows the surface turbulent heat flux, with slightly negative values when there are thick clouds and positive values in the presence of strong inversions. Because the surface inversions are much weaker for higher values of T 2 (0), the difference between surface skin temperature and surface air temperature is much reduced for the warmest simulations. Thus, a cooling metric defined in terms of time-mean surface skin temperature would be even more sensitive to the initial state than T Discussion 255 a. Comparison of cloud-resolving and single-column model results The results above are both qualitatively and quantitatively consistent with the findings of Cronin and Tziperman (2015), who used a single-column setup of WRF. A key conclusion of this paper is to support the single-column model result that Arctic air formation is suppressed for a warm initial maritime profile. Nonetheless, it is useful to analyze in depth the differences between single-column and cloudresolving results, to determine where differences lie. Our Figure 5 can be compared to Figure 2 of Cronin and Tziperman (2015). For the cloud-resolving simulation results presented here, timemean surface cooling over two weeks is slightly reduced (by 1-3 C) and the feedback γ is slightly larger relative to the single-column results. The cooling curves are less flat for warm T 2 (0) in the 12

13 simulations of Cronin and Tziperman (2015) as compared to the results found here, so the sharp jump in τ 0 around T 2 (0)=10 C was not found in Cronin and Tziperman (2015). These differences could result from numerical issues such as changes in domain height and vertical level spacing, or from differences in the physical mechanism of Arctic air formation between the cloud-resolving and single-column models. To compare single-column and cloud-resolving results more directly, we have re-run all of the 2- dimensional simulations described here using a single-column model configuration with the same vertical level spacing (301 vertical levels, model top at 15 km). We define a bulk root-mean-square (RMS) temperature error statistic δ ˆT by: { n 1 t δ ˆT = Mn z n t n z i=1 k=1 m k [ T 2D x (i,k) T SCM (i,k) ] 2} 1/2, (4) where M is the total atmospheric mass, n z is the number of vertical levels, n t is the number of time steps, m k is the atmospheric mass in vertical level k, Tx 2D (k,t) is the temperature at vertical level k and time step i averaged over the horizontal coordinate for the cloud-resolving simulation, and T SCM (k,t) is the temperature in the single-column run at vertical level k and time step i. An analogous statistic, δtˆ 2, is defined by comparing only the 2-meter temperatures: { n δtˆ 1 t 2 = n t i=1 [ T 2D 2 (i) T SCM 2 (i) ] 2} 1/2 (5) where T 2D 2 (i) is the horizontally averaged two-meter temperature at time step i for the cloud- resolving run and T SCM 2 (i) is defined similarly for the single-column run. We also define a simple time-mean surface air temperature difference between cloud-resolving and single-column simula- tions as δt 2 = T 2 2D T2 SCM. We find that differences between cloud-resolving and single-column results are small at low T 2 (0), but generally grow for warmer initial atmospheric states (Figure 6; some schemes have greatest near-surface disagreement for T 2 (0) = 10 C). The magnitude of the temperature errors is < 2 C for δ ˆT, but can be up to 7 C for δ ˆ T 2, although δ ˆ T 2 is only > 4 C for 13

14 two microphysics schemes (Thompson and Morrison) and some warmer initial temperatures. RMS differences in surface air temperature are mostly linked to time-mean temperature differences, as cloud-resolving simulations simulations are generally warmer near the surface than single-column simulations (Figure 6c). Surface temperatures in the cloud-resolving model can be 5 C warmer than in the single-column model around days 10-14, especially for the Thompson and Morrison schemes. Disagreement between the cloud-resolving and single-column simulations may occur due to turbulent mixing near the tops of layered clouds, as well as the increasing occurrence of cumulus convection at warmer temperatures, which is handled by a parameterization in the single-column model but by resolved small-scale motions in the cloud-resolving model. The greater warmth of cloud-resolving simulations (relative to corresponding single-column simulations) near the surface is offset by colder conditions near the cloud-top inversion (not shown). The Morrison scheme is warmer at the surface and colder over a deep lower-tropospheric layer in the cloud-resolving 299 configuration even for low T 2 (0). Some of these differences are associated with more cloud condensate in the cloud-resolving than in the single-column configuration in part because the upward-propagating stratus layers persist longer in the cloud-resolving than in the single-column simulations (especially for the Thompson and Morrison schemes). The pattern of overall differences in both temperature and cloud condensate between cloud-resolving and single-column simulations indicates more active cloud-top turbulence in the cloud-resolving simulations, leading to cloud layers that grow more rapidly and ultimately become deeper than in the single-column simulations (this difference occurs for all microphysics schemes at T 2 (0) = 20 C). Because the radiative cooling to space from lower-tropospheric cloud tops is spread over a deeper layer, cooling is weaker at the surface but extends to greater height. Thus, in spite of our initial expectation that 14

15 a cloud-resolving model might give more surface cooling because it allows for cloud layers with less than 100% cover, it appears that the reverse occurs due to increasing cloudy layer thickness. Taking a step back, we reiterate that the qualitative differences between cloud-resolving and single-column model simulations are small. Use of a high-resolution 2-dimensional cloud resolving model alters little the conclusions reached with the single-column model. 314 b. Vertical structure of cooling As the initial atmospheric state is warmed, the surface cooling rate decreases, but the top-ofatmosphere outgoing longwave radiation increases. Reconciling these two opposing trends requires that the cooling rate of the atmosphere must increase with T 2 (0) at some height above the surface. Plotting the profile of average cooling rate, we indeed see that cooling decreases with T 2 (0) at and just above the surface, but increases with T 2 (0) above the lowermost troposphere (Figure 7). The strongest reduction in surface cooling as T 2 (0) is increased occurs over the first week of the simulation (Figure 7a), with a non-monotonic response of surface cooling to T 2 (0) during the second week (Figure 7b). Colder initial atmospheres have a surface cooling rate of 4 C d 1 over the two-week period and 5 C d 1 during the first week, but the atmosphere above 850 hpa cools at 2 C d 1 or less. The warmest cases (T 2 (0) = 20 C) have a cooling rate of about 2 C d 1 that is relatively constant in time and height over a deep layer (up to approximately 300 hpa). There is significant spread across microphysics schemes in the timing of cooling as shown by the shaded areas in the plots of cooling broken down by week (Figure 7a,b) but the total amount of cooling over the two-week period differs much less across microphysics schemes. The massaveraged cooling rate of the atmosphere increases with T 2 (0), from 1.4 C d 1 at T 2 (0) = 0 C to 1.8 C d 1 at T 2 (0) = 20 C (Table 1). This cooling rate is an average temperature change from the sum of all physical processes simulated (radiation, condensation, convection), and although it is 15

16 dominated by longwave radiative cooling, it should not be interpreted as a radiative cooling rate alone. Surface cooling rates in the no-crf simulations show much less sensitivity to the initial atmospheric state, with 4 5 C d 1 surface cooling over the first week and 2 3 C d 1 surface cooling over the second week, and surface-amplified cooling over the whole two-week period (Figure 8). An upward shift and increase in magnitude of mid- and upper-tropospheric cooling with warming of the initial atmosphere is seen in simulations with and without cloud-radiation interactions (compare Figures 7 and 8 above 600 hpa). The energy loss of the atmosphere and surface by radiation to space can be divided into contributions from changes in internal heat, latent, and gravitational potential energy of the atmosphere, and changes in heat content of the surface (Table 1; angle brackets indicate mass-weighted vertical integrals). Condensation (L v q v / t) plays an increasingly important role in the column energy budget at the warmest temperatures, amounting to 40 W m 2 of heating in the warmest cases. For extremely warm initial temperatures, the role of condensation alone in increasing the effective heat capacity of the atmosphere could lead to a reduction in average tropospheric cooling rates with increasing T 2 (0) (Cronin and Emanuel 2013), but our simulations do not reach that limit, in part because our initial soundings are rather dry. Note that changes in internal heat energy (c v T / t) and gravitational potential energy ( gz / t) of the column do not sum to c p T / t, because the upper bound of integration is only 15 km and the equality only holds for a full column integral (e.g., Peixoto and Oort 1992, chapter 13). 351 c. Top-of-atmosphere radiation and feedbacks To attempt to compare our results with the feedbacks diagnosed from global climate models (e.g., Pithan and Mauritsen 2014), we can analyze how top-of-atmosphere radiative fluxes depend on surface temperature. Because our model for Arctic air formation is an idealized depiction of 16

17 a complex transient process, the analysis presented is not equivalent to a climate model feedback analysis, and we do not decompose the sensitivity of top-of-atmosphere outgoing longwave radiation (OLR) to surface temperature T S into specific feedbacks (this would also require additional radiative transfer calculations outside of WRF). Figure 9 shows the surface temperaturedependence of three choices of OLR: initial OLR(0) plotted against initial surface temperature, time-mean OLR plotted against time-mean surface temperature, and time-mean clear-sky OLR clear plotted against time-mean surface temperature (values also given in Table 1). A blackbody with temperature 25 degrees less than the surface is also plotted for reference. All three values of OLR appear fairly linear as functions of T S (Figure 9a), but closer examination of the slopes of OLR against surface temperature reveals more nuance (Figure 9b). These slopes are plotted with negative sign as they represent a total longwave feedback that is stabilizing. The contrast in slope between the time-mean and initial OLR values provides a measure of how the suppression of cold air formation alters the local top-of-atmosphere longwave feedback. We wish to emphasize a few features of Figure 9b: The apparent linearity of OLR(0) in Figure 9a is deceptive. The longwave feedback from the initial state increases in magnitude from 2.2 W m 2 K 1 for the coldest initial temperatures to 2.8 W m 2 K 1 for the warmest The clear-sky time-mean OLR is quite linear. The reduced magnitude of slope of OLR clear by 0.5 W m 2 K 1 relative to the slope of OLR(0) indicates that there are positive clearsky OLR feedbacks associated with the suppression of Arctic air formation. We interpret this offset between slopes of OLR clear and OLR(0) as primarily a positive lapse rate feedback, though we cannot rule out a water vapor feedback component. 17

18 The most striking nonlinearity in Figure 9a is the negative curvature in the plot of OLR; figure 9b shows a full halving of slope of OLR from the coldest to the warmest simulations. The reduced magnitude of the slope of OLR with warming is due to a positive top-of-atmosphere cloud longwave feedback that rapidly increases to 1 W m 2 K 1 for the warmest initial conditions (compare slopes of OLR and OLR clear in figure 9b) The strong top-of-atmosphere cloud feedback under warm conditions shown in Figure 9b can also be inferred from time-mean top-of-atmosphere cloud radiative forcing, which is generally small compared to the surface cloud radiative forcing (and can even be negative), but which increases rapidly with warming for warm initial atmospheres (Table 1, last two rows). From a conventional top-of-atmosphere standpoint, clouds may thus act as a stronger positive feedback than was realized by Cronin and Tziperman (2015). 388 d. Sensitivity to model resolution To test the sensitivity of the results to horizontal and vertical resolution ( x, z), we conduct simulations with varied resolution using the Lin-Purdue scheme at T 2 (0) of 0 and 20 C. RMS er- ror metrics δ ˆT and δ ˆ T 2 are defined based on differences between the control simulation and the simulation with varied resolution. Overall, these sensitivity tests do not show clear convergence with increasing resolution, but they do confirm that the results change relatively little with resolu- tion (Table 2). Root-mean-square temperature deviations from the control simulation (which has x = 100 m, x = 50 m) are < 1 C for the bulk atmosphere, and < 3 C for the surface (Table 2). Table 2 also shows the time-mean 2-meter temperature difference, the mean surface cloud radia- tive forcing, and the statistic σ u, which is defined as the standard deviation of instantaneous zonal wind across the horizontal dimension, averaged over all vertical levels between 1000 and 850 hpa and the entire two-week period. This statistic is intended to measure low-level turbulence, which 18

19 is particularly relevant to the warmer simulations in which there appears to be significant low-level convection. One interesting aspect of these simulations is that varying resolution has different effects for warm and cold initial conditions. For cold initial conditions (T 2 (0) = 0 C), sensitivity to horizontal resolution is modest, except that when x is lowered to 50 m, a much stronger cloud layer develops early in the simulation, leading to an increase in surface CRF and an average surface warming of 1.5 C. Increasing vertical resolution leads to a sharper inversion and a colder surface (despite stronger low-level turbulence), whereas decreasing vertical resolution leads to a smoother inversion and a warmer surface. For warm initial conditions (T 2 (0) = 20 C), sensitivity to decreasing horizontal resolution is stronger, and leads to surface cooling of 1.5 C, along with a decrease in turbulence and surface CRF. Doubling horizontal resolution has relatively little effect. Vertical resolution changes have the opposite effect in the warm simulation as in the cold one; increasing vertical resolution leads to (small) surface warming, and decreasing vertical resolution leads to surface cooling. This reversal occurs because clouds are much more important in determining the surface air temperature in the warm simulation, and sharp clear-sky inversions do not develop as in the cold simulation. 416 e. Treatment of the surface and other limitations The surface in our model is treated very simply essentially as a heat-storing slab that is dragged along with the atmosphere as it moves. By using identical values of T S (0) and T 2 (0), and giving the surface a relatively low heat capacity, we have tried to minimize biases in sensitivity γ = T 2 T 2 (0) that might be related to the surface. Cronin and Tziperman (2015) found that a surface with higher heat capacity leads to smaller values of γ, whereas a surface with a lower heat capacity leads to a larger γ. We suspect this indicates a general rule: the more thermal memory the surface has, the 19

20 less sensitive surface temperatures will be to changing the initial atmospheric state. For instance, previous work by Curry (1983) and Pithan et al. (2014) both used a sea ice-like surface, with a prescribed thickness and temperature profile. This structural choice makes sense for exploring Arctic air formation in the present climate, but likely makes γ smaller than in our work, because ice with a prescribed temperature will conduct heat out of a warm initial atmosphere or into a cold initial atmosphere. Another limitation of this work is the lack of large-scale subsidence or wind shear. Moderate subsidence in single-column simulations of Cronin and Tziperman (2015) was found to limit the upward growth of the cloud layer, but did little to modify the suppression of Arctic air formation in a warmer initial atmosphere; we anticipate similar sensitivity to subsidence in the cloud-resolving model used here. A stochastically varying vertical velocity profile that includes stronger ascent and stronger subsidence, as in Brient and Bony (2013), might provide a stronger and more realistic test of our mechanism than steady subsidence. Regarding wind shear, we expect more rapid horizontal advection of air aloft than near the surface, so realistic vertical shear would likely lead to less cooling in the mid- and upper-troposphere as an air mass traverses a continent than we have simulated here. The 2-week time period during which we follow the cold air formation process is also somewhat arbitrary, and should be informed by investigation of the observed time scales of continental traversal for air parcels in the lower troposphere, and projections of how these time scales may change with warming. Recent work by Woods and Caballero (2016) has suggested a link between observed Arctic warming and increasing frequency of injection events of very warm and moist air into the polar region a result consistent with the ideas presented in this paper. Questions about the role of large-scale dynamics both vertical advection and the statistics of horizontal flow point to investigation of cold air formation in a GCM as a productive future research direction. 20

21 A third limitation was noted above: in the version of WRF we use, the coupling between radiation and microphysics is incomplete. Only the total water and ice content in each column and vertical level are passed from the microphysics scheme to the radiation scheme, and the radiation scheme makes its own assumptions about particle sizes. The spread across microphysics schemes shown here thus includes temperature-dependent differences in liquid condensate fraction and microphysical removal rates, but does not include variation in particle sizes. Investigation of cloud ice effective radii in the Thompson and Morrison scheme simulations (not shown) reveals large differences between the two schemes, but only weak sensitivity to T 2 (0) in each. Lack of temperature-dependence within each scheme is reassuring for our overall mechanism for suppression of Arctic Air formation, but the large difference between schemes indicates that we have underestimated the spread in cooling rates that would occur for complete coupling of radiation and microphysics. Finally, we do not include in our simulations any link between aerosols and clouds or precipitation interaction, although interactions between aerosol, cloud, and precipitation may be important for determining cloud particle size and lifetime in the real Arctic (Mauritsen et al. 2011) Conclusions We have used a 2-dimensional cloud-resolving configuration of the WRF model to investigate the idea that Arctic air formation is suppressed in warmer climates. Our results indicate that warming of the initial state leads to substantial inhibition of Arctic air formation via the development of optically thick low-level liquid clouds that hamper surface radiative cooling, and are consistent with single-column model simulations in Cronin and Tziperman (2015). Two-week averaged cooling decreases by roughly 0.6 degrees for each degree warming of the initial state at initial air temperatures near 0 C, and this amplification factor rises for very warm initial air temperatures 21

22 to as much as 1.7 degrees of reduced cooling for each degree warming of the initial state. These results are robust across several different cloud microphysics schemes. The low-level cloud tops for the warmer cases in the cloud-resolving simulations extend to greater altitude as compared to analogous single-column simulations, which slightly increases the strength of the cloud feedback by spreading cooling over a deeper layer of the lower troposphere. The greater altitude reached and faster growth of the lower-tropospheric cloud layer appears related to cloud-top turbulence, which is not resolved in the single-column model. This paper was able to focus on smaller-scale processes than was possible in the single-column simulations of Cronin and Tziperman (2015). Many questions for future research on Arctic air formation relate to larger spatial scales, and the interaction of Arctic air formation with the general circulation of the mid- and high-latitude atmosphere. How does the upward shift in cooling during the formation of cold air affect mid- and high-latitude dynamics? What pressure levels in the Arctic atmosphere are most linked to extreme cold outbreaks in mid-latitudes? How robust is the low-cloud insulation mechanism to full 3-dimensional wind variability in a global model? What is the joint probability density function of age of terrestrial air and sea surface temperature last encountered, and how does this joint distribution change with global warming? Addressing these questions may offer new ways of understanding Arctic amplification and its coupling to changes in mid-latitude extreme weather. 488 Acknowledgments. This work was supported by a Harvard undergraduate PRISE fellowship (HL), NOAA Climate and Global Change Postdoctoral Fellowship and by the Harvard Univer- sity Center for the Environment (TWC), and by the NSF climate dynamics program under grant AGS ET thanks the Weizmann institute for its hospitality during parts of this work. 492 APPENDIX 22

23 493 Cloud microphysics schemes used We use six different microphysics schemes in this paper; references are given in Table 5. Most of the models are bulk schemes that use a single prognostic variable mass mixing ratio to model six classes of water: vapor, cloud liquid, cloud ice, rain, snow, and graupel. Exceptions are listed in the Notes column of Table 5 for example, the Thompson scheme tracks both number and mass of the rain class (and thus has two-moment rain). Previous work highlights the importance of liquid-ice partitioning (as a function of temperature) in determining the magnitude of low cloud optical thickness feedback over the Southern Ocean in global climate models (McCoy et al. 2015). Table 5 shows the glaciation temperature (T ) metric from McCoy et al. (2015) for each microphysics scheme, or the temperature at which half of cloud water is ice and half is liquid. Figure A1 shows the mean liquid cloud condensate fraction as a function of temperature for each of the microphysics schemes examined in this study. Both the glaciation temperature and the dependence of liquid condensate fraction on temperature were determined by aggregating the liquid cloud condensate fraction for all model gridpoints with at least 10 4 g kg 1 of total cloud condensate among the simulations with initial surface temperatures in { 10, 5,0,5,10,15,20} C into bins of width 1K. Compared with the GCMs in McCoy et al. (2015), the WRF microphysics schemes here tend to have a more rapid liquid-ice transition (compare the steepness of the curves in Figure A1 with those in Figure 1 of McCoy et al. 2015). In addition, the temperatures at which the phase transition occurs are around 10 C higher here compared to the observations and multi-model mean in McCoy et al. (2015). The implications of this bias are unclear; McCoy et al. (2015) suggest that higher glaciation temperature corresponds to a stronger cloud optical thickness feedback over the Southern Ocean, but since clouds in our model setup often form at a much lower temperature than experienced in the lower troposphere over the Southern Ocean, a lower glaciation temperature 23

24 might simply imply larger cloud optical thickness changes at lower T 2 (0). Overall, there does not appear to be a strong association between the liquid-ice transition temperature and the strength of the radiative feedback across the six microphysics schemes used here. 519 References Alexeev, V. A., and C. H. Jackson, 2013: Polar amplification: is atmospheric heat transport im- portant? Climate Dynamics, 41, , doi: /s z Brient, F., and S. Bony, 2013: Interpretation of the positive low-cloud feedback predicted by a climate model under global warming. Climate Dynamics, 40, , doi: / s Chylek, P., C. K. Folland, G. Lesins, M. K. Dubey, and M. Wang, 2009: Arctic air temperature change amplification and the atlantic multidecadal oscillation. Geophysical Research Letters, 36, L14 801, doi: /2009gl Cronin, T. W., and K. A. Emanuel, 2013: The climate time scale in the approach to radiative- convective equilibrium. Journal of Advances in Modeling Earth Systems, 5, , doi: /jame Cronin, T. W., and E. Tziperman, 2015: Low clouds suppress Arctic air formation and amplify high-latitude continental winter warming. Proceedings of the National Academy of Sciences, doi: /pnas Curry, J., 1983: On the formation of continental polar air. Journal of the Atmospheric Sciences, 40 (9), Emanuel, K., 2008: Back to Norway: an essay. Meteorological Monographs, 33,

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