Further Probing the Mechanisms Driving Projected 1 Subtropical Decreases of Extreme Precipitation Intensity 2

Regional projections of extreme precipitation intensity (EPI) are strongly 6 inﬂuenced by regional projections of “extreme ascent,” i.e. ascending air during peri- 7 ods of extreme precipitation. Earlier studies have performed analysis suggesting that 8 long-term changes in eddy length scale and vertical stability are key factors inﬂuenc- 9 ing extreme ascent projections, but these mechanisms have yet to be conﬁrmed with 10 controlled model experiments. In this study, we perform such controlled experiments 11 using a cloud-resolving model (CRM). The selected CRM domains are two locations 12 over the subtropical South Atlantic Ocean where global climate models consistently 13 project weakening of extreme ascent with accordingly decreased EPI. At each study 14 location, three pairs of 20-year maximum precipitation events are simulated with the CRM, with each pair consisting of an event during the historical period (1981-2000) 16 and an event during the future period (2081-2100), with large-scale forcings for the 17 three pairs derived from three different members of an initial condition ensemble of 18 the Canadian Earth System Model version 2 (CanESM2). These experiments reveal 19 that, in both study locations, weakening of differential cyclonic vorticity advection 20 (dCVA) is a key driver of projected decreases in extreme ascent and EPI. Weakening 21 of dCVA is expected in accordance with hydrostatic balance because, as temperatures 22 warm, the pressure spacing between geopotential surfaces increases. Although there 23 is evidence that the CRM is more sensitive to dCVA changes than CanESM2, such a 24 dCVA mechanism may nonetheless be important to consider for EPI changes in the 25 real world. 26

long-term decreases in EPI are projected. This regional variability has been linked to 84 regional variations in projections of vertical velocity during EPEs (Pfahl et al, 2017; 85 Tandon et al, 2018a), referred to as "extreme ascent." The contribution of extreme 86 ascent to EPI is often referred to as the "dynamical component" of EPI. 87 In addition to the regional variability of EPI projections, Pfahl et al (2017) have 88 shown that the pattern and magnitude of the dynamical component is very different 89 during summer than during winter. For this reason, climate change might also influ-  Earlier studies have performed analysis suggesting that long-term changes in the 99 horizontal scale of vertical velocity anomalies, referred to as "eddy length," are a 100 key factor influencing regional extreme ascent projections (Tandon et al, 2018a,b). 101 Projected increases in eddy length are expected to weaken the coupling between con-  Despite the valuable insights gained from GCMs, understanding regional pro-111 cesses in GCMs is challenging due to the complexity of the models. Thermodynamic 112 and dynamical coupling between adjacent atmospheric grid cells, as well as coupling 113 between the atmosphere and the surface, makes it difficult to isolate mechanisms re-114 sponsible for the projected EPI changes. Furthermore, while GCMs are capable of 115 capturing the long-term statistics of many EPEs (Randall et al, 2007;Pierce et al, 116 2009), they are limited in their ability to simulate individual EPEs in the observa-117 tional record, as the precise initialization and pre-conditioning required is typically 118 not attainable with a GCMs limited spatial and temporal resolutions. Finer resolu-119 tion regional models allow for controlled experimentation that can more easily isolate 120 physical mechanisms relevant to extreme ascent in both observations and GCMs (Nie 121 and Sobel, 2016; Nie et al, 2016bNie et al, , 2018. 122 In this study, a dynamical downscaling approach is implemented using a cloud- where p is pressure, σ is the dry static stability, f 0 is the reference value of the Cori-

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olis parameter ( f ), ∇ 2 is the horizontal Laplacian operator, R is the gas constant 151 for dry air, ζ is the geostrophic absolute vorticity, T is temperature and Q is the 152 diabatic heating. Here, Adv(·) = −u g ∂ x (·) − v g ∂ y (·) is the horizontal geostrophic 153 advection operator, where u g and v g are the horizontal geostrophic winds in the 154 x (zonal) and y (meridional) directions, respectively. The dry stability is given by 155 σ = −(RT /p)∂ p ln θ , where θ is potential temperature. The geostrophic vorticity is 156 given by ζ = f −1 0 ∇ 2 φ + f , where φ is the geopotential.
gradients. As a result, in synoptic scale motions, ω is representative of uplift taking 163 place in a column of air rather than small plumes.

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The QGω equation has three forcing terms on its right-hand side (RHS). The first 165 forcing term is the differential VA. When VA is increasing with height [∂ p Adv(ζ ) < 166 0], referred to as differential cyclonic vorticity advection (dCVA), that implies that at 167 a given location, the relative vorticity is increasing more at higher levels compared 168 to lower levels, which implies that the curvature of height surfaces is increasing at 169 higher levels more than at lower levels. then ∇ 2 Q < 0, so convective heating will force upward motion. On the LHS of (1),

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the key parameter is static stability (σ ). For a given positive forcing, smaller values 180 of σ imply a less stable atmosphere and accordingly larger (more negative) values of 181 ω.

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The QGω equation can be solved numerically with just a single forcing term 183 from the RHS of (1) to obtain the particular ω solution associated with that forcing.

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Because the QGω equation is linear, the total ω solution is just the sum of the three 185 particular solutions, i.e.
where ω ζ is the solution with only differential VA forcing applied, ω T is the solution 187 with only TA forcing applied and ω Q is the solution with only diabatic forcing applied 188 (Nie and Sobel, 2016). Assuming ω has wavelike structure with horizontal length scale L (where L is an 190 inverse wavenumber), then the Laplacian in (1) can be replaced by −1/L 2 , yielding  In this study, the CQG framework is implemented in a specific CRM called the   applicable to other models.

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The specific CanESM2 output fields used to force the CRM forcing are as follows:

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Monthly mean surface air temperature is used for the prescribed surface temperature.

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Daily and 6-hourly output of air temperature (T ), wind (u), specific humidity (q) 284 and geopotential height (φ /g, where g is the acceleration due to gravity) are used.

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The 6-hourly data are archived on model sigma levels, and these are linearly inter-  Daily CanESM2 output is used to construct vertical profiles of potential temper-293 ature and moisture, which are additional large-scale forcings required by the CRM.

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All time-varying forcings are supplied to the CRM at the same temporal resolution 295 as the CanESM2 output, and the CRM linearly interpolates these forcings in time.

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The surface boundary condition is prescribed as the seasonal mean of monthly sur-   The second-last step in this procedure is a refinement of the procedure used in Tan forcing.

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In order for the CRM to run without numerical instability, we increase the eddy 343 length by a factor of 3-6 compared to its CanESM2-derived value. This adjustment is 344 applied to both the historical and future L E values so that δ L 2 E /L 2 E0 in the CRM runs 345 matches δ L 2 E /L 2 E0 in the GCM runs. (We use δ hereafter when referring to "climatic 346 changes" between the historical and future periods.) The specific adjustment factor 347 for each experiment is provided in  The stars indicate the locations used for the dynamical downscaling experiments in the current study. The black star corresponds to the "S27" study location, and the green star corresponds to the "S18" study location.
ability, we can essentially pre-filter the internal variability by selecting CanESM2 383 ensemble members whose EPI projections resemble the ensemble mean projections, 384 thus requiring fewer CRM experiments to produce clear results.
385 Table 1 describes the CanESM2 EPEs examined with our CRM experiments.

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Case names are constructed starting with the study location name (e.g. S27 or S18), 387 followed by the CanESM2 ensemble group label, followed by the epoch ("Hist" for 388 historical, "Fut" for future). "GCM" is appended to the case name when examining 389 CanESM2 output directly; otherwise it is assumed that the case is a CRM experi-390 ment driven by an ensemble member in the indicated ensemble group of CanESM2.

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As we use only one CanESM2 ensemble member from a given ensemble group, the 392 ensemble group number provides a distinctive label for each case, and the specific 393 CanESM2 ensemble member number used for each case is also provided in Table 1 394 for reference. For example, the S27r1-Hist case is the CRM experiment in the S27 lo-395 cation driven by ensemble member r4 in ensemble group r1 of CanESM2. When con-396 sidering ensemble means, the ensemble group number is omitted (e.g., "S27-Hist").
397 from internal variability rather than externally-forced climate change. We will discuss 409 the implications of these details further below.

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To visualize our case selection process, Fig. 3 shows timeseries of annual maxi-   S18r2-Hist, S18r2-Fut, S18r4-Hist, S18r4-Fut, S18r5-Hist and S18r5-Fut. In each 424 case, we run the model for 10 days with only the temperature and moisture profiles 425 applied, which allows the CRM to reach a state of radiative-convective equilibrium.  Table 2 and subsequent figures.

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For reference,   As mentioned earlier, all six pairs of ensemble members show climatic weakening 436 of EPI. Interestingly, for one ensemble member pair (S18r5), the future EPE occurs at 437 a cooler temperature than the historical event, likely related to the fact that the future 438 and historical events occur in different seasons (see Table 1). This result gives a sense 439 of the range of behaviour sampled by our ensemble, and we will discuss additional 440 details of individual ensemble members below.   (Table 3).

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Further examining individual ensemble members, we found that the peak pre-455 cipitation in some CRM experiments occurred 1-2 days earlier than in the GCM.

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Such a difference in timing is not surprising, as the GCM parameterizes convection 457 whereas the CRM explicitly resolves convection. Khairoutdinov and Randall (2003) 458 also noted a precipitation timing mismatch of approximately one day when evaluating 459 SAM against observations. Our focus in this study is on EPI rather than the precise  Table 3. In this and subsequent figures, some CRM timeseries have been time shifted by 1-2 days prior to ensemble averaging so that the day of maximum precipitation aligns with that in the GCM runs. Additional details are provided in Table 3 and the text.
The CRM exhibits similar behaviour at the S18 location (Fig. 5)  the S18r2 and S18r5 CRM experiments produce increases in EPI, in contrast to the 469 deceases produced by CanESM2 (Table 3). These contrasts notwithstanding, the abil-   Fig. 4 for the S18 study location.

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To investigate the mechanisms responsible for the changes in EPI, we have performed  Section 2 for discussion of these concepts.) Over the S18 location, eddy length change in isolation produces a decrease in 490 EPI ( Fig. 7a and Table 2), indicating that changes in eddy length may contribute to 491 decreased EPI in the middle of the subtropical dry zone. Since the ensemble mean 492 eddy length decreases over the S18 location (see Table 1), this result suggests that the S18-Hist S18-Fut S18-Adv Ensemble Mean: Isolation Runs Fig. 7 As in Fig. 6 but over the S18 study location.

Eddy length Isolation
Next we consider the effect of changing only surface temperature and vertical 507 stability. Over the S27 location (Fig. 6b), this S27-∆Stab run (yellow) produces a 508 slight increase in EPI in contrast with the EPI decrease produced when all forcings are 509 changed (red). Over the S18 location, however (Fig. 7b), the S18-∆Stab run produces 510 a decrease in EPI, albeit weaker than the decrease produced by S18-∆L ( Fig. 7a; see 511 also Table 2). This result suggests that the effect of vertical stability change may  horizontal advection are the dominant driver of EPI changes in this location. Over the 520 S18 location (Fig. 7c), advection changes (yellow) also produce a decrease in EPI, but 521 this effect is weaker than the the effect of eddy length change (Fig. 7a) and compara-522 ble to the effect of stability change ( Fig. 7b; see also Table 2). However, as mentioned response to horizontal advection changes, but not all of the S18 ensemble members 531 behave this way (Table 3). However, the two S18 ensemble members that produce EPI  turbed TA is quantitatively comparable to the historical EPI over both the S27 (Fig. 8) 544 and S18 (Fig. 9) locations. These results suggest that changes in TA alone do not 545 appear to influence the decrease of EPI in these locations. Changes in moisture ad-546 vection produce an increase in EPI over S27 (Fig. 8b) but a small decrease over S18 547 (Fig. 9). However, changes in differential VA alone produce strong decreases in EPI 548 over both S27 (Fig. 8c) and S18 (Fig. 9c). In combination with the results of our other 549 isolation runs (Figs. 6-7), we can conclude that changes in differential VA are a key 550 driver of EPI decrease in the study locations.

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To further illuminate the dynamics responsible for the EPI changes, we can lin-557 early decompose the contributions of each large-scale forcing to ω, as detailed in 558 Section 2. Fig. 10 shows vertical profiles of ω ζ , ω T and ω Q for each simulation day S18-Hist S18-Fut S18-AdvT Ensemble Mean: Isolation of Horizontal Advective Forcings Fig. 9 As in Fig. 8 for the S18 study location.
in the S27-Hist and S27-Fut experiments. Fig. 10a shows that during the EPE, ω ζ is 560 strongly negative in the upper troposphere, reiterating its key role in generating ex-561 treme precipitation. Furthermore, the negative ω ζ anomaly in S27-Fut (Fig. 10b) is

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Comparing the first and third rows of Fig. 10, we find that ω ζ anomalies are also 574 much larger than ω Q anomalies. However, the ω Q anomalies are also larger than the  ω T anomalies, so ω Q appears to play a more significant role than ω T . Furthermore, in CanESM2 could have also been explained by differential VA changes, although 581 it also appears (as mentioned above) that CanESM2 is less sensitive to horizontal 582 advective forcing than the CRM.

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Over the S18 study location (Fig. 11), ω ζ is an order of magnitude larger than 584 ω T , and it is also somewhat larger than ω Q , qualitatively resembling the S27 results.

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However, in contrast with S27, ω ζ and ω Q over S18 are the same order of magnitude, 586 and the climatic fractional decrease of |ω Q | (approximately 50%) is larger than that of  that EPI in the CRM is also greater than in CanESM2 (Figs. 4-5), which as men-601 tioned above, is likely because the CRM is more sensitive to horizontal advective 602 forcing than CanESM2.
Thus, an increase in temperature produces an increase in pressure spacing between 636 geopotential surfaces. We can expect such a change to have a direct effect on dif-637 ferential VA because QG vorticity depends on the horizontal curvature of geopoten-638 tial surfaces. Furthermore, if ω changes then mass conservation requires that the ω 639 change be non-uniform in space (e.g., weaker ascent in one location requires weaker 640 descent in another location), which requires that the horizontal curvature of geopo-641 tential surfaces must change as well.

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With these constraints in mind, an increase in pressure spacing between geopo-643 tential surfaces requires the circulation to advect geopotential disturbances whose to decreased EPI over the S18 study location. This finding agrees with the analysis 658 of Nie et al (2020), who found that vertical stability change contributes to projected 659 decrease of EPI in some subtropical locations.

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Over both study locations, weakening of dCVA is a key driver of the ensemble 661 mean EPI changes. Over the S18 study location, this decreased dCVA combines with 662 decreased eddy length to produce the projected decrease in EPI. Furthermore, over 663 S18, decreased eddy length on its own contributes a stronger EPI decrease than dCVA 664 weakening. However, decreased eddy length over S18 is likely a result of internal cli- standing that can be used to further assess climate models and improve confidence in 685 regional projections of extreme precipitation.