The temperature dependence of ice-nucleating particle 1 concentrations affects the radiative properties of tropical 2 convective cloud systems

15 Convective cloud systems in the maritime tropics play a critical role in global climate, but accurately representing 16 aerosol interactions within these clouds persists as a major challenge for weather and climate modelling. We quantify 17 the effect of ice-nucleating particles (INP) on the radiative properties of a complex Tropical Atlantic deep convective 18 cloud field using a regional model with an advanced double-moment microphysics scheme. Our results show that the 19 domain-mean daylight outgoing radiation varies by up to 18 W m -2 depending on the chosen INP parameterisation. 20 The key distinction between different INP parameterisations is the temperature dependence of ice formation, which 21 alters the vertical distribution of cloud microphysical processes. The controlling effect of the INP temperature 22 dependence is substantial even in the presence of Hallett-Mossop secondary ice production, and the effects of 23 secondary ice formation depend strongly on the chosen INP parameterisation. Our results have implications for 24 climate model simulations of tropical clouds and radiation, which currently do not consider a link between INP particle 25 type and ice water content. The results also provide a challenge to the INP measurement community, since we 26 demonstrate that INP concentration measurements are required over the full mixed-phase temperature regime, 27 which covers around 10 orders of magnitude.


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Deep convective clouds are important drivers of local, regional and global climate and weather (Arakawa, 2004; 30 Lohmann et al., 2016). They produce substantial precipitation (Arakawa, 2004) and the associated phase changes 31 release latent heat that helps to drive global atmospheric circulation (Fan et al., 2012). Convective clouds have a direct 32 impact on climate through interactions with incoming shortwave and outgoing longwave radiation (Lohmann et al., 33 2016), for example by producing radiatively important long-lived cirrus clouds (Luo and Rossow, 2004). The clouds 34 extend from the warmer lower levels of the atmosphere where only liquid exists to the top of the troposphere where 35 only ice exists (Lohmann et al., 2016). Between these levels is the mixed-phase region where both liquid and ice 36 coexist and interact (Seinfeld and Spyros, 2006). Within the mixed-phase region, primary ice particles can form    Meyers et al., 1992). We hypothesise that such large differences in ice production 77 rates between INP parameterisations are likely to affect cloud properties. In simulations of deep convective clouds 78 over North America (Takeishi and Storelvmo, 2018) there were differences in the magnitude and altitude of droplet 79 depletion depending on INP parameterisation choice (Bigg, 1953;DeMott et al., 2010DeMott et al., , 2015.

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Uncertainty in mixed-phase cloud properties is compounded further by a lack of quantification of the interaction of 81 heterogeneous freezing with other ice production mechanisms. Ice crystals in the mixed-phase region can also be 82 formed by secondary ice production (SIP) from existing hydrometeors (Field et al., 2017) and droplets can freeze 83 homogeneously below around -33°C (Herbert et al., 2015). In observations of convective clouds with relatively warm

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suggesting that secondary ice production is the dominant small-ice formation mechanism in mixed-phase regions 87 (Ladino et al., 2017). The importance of heterogeneous ice production relative to secondary and homogeneous 88 freezing has therefore been questioned (Ladino et al., 2017;Phillips et al., 2007) (Hallett and Mossop, 1974). If this is the case, in clouds where SIP may also be initiated by the primary freezing of a   Table 2 Bigg (1953). For reference, the modelled domain-mean out-of-cloud temperature and relative humidity are shown in

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Homogeneous freezing of cloud droplets is parameterised according to Jeffery and Austin (1997).

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The INP parameterisations tested in this study represent only immersion freezing. Heterogeneous ice nucleation by    Mossop, 1985). In-situ cloud observations have frequently observed ICNC that could be explained by the Hallett-

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Mossop process, but the mechanism underlying the Hallett-Mossop process as well as the ice particle production rate 185 remain uncertain and not well quantified (Field et al., 2017). A maximum splinter production rate of 350 per milligram 186 of rimed material has been measured in a number of laboratory studies (Hallett and Mossop, 1974;Mossop, 1985) 187 and has been applied as the best estimate here and in previous modelling studies (Connolly et al., 2006), although 188 other rates have also been measured (Heymsfield and Mossop, 1984;Saunders and Hosseini, 2001). Uncertainties

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Changes to outgoing radiation from cloudy regions and changes in cloud fraction both contribute to the total overall 217 change in outgoing radiation between two simulations. The contributions from changes in outgoing radiation from 218 cloudy regions and cloud fraction to the overall radiative differences between simulations were calculated separately 219 as described below. The cloudy regions contribution, i.e. the difference in outgoing radiation between two cloudy 220 regions due to changes in cloud albedo or thickness ignoring any changes in cloud fraction, (∆ ) to a 221 9 domain radiative difference between a sensitivity simulation (s) and a reference simulation (r) (s -r) is calculated Where , is the mean outgoing radiation from cloudy regions in simulation r and , is the mean outgoing 233 radiation from clear sky regions in simulation r and ∆ is the difference in domain cloud fraction between simulations 234 s and r (s-r). There is interaction between the outgoing radiation from cloudy regions and cloud fraction changes The contribution of changes in the outgoing radiation from clear sky areas (∆ ) can be calculated as shown in

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Where ∆ is the change in mean outgoing radiation from clear sky areas between simulations s and r and is 241 the cloud fraction of simulation s.

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The total outgoing radiation difference between simulations s and r (∆ − ) is therefore as shown in Eq. (5). 243 The interaction term ∆ and the clear sky term (∆ ) were found to be negligible and are therefore 245 ignored for the purposes of this paper.

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When analysing the simulation output, cloudy grid boxes were classed as those containing more than 10 -5 kg kg -1 265 condensed water from cloud droplets, ice crystals, graupel and snow. Rain was not included to ensure analysis did not 266 include areas below cloud base. Other cloud thresholds were tested and found to have no notable effect on the 267 results. For cloud categorisation into low, mid and high clouds, model vertical columns containing cloudy grid boxes 268 were categorised by cloud altitude. Low cloud occurs below 4km, mid cloud between 4 and 9 km and high cloud above 269 9 km. Columns with cloudy grid boxes in two or more cloud categories were classified as mixed category columns 270 according to the vertical placement of the cloudy grid boxes, e.g. low/high for columns containing cloud below 4 km 11 and above 9 km. 4 and 9 km were chosen as the low/mid and mid/high division points because they are just below 272 two well-defined peaks in cloud base heights (not shown) and roughly correspond to the beginning of the        in all cases (Fig. 4a). The enhancement in outgoing radiation varies between 2.6 W m -2 for D10 and 20.8 W m -2 for A13 328 relative to the NoINP simulation. There is a variation of up to 18.2 W m -2 depending on the chosen representation of 329 heterogeneous ice nucleation, which shows that the INP parameterisation can affect outgoing radiation as much as 330 excluding or including heterogeneous freezing altogether. The difference in radiation between the NoINP and the 331 simulations where INP are present are caused mainly by changes to outgoing shortwave radiation. The inclusion of INP 332 enhances outgoing shortwave radiation by between 5.3 W m -2 for D10 and 26.6 W m -2 for A13 (Fig. A3a). Differences 333 in outgoing longwave radiation are comparatively small (-2.7 W m -2 for D10 to -5.8 W m -2 for A13; Fig. A3b) due to 334 similar cloud top heights between simulations of these thermodynamically limited clouds. Bear in mind that SIP was 335 active (SIP_active) in the simulations summarised in Fig. 4a, including in the NoINP simulation in which the Hallett-

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Mossop process can be initiated by settling ice-phase hydrometeors (either by settling homogeneously frozen ice 337 crystals subsequently converted to snow or graupel, or by settling snow or graupel formed from homogeneously 338 frozen ice crystals at upper cloud levels), indicating that these cloud systems are sensitive to INP even in the presence 339 of SIP. This is consistent with a comparatively small change in TOA radiation when SIP is active relative to when it is 340 inactive (Fig. 4b and 3c) (we discuss the role of SIP in more detail in Sect. 3.5).

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The slope of the INP parameterisation (i.e. the dependence of INP number concentration on temperature) is a key 342 determinant of the outgoing radiation. There is a statistically significant correlation between INP parameterisation 343 slope and total TOA outgoing radiation (r 2 = 0.75, p < 0.01, n = 10) (Fig. 4c). Changes in outgoing radiation due to the 344 presence of INP are caused by a combination of changes to the outgoing radiation from cloudy regions, caused by 345 changes in cloud structure and microphysical properties, and changes to domain cloud fraction, whose contributions 346 to the total radiative difference are shown in Fig. 4a (left and centre). In order to appreciate the reasons for these 347 trends, we will now take a closer look at the effect of INP on outgoing radiation from cloudy regions only, domain 348 cloud fraction and cloud type.

Effect of INP and INP parameterisation on outgoing radiation from cloudy regions 350
Here we discuss the changes in daytime outgoing radiation from cloudy regions only due to INP parameterisation 351 choice. Daytime outgoing radiation from cloudy regions increases due to INP for all but one INP parameterisation (Fig.   352 5a). The absolute change in outgoing radiation from cloudy regions is between -0.8 (D10) and +28.1 (A13) W m -2 , and 353 the larger values are a result of large increases in reflected shortwave (up to +37.2 W m -2 ) and relatively moderate 354 decreases in outgoing longwave radiation (up to -11.1 W m -2 ) from cloudy regions. The above absolute changes in 14 outgoing radiation from cloudy regions contribute between -0.7 and +11.4 W m -2 to the domain-mean change in 356 outgoing radiation due to the presence of INP (Fig. 4a, cloudy regions contribution).

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The enhancement of outgoing radiation from cloudy regions due to INP is caused primarily by increases in cloud 358 condensate relative to the NoINP simulation (Fig. 5b). When INP are included in a simulation, snow and cloud droplet 359 water path are enhanced, causing increases in total cloud condensate, despite decreases (in all except A13) in ice 360 crystal water path due to a reduction in ice crystal number and mass concentrations caused by a reduction in the 361 availability of cloud droplets for homogeneous freezing. Snow, cloud droplets and ice crystals are the hydrometeors 362 that affect outgoing radiation in CASIM and the combined water path of these three species is significantly positively 363 correlated with cloud shortwave reflectivity (r 2 = 0.62, p < 0.01, n = 11) (Fig. 5c). The mechanism for this INP induced 364 increase in cloud condensate and consequently cloud shortwave reflectivity is as follows: When heterogeneous ice 365 nucleation is active, liquid is consumed in the warmer regions of mixed-phase clouds because of increased 366 heterogeneous ice nucleation (Fig. 2) and SIP (Fig. A4a). The resultant additional ice crystals in mixed-phase regions 367 facilitate riming causing increases in snow and graupel (Fig. A4c, d), increasing snow water path and reflectivity in 368 mixed-phase and ice clouds. At the same time, the enhanced production of relatively heavy snow and graupel 369 increases precipitation which on melting to form rain below the freezing level and subsequent evaporation below 4 370 km, reduces out-of-cloud temperature and increases relative humidity (Fig. A5a, b). This leads to increases in water 371 path in low-level liquid clouds and thus an enhancement in their shortwave reflectivity.

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However, increases in total cloud condensate alone cannot account for the differences in outgoing radiation from 373 cloudy regions between simulations using different INP parameterisations, which are caused by a combination of 374 cloud microphysical responses. We find that outgoing radiation from cloudy regions is significantly negatively 375 correlated with INP parameterisation slope (r 2 = 0.63, p < 0.01, n = 10) (Fig. 6a) Fig. 2) and SIP at high temperatures (Fig. A4a). This, combined with higher INP concentrations at low 15 temperatures (Fig. 2), increases ICNC at upper mixed-phase altitudes, as well as enhancing the lifetime of liquid cloud 385 droplets at lower altitudes in the mixed-phase region when compared to shallower INP parameterisations.

Effect of INP and INP parameterisation on cloud fraction 387
Overall cloud fraction is increased by INP for all INP parameterisations and these increases in cloud fraction contribute 388 about as much to changes in domain-mean daytime radiation as the changes in outgoing radiation from cloudy 389 regions (Fig. 4a, cloud fraction contribution). Increases in domain cloud fraction due to INP are driven by cloud cover 390 increases in the warm and mixed-phase regions of the cloud (~ 4 -6 km), offset somewhat by decreases in the cloud 391 fraction due to reduced homogeneous freezing in the ~ 10 -14 km regime (Fig. 7a). Cloud fraction increases at mid-392 levels occur because heterogeneous ice nucleation induces an increase in precipitation-sized particles (snow and 393 graupel) which sediment to lower levels and moisten the atmosphere by evaporation (Fig. A5a, b). This increases new 394 cloud formation and may prolong the lifetime of existing cloud cells. Additionally, increased droplet freezing and 395 riming in the mixed-phase cloud region releases latent heat and invigorates cloud development with increases in 396 updraft speed just above 4 km (Fig. A5c). The increased cloud fraction at mid-levels due to INP are partially offset by a 397 reduced cloud fraction above 10 km (Fig. 7a)

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The effects of INP on the altitude profile of cloud fraction are strongest for shallow INP parameterisation slopes, which 403 have a freezing profile most different to that of the NoINP simulation (Fig. 7a). At 5 km, the shallowest 404 parameterisation (M92) causes the largest increase in cloud fraction, while the steepest parameterisation (A13) 405 causes the smallest (r 2 = 0.83, p < 0.05, n = 5). At 12 km, the order is reversed, and steep parameterisations exhibit the 406 highest cloud fraction (r 2 = 0.94, p < 0.01, n = 5). The largest cloud fraction-induced increases in outgoing radiation 407 relative to the NoINP simulation (Fig. 4a) are seen in simulations using steeper INP parameterisations because these 408 simulations exhibit higher cloud fractions at high altitudes (~12 km), translating into the higher total cloud fraction.

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These slope dependent changes in cloud fraction are explained by a relationship between cloud fraction and several 410 microphysical properties affecting cloud fraction. For example, steeper INP parameterisations produce higher ICNC at 411 the top of the mixed-phase region (10 km) as well as higher ratios of ice crystal mass to snow and graupel mass within 412 the homogeneous freezing region (12 km) (Fig. 7b, c). A higher number and mass of ice crystals relative to those of 16 larger precipitation-sized hydrometeors with the steepest parameterisations results in lower frozen hydrometeor 414 sedimentation, a longer cloud lifetime and a higher cloud fraction.

Effect of INP and INP parameterisation on cirrus anvils 416
Our results show that the INP parameterisation affects the properties and spatial extent of cirrus anvils. We define 417 cirrus anvils to be regions where cloud is present above 9 km only (further details available in Sect. 2.1.4). 2D aerial 418 images of cloud categorisation (Fig. 8a-f) show well-defined regions of anvil cloud (light blue -H) surrounding a large 419 convective system containing clouds at a range of altitudes from <4 km to >9 km. There are clearly differences in the 420 extent and position of cloud categories between simulations (Fig. 8a -f).

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The presence of INP reduces convective anvil extent by between 2.1 and 4.1% of the domain area depending on the 422 choice of INP parameterisation (Fig. 8 g), corresponding to a decrease in anvil cloud of between 22 and 53% relative to 423 the NoINP simulation (not shown). The reduction in anvil extent in the presence of INP is caused by increased liquid 424 consumption at all mixed-phase levels, due to heterogeneous freezing, enhanced SIP and increased graupel and snow 425 production, reducing the availability of cloud droplets for homogeneous freezing (Fig. A4b), reducing ICNC at cloud-426 top, and reducing cloud anvil extent (Fig. 8g)

Importance of secondary ice production 435
It has been argued that the observed (or derived) primary ice particle production rate is unimportant for convective

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Mossop process is +2.9 W m -2 . Therefore, rather than primary ice being simply overwhelmed by SIP, it actually

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The effect of SIP on the radiative properties of the cloud field is dependent on INP parameterisation choice, both in 451 magnitude and sign of change (Fig. 4b). SIP makes the clouds more reflective independent of the chosen 452 parameterisation (Fig. 4b, cloudy regions contribution) due to increases in snow and cloud droplet water path. N12 453 and A13 have the largest overall radiative response to SIP because changes to the radiative forcing from cloudy 454 regions and cloud fraction contributions act to increase outgoing radiation (Fig. 4b). However, the cloud fraction 455 response to SIP is opposite for C86, M92 and D10 meaning the cloudy regions and cloud fraction contributions act in 456 opposite directions, reducing the total radiative forcing.

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The different response of the domain cloud fraction to the presence of SIP is caused by substantial variation between 458 simulations in the anvil cloud extent (Fig. 8h), from an increase of 10% (+0.9% of the domain area) in N12 to a 459 decrease of 40% (-3.6% of the domain area) in M92 (Fig. 8h). These non-uniform changes in cloud fraction and 460 outgoing radiation can be explained by differences in the response of cloud freezing profiles to SIP due to variations in

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The SOCRATES representation of radiation with a dependence on ice mass is a more accurate and realistic 481 representation of radiation than is seen in many climate models which often derive bulk optical properties using 482 empirically derived deterministic relationships between ice particle size and environmental temperature and/or ice

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Another limitation of the SOCRATES radiation code is its lack of consideration of rain and graupel particles. The effects 489 of these hydrometeors are expected to be less than that of ice, snow and cloud droplets as they precipitate faster and 490 therefore have a shorter lifetime. Furthermore, the effect of graupel on the tropical longwave radiative effect has 491 been found to be negligible and dwarfed by that of snow (Chen et al., 2018). The global radiative effect of rain has also 492 been found to be small in the vast majority of cases even at high temporal and spatial resolution (Hill et al., 2018). The 493 effect of the incorporation of these hydrometeors into radiative transfer parameterisations should however be tested 494 in future studies.

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The use of both aerosol-dependent (D10, N12, A13) and solely-temperature dependent (C86, M92) parameterisations 496 in this study means that we have examined the radiative sensitivity of a complex cloud field to a larger variety of INP 19 parameterisations used in weather and climate models than if we had exclusively used parameterisations that 498 consider aerosol concentration. However, this experimental design has limitations. For example, due to the lack of 499 aerosol dependence of the C86 and M92 schemes a 'presumed 'dust concentration is implicitly present in these two 500 cases and remains uniform throughout the simulation period. The effect of INP parameterisation choice on convective 501 cloud field properties should also be examined with the inclusion of aerosol scavenging but this was beyond the scope 502 of this study. Aerosol scavenging would allow the aerosol number concentration to be reduced by cloud droplet 503 activation and the number of dust particles within cloud droplets to be tracked and depleted when frozen 504 heterogeneously. In the simulations presented here, the heterogeneous freezing rate is calculated using the 505 interstitial aerosol number concentration and the ICNC of the gridbox in question meaning that ice crystals advected 506 into the gridbox will reduce the heterogeneous nucleation rate even if they were frozen elsewhere in the domain.

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The results presented here also present a new framework for understanding the effect of SIP by identifying a potential

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The datasets generated and analysed in this study are available from the corresponding author on reasonable request.