Effect of Ice Number Concentration on the Evolution of Boundary Layer Clouds During Arctic Marine Cold-Air Outbreaks

Abstract

Marine cold-air outbreaks (MCAOs) are crucial for Arctic Ocean heat loss, featuring convective cloud rolls that transition into convection cells downstream. Understanding factors controlling this transformation is the key for improving MCAO cloud representation in climate models. This study employs large-eddy simulations to investigate how cloud ice number concentrations ($${N}_{i}$$) affect cloud evolution using a case from the Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) campaign. The simulations, performed in a Lagrangian framework following an air mass trajectory, are driven by ERA5 reanalysis data. Initially, all simulations produce similar cloud patterns, but higher $${N}_{i}$$ leads to earlier breakup of cloud rolls. Between 4 and 10 hr, surface precipitation rates are similar across simulations, but precipitation initiates earlier, and the cloud-base precipitation rates are higher when $${N}_{i}$$ is higher. The stronger precipitation evaporation leads to increased stability of the boundary layer and reduced intensity of vertical mixing between the surface and cloud layer. An increased sink of cloud layer moisture via precipitation and decreased source through diminished vertical transport result in earlier cloud breakup in higher $${N}_{i}$$ conditions. Simulations with different sea surface temperatures (SST) indicate that this cloud breakup mechanism remains valid for MCAOs of different strengths, although the cloud organization is more sensitive to SST changes in low $${N}_{i}$$ environments. This work highlights the importance of accurate representations of ice processes in simulating MCAO clouds and suggests the need for observational constraints of ice nucleating particles and $${N}_{i}$$ over the mixed-phase cloud regimes.

Key Points

• Roll cloud structures are well captured by a large eddy simulation model with different ice number concentrations ($${N}_{i}$$)

• In higher $${N}_{i}$$ cases, precipitation depletes more cloud water and the boundary layer is less coupled, leading to earlier roll cloud breakup

• Clouds with lower $${N}_{i}$$ are more sensitive to the sea surface temperature

Plain Language Summary

In this study, we use computer simulations to understand how the presence of ice particles affects the behavior of clouds during marine cold-air outbreaks (MCAOs), which are usually formed with strong and cold winds over the sea. We find that clouds with more ice particles start precipitating earlier and break up faster than those with fewer ice particles. Precipitation evaporation below the cloud cools the sub-cloud layer, making it more stable and reducing the vertical mixing of moisture, which accelerates the cloud breakup. By varying the sea surface temperature, we also find that the impact of ice particles on cloud evolution is consistent for MCAOs of different strengths. Our findings emphasize the need for accurate representations of cloud ice and its interactions with the dynamics in weather and climate models.

1 Introduction

The Arctic has been warming at a faster rate than the lower latitudes in the past several decades, known as Arctic amplification (Holland & Bitz, 2003; Pithan & Mauritsen, 2014). A phenomenon associated with Arctic amplification that has drawn considerable societal attention and research interest is the Arctic sea-ice retreat and sea-ice extent minimum in September that influences sea-ice coverage in the months following (Holland & Bitz, 2003; Kopec et al., 2016; Kumar et al., 2010; Screen & Simmonds, 2010; Tilling et al., 2020). Among other factors, clouds have been found to play a key role in mediating sea-ice extent by impacting Arctic radiation balance (Curry, 1996; Huang et al., 2021; Kay & Gettelman, 2009; Sledd et al., 2023) through feedback mechanisms that involve sea ice, surface albedo, ocean temperature, surface heat flux, and cloud cover (Cox et al., 2016; Huang et al., 2019; Kay & Gettelman, 2009; Monroe et al., 2021). The response of clouds to global warming, however, remains one of the major uncertainties in climate projections (Section 8.6.2 of IPCC, 2021) especially over the Arctic, where observations are sparse.

With the projected sea-ice extent decline, more open ocean areas will be exposed to cold and dry Arctic air especially in autumn (e.g., Holland & Bitz, 2003). A particular phenomenon occurring at the air-sea interface is the marine cold-air outbreak (MCAO), where cold central Arctic air is advected southward across the ice edge to over relatively warm open ocean and induces rapid air-sea exchange. The strong temperature gradients in the lower troposphere lead to intense sensible and latent heat fluxes from the ocean to the atmosphere and result in boundary layer deepening and moist convection. In strong MCAO events, the air-sea temperature difference can exceed 20 K and the surface sensible heat flux near the ice edge can be greater than 500 W m⁻² (Geerts et al., 2022; Pithan et al., 2018; Wu & Ovchinnikov, 2022). During cold seasons, MCAO events account for more than half of the ocean heat loss over the Norwegian Sea (Papritz et al., 2015). When seen in satellite data, MCAO events have a characteristic feature known as cloud streets extending hundreds of kilometers from the ice edge before transitioning to convection cells further downstream (e.g., Figure 1). Due to the low temperature, clouds formed during Arctic MCAO events are mostly mixed phase, that is, contain liquid and ice hydrometeors (Abel et al., 2017; Lloyd et al., 2015; Mateling et al., 2023).

Figure 1

MODIS visible reflectance image from the overpass at 9:50 UTC on 13 March 2020. The magenta line shows the backward trajectory ending at 18:00 UTC at 1 km at the AMF1 site at Andenes, Norway (marked as the star). MODIS data is downloaded from https://ladsweb.modaps.eosdis.nasa.gov/archive/allData//61/.

Modeling mixed-phase clouds during MCAO events in global climate models (GCMs) is challenging especially over the first several hundred kilometers downwind of the sea ice edge where the boundary layer is shallow and highly convective (Gryschka et al., 2014). Convective processes occur on a much smaller scale than most climate model grid spacings requiring the parameterization of shallow convection, which may be part of the boundary layer parameterization (Tomassini et al., 2017) even though MCAO convection may grow much deeper than the typical boundary layer. As a result, many GCMs struggle to accurately represent mixed-phase cloud processes in MCAO clouds, leading to uncertainties in predicting their responses to climate change (Abel et al., 2017; Landgren et al., 2019).

To mitigate GCM errors and uncertainties arising from the unresolved sub-grid scale variability, cloud-resolving and large-eddy simulations (LES) models have been employed to develop and test parameterizations of MCAO cloud physical processes and their sensitivities to the environment (Abel et al., 2017; Chen et al., 2022; Eirund, Lohmann, et al., 2019; Eirund, Possner, et al., 2019; Li et al., 2022; Tomassini et al., 2017; Tornow et al., 2021; Wacker et al., 2005). Due to their large areal coverage and distinct morphological differences along the cold-air fetch, MCAO cloud organizations and the underlying controlling factors have drawn research interest in the past several decades.

Recent studies have emphasized the importance of mixed-phase microphysical processes in MCAO cloud organization. In an observational and modeling study of an MCAO case north of the United Kingdom by Abel et al. (2017), the roll-to-cell transition was found to be accompanied by enhanced precipitation with secondary ice processes becoming active and greater thermodynamic gradients in the sub-cloud layer. Precipitation is found to be responsible for the cloud morphology transition by depleting liquid water from the cloud and by decoupling the boundary layer from the surface (Abel et al., 2017). By simulating a mixed-phase stratocumulus case over the Arctic Ocean, Eirund, Lohmann et al. (2019) concluded that higher ice nucleating particle concentrations ($${N}_{\text{inp}}$$) can induce the stratocumulus breakup by enhancing the development of a sub-cloud circulation from precipitation evaporation and cold pool formation that forces updrafts driving new convective cells. From LES simulations of a North-West (NW) Atlantic MCAO case, Tornow et al. (2021) found the roll-to-cell transition is regulated by $${N}_{\text{inp}}$$ through the “preconditioning by riming” effect prior to substantial rain: increasing $${N}_{\text{inp}}$$ results in reduced cloud liquid water and early consumption of cloud concentration nuclei (CCN) as well as early cooling and moistening of the sub-cloud layer.

In this study, we use LES to investigate how the MCAO cloud organization responds to changes in cloud ice number concentrations ($${N}_{i}$$) and whether this response is sensitive to the sea surface temperature (SST). Note that this study constrains $${N}_{i}$$ directly and does not address the connection of $${N}_{i}$$ to $${N}_{\text{inp}}$$ through a specific ice nucleation mechanism or secondary ice production. Surface conditions and SST are found to be important for Arctic mixed-phase stratocumulus cloud microphysics (Eirund, Possner, et al., 2019) and for MCAO cloud organizations over the NW Atlantic (Chen et al., 2022). By modifying SST, we test the impact of cloud ice processes on cloud organization under a wider range of possible MCAO conditions. This study differs from investigations mentioned above in the following aspects: (a) the meteorological conditions (e.g., mean horizontal wind and boundary layer stability) in MCAO cases are different from those producing Arctic mixed-phase stratocumulus, which have relatively stable boundary layer and much weaker horizontal wind (Eirund, Lohmann, et al., 2019; Eirund, Possner, et al., 2019), (b) the cold air is advected from an ice-covered ocean to an open ocean and is cleaner than MCAO events over the NW Atlantic in which the cold air is mainly advected from North America and contains more anthropogenic emissions (Li et al., 2023; Tornow et al., 2021, 2022). The air mass in the present study is also colder, which is expected to facilitate clouds that contain greater amounts of frozen over liquid condensate compared to previous studies, and (c) we dedicate a great portion of our analysis, as presented below, to cloud morphology and its drivers. The rest of the manuscript is organized as follows: Section 2 describes the simulated cases and model specifications, whereas evaluation of the simulated cloud properties and analysis of the effects of changing $${N}_{i}$$ on cloud evolutions are presented in Section 3. The results are further discussed in Section 4 and summarized in Section 5.

2 Simulations of a Cold-Air Outbreak Case

In this section, we describe the simulated MCAO case, the LES model and simulation setup, and observational constraints from satellite retrievals.

2.1 Case Description

From December 2019 to May 2020, the U.S. Department of Energy (DOE) deployed the first Atmospheric Radiation Measurement (ARM) Mobile Facility (AMF1) during the Cold-Air Outbreaks in the Marine Boundary Layer Experiment (COMBLE) field campaign in Andenes, Norway (Geerts et al., 2022). A major objective of COMBLE was to collect observational data sets during MCAO events, which happen frequently over the Greenland and Norwegian Seas (Landgren et al., 2019). During COMBLE, MCAO conditions were observed nearly 20% of the time at the AMF1 site, located on the northern Norwegian coast some 1,000 km from the Arctic ice edge (Geerts et al., 2022). For this study, we focus on one event that occurred around 13 March 2020 (Lackner et al., 2023; Wu & Ovchinnikov, 2022). The cloud top temperatures at the AMF1 site were below −40$${}^{\circ}\mathrm{C}$$ for most of the day. During this strong MCAO case, a cloud field advected from the sea ice edge to the AMF1 site in about 18 hr exhibited a complete transformation from roll to cell structure (Figure 1). The surface heat fluxes exceed 800 W m⁻² near the ice edge, which leads to rapid boundary layer deepening and cloud formation (Wu & Ovchinnikov, 2022). Organized cloud streets transform into broken cellular clouds after a sufficient fetch off the ice edge as seen in the satellite image (Figure 1). We simulate this case using an LES model to test the response of cloud evolution to changing ice number concentrations.

2.2 Model Description and Simulation Setup

The LES model used in this study is the System for Atmospheric Modeling (Khairoutdinov & Randall, 2003), version 6.10.11. The model is employed in a Lagrangian framework in which a domain with periodic lateral boundary conditions is translated along a trajectory (magenta line in Figure 1) obtained from the Hybrid Single Particle Lagrangian Integrated Trajectory Model (HYSPLIT) and informed by Global Forecast System 0.25-degree analysis data. The back trajectory is initiated at 1800 UTC, 13 March 2020, at Andenes (69.141°N, 15.519°E), when the MCAO strength is near its peak at the AMF1 site.

To drive the LES model, we extract hourly vertical profiles of meteorological variables (potential temperature, specific humidity, and wind as shown in Figure 2) along the 20-hr trajectory from the fifth generation European Center for Medium-Range Weather Forecasting (ECMWF) atmospheric reanalysis (ERA5). Sea surface temperature (SST) is extracted in the same way except that the surface temperature before and near the sea ice edge (hours −2 to +1 in Figure 2c) is adjusted to match the surface sensible heat flux in ERA5 (Figure 2f). The surface sensible and latent heat fluxes in the simulations are computed from wind, near-surface temperature, and SST based on Monin-Obukhov similarity theory (Monin & Obukhov, 1954). Hour 0 in Figure 2 denotes the time at which the trajectory transitions from the sea ice to the open ocean. The marginal ice zone (MIZ) is important in simulating convective roll structures in MCAO events (Gryschka et al., 2008, 2014). The adjusted SST has a more gradual transition from sea-ice to open ocean than the original ERA5 values, which mimics the effect of MIZ on surface heat fluxes although the surface heterogeneity is not reflected in this adjustment. Large-scale subsidence is from ERA5 vertical velocity. Because the model domain is moving with the mean boundary layer wind, no large-scale advective tendencies are included.

Figure 2

Time series of ERA5 forcing along the backward trajectory. (a) Potential temperature, (b) specific humidity, (c) surface temperature, (d) eastward wind, (e) northward wind, and (f) surface sensible (solid line) and latent (dashed line) heat fluxes. The X-axis shows hours relative to the time that the air mass passes the sea ice edge. Hour 18 corresponds to the time the air mass passes the AMF1 site. The gray line in (c) shows the surface temperature from ERA5, and the black line shows the surface temperature adjusted by matching calculated surface fluxes with the ones in ERA5. The dotted line in (c) shows the cold air outbreak index, M values, which are calculated as the difference in SST and potential temperature at 850 hPa ($$M=\text{SST}-{\theta }_{850\text{hPa}}$$). Note that the surface heat fluxes in the simulations are not prescribed as those in (f) but are computed interactively from wind, near-surface temperature, and SST.

Simulations are initiated at 2000 UTC on 12 March 2020, with the extracted ERA5 profiles. The first 2 hours are treated as spin-ups and are not included in the analysis. Horizontal mean wind profiles are nudged toward ERA5 from 500 m above the surface to the model top with a timescale of $$\tau =2$$ hours, following Tornow et al. (2021). Horizontal mean temperature and moisture profiles are nudged above the domain-mean inversion height with the same timescale.

The model uses a two-moment microphysics scheme (Morrison et al., 2005). Cloud condensation nuclei number concentration ($${N}_{\text{CCN}}$$) is prescribed as 20 cm⁻³ based on the ground-based measurement at the AMF1 site. Ice particle number concentration is maintained near a prescribed value, $${N}_{i0}$$, within a mixed-phase cloud, that is, when the temperature is below $$0\mathit{^{\circ}\mathrm{C}}$$, the fractional supersaturation over ice ($${S}_{i}$$) is at least 0.05, and the liquid water mixing ratio ($${q}_{l}$$) is at least 0.001 $$\mathrm{g}\,\mathrm{k}{\mathrm{g}}^{-1}$$ (Ovchinnikov et al., 2014). If under these conditions $${N}_{i}$$ is below $${N}_{i0}$$, then new ice crystals are produced at a rate $$\frac{\mathit{\partial }{N}_{i}}{\mathit{\partial }t}=\frac{{N}_{i0}-{N}_{i}}{\mathit{{\increment}}t}$$, where $$\mathit{{\increment}}t$$ is the model time step (Ovchinnikov et al., 2014). Primary ice nucleation or secondary ice production mechanisms leading to the formation of the ice particles are not specified in this study. Rather, this study assesses the effects of changing $${N}_{i}$$ on cloud evolution.

In the presented simulations, $${N}_{i0}$$ is specified to be 1, 10, and 25 $${\mathrm{L}}^{-1}$$, which covers a range of $${N}_{i}$$ observed in the Arctic (Creamean et al., 2018; Klein et al., 2009; Ovchinnikov et al., 2014). We refer to the above three $${N}_{i0}$$ conditions as ice01, ice10, and ice25. An additional simulation with no ice (supercooled liquid cloud only) is also performed and referred to as ice00. There are three ice phase species in the simulations: cloud ice, graupel, and snow. In the rest of the paper, we refer to the ice water path (IWP) as the sum of water paths from these three ice species and the liquid water path (LWP) as the sum of the cloud liquid water path and rain water path (RWP). The total water path (TWP) is the sum of IWP and LWP and includes all condensed water species in the atmospheric column. In addition to the simulations with varying $${N}_{i}$$, we conduct an additional simulation to isolate the effects of precipitation evaporation, specifically snow sublimation, on boundary layer structure, and cloud regime transitions. This simulation is identical to the ice25 configuration except that snow sublimation below the cloud base is set to zero. In the following analysis, we will refer to this simulation as ice25_noSublim.

The longwave radiative cooling rate is parameterized as a function of the liquid water mixing ratio profile as detailed by Ovchinnikov et al. (2014). Because of the high latitude and the time of year for the case (early March), the sun angle is low. Under these conditions, the shortwave radiation has little impact on the cloud fields and is not included in the simulations to speed up the computations.

In all simulations, we use a domain size of (25.6 km)² with horizontal grid spacings of $$dx=dy=100\,\mathrm{m}$$. From satellite image analysis of the considered MCAO case, Wu and Ovchinnikov (2022) found the horizontal cloud sizes to be smaller than 25 km in roll cloud and transition regimes, which are the primary focus of our analysis. The vertical grid spacing is $$dz=50\,\mathrm{m}$$ and the model top is at 6.4 km. The model top height is adequate for the roll clouds and roll breakup regimes, where the inversion height is lower than 3 km. Grid spacing is a key parameter for LES, affecting the variances of temperature, moisture, and vertical velocity across spatial scales (Ovchinnikov et al., 2022). Previous studies (e.g., Honnert et al., 2020; Wurps et al., 2020) have shown that, when the convective boundary layer is well developed, the resolved fraction of the turbulent kinetic energy remains high enough for simulations with horizontal grid spacings on the order of 100–300 m. The time step is set to $$\mathit{{\increment}}t=1\,\mathrm{s}$$ but adjusted dynamically if needed to meet the Courant–Friedrichs–Lewy (CFL) condition (Courant et al., 1967). Note that a wider and taller model domain may be needed for an adequate representation of a deeper convection regime occurring in the last part of the trajectory where the cloud top height can exceed 5 km (Geerts et al., 2022; Lackner et al., 2023).

2.3 Observational Constraint on Model Using MAC-LWP Satellite Retrievals

To provide observational constraints for model simulations over the Norwegian Sea, upwind of the COMBLE site, we rely on satellite retrievals of LWP. For the duration of the CAO, we find that the solar zenith angle is greater than 70°, rendering imager-based retrievals too uncertain. Instead, we use LWP retrievals from spaceborne microwave radiometers hosted on multiple earth-orbiting satellite platforms. Specific sensors and satellites observing the COMBLE region include the Special Sensor Microwave Imager (SSMI) -F16, -F17, and -F18 on Defense Meteorological Satellite Program (DMSP) satellites, Global Precipitation Measurement (GPM) satellite microwave radiometer GMI, the Advanced Microwave Scanning Radiometer 2 (AMSR2) onboard Global Change Observation MIssion water specializing satellite (GCOM-W1), and WindSat on Coriolis. The Multisensor Advanced Climatology of Liquid Water Path algorithm (MAC-LWP; Elsaesser et al., 2017) provides the column-integrated total liquid (i.e., cloud and rain water combined) from these instruments using as initial input the latest cloud liquid water retrieval inputs from Remote Sensing Systems (Hilburn & Wentz, 2008). Since all liquid categories are combined, MAC retrievals are directly comparable to the total LWP computed from the model simulations. The MAC algorithm applies a number of bias corrections and enhancements to inputs to arrive at the final combined LWP with a systematic uncertainty estimate of less than 20% on retrievals. Errors from MAC are much smaller than typical LWP estimates in which substantial uncertainties are introduced by typical cloud-rain partitioning efforts or by signal attenuation issues from the remote sensing method utilized (Elsaesser et al., 2017; Greenwald et al., 2018). We use hourly resolved LWP data and collocate pixels at a resolution of (∼25 km)² to domains of (∼50 km)² along the trajectory to produce domain-mean LWP values that include cloudy and clear regions. This LWP data set was recently employed as an observational constraint by Tornow et al. (2023).

3 Results

In this section, we analyze simulations with four $${N}_{i}$$ values (ice00, ice01, ice10, and ice25) and three surface temperatures. First, we evaluate the LWP evolution and spatial cloud patterns in simulations with different $${N}_{i}$$ using satellite observations and retrievals. Then, the mechanisms of cloud response to changing $${N}_{i}$$ are discussed. Finally, to test the sensitivity of these microphysically driven mechanisms to the surface forcing, simulations with the SSTs increased or decreased by 2K are examined and compared with the default setup.

3.1 Evaluating SAM Simulations With Observations

Figure 3 shows TWP snapshots in different simulations (rows) and at several time steps (columns). All the panels in Figure 3 share the same color scale with bright colors representing higher TWP. In general, the simulations capture the observed cloud patterns as shown in Figure 1. TWP values increase with time in all simulations. The simulations tend to produce higher TWP with lower $${N}_{i}$$ with the highest TWP in ice00. This is confirmed by the domain mean TWP values shown in Figure 4c that the values in ice00 are much higher than in other simulations between hours 2 and 14. At 1 hour after passing the ice edge roll clouds with orientations approximately along the y-direction (equivalent to a north-south direction) appear in all simulations. The 2 × 2 tiled TWP fields for the ice25 simulation are shown in Figure S1 in Supporting Information S1 in which the roll patterns are clearer and comparable with those from the simulation with a larger domain of $${(51.2\,\text{km})}^{2}$$. The roll clouds grow wider with prolonged air mass exposure to large sensible and latent heat fluxes from the open ocean. After a sufficient fetch from the ice edge, for example, at 8–10 hr in the ice25 simulation, roll clouds start to disorganize and break up into cellular convection. The timing of the cloud breakup is different in simulations with different $${N}_{i}$$ as will be further discussed below.

Figure 3

Panels (a–x) show snapshots of total water path from simulations with different ice number concentrations ($${N}_{i}$$, columns) at different hours since the sea ice edge (rows). All panels share the same color scale.

Figure 4

Time series of domain-mean (a) liquid water path (LWP = cloud water path + rain water path), (b) ice water path (IWP = cloud ice water path + snow water path + graupel water path), (c) total water path (TWP = LWP + IWP), (d) inversion height (z_i, solid lines) and cloud base height estimated from liquid water mixing ratio (CBH, dashed lines), (e) precipitation rate at cloud base (dotted lines) and surface (solid lines), (f) precipitation evaporation rate from the difference of precipitation rates at the cloud base height and at the surface, (g) cloud fraction, and (h) total water homogeneity parameter ($$\nu $$) calculated from grids with TWP greater than 100 g m⁻². Black dots in (a) are LWP retrieved from satellite observations. An additional sensitivity experiment based on ice25 with snow sublimation turned off (“ice25_noSublim”) is shown as the purple line in (f). Note that zero values are included in calculating the domain-mean values. Most of the analysis in this study focuses on simulations within 10 hr after the ice edge.

In addition to the qualitative comparison of the simulated cloud patterns with satellite images, we evaluate simulated cloud properties quantitatively using the MAC-LWP retrievals. Figure 4a shows the time series of simulated domain mean LWP with black dots showing MAC estimates matched in time and space with the SAM domain (details on matching in Section 2.3). Due to the possibility of ice contamination in retrievals near the ice edge, we only use retrieved LWP values after 2 hr off the ice edge. The retrieved LWP values increase quickly between 2 and 3 hr and then stay relatively stable until 10 hr before decreasing slowly toward the end of the simulation (at the AMF1 site in Andenes). The LWP in the ice25 simulation exhibits the best agreement with satellite retrievals among the analyzed simulations.

3.2 Sensitivity of Cloud Properties to Ice Number Concentration

Increasing $${N}_{i}$$ leads to larger IWP (Figure 4b) in the first 10 hr as expected (Eirund, Lohmann, et al., 2019; Ovchinnikov et al., 2014; Tornow et al., 2021). The growth of more ice particles leaves less moisture available for liquid droplets, which lead to a decrease in LWP (Figure 4a). The TWP values (Figure 4c) show smaller differences among simulations than the LWP and IWP components with the highest TWP in ice00 and the lowest in ice25 and ice10. Little difference is found in TWP between ice10 and ice25 before 6 hr, although the liquid-to-ice partitioning differs between these cases, and LWP and IWP diverge from each other as soon as clouds form. The domain mean inversion heights (Figure 4d), estimated as the height of the maximum gradient of potential temperature, are close to each other in the first 3 hours and gradually diverge afterward. The inversion height in ice25 is the lowest before hour 10 but increases sharply afterward.

Precipitation initiates the earliest in ice25 and the latest in ice00 (Figures 4e and 4f). After initiation, precipitation rates increase at a similar rate for the next ∼1.5 hr in simulations with ice, whereas in ice00, the precipitation rate increases slower. Precipitation rates at the cloud base (Figure 4e) increase almost monotonically with time until ∼10 hr in all the simulations after their initial peaks with the highest precipitation rate in ice25. Note that the cloud base heights are estimated from liquid water mixing ratios. Although ice00 has the highest TWP, its precipitation rate is the lowest, suggesting a lower precipitation efficiency in ice00 compared to the ice-containing simulations. The precipitation rates at the surface (Figure 4f), however, show much smaller differences with the values oscillating near 6 mm day⁻¹ in all mixed-phase cases after their initial peaks. The comparison of the precipitation rates at the cloud base and surface (Figures 4e and 4f) implies that the sublimation rate below the cloud base is greater in higher $${N}_{i}$$ simulations. The cloud base is relatively high (Figure 4d), implying much sublimation potential.

For the purpose of computing the cloud fraction, model grid columns with the TWP greater than 15 g m⁻² are considered as cloudy. The domain mean cloud fraction and TWP homogeneity parameter ($$\nu =\text{variance}(\text{TWP})/{\overline{\text{TWP}}}^{2}$$, where only TWP values greater than 100 g m⁻² are taken into the calculation) are shown in Figures 4g and 4h, respectively. Note that a reduction of cloud fraction to below 0.75 has been used previously to indicate the breakup of an overcast cloud deck (Tornow et al., 2021). The homogeneity parameter is used to identify regions of roll-to-cell transition in satellite retrieved cloud water path by Wu and Ovchinnikov (2022) for the same MCAO case. However, as shown in Wu and Ovchinnikov (2022), it is hard to pinpoint an exact time or location that the majority of roll clouds break up into convective cells given this transition takes place over a distance of several hundred kilometers. In this study, we use both cloud fraction and $$\nu $$ to describe the breakup of roll clouds in a qualitative manner.

Cloud fractions increase sharply in all simulations as the cold air is advected off the ice edge (Figure 4g) as also been found in satellite studies (e.g., Murray-Watson et al., 2023). In ice00, the cloud fraction remains close to 100% throughout the simulation. In simulations with ice, cloud fraction is higher when $${N}_{i}$$ is lower. A relatively quick decrease in cloud fraction is an indication of cloud breakup, for example, during hours 8–10 in ice25. Figure 4g shows that clouds with higher $${N}_{i}$$ breakup earlier. This is confirmed by the $$\nu $$ parameter in Figure 4h where in higher $${N}_{i}$$ simulations, $$\nu $$ falls to below an arbitrary $$\nu $$ threshold earlier.

The simulated cloud properties, for example, those from ice25, resemble those from the larger domain as shown in Figure S2 in Supporting Information S1 in the first ∼10 hr of simulation since the ice edge, suggesting the adequacy of the $${(25.6\,\text{km})}^{2}$$ domain size in capturing the general features of cloud properties and meteorological conditions.

3.3 Mechanisms of Cloud Structure Response to $${N}_{i}$$

To examine the distribution of water in cloud and precipitation hydrometers, we show the probability density functions (PDFs) of cloud water path (CWP, left column) and precipitation water path (PWP, right column) in Figure 5. CWP includes cloud water and cloud ice, and PWP includes rain, snow, and graupel. In simulations with higher $${N}_{i}$$, the cloud water path distributions are narrower, and the mean values are smaller. The effect of $${N}_{i}$$ on precipitation water is more complicated. In the early hours of cloud evolution, higher $${N}_{i}$$ corresponds to broader precipitation water distributions with larger mean values. The differences among the precipitation water path distributions, however, are not as pronounced as among the cloud-water path distributions and become smaller with time. The precipitation water path distributions for ice00 resemble those from ice01 most of the time, but the corresponding cloud-water path distributions are broader in ice00, making the overcast clouds without ice to persist for longer. The PWP/TWP ratios increase with time and are higher with higher $${N}_{i}$$, implying the role of precipitation depletion of cloud water in cloud breakup.

Figure 5

Probability density functions (PDFs) of cloud water path (CWP = cloud liquid + ice water paths, left column, panels a, c, e, and g) and precipitation water path (PWP = rain + snow + graupel water paths, right column, panels b, d, f, and h) at different times since the sea ice edge (rows). The means (standard deviations) of CWP and PWP are shown in each panel, and the ratios of PWP and TWP are shown in the right column.

Figure 6 shows the time series of the mean vertical velocity variance ($$\overline{{w}^{\prime }{w}^{\prime }}$$) below the inversion height. The boundary layer turbulence is generated by buoyancy and wind shear, but here we focus on $${w}^{\prime }{w}^{\prime }$$, which corresponds to the vertical component of the turbulence kinetic energy (TKE) and indicates the strength of the vertical mixing. Ice00 has the largest $$\overline{{w}^{\prime }{w}^{\prime }}$$ throughout most of the simulation time. In simulations with higher $${N}_{i}$$, $$\overline{{w}^{\prime }{w}^{\prime }}$$ is lower than in those with lower $${N}_{i}$$, highlighting a weaker vertical mixing in the former case. Precipitation evaporation and corresponding cooling in the sub-cloud layer can increase the stability of the boundary layer, modify its dynamics, and, subsequently, impact cloud organization. These relationships are supported by the profiles shown in Figure 7, where increased snow sublimation with increasing $${N}_{i}$$ (Figure 7 left column) corresponds with a weakening of the vertical mixing or decrease in $$\overline{{w}^{\prime }{w}^{\prime }}$$ (Figure 7 right column). Tornow et al. (2021) found similar mechanisms in a liquid-dominated case where substantial rain triggers the regime transition: increasing ice number concentration enhances MCAO cloud breakup through boundary stratification by snow sublimation or melting and evaporation. Several previous studies of the effect of precipitation on mixed-phase cloud organization found that precipitation evaporation below the cloud can lead to the decoupling of the boundary layer (Abel et al., 2017; Lloyd et al., 2015). In our study, the boundary layer remains largely coupled to the surface in all the simulations presumably due to the large surface heat fluxes and strongly convective boundary layer, but the liquid water potential temperature profiles become more stable with time particularly in the ice25 simulation (Figures 7b, 7f, 7j, and 7n). As a result, the domain mean water vapor mixing ratio ($${q}_{v}$$, third column in Figure 7) is the lowest in ice25 near the cloud layer despite the highest precipitation evaporation rate. A sensitivity simulation (“ice25_noSublim”) with the same configuration as ice25 but without snow sublimation demonstrates an increase in $$\overline{{w}^{\prime }{w}^{\prime }}$$ over that in ice25 (purple lines in Figures 6 and 7), thereby confirming the effect of precipitating ice sublimation on sub-cloud vertical mixing. Also, although ice25_noSublim increases intensity of the mixing below the cloud base, it does not come closer to ice01 or ice00 simulations within the cloud layer. This suggests that the deposition of vapor on ice also plays a role in stabilizing the BL through the release of extra latent heat. Note that although precipitation evaporation in ice25_noSublim is the lowest among all simulations (Figure 4f), it is not zero. Although snow constitutes most of the precipitating hydrometeors, rain evaporation and cloud ice sublimation still occur below the liquid cloud base.

Figure 6

Time series of domain-mean vertical velocity variance below z_i.

Figure 7

Left to right columns show domain-mean profiles of snow sublimation (panels a, e, i, and m), liquid potential temperature ($${\theta }_{l}$$, panels b, f, j, and n), water vapor mixing ratio (q_v, panels c, g, k, and o), and vertical velocity variance ($$\overline{{w}^{\prime }{w}^{\prime }}$$, panels d, h, l, and p) at different times (rows) since the air mass passes the sea ice edge. The experiment with no snow sublimation is shown as purple lines in the right column.

Figure 8 shows the domain mean $${\theta }_{v}$$ variance at the lowest model level (25 m above the surface), which is an indication of convergence-driven buoyant updrafts and evaporation-driven downdrafts. $${\theta }_{v}$$ variance has also been used to identify cold pools, including in marine stratocumulus-topped boundary layers (e.g., Terai & Wood, 2013). The $${\theta }_{v}$$ variances in ice00 are slightly higher than the simulations with ice in the roll cloud regime (e.g., hours 2–6). However, because of the high TWP and cloud fraction in ice00, clouds do not fully break up even after 18 hr of simulation. After hour 6, $${\theta }_{v}$$ variances in all the simulations start to increase with ice25 having the largest increase rate. Near the time of roll breakup (e.g., after hour 10), ice25 has the highest $${\theta }_{v}$$ variance, indicating the strongest mesoscale updraft and downdraft among the simulations. This is consistent with the larger sub-cloud sublimation rate in ice25 at this time. The $${\theta }_{v}$$ variance in ice00 remains generally low compared to the simulations with ice after cloud breakup. This is consistent with the results by Eirund, Lohmann, et al. (2019) and Eirund, Possner, et al. (2019) that they found the lowest $${\theta }_{v}$$ variance in the no-ice simulation when testing the role of cloud ice processes in Arctic stratocumulus spatial organizations.

Figure 8

Time series of virtual potential temperature ($${\theta }_{v}$$) variance at the lowest model level (25 m above the surface).

3.4 Sensitivity to Surface Temperature

A reason for the intense convection during MCAO events is the large temperature contrast between the sea surface and the atmosphere. The MCAO case in this study is a very strong event over the Fram Strait (Dahlke et al., 2022). To test the robustness of the ice number impact on cloud organization under different MCAO intensities, for example, stronger or weaker MCAO scenarios and thus different boundary layer dynamics, we conduct a set of simulations by changing the SST by $$\mathit{\pm }$$2 K in ice01 and ice25. We label simulations with SST reduced or increased by 2 K compared to the default configuration as “−2K” and “2K,” respectively, and simulations with unperturbed SST as “0K.”

Cloud patterns in simulations with all SSTs show roll structures, mimicking those in satellite observations (Figure S3 in Supporting Information S1). TWP in −2K simulations are lower than those in 0k and +2K simulations as shown in Figure S3 in Supporting Information S1 and Figure 9c. The partitioning of TWP into LWP (Figure 9a) and IWP (Figure 9b) follows those in the $${N}_{i}$$ sensitivity simulations that higher $${N}_{i}$$, in general, leads to higher IWP and lower LWP. Relative to 0K, the SHF and LHF in the +2K simulations changed by 8% and 20%, respectively, whereas the SHF and LHF in the −2K simulations changed by −8% and −16%, respectively. In the −2K simulations, the LWP and IWP values are all smaller than in the +2K simulations because of lower latent heat flux from the surface with decreased SST. The inversion height shows a larger sensitivity to changing SST (Figure 9d) than to changes in $${N}_{i}$$ (Figure 4d). Precipitation is initiated earlier in +2K simulations, although precipitation evaporation below the cloud is roughly the same between −2K and +2K simulations as inferred from Figures 9e and 9f. The ice25 simulations, however, have stronger precipitation evaporation than their ice01 counterparts, implying a greater sensitivity of precipitation evaporation to changing $${N}_{i}$$ than to changing SST.

Figure 9

Same as Figure 4, except for simulations in ice01 (orange lines) and ice25 (red lines) with SST change by −2 K (dotted lines) and 2 K (dashed lines).

Clouds above higher SST (+2K) break up earlier than those over cooler SST (−2K) in both ice01 and ice25 (Figures 9f and 9g). The cloud breakup times closely match the times when the inversion heights increase sharply (Figure 9d). The effects of SST on cloud break up are, however, different under different $${N}_{i}$$: the advancement and delay of cloud breakup time with 2K increase and decrease, respectively, in SST in ice01 are greater than those in ice25, suggesting a weaker sensitivity of cloud organization to SST under higher $${N}_{i}$$.

Increases in SST result in higher $$\overline{{w}^{\prime }{w}^{\prime }}$$, whereas decreases in SST result in lower $$\overline{{w}^{\prime }{w}^{\prime }}$$, as expected, but all ice25 simulations have lower $$\overline{{w}^{\prime }{w}^{\prime }}$$ than ice01 simulations (Figure S4 in Supporting Information S1) before the cloud breakup (10–12 hr) especially in the sub cloud layer (right column in Figure 10). For the same SST, the vertical mixing strength is weaker with higher $${N}_{i}$$ which leads to weaker coupling of the cloud layer to the surface (second column in Figure 10) and lower $${q}_{v}$$ (third column in Figure 10) in the boundary layer consistent with the findings in Section 3.3.

Figure 10

Same as Figure 7, except for the same set of SST simulations shown in Figure 9.

4 Discussion

Traditionally, the roll-to-cell transition is explained in terms of shifts in thermal and dynamical instabilities in different cloud regimes. For example, the vertical wind shear (Asai, 1970) and curvature of the wind profile (Kuettner, 1971) of the primary flow (along the roll cloud alignment) are found to be important for the organization of the convective patterns. The shift toward a more convective boundary layer and, thus, increasing latent heat release in clouds relative to surface heating is found during the roll-to-cell transition (Brümmer, 1999). A dimensionless stability parameter, $${-}{z}_{i}/L$$, where $${z}_{i}$$ is the boundary layer depth and $$L$$ is the Obukhov length, can be used to describe the relative importance of wind shear and buoyancy in the turbulent kinetic energy production, and a range of characteristic numbers (from <10 to >25) has been proposed to differentiate between roll and cell cloud regimes (Baik & Park, 2014; Deardorff, 1972; Khanna, 1997; Salesky et al., 2017; Weckwerth et al., 1999). In a case study by Wu and Ovchinnikov (2022), however, the magnitude of $${-}{z}_{i}/L$$ values in roll and cell cloud regimes is found to depend on meteorological conditions: the values in the cell cloud region can be smaller than in the roll cloud region in certain conditions, which is contrary to previous findings. One of the possible explanations of this counterintuitive trend in $${-}{z}_{i}/L$$ is that microphysical processes especially the convective precipitation process, are not reflected in this traditional stability analysis.

This study investigates the roles of $${N}_{i}$$ on cloud regime transition. From the above analysis, we can conclude that ice processes are not a necessary component in forming convective roll structures during an MCAO event (e.g., Figure 4) but are important for cloud regime transition from rolls to broken cells. Higher $${N}_{i}$$ leads to a stronger precipitation rate at the cloud base, which depletes more cloud water. The boundary layer is less coupled to the surface with higher $${N}_{i}$$, and the transport of surface moisture and heat to the cloud layer is less efficient. The stronger snow sublimation in simulations with higher $${N}_{i}$$ act to strengthen the mesoscale updraft and downdraft evidenced by larger $${\theta }_{v}$$ variance.

The effects of precipitation on cloud organization are not unique to the MCAO cloud system in this case. Similar mechanisms have been found in midlatitude oceanic stratocumulus-to-cumulus transitions (Yamaguchi et al., 2017) and Arctic mixed-phase cloud organization transitions (Abel et al., 2017; Eirund, Lohmann, et al., 2019). There is, however, a decoupling process involved in previous case studies even in marine MCAO events (Eirund, Lohmann, et al., 2019; Lloyd et al., 2015). In the MCAO case discussed in this study, the surface heat fluxes are so strong (e.g., Figure 2f) that the boundary layer remains coupled, as suggested by $${\theta }_{l}$$ profiles, at least up to the cloud break up.

The mechanisms of ice/snow and precipitation on MCAO cloud organization have also been studied over the northwest Atlantic Ocean by Tornow et al. (2021). Their study found that precipitation evaporation induced boundary layer stratification. However, there are important differences between the two studies. The clouds by Tornow et al. (2021) are dominated by liquid, as indicated by a much higher liquid water path than ice water path, and the warm-rain process is active, resulting in comparable amounts of rain water path and ice water path (see their Figure 2).

In Tornow et al. (2021), cloud top temperatures are mostly above −12°C, whereas in our case, the cloud top temperatures are mostly below −30°C. Colder clouds that are not necessarily driven by rain may behave differently than warmer ones (e.g., our case does not show a sharp cloud fraction transition as in the Tornow work). The cloud liquid droplet number concentrations by Tornow et al. (2021) are several times higher (50–150 $$\mathrm{c}{\mathrm{m}}^{-3}$$) than those in our simulations (∼20 $$\mathrm{c}{\mathrm{m}}^{-3}$$), which is presumably due to relatively polluted air masses from the North American continent compared to the cleaner air from the Arctic.

The sensitivity of MCAO cloud evolutions to $${N}_{i}$$ described above is investigated using prescribed and time-invariant $${N}_{i}$$ and $${N}_{\text{CCN}}$$. ice25 produces LWP that is most comparable to satellite retrievals. $${N}_{i}$$ of 25 $${\mathrm{L}}^{-1}$$ is close to the measurements documented in the literature for MCAO cases in the high latitude. For example, Field et al. (2014) reported aircraft measured $${N}_{i}$$, for particle diameters greater than 100 $$\mu \mathrm{m}$$, to be in the order of 10 $${\mathrm{L}}^{-1}$$ for an MCAO case occurred near Scotland, which is further south and under warmer conditions than the case considered in this study. Raif et al. (2024) showed that the concentration of ice-nucleating particles (INPs), $${N}_{\text{INP}}$$ over the Norwegian and Barents seas can sometimes reach 10 $${\mathrm{L}}^{-1}$$ and higher. However, $${N}_{\text{INP}}$$ from their measurements are often on the order of 1 $${\mathrm{L}}^{-1}$$, meaning that secondary ice production would be needed to produce $${N}_{i}$$ to ∼20 $${\mathrm{L}}^{-1}$$. Partitioning $${N}_{i}$$ between primary and secondary ice production is complicated and is a good research topic for future work. The idealized approach of prescribed $${N}_{i}$$ in this study avoids uncertainties in ice nucleation and secondary ice production rates and is chosen to isolate the effect of microphysics on cloud structure given the lack of in situ microphysics measurements during COMBLE.

In reality, aerosol properties, including $${N}_{\text{CCN}}$$ and the concentration of ice-nucleating particles (INPs), can vary along the trajectory of the air mass (e.g., Figure 7 in Murray-Watson et al., 2023). These variations can stem from local sources, such as sea spray aerosol (McCluskey et al., 2018), as well as remote sources, such as midlatitude dust emissions (Najafi et al., 2015). Additionally, different ice formation mechanisms, such as contact freezing or rime-splintering, may affect $${N}_{i}$$ beyond the immersion freezing considered in our model simulations. Those processes are not explicitly represented in our current model specifications, underscoring the need for future studies incorporating prognostic aerosol treatments and more realistic ice formation mechanisms.

$${N}_{\text{CCN}}$$ measured at the AMF1 site for the entire trajectory may differ from $${N}_{\text{CCN}}$$ in the early stages of the simulation and although ice processes and snow sublimation are key factors in cloud regime transitions, the role of initial and time-varying $${N}_{\text{CCN}}$$ remains to be fully investigated.

The SST perturbation experiments allow us to conclude that the effects of $${N}_{i}$$ on MCAO cloud structure and roll cloud breakup through the depletion of cloud water and decreased vertical mixing in the sub-cloud layer occur similarly in MCAO events of different strengths. Those CAO events, however, are all strong compared to the overall CAO cases during COMBLE (Geerts et al., 2022). The weaker sensitivity of cloud patterns to SST under lower $${N}_{i}$$ conditions might be due to the fast water mass transfer process from liquid to ice even with a small amount of ice particles introduced in mixed-phase clouds. The relative roles of microphysics (e.g., ice processes) and boundary layer dynamics (e.g., surface heat fluxes) in MCAO cloud organization warrant further studies.

5 Summary

MCAO events in the Arctic are characterized by rapid and intense heat and moisture transfer from the open ocean to the atmosphere, leading to the deepening of the boundary layer and cloud formation. Over half of the Arctic Ocean's heat loss during the cold season occurs under MCAO conditions (Papritz et al., 2015). Despite their climatic significance, MCAO clouds pose a challenge for representation in large-scale models, partly because the scales of the boundary layer and cloud are much smaller than the grid sizes used in traditional climate models. The transition from convective rolls to broken cellular clouds is a process within MCAO that is not well-captured. Understanding the mechanisms responsible for this transition in cloud organization is critical for improving the representation of convective clouds over the Arctic.

In this study, we perform LES simulations of a strong MCAO case documented during the ARM COMBLE campaign. We investigate the response of cloud organization, focusing on the roll-to-cell transition, to a set of prescribed cloud ice number concentration $${N}_{i}$$ (ice00, ice01, ice10, and ice25). Clouds appear as roll structures in all the simulations similar to those from observations, including the ice-free simulation ice00. Simulated LWP values decrease with increasing $${N}_{i}$$, with ice25 simulated LWP most closely aligned with the satellite retrieved LWP. Conversely, the simulated IWP values increase with the increase of $${N}_{i}$$ due to the growth of ice at the expense of cloud liquid. Precipitation initiates earlier, and the precipitation rate at the cloud base is higher in simulations with higher $${N}_{i}$$. However, precipitation rates at the surface vary little across simulations, indicating enhanced evaporation (sublimation) below the cloud in higher $${N}_{i}$$ simulations. Mean vertical velocity variance ($$\overline{{w}^{\prime }{w}^{\prime }}$$) in the boundary layer is reduced in higher $${N}_{i}$$ simulations, implying weaker vertical mixing. This is consistent with the less coupled state of the boundary layer in higher $${N}_{i}$$ simulations. The combined effects of enhanced precipitation evaporation, weaker vertical mixing, and a less coupled boundary layer restrict water vapor vertical transport, contributing to the earlier breakup of roll clouds. A sensitivity simulation with no sublimation verifies the role of precipitation evaporation in cloud regime transitioning (e.g., Figure 6). A similar mechanism has been documented in midlatitude stratocumulus-to-cumulus transitions and in the development of Arctic mixed-phase stratocumulus but has not been observed in MCAO cases with strong surface heating. The atmospheric temperatures in the case presented here are much colder than in other MCAO cloud morphology studies.

To test the sensitivity of the aforementioned mechanism to different MCAO conditions, we conduct another set of simulations with altered SST by decreasing or increasing SST by 2K. The ice01 and ice25 conditions are examined in this SST sensitivity analysis. Independent of the $${N}_{i}$$ and SST scenarios, all simulations produce the roll cloud structures, reaffirming the effectiveness of the model setup in capturing cloud organization. At constant $${N}_{i}$$, higher SST results in faster deepening of the boundary layer and earlier cloud break up. Similarly, at constant SST, increased $${N}_{i}$$ leads to earlier cloud break up with cloud and boundary layer properties echoing the $${N}_{i}$$-sensitivity analysis: stronger precipitation evaporation and a boundary layer weakly coupled to the surface in higher $${N}_{i}$$ simulations. The dependence of cloud organization on SST is stronger in environments with lower $${N}_{i}$$.

Traditionally, research on the mechanisms controlling cloud morphology at both mid and high latitudes has prioritized thermodynamic and dynamic factors. This study, along with several other recent ones, underscores the role of cloud and precipitation microphysics in determining cloud organization. In the high latitudes, the distinct microphysics of mixed-phase clouds necessitates that ice processes be accurately represented for realistic simulations of MCAO clouds. The liquid-ice partition can alter ice-phase hydrometeor water mass and impact the precipitation rate. Although we did not examine the secondary ice production (SIP) process in this study due to the much colder temperatures (cloud top temperature around −30$${}^{\circ}\mathrm{C}$$ in the first ∼10 hr of simulations) compared to the typical SIP temperature range (e.g., between −8$${}^{\circ}\mathrm{C}$$ and −3$${}^{\circ}\mathrm{C}$$), the SIP process can enhance $${N}_{i}$$ and impact cloud patterns through the mechanisms described above.

The presented results, however, are all derived from a model environment with a very simplified treatment of the interactions between clouds and their environment. For example, we prescribed CCN and ice number concentrations in the simulations. The extent to which these conclusions apply to the real world remains to be verified through further study.

Acknowledgments

This research is supported by the U.S. Department of Energy Office of Science Atmospheric System Research (ASR) program at PNNL. PNNL is operated for the Department of Energy by Battelle Memorial Institute under Contract DE-AC05-76 RL01830. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award BER-ERCAP0030247. We would like to thank Marat Khairoutdinov for developing and maintaining the SAM code and for making it publicly available. We would also like to thank Aaron Wang for helping to setup SAM on NERSC. Ann Fridlind, Tim Juliano, Branko Kosovic, Lulin Xue, Yunyan Zhang, and Xue Zheng are acknowledged for discussions.

Open Research

Data Availability Statement

The source code used for the simulations of this study, the System for Atmospheric Modeling (SAM) model, is publicly available (SAM, 2020). ERA5 reanalysis data is provided by ECMWF through Copernicus (ERA5, 2020). HYSPLIT backward trajectories for each CAO hour during the COMBLE field campaign are archived in the ARM data center (Wu & Ovchinnikov, 2019). The MAC-LWP retrievals for the case can be accessed at COMBLE-MIP GitHub page (MAC-LWP, 2023).