Coastal Clouds at the Eastern Margin of the Southeast Pacific: Climatology and Trends

Abstract The climatology and recent trends of low-level coastal clouds at three sites along the northern Chilean coast (18.3°–23.4°S) are documented based upon up to 45 years of hourly observations of cloud type, coverage, and heights. Consistent with the subtropical location, cloud types are dominated by stratocumuli having greatest coverage (>7 oktas) and smaller heights (600–750 m) during the nighttime of austral winter and spring. Meridionally, nighttime cloud fraction and cloud-base heights increase from south to north. Long-term trends in mean cloud cover are observed at all sites albeit with a seasonal modulation, with increasing (decreasing) coverage in the spring (fall). Consistent trend patterns are also observed in independent sunshine hour measurements at the same sites. Cloud heights show negative trends of about 100 m decade−1 (1995–2010), although the onset time of this tendency differs between sites. The positive cloud fraction trends during the cloudy season reported here disagree with previous studies, with discrepancies attributed to differences in datasets used or to methodological differences in data analysis. The cloud-base height tendency, together with a less rapid lowering of the subsidence inversion base height, suggests a deepening of the coastal cloud layer. While consistent with the tendency toward greater low-level cloud cover and the known cooling of the marine boundary layer in this region, these tendencies are at odds with a drying trend of the near-surface air documented here as well. Assessing whether this intriguing result is caused by physical factors or by limitations of the data demands more detailed observations, some of which are currently under way.

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Mind the gap – Part 1: Accurately locating warm marine boundary layer clouds and precipitation using spaceborne radars

Atmospheric Measurement Techniques ◽

10.5194/amt-13-2363-2020 ◽

2020 ◽

Vol 13 (5) ◽

pp. 2363-2379 ◽

Cited By ~ 3

Author(s):

Katia Lamer ◽

Pavlos Kollias ◽

Alessandro Battaglia ◽

Simon Preval

Keyword(s):

Boundary Layer ◽

Cloud Cover ◽

Marine Boundary Layer ◽

Short Pulse ◽

Pulse Mode ◽

Cloud Base ◽

Boundary Layer Clouds ◽

Highly Sensitive ◽

Eastern North Atlantic ◽

Long Pulse

Abstract. Ground-based radar observations show that, over the eastern North Atlantic, 50 % of warm marine boundary layer (WMBL) hydrometeors occur below 1.2 km and have reflectivities of < −17 dBZ, thus making their detection from space susceptible to the extent of surface clutter and radar sensitivity. Surface clutter limits the ability of the CloudSat cloud profiling radar (CPR) to observe the true cloud base in ∼52 % of the cloudy columns it detects and true virga base in ∼80 %, meaning the CloudSat CPR often provides an incomplete view of even the clouds it does detect. Using forward simulations, we determine that a 250 m resolution radar would most accurately capture the boundaries of WMBL clouds and precipitation; that being said, because of sensitivity limitations, such a radar would suffer from cloud cover biases similar to those of the CloudSat CPR. Observations and forward simulations indicate that the CloudSat CPR fails to detect 29 %–43 % of the cloudy columns detected by ground-based sensors. Out of all configurations tested, the 7 dB more sensitive EarthCARE CPR performs best (only missing 9.0 % of cloudy columns) indicating that improving radar sensitivity is more important than decreasing the vertical extent of surface clutter for measuring cloud cover. However, because 50 % of WMBL systems are thinner than 400 m, they tend to be artificially stretched by long sensitive radar pulses, hence the EarthCARE CPR overestimation of cloud top height and hydrometeor fraction. Thus, it is recommended that the next generation of space-borne radars targeting WMBL science should operate interlaced pulse modes including both a highly sensitive long-pulse mode and a less sensitive but clutter-limiting short-pulse mode.

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Mass flux estimates and their relationship to cloud-base cloudiness during the EUREC4A campaign

10.5194/egusphere-egu21-4804 ◽

2021 ◽

Author(s):

Raphaela Vogel ◽

Sandrine Bony ◽

Anna Lea Albright ◽

Bjorn Stevens ◽

Geet George ◽

...

Keyword(s):

Mass Flux ◽

Cloud Cover ◽

Climate Models ◽

Cloud Fraction ◽

Cloud Feedback ◽

Surface Fluxes ◽

Cloud Base ◽

Entrainment Rate ◽

Cumulus Cloud ◽

Total Cloud Cover

The trade-cumulus cloud feedback in climate models is mostly driven by changes in cloud-base cloudiness, which can largely be attributed to model differences in the strength of lower-tropospheric mixing. Using observations from the recent EUREC4A field campaign, we test the hypothesis that enhanced lower-tropospheric mixing dries the lower cloud layer and reduces near-base cloudiness. The convective mass flux at cloud base is used as a proxy for the strength of convective mixing and is estimated as the residual of the subcloud layer mass budget, which is derived from dropsondes intensively launched along a circle of ~200 km diameter. The cloud-base cloud fraction is measured with horizontally-pointing lidar and radar from an aircraft flying near cloud base within the circle area. Additional airborne, ground- and ship-based radar, lidar and in-situ measurements are used to estimate the total cloud cover, the surface fluxes and to validate the consistency of the approach.Preliminary mass flux estimates have reasonable mean values of about 15 mm/s. 3- circle (i.e. 3h) averaged estimates range between 0-40 mm/s and reveal substantial day-to-day and daily variability. The day-to-day variability in the mass flux is mostly due to variability in the mesoscale vertical velocity, whereas the entrainment rate mostly explains variability on the daily timescale, consistent with previous large-eddy simulations. We find the mass flux to be positively correlated to both the cloud-base cloud fraction and the total cloud cover (R=0.55 and R~0.4, respectively). Other indicators of lower-tropospheric mixing due to convection and mesoscale circulations also suggest positive relationships between mixing and cloudiness. Implications of these analyses for testing the hypothesized mechanism of positive trade-cumulus cloud feedback will be discussed.

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What controls the formation of nocturnal low-level stratus clouds over southern West Africa during the monsoon season?

Atmospheric Chemistry and Physics ◽

10.5194/acp-19-13489-2019 ◽

2019 ◽

Vol 19 (21) ◽

pp. 13489-13506 ◽

Cited By ~ 3

Author(s):

Karmen Babić ◽

Norbert Kalthoff ◽

Bianca Adler ◽

Julian F. Quinting ◽

Fabienne Lohou ◽

...

Keyword(s):

Boundary Layer ◽

West Africa ◽

Climate Models ◽

Marine Boundary Layer ◽

Monsoon Season ◽

Onset Time ◽

Data Set ◽

Cold Air ◽

Low Level ◽

Stratus Clouds

Abstract. Nocturnal low-level stratus clouds (LLCs) are frequently observed in the atmospheric boundary layer (ABL) over southern West Africa (SWA) during the summer monsoon season. Considering the effect these clouds have on the surface energy and radiation budgets as well as on the diurnal cycle of the ABL, they are undoubtedly important for the regional climate. However, an adequate representation of LLCs in the state-of-the-art weather and climate models is still a challenge, which is largely due to the lack of high-quality observations in this region and gaps in understanding of underlying processes. In several recent studies, a unique and comprehensive data set collected in summer 2016 during the DACCIWA (Dynamics-aerosol-chemistry-cloud interactions in West Africa) ground-based field campaign was used for the first observational analyses of the parameters and physical processes relevant for the LLC formation over SWA. However, occasionally stratus-free nights occur during the monsoon season as well. Using observations and ERA5 reanalysis, we investigate differences in the boundary-layer conditions during 6 stratus-free and 20 stratus nights observed during the DACCIWA campaign. Our results suggest that the interplay between three major mechanisms is crucial for the formation of LLCs during the monsoon season: (i) the onset time and strength of the nocturnal low-level jet (NLLJ), (ii) horizontal cold-air advection, and (iii) background moisture level. Namely, weaker or later onset of NLLJ leads to a reduced contribution from horizontal cold-air advection. This in turn results in weaker cooling, and thus saturation is not reached. Such deviation in the dynamics of the NLLJ is related to the arrival of a cold air mass propagating northwards from the coast, called Gulf of Guinea maritime inflow. Additionally, stratus-free nights occur when the intrusions of dry air masses, originating from, for example, central or south Africa, reduce the background moisture over large parts of SWA. Backward-trajectory analysis suggests that another possible reason for clear nights is descending air, which originated from drier levels above the marine boundary layer.

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Simulation of Seasonal Variation of Marine Boundary Layer Clouds over the Eastern Pacific with a Regional Climate Model*

Journal of Climate ◽

10.1175/2010jcli3935.1 ◽

2011 ◽

Vol 24 (13) ◽

pp. 3190-3210 ◽

Cited By ~ 23

Author(s):

Lei Wang ◽

Yuqing Wang ◽

Axel Lauer ◽

Shang-Ping Xie

Keyword(s):

Boundary Layer ◽

Heat Flux ◽

Seasonal Cycle ◽

Marine Boundary Layer ◽

Eastern Pacific ◽

Cloud Base ◽

Low Level ◽

Surface Latent Heat Flux ◽

Cloud Regime ◽

Low Cloud

Abstract The seasonal cycle of marine boundary layer (MBL) clouds over the eastern Pacific Ocean is studied with the International Pacific Research Center (IPRC) Regional Atmospheric Model (iRAM). The results show that the model is capable of simulating not only the overall seasonal cycle but also the spatial distribution, cloud regime transition, and vertical structure of MBL clouds over the eastern Pacific. Although the modeled MBL cloud layer is generally too high in altitude over the open ocean when compared with available satellite observations, the model simulated well the westward deepening and decoupling of the MBL, the rise in cloud base and cloud top of the low cloud decks off the Peru and California coasts, and the cloud regime transition from stratocumulus near the coast to trade cumulus farther to the west in both the southeast and northeast Pacific. In particular, the model reproduced major features of the seasonal variations in stratocumulus decks off the Peru and California coasts, including cloud amount, surface latent heat flux, subcloud-layer mixing, and the degree of MBL decoupling. In both observations and the model simulation, in the season with small low-level cloudiness, surface latent heat flux is large and the cloud base is high. This coincides with weak subcloud-layer mixing and strong entrainment at cloud top, characterized by a high degree of MBL decoupling, while the opposite is true for the season with large low-level cloudiness. This seasonal cycle in low-cloud properties resembles the downstream stratocumulus-to-cumulus transition of marine low clouds and can be explained by the “deepening–decoupling” mechanism proposed in previous studies. It is found that the seasonal variations of low-level clouds off the Peru coast are mainly caused by a large seasonal variability in sea surface temperature, whereas those off the California coast are largely attributed to the seasonal cycle in lower-tropospheric temperature.

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Shallow cumulus cloud feedback in large eddy simulations – bridging the gap to storm-resolving models

Atmospheric Chemistry and Physics ◽

10.5194/acp-21-3275-2021 ◽

2021 ◽

Vol 21 (5) ◽

pp. 3275-3288

Author(s):

Jule Radtke ◽

Thorsten Mauritsen ◽

Cathy Hohenegger

Keyword(s):

Cloud Cover ◽

Horizontal Resolution ◽

Cloud Fraction ◽

Cloud Feedback ◽

Cloud Base ◽

Trade Wind ◽

Cumulus Cloud ◽

Shallow Cumulus ◽

Large Eddy ◽

Carry Over

Abstract. The response of shallow trade cumulus clouds to global warming is a leading source of uncertainty in projections of the Earth's changing climate. A setup based on the Rain In Cumulus over the Ocean field campaign is used to simulate a shallow trade wind cumulus field with the Icosahedral Nonhydrostatic Large Eddy Model in a control and a perturbed 4 K warmer climate, while degrading horizontal resolution from 100 m to 5 km. As the resolution is coarsened, the base-state cloud fraction increases substantially, especially near cloud base, lateral mixing is weaker, and cloud tops reach higher. Nevertheless, the overall vertical structure of the cloud layer is surprisingly robust across resolutions. In a warmer climate, cloud cover reduces, alone constituting a positive shortwave cloud feedback: the strength correlates with the amount of base-state cloud fraction and thus is stronger at coarser resolutions. Cloud thickening, resulting from more water vapour availability for condensation in a warmer climate, acts as a compensating feedback, but unlike the cloud cover reduction it is largely resolution independent. Therefore, refining the resolution leads to convergence to a near-zero shallow cumulus feedback. This dependence holds in experiments with enhanced realism including precipitation processes or warming along a moist adiabat instead of uniform warming. Insofar as these findings carry over to other models, they suggest that storm-resolving models may exaggerate the trade wind cumulus cloud feedback.

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Heuristic estimation of low-level cloud fraction over the globe based on a decoupling parameterization

Atmospheric Chemistry and Physics ◽

10.5194/acp-19-5635-2019 ◽

2019 ◽

Vol 19 (8) ◽

pp. 5635-5660 ◽

Cited By ~ 2

Author(s):

Sungsu Park ◽

Jihoon Shin

Keyword(s):

General Circulation ◽

Cloud Amount ◽

Cloud Fraction ◽

Spatiotemporal Variation ◽

Interannual Variations ◽

Marine Stratocumulus ◽

Near Surface ◽

Low Level ◽

Inversion Strength ◽

Lifting Condensation Level

Abstract. Based on the decoupling parameterization of the cloud-topped planetary boundary layer, a simple equation is derived to compute the inversion height. In combination with the lifting condensation level and the amount of water vapor in near-surface air, we propose a low-level cloud suppression parameter (LCS) and estimated low-level cloud fraction (ELF), as new proxies for the analysis of the spatiotemporal variation of the global low-level cloud amount (LCA). Individual surface and upper-air observations are used to compute LCS and ELF as well as lower-tropospheric stability (LTS), estimated inversion strength (EIS), and estimated cloud-top entrainment index (ECTEI), three proxies for LCA that have been widely used in previous studies. The spatiotemporal correlations between these proxies and surface-observed LCA were analyzed. Over the subtropical marine stratocumulus deck, both LTS and EIS diagnose seasonal–interannual variations of LCA well. However, their use as a global proxy for LCA is limited due to their weaker and inconsistent relationship with LCA over land. EIS is anti-correlated with the decoupling strength more strongly than it is correlated with the inversion strength. Compared with LTS and EIS, ELF and LCS better diagnose temporal variations of LCA, not only over the marine stratocumulus deck but also in other regions. However, all proxies have a weakness in diagnosing interannual variations of LCA in several subtropical stratocumulus decks. In the analysis using all data, ELF achieves the best performance in diagnosing spatiotemporal variation of LCA, explaining about 60 % of the spatial–seasonal–interannual variance of the seasonal LCA over the globe, which is a much larger percentage than those explained by LTS (2 %) and EIS (4 %). Our study implies that accurate prediction of inversion base height and lifting condensation level is a key factor necessary for successful simulation of global low-level clouds in general circulation models (GCMs). Strong spatiotemporal correlation between ELF (or LCS) and LCA identified in our study can be used to evaluate the performance of GCMs, identify the source of inaccurate simulation of LCA, and better understand climate sensitivity.

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What controls the formation of nocturnal low-level stratus clouds over southern West Africa during the monsoon season?

10.5194/acp-2019-537 ◽

2019 ◽

Cited By ~ 1

Author(s):

Karmen Babić ◽

Norbert Kalthoff ◽

Bianca Adler ◽

Julian F. Quinting ◽

Fabienne Lohou ◽

...

Keyword(s):

Boundary Layer ◽

West Africa ◽

Climate Models ◽

Marine Boundary Layer ◽

Monsoon Season ◽

Onset Time ◽

Data Set ◽

Cold Air ◽

Low Level ◽

Stratus Clouds

Abstract. Nocturnal low-level stratus clouds (LLC) are frequently observed in the atmospheric boundary layer (ABL) over southern West Africa (SWA) during the summer monsoon season. Considering the effect these clouds have on the surface energy and radiation budgets as well as on the diurnal cycle of the ABL, they are undoubtedly important for the regional climate. However, an adequate representation of LLC in the state–of–the–art weather and climate models is still a challenge, which is largely due to the lack of high-quality observations in this region. In several recent studies, a unique and comprehensive data set collected in summer 2016 during the DACCIWA (Dynamics-Aerosol-Cloud-Chemistry Interactions in West Africa) ground-based field campaign was used for the first observational analyses of the parameters and physical processes relevant for the LLC formation over SWA. However, occasionally stratus-free nights occur during the monsoon season as well. Using observations and ERA5 reanalysis, we investigate differences in the boundary layer conditions during 6 stratus-free and 20 stratus nights observed during the DACCIWA campaign. Our results suggest that the interplay between three major mechanisms is crucial for the formation of LLC during the monsoon season: (i) the onset time and strength of the nocturnal low-level jet (NLLJ), (ii) horizontal cold-air advection and (iii) background moisture level. Namely, weaker or later onset of NLLJ leads to reduced contribution from horizontal cold-air advection. This in turn results in a weaker cooling and thus saturation is not reached. Such deviation in the dynamics of NLLJ is related to the arrival of cold air mass propagating northwards from the coast called Gulf of Guinea maritime inflow. Additionally, stratus-free nights occur when the intrusions of dry air masses, originating from e.g. central or south Africa, reduce the background moisture over the large parts of SWA. Based on the backward trajectories analysis, another possible reason for clear nights is descending of air originating from drier levels above the marine boundary layer.

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An overview of the diurnal cycle of the atmospheric boundary layer during the West African monsoon season: results from the 2016 observational campaign

Atmospheric Chemistry and Physics ◽

10.5194/acp-18-2913-2018 ◽

2018 ◽

Vol 18 (4) ◽

pp. 2913-2928 ◽

Cited By ~ 30

Author(s):

Norbert Kalthoff ◽

Fabienne Lohou ◽

Barbara Brooks ◽

Gbenga Jegede ◽

Bianca Adler ◽

...

Keyword(s):

Boundary Layer ◽

West Africa ◽

Atmospheric Boundary Layer ◽

Radiation Budget ◽

Cloud Base ◽

Data Set ◽

Near Surface ◽

Low Level ◽

Synoptic Conditions ◽

Low Level Jet

Abstract. A ground-based field campaign was conducted in southern West Africa from mid-June to the end of July 2016 within the framework of the Dynamics–Aerosol–Chemistry–Cloud Interactions in West Africa (DACCIWA) project. It aimed to provide a high-quality comprehensive data set for process studies, in particular of interactions between low-level clouds (LLCs) and boundary-layer conditions. In this region missing observations are still a major issue. During the campaign, extensive remote sensing and in situ measurements were conducted at three supersites: Kumasi (Ghana), Savè (Benin) and Ile-Ife (Nigeria). Daily radiosoundings were performed at 06:00 UTC, and 15 intensive observation periods (IOPs) were performed during which additional radiosondes were launched, and remotely piloted aerial systems were operated. Extended stratiform LLCs form frequently in southern West Africa during the nighttime and persist long into the following day. They affect the radiation budget and hence the evolution of the atmospheric boundary layer and regional climate. The relevant parameters and processes governing the formation and dissolution of the LLCs are still not fully understood. This paper gives an overview of the diurnal cycles of the energy-balance components, near-surface temperature, humidity, wind speed and direction as well as of the conditions (LLCs, low-level jet) in the boundary layer at the supersites and relates them to synoptic-scale conditions (monsoon layer, harmattan layer, African easterly jet, tropospheric stratification) in the DACCIWA operational area. The characteristics of LLCs vary considerably from day to day, including a few almost cloud-free nights. During cloudy nights we found large differences in the LLCs' formation and dissolution times as well as in the cloud-base height. The differences exist at individual sites and also between the sites. The synoptic conditions are characterized by a monsoon layer with south-westerly winds, on average about 1.9 km deep, and easterly winds above; the depth and strength of the monsoon flow show great day-to-day variability. Within the monsoon layer, a nocturnal low-level jet forms in approximately the same layer as the LLC. Its strength and duration is highly variable from night to night. This unique data set will allow us to test some new hypotheses about the processes involved in the development of LLCs and their interaction with the boundary layer and can also be used for model evaluation.

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Low Level Cloud and Dynamical Features within the Southern West African Monsoon

10.5194/acp-2018-1149 ◽

2018 ◽

Cited By ~ 3

Author(s):

Cheikh Dione ◽

Fabienne Lohou ◽

Marie Lothon ◽

Bianca Adler ◽

Karmen Babić ◽

...

Keyword(s):

West Africa ◽

Onset Time ◽

Boreal Summer ◽

Cloud Base ◽

Time Range ◽

Low Level ◽

Stratus Clouds ◽

Monsoon Flow ◽

Low Level Jet ◽

Core Height

Abstract. During the Boreal summer, the monsoon season that takes place in West Africa is accompanied by low stratus clouds over land, that stretch from the Guinean coast several hundred kilometers inland. These clouds form during the night and dissipate during the following day. Inherently linked with the diurnal cycle of monsoon flow, those clouds still remain poorly documented and understood.Moreover, numerical climate and weather models lack fine quantitative documentation of cloud macrophysical characteristics and the dynamical and thermodynamical structures occupying the lowest troposphere. The Dynamics–Aerosol–Chemistry–Cloud Interactions in West Africa (DACCIWA) field experiment, which took place in summer 2016, addresses this knowledge gap. Low level atmospheric dynamics and low-level cloud macrophysical properties are analyzed using in-situ and remote sensing continuous measurements collected from 20 June to 30 July at Savè, Benin, roughly 180 km from the coast. The macrophysical characteristics of the stratus clouds are deduced from a ceilometer, an infrared cloud camera and cloud radar. Onset times, evolution, dissipation times, base heights and thickness are evaluated. The Data from a UHF (Ultra High Frequency) wind profiler, a microwave radiometer and an energy balance station are used to quantify the occurrence and characteristics of the monsoon flow, the nocturnal low-level jet and the cold air mass inflow propagating northwards from the coast of the Gulf of Guinea. The results show that these dynamical structures are very regularly observed during the entire 41-day documented period. Monsoon flow is observed 100 % of the time. The so-called maritime inflow and the nocturnal low level jet are also systematic features in this area. According to monsoon flow conditions, the maritime inflow reaches Savè around 18:00–19:00 UTC on average: this timing is correlated with the strength of the monsoon flow. This time of arrival is close to the time range of the nocturnal low level jet settlement. As a result, these phenomena are difficult to distinguish at the Savè site. The low level jet occurs every night, except during rain events, and is associated 65 % of the time with low stratus clouds. Stratus cloud form between 22:00 UTC and 06:00 UTC at an elevation close to the nocturnal low level jet core height. The cloud base height, 310 ± 30 m above ground level (a.g.l.) is rather stationary during the night and remains below the jet core height. The cloud top height, at 640 ± 100 m a.g.l., is typically found above the jet core. The nocturnal low level jet, low level clouds, monsoon flow and maritime inflow reveal significant day-to-day variability during the summer. Distributions of strength, depth, onset time, break up time, etc. are quantified here.

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Modelling atmospheric structure, cloud and their response to CCN in the central Arctic: ASCOS case studies

Atmospheric Chemistry and Physics ◽

10.5194/acp-12-3419-2012 ◽

2012 ◽

Vol 12 (7) ◽

pp. 3419-3435 ◽

Cited By ~ 32

Author(s):

C. E. Birch ◽

I. M. Brooks ◽

M. Tjernström ◽

M. D. Shupe ◽

T. Mauritsen ◽

...

Keyword(s):

Surface Temperature ◽

Cloud Cover ◽

Cloud Condensation Nuclei ◽

Late Summer ◽

Surface Radiation ◽

The Arctic ◽

Temperature Structure ◽

Near Surface ◽

Low Level ◽

Arctic Summer

Abstract. Observations made during late summer in the central Arctic Ocean, as part of the Arctic Summer Cloud Ocean Study (ASCOS), are used to evaluate cloud and vertical temperature structure in the Met Office Unified Model (MetUM). The observation period can be split into 5 regimes; the first two regimes had a large number of frontal systems, which were associated with deep cloud. During the remainder of the campaign a layer of low-level cloud occurred, typical of central Arctic summer conditions, along with two periods of greatly reduced cloud cover. The short-range operational NWP forecasts could not accurately reproduce the observed variations in near-surface temperature. A major source of this error was found to be the temperature-dependant surface albedo parameterisation scheme. The model reproduced the low-level cloud layer, though it was too thin, too shallow, and in a boundary-layer that was too frequently well-mixed. The model was also unable to reproduce the observed periods of reduced cloud cover, which were associated with very low cloud condensation nuclei (CCN) concentrations (<1 cm−3). As with most global NWP models, the MetUM does not have a prognostic aerosol/cloud scheme but uses a constant CCN concentration of 100 cm−3 over all marine environments. It is therefore unable to represent the low CCN number concentrations and the rapid variations in concentration frequently observed in the central Arctic during late summer. Experiments with a single-column model configuration of the MetUM show that reducing model CCN number concentrations to observed values reduces the amount of cloud, increases the near-surface stability, and improves the representation of both the surface radiation fluxes and the surface temperature. The model is shown to be sensitive to CCN only when number concentrations are less than 10–20 cm−3.

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