A Flux Method for the Numerical Solution of the Stochastic Collection Equation

Bott, Andreas

doi:10.1175/1520-0469(1998)055<2284:afmftn>2.0.co;2

Cited by 152 publications

(180 citation statements)

References 12 publications

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“…This increase in mean droplet size may promote the development of precipitable droplets by increased collision and coalescence efficiency and the size calculated for 200 m uplift is consistent with cloud-top mean droplet sizes observed in drizzling marine Sc (e.g. Bott, 1998). This leads to the suggestion that the observed gravity waves may not always be expected to induce drizzle and only those lifting cloud by the upper range of that observed may lead to precipitation.…”

Section: Conceptual Model and Microphysical Process Interactionssupporting

confidence: 83%

Gravity‐wave‐induced perturbations in marine stratocumulus

Allen

Vaughan

Toniazzo

et al. 2012

Quart J Royal Meteoro Soc

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We discuss the role of atmospheric gravity waves in modulating cloud radiative and dynamical properties over the southeast Pacific. Satellite imagery and satelliteretrieved cloud properties during October 2008 illustrate three distinct episodes of horizontal propagation of gravity wave trains across the large-scale stratocumulus (Sc) cloud deck capping the local marine boundary layer. In one period, 7-9 October 2008, the waves modulated cloud-top-height by up to 400 m peak-to-trough, propagating perpendicular to the synoptic boundary layer flow with phase speed 15.3 m s −1 , period ∼1 h and horizontal wavelength 55 km. The gravity waves were observed to be non-dispersive. These waves were first evident in the cloud deck near 30• S, 85• W during a 24 h period beginning at midday on 7 October 2008, and propagated northeastward toward the Peruvian coast for the following 48 h. During this time they induced both reversible and non-reversible changes in cloud-radiative and cloud-dynamic properties, such that areas of clear sky developed in the troughs of passing wave-fronts. These pockets of open cells persisted long after the passage of the gravity waves, advecting northwestward with the background wind. Using the analysis fields of the European Centre for Medium-Range Weather Forecasts in conjunction with infrared and microwave satellite imagery, we show that these gravity waves emerged from a disturbed subtropical jet stream. The radiant of the waves was coincident in all cases with centres of large negative residuals in nonlinear balance, suggesting that geostrophic readjustment of sharply divergent flows associated with the disturbed jet provided a source for the wave energy. Conversely, gravity waves were not observed in more quiescent jet conditions. This case study highlights the important and irreversible effects that gravity waves propagating in the troposphere can have on cloud radiative properties (and hence surface radiation budgets) over a very wide area. It also highlights the importance of synoptic influence on Sc-covered marine boundary layers.

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Section: Conceptual Model and Microphysical Process Interactionssupporting

confidence: 83%

Gravity‐wave‐induced perturbations in marine stratocumulus

Allen

Vaughan

Toniazzo

et al. 2012

Quart J Royal Meteoro Soc

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“…Moreover, due to the large difference in timescales between the collection process and vapor deposition, we separate the collection calculations from the vapor deposition. The former occurs over 10s of minutes (e.g., Tzivion et al, 1987;Bott, 1998) while the latter occurs over the course of a few seconds (e.g., Chuang et al, 1997;Pruppacher and Klett, 1997) Another reason for doing so is that the collection process does not affect the ambient water vapor mixing ratio (note that the equilibrium vapor pressure will change slightly since larger drops require less water vapor in the gas phase to maintain equilibrium), temperature, or supersaturation directly. The calculations are performed as follows.…”

Section: Collision-coalescence and Aerosol Scavengingmentioning

confidence: 99%

“…The calculations are performed as follows. For numerical implementation, we employ the flux method of Bott (1998). (Bott, 2000, proposed a method by which the 2-D collection problem can be reduced to a 1-D problem and then extrapolated back to 2-D. We find that it is best to apply the 1-D method of Bott, 1998, in two-dimensions to minimize the loss of information when the problem is simplified to a 1-D collection problem.)…”

Section: Collision-coalescence and Aerosol Scavengingmentioning

confidence: 99%

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A continuous spectral aerosol-droplet microphysics model

Lebo

Seinfeld

2011

Atmos. Chem. Phys.

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Abstract.A two-dimensional (2-D) continuous spectral aerosol-droplet microphysics model is presented and implemented into the Weather Research and Forecasting (WRF) model for large-eddy simulations (LES) of warm clouds. Activation and regeneration of aerosols are treated explicitly in the calculation of condensation/evaporation. The model includes a 2-D spectrum that encompasses wet aerosol particles (i.e., haze droplets), cloud droplets, and drizzle droplets in a continuous and consistent manner and allows for the explicit tracking of aerosol size within cloud droplets due to collision-coalescence. The system of differential equations describing condensation/evaporation (i.e., mass conservation and energy conservation) is solved simultaneously within each grid cell. The model is demonstrated by simulating a marine stratocumulus deck for two different aerosol loadings (100 and 500 cm −3 ), and comparison with the more traditional microphysics modeling approaches (both 1-D bin and bulk schemes) is evaluated. The simulations suggest that in a 1-D bin microphysics scheme, without regeneration, too few particles are produced and hence the mode of the droplet size spectrum occurs at a larger size relative to the 2-D bin model results. Moreover, with regeneration, the 1-D scheme produces too many small droplets and thus shifts the mode toward smaller sizes. These large shifts in the droplet size distribution can potentially have significant effects on the efficiency of the collision-coalescence process, fall speeds, and ultimately precipitation.

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“…The continuous SCE is discretized and numerically solved by a linear flux method as outlined by Bott (1998). This method is mass conservative, introduces minimal numerical diffusion, and is highly computationally efficient (Kerkweg et al, 2003;Pinsky and Khain, 2002).…”

Section: Condensation Growth With Entrainmentmentioning

confidence: 99%

Understanding aerosol-cloud interactions in the development of orographic cumulus congestus during IPHEx

Duan

Petters

Barros

2017

Preprint

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Abstract.A new cloud parcel model (CPM) including activation, condensation, collision-coalescence, and lateral entrainment processes is presented here to investigate aerosol-cloud interactions (ACI) in cumulus development prior to rainfall onset. The CPM was employed along with ground based radar and surface aerosol measurements to predict the vertical structure of cloud formation at early stages and evaluated against airborne observations of cloud microphysics and 10 thermodynamic conditions during the Integrated Precipitation and Hydrology Experiment (IPHEx) over the Southern Appalachian Mountains. Further, the CPM was applied to explore the space of ACI physical parameters controlling cumulus congestus growth not available from measurements, and to examine how variations in aerosol properties and microphysical processes influence the evolution and thermodynamic state of clouds over complex terrain via sensitivity analysis. Modelling results indicate that aerosol-cloud droplet number concentration (CDNC) closure is achieved optimally to ~ 1.3% of the 15 observations for condensation coefficient ( ) = 0.01 and within 5% for 0.01< < 0.015, and the corresponding spectra in the predictions are in good agreement with IPHEx aircraft observations around the same altitude. This is in contrast with larger closure errors and high values reported in previous studies assuming adiabatic conditions. Entrainment is shown to govern the vertical development of clouds and the change of droplet numbers with height, and the sensitivity analysis suggests that entrainment strength and condensation process are mutually compensating to attain aerosol-CDNC closure. 20Simulated CDNC also exhibits high sensitivity to variations in initial aerosol concentration at cloud base, but weak sensitivity to aerosol hygroscopicity. Exploratory multiple-parcel simulations capture realistic time-scales of vertical development of cumulus congestus (deeper clouds and faster droplet growth). These findings provide new insights into determinant factors of mid-day cumulus congestus formation that can explain a large fraction of warm season rainfall in mountainous regions. 25

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A Flux Method for the Numerical Solution of the Stochastic Collection Equation

Cited by 152 publications

References 12 publications

Gravity‐wave‐induced perturbations in marine stratocumulus

Gravity‐wave‐induced perturbations in marine stratocumulus

A continuous spectral aerosol-droplet microphysics model

Understanding aerosol-cloud interactions in the development of orographic cumulus congestus during IPHEx

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