Dynamic Entrainment Research Articles

Dynamic entrainment: A deep learning and data-driven process approach for synchronization in the Hodgkin-Huxley model.

Resonance and synchronized rhythm are significant phenomena observed in dynamical systems in nature, particularly in biological contexts. These phenomena can either enhance or disrupt system functioning. Numerous examples illustrate the necessity for organs within the human body to maintain their rhythmic patterns for proper operation. For instance, in the brain, synchronized or desynchronized electrical activities can contribute to neurodegenerative conditions like Huntington's disease. In this paper, we utilize the well-established Hodgkin-Huxley (HH) model, which describes the propagation of action potentials in neurons through conductance-based mechanisms. Employing a "data-driven" approach alongside the outputs of the HH model, we introduce an innovative technique termed "dynamic entrainment." This technique leverages deep learning methodologies to dynamically sustain the system within its entrainment regime. Our findings show that the results of the dynamic entrainment technique match with the outputs of the mechanistic (HH) model.

Live music stimulates the affective brain and emotionally entrains listeners in real time

Music is powerful in conveying emotions and triggering affective brain mechanisms. Affective brain responses in previous studies were however rather inconsistent, potentially because of the non-adaptive nature of recorded music used so far. Live music instead can be dynamic and adaptive and is often modulated in response to audience feedback to maximize emotional responses in listeners. Here, we introduce a setup for studying emotional responses to live music in a closed-loop neurofeedback setup. This setup linked live performances by musicians to neural processing in listeners, with listeners' amygdala activity was displayed to musicians in real time. Brain activity was measured using functional MRI, and especially amygdala activity was quantified in real time for the neurofeedback signal. Live pleasant and unpleasant piano music performed in response to amygdala neurofeedback from listeners was acoustically very different from comparable recorded music and elicited significantly higher and more consistent amygdala activity. Higher activity was also found in a broader neural network for emotion processing during live compared to recorded music. This finding included observations of the predominance for aversive coding in the ventral striatum while listening to unpleasant music, and involvement of the thalamic pulvinar nucleus, presumably for regulating attentional and cortical flow mechanisms. Live music also stimulated a dense functional neural network with the amygdala as a central node influencing other brain systems. Finally, only live music showed a strong and positive coupling between features of the musical performance and brain activity in listeners pointing to real-time and dynamic entrainment processes.

An Analysis of the Impact of Vertical Wind Shear on Convection Initiation Using Large-Eddy Simulations: Importance of Wake Entrainment

Abstract The initiation of thunderstorms in environments characterized by strong wind shear presents a forecast challenge because of the complexities of the interactions between growing cumulus clouds and wind shear. Thunderstorms that develop in such environments are often capable of producing high-impact hazards, highlighting the importance of convection initiation in sheared environments. Although recent research has greatly improved understanding of the structure and evolution of rising thermals in unsheared environments, there remains uncertainty in how wind shear influences the convection initiation process. Two large-eddy simulations (75-m horizontal grid spacing) were performed to study this problem. Convection initiation attempts are forced in the simulations through prescribed surface heat fluxes (the initial boundary layers are statistically horizontally homogeneous and quasi–steady state but contain turbulent eddies as a result of random initial temperature perturbations). The only difference between the two simulations is the presence or absence of wind shear above 2 km. Important differences in the entrainment patterns are present between sheared and unsheared growing cumulus clouds. As found in previous research, the overturning circulation associated with rising thermals drives dynamic entrainment in the unsheared clouds. However, in sheared clouds, wake entrainment resulting from the tilting of environmental vorticity is an important dynamic entrainment pathway. This result has implications for both the structure of sheared growing cumulus clouds and for convection initiation in sheared environments. Significance Statement Forecasts of thunderstorm hazards such as tornadoes, hail, and strong winds, require the accurate prediction of when and where thunderstorms form. Unfortunately, predicting thunderstorm formation is not easy, as there are a lot of different factors to consider. One such factor is environmental vertical wind shear, which describes how winds change speed and direction with height. The purpose of this study is to better understand how wind shear impacts developing clouds. Our results demonstrate a specific mechanism, called “wake entrainment,” through which wind shear can weaken developing clouds and potentially prevent them from becoming strong thunderstorms entirely. Understanding this mechanism may be useful for thunderstorm prediction in environments characterized by wind shear.

Characteristics and dynamic analysis of the February 2021 long-runout disaster chain triggered by massive rock and ice avalanche at Chamoli, Indian Himalaya

A massive rock and ice avalanche occurred on the western slope of the Ronti Gad valley in the northern part of Chamoli, Indian Himalaya, on 7 February 7, 2021. The avalanche on the high mountain slope at an elevation of 5600 m above sea level triggered a long runout disaster chain, including rock mass avalanche, debris avalanche, and flood. The disaster chain had a horizontal travel distance of larger than 17,600 m and an elevation difference of 4300 m. In this study, the disaster characteristics and dynamic process were analyzed by multitemporal satellite imagery. The results show that the massive rock and ice avalanche was caused by four large expanding discontinuity planes. The disaster chain was divided into five zones by satellite images and field observation, including source zone, transition zone, dynamic entrainment zone, flow deposition zone, and flood zone. The entrainment effect and melting water were recognized as the main causes of the long-runout distance. Based on the seismic wave records and field videos, the time progress of the disaster was analyzed and the velocity of frontal debris at different stages was calculated. The total analyzed disaster duration was 1247 s, and the frontal debris velocity colliding with the second hydropower station was approximately 23 m/s. This study also carried out the numerical simulation of the disaster by rapid mass movement simulation (RAMMS). The numerical results reproduced the dynamic process of the debris avalanche, and the mechanism of long-runout avalanche was further verified by parametric study. Furthermore, this study discussed the potential causes of disaster and flood and the roles of satellite images and seismic networks in the monitoring and early-warning.

Characteristics of a pre-monsoon dryline atmospheric boundary layer over the rain shadow region: A case study

A dryline is the zone of distinct moisture gradient separating warm, moist, and hot, dry air masses. It is usually associated with mesoscale phenomena and plays a significant role in atmospheric boundary layer (ABL) dynamics including initiation of convection/thunderstorms. In the tropical Indian region, these dryline conditions are normally associated with the pre-monsoon season. In the present study, dryline characteristics over a rain shadow region in the Indian subcontinent were investigated utilizing observations and Weather Research and Forecasting (WRF) model from 28 to 30 May 2019. Based upon Wind Profiler Radar and MicroWave Radiometer Profiler measurements, the ABL characteristics were investigated. Interestingly, the ABL height was found to evolve up to 5 km with the horizontal wind vectors oscillating between north-westerly and north-easterly flow. During the intense ABL deepening, stronger downdraft cores were observed in comparison with the updraft cores. The stronger downdrafts entrained free-tropospheric dry air thereby further deepening the ABL. Based upon the entrainment velocity estimates at the ABL top and the variations in potential temperature, the dynamic entrainment fluxes were estimated and further implemented for evaluating two slab models to recreate the ABL growth. With this analysis, we demonstrate the significant contribution of entrainment fluxes on ABL growth during dryline conditions.

Roton instabilities in the superfluid outer core of neutron stars

We study the superfluid dynamics of the outer core of neutron stars by means of a generalized hydrodynamic model made of a neutronic superfluid and a protonic superconductor, coupled by both the dynamic entrainment and the Skyrme SLy4 nucleon-nucleon interactions. The resulting nonlinear equations of motion are probed in the search for dynamical instabilities triggered by the relative motion of the superfluids that could be of potential relevance to observational features of neutron stars. Through linear analysis, the origin and expected growth of the instabilities is explored for varying nuclear-matter density. Differently from previous findings, the dispersion of linear excitations in our model shows rotonic structures below the pair-breaking energy threshold, which lies at the origin of the dynamical instabilities and could eventually lead to emergent vorticity along with modulations of the superfluid density.

A progressive entrainment runout model for debris flow analysis and its application

A progressive entrainment model has been incorporated into an energy-based runout model to calculate the kinematic characteristics of debris flow. The progressive entrainment model considers both rolling and sliding motions of erodible material. To study the effect of the controlling parameters in the entrainment model, sensitivity analyses have been carried out by varying model parameters such as the internal friction angle of the debris, the basal friction angle of the channel, the turbulent flow coefficient, and the mean value of the probabilistic density function (PDF) for the resting angle. The results are evaluated by calculating the change of the maximum entrainment rate, the maximum frontal velocity, the final total volume, the longitudinal length of deposition, the maximum debris flow height, and the runout distance of the debris. The progressive entrainment runout model is sensitive to the characteristic particle size, basal friction angle and turbulent coefficient. Measurements from the 1990 Tsingshan debris flow, Hong Kong, China, are used to validate the model. Velocities at different channel sections estimated using the super-elevation method and entrainment depth are used to evaluate the simulation results. Comparing the results between simulated and observed maximum velocity and entrainment depth indicate that the progressive entrainment model together with the runout model can capture the erosion characteristics of the granular material. The results are also compared with that using a dynamic entrainment model. The results demonstrate that the progressive entrainment model provides a more realistic calculation of entrainment for this case compared with the dynamic entrainment model.

An Analytic Description of the Structure and Evolution of Growing Deep Cumulus Updrafts

Abstract New theoretical analytic expressions are derived for the evolution of a passive scalar, buoyancy, and vertical velocity in growing, entraining moist deep convective updrafts. These expressions are a function of updraft radius, height, convective available potential energy (CAPE), and environmental relative humidity RH. They are quantitatively consistent with idealized three-dimensional moist updraft simulations with varying updraft sizes and in environments with differing RH. In particular, the analytic expressions capture the rapid decrease of buoyancy with height due to entrainment for narrow updrafts in a dry environment despite large CAPE. In contrast to the standard entraining-plume model, the theoretical expressions also describe the effects of engulfment of environmental air between the level of free convection (LFC) and height of maximum buoyancy (HMB) required by mass continuity to balance upward acceleration of updraft air (i.e., dynamic entrainment). This organized inflow sharpens horizontal gradients, thereby enhancing smaller-scale lateral turbulent mixing below the HMB. For narrow updrafts in a dry environment, this enhanced mixing leads to a negatively buoyant region between the LFC and HMB, effectively cutting off the region of positive buoyancy at the HMB from below so that the updraft structure resembles a rising thermal rather than a plume. Thus, it is proposed that a transition from plume-like to thermal-like structure is driven by dynamic entrainment and depends on updraft width (relative to height) and environmental RH. These results help to bridge the entraining-plume and rising-thermal conceptual models of moist convection.

Temperature–Moisture Dependence of the Deep Convective Transition as a Constraint on Entrainment in Climate Models

AbstractProperties of the transition to strong deep convection, as previously observed in satellite precipitation statistics, are analyzed using parcel stability computations and a convective plume velocity equation. A set of alternative entrainment assumptions yields very different characteristics of the deep convection onset boundary (here measured by conditional instability and plume vertical velocity) in a bulk temperature–water vapor thermodynamic plane. In observations the threshold value of column water vapor above which there is a rapid increase in precipitation, referred to as the critical value, increases with temperature, but not as quickly as column saturation, and this can be matched only for cases with sufficiently strong entrainment. This corroborates the earlier hypothesis that entraining plumes can explain this feature seen in observations, and it places bounds on the lower-tropospheric entrainment. Examination of a simple interactive entrainment scheme in which a minimum turbulent entrainment is enhanced by a dynamic entrainment (associated with buoyancy-induced vertical acceleration) shows that the deep convection onset curve is governed by the prescribed minimum entrainment. Results from a 0.5° resolution version of the Community Climate System Model, whose convective parameterization includes substantial entrainment, yield a reasonable match to satellite observations in several respects. Temperature–water vapor dependence is seen to agree well with the plume calculations and with offline simulations performed using the convection scheme of the model. These findings suggest that the convective transition characteristics, including the onset curve in the temperature–water vapor plane, can provide a substantial constraint for entrainment assumptions used in climate model deep convective parameterizations.

Walking Is Not Like Reaching: Evidence from Periodic Mechanical Perturbations

The control architecture underlying human reaching has been established, at least in broad outline. However, despite extensive research, the control architecture underlying human locomotion remains unclear. Some studies show evidence of high-level control focused on lower-limb trajectories; others suggest that nonlinear oscillators such as lower-level rhythmic central pattern generators (CPGs) play a significant role. To resolve this ambiguity, we reasoned that if a nonlinear oscillator contributes to locomotor control, human walking should exhibit dynamic entrainment to periodic mechanical perturbation; entrainment is a distinctive behavior of nonlinear oscillators. Here we present the first behavioral evidence that nonlinear neuro-mechanical oscillators contribute to the production of human walking, albeit weakly. As unimpaired human subjects walked at constant speed, we applied periodic torque pulses to the ankle at periods different from their preferred cadence. The gait period of 18 out of 19 subjects entrained to this mechanical perturbation, converging to match that of the perturbation. Significantly, entrainment occurred only if the perturbation period was close to subjects' preferred walking cadence: it exhibited a narrow basin of entrainment. Further, regardless of the phase within the walking cycle at which perturbation was initiated, subjects' gait synchronized or phase-locked with the mechanical perturbation at a phase of gait where it assisted propulsion. These results were affected neither by auditory feedback nor by a distractor task. However, the convergence to phase-locking was slow. These characteristics indicate that nonlinear neuro-mechanical oscillators make at most a modest contribution to human walking. Our results suggest that human locomotor control is not organized as in reaching to meet a predominantly kinematic specification, but is hierarchically organized with a semi-autonomous peripheral oscillator operating under episodic supervisory control.

The effects of water velocity and sediment size on Acroneuria abnormis (Plecoptera: Perlidae) entrainment

We investigated the roles that velocity and substrate size play in the drift of stonefly larvae (Acroneuria abnormis). Acroneuria were introduced into an experimental flume containing homogeneous substrates of different size (small gravel, large gravel, or cobble), or a mixture of various substrate sizes. For each substrate Acroneuria were subjected to three different velocities (0.3, 0.6 and 0.9 ms−1) corresponding to base flow conditions in real streams, and the number of individuals entrained into the water column was measured. Entrainment was nearly two times higher from the smallest substrates than larger substrates and the heterogeneous mixture of substrate sizes. Higher entrainment from the small particles appeared to result from lower availability of refugia among particles and movement of particles under the higher water velocities. Entrainment generally increased with increasing discharge on small and large, but not intermediate-sized, particles. Our results suggest there may be dynamic Acroneuria entrainment under low flow conditions in streams.

Numerical modelling of the entrainment of particles in inviscid supersonic flow

The interaction between particles situated in close proximity and moving at supersonic speeds is investigated computationally. The simplest case of the motion of a single particle travelling behind a lead particle is used to elucidate the role of aerodynamic forces in the motion of a group of particles. The effect of the following parameters on the drag and lift forces acting on each of two particles of equal diameter in proximity is investigated: the free-stream Mach number, and the axial and lateral displacements of the trailing particle. The two-dimensional flow field is numerically simulated using an unsteady Euler CFD code to find the steady-state drag and lift coefficients for both particles. Three static zones of aerodynamic influence in the wake of the lead particle are identified, which are denoted as the entrainment, lateral attraction, and ejection zones. A non-dimensional representation of the zones of influence is given. It is shown that the dynamic entrainment of particles can occur even when the path of the trailing particle originates outside the entrainment and lateral attraction zones.

Synchronization of Ion Exchangers by an Oscillating Electric Field: Theory

Can we physically manipulate functions of membrane proteins, such as ion exchangers, especially the active transporters? This is a fascinating question which has attracted many scientists. Recently, we developed a new technique that we call synchronization modulation with which we realized significant (many-folds) activation of Na/K pumps by a well-designed oscillating electric field. In this technique, we consider activation of the pump molecules as a dynamic entrainment procedure, where individual pumps are first entrained to run at the same pumping rate and phase as the oscillating electric field and then the two transports are electrically facilitated separately and alternately by gradually increasing the field oscillating frequency. The procedure consists of two steps: synchronization and modulation. In this paper, we discuss the underlying mechanism involved in the first step: synchronization of the pump molecules.

Dust emissions from undisturbed and disturbed supply‐limited desert surfaces

Aeolian sediment transport systems have been treated frequently as transport limited, where transport is governed by the force of the wind, or as supply limited, where sediment transport is controlled by the availability of surface grains. Although many arid environments are dominated by supply‐limited surfaces, almost all available dust emission and sand transport models are restricted to transport‐limited conditions. To examine the emission of PM10 (particulate matter ≤10 μm aerodynamic diameter) and horizontal sand transport from supply‐limited environments, a series of wind tunnel tests were conducted in the Mojave Desert, California. In situ testing was conducted with an open‐floored, portable wind tunnel (12 × 1 × 0.75 m) on a variety of natural soils having disturbed and undisturbed surface conditions. Results indicate that for these supply‐limited environments, PM10 emissions are primarily driven by the aerodynamic resuspension of loose surface material as opposed to the dynamic entrainment mechanisms associated with saltating grains. Emission rates were directly influenced by wind shear and mechanical disturbance and indirectly influenced by soil texture. In addition, disturbance of the surface was found to increase the potential for multiple emission events, which may affect the temporal accumulation of atmospheric dust.

Synchronous speech and speech rate

Synchronously read speech has shown to reduce a high degree of speaker variability of reading exhibited by speakers in laboratory recording; e.g., pause placement and duration, and speech rate. However, quantitative analysis of speech rate has rarely been found in studies on synchronous speech. This study examines Mandarin Chinese (2 dialects from Taiwan and Shanghai), which is a syllable‐time language and thus expected to exhibit a relatively stable speech rate, in both read‐alone and read‐together speech. Consistency and variability of speech rate are compared in both reading types across repetitions within a subject, across subjects, and across dialects. The results show that speech rate is more stable in read‐together than in read‐alone speech, and that speech rate in synchronous reading falls on a constant value of speech rate rather than on the average between the speakers' rates in pair. This global pattern is consistent across dialects, and stylized local variation of speech rate over prosodic units (Intonational phrase) is also observed unique to each dialect. We discuss how timing in synchronous speech cannot be accounted for only by dynamic entrainment of speakers with different speech rates and how there should also be rhythmic information shared by speakers of a language.

Membrane Potential Hyperpolarization in Mammalian Cardiac Cells by Synchronization Modulation of Na/K Pumps

In previously reported work, we developed a new technique, synchronization modulation, to electrically activate Na/K pump molecules. The fundamental mechanism involved in this technique is a dynamic entrainment procedure of the pump molecules, carried out in a stepwise pattern. The entrainment procedure consists of two steps: synchronization and modulation. We theoretically predicted that the pump functions can be activated exponentially as a function of the membrane potential. We have experimentally demonstrated synchronization of the Na/K pump molecules and acceleration of their pumping rates by many fold through use of voltage-clamp techniques, directly monitoring the pump currents. We further applied this technique to intact skeletal muscle fibers from amphibians and found significant effects on the membrane resting potential. Here, we extend our study to intact mammalian cardiomyocytes. We employed a noninvasive confocal microscopic fluorescent imaging technique to monitor electric field-induced changes in ionic concentration gradient and membrane resting potential. Our results further confirm that the well-designed synchronization modulation electric field can effectively accelerate the Na/K pumping rate, increasing the ionic concentration gradient across the cell membrane and hyperpolarizing the membrane resting potential.

SYMPATHETIC RHYTHMS AND NERVOUS INTEGRATION

1. The present review focuses on some of the processes producing rhythms in sympathetic nerves influencing cardiovascular functions and considers their potential relevance to nervous integration. 2. Two mechanisms are considered that may account for rhythmic sympathetic discharges. First, neuronal elements of peripheral or central origin produce rhythmic activity by phasically exciting and/or inhibiting neurons within central sympathetic networks. Second, rhythms arise within central sympathetic networks. Evidence is considered that indicates the operation of both mechanisms; the first in muscle and the second in skin sympathetic vasoconstrictor networks. 3. Sympathetic activity to the rat tail, a model for the nervous control of skin circulation, is regulated by central networks involved in thermoregulation and those associated with fear and arousal. In an anaesthetized preparation, activity displays an apparently autonomous rhythm (T-rhythm; 0.4-1.2 Hz) and the level of activity can be manipulated by regulating core body temperature. This model has been used to study rhythm generation in central sympathetic networks and possible functional relevance. 4. A unique insight provided by the T rhythm, into possible physiological function(s) underlying rhythmic sympathetic discharges is that the activity of single sympathetic post-ganglionic neurons within a population innervating the same target can have different rhythm frequencies. Therefore, the graded and dynamic entrainment of the rhythms by inputs, such as central respiratory drive and/or lung inflation-related afferent activity, can produce graded and dynamic synchronization of sympathetic discharges. The degree of synchronization may influence the efficacy of transmission in a target chain of excitable cells. 5. The T-rhythm may be generated within the spinal cord because the intrathecal application of 5-hydroxytryptamine at the L1 level of the spinal cord of a rat spinalized at T10-T11 produces a T-like rhythm. Thus, induction and modulation of spinal cord oscillators may be mechanisms that influence ganglionic and neuroeffector transmission. 6. The study of sympathetic rhythms may not only further understanding of sympathetic control, but may also inform on the relevance of rhythmic nervous activities in general.

Comparison of Glass Vessels and Plastic Bags for Enclosing Living Plant Parts for Headspace Analysis

Plants release volatile chemicals into their surrounding air space that can affect the physiology of neighboring plants and influence the behavior of insects. In studying these interactions, it is desirable to collect volatiles from plants that have not been excised and are growing under as natural conditions as possible. We compared a vessel of borosilicate glass and Nylon-6 or polyester [poly(ethyleneterephthalate) or PET] cooking bags for enclosing plants during collection of volatiles. A push-pull airflow system was used, and volatiles were trapped on Tenax TA and analyzed by gas chromatography after thermal desorption. Low levels of impurities were found for the glass vessel and polyester bags. Nylon bags contained higher levels and more impurities. Recoveries of standards of 10 plant volatiles were measured in static and dynamic systems. In a static air system, there was good recovery only from the glass vessel. In a dynamic system, there was generally good recovery from both the glass vessel and polyester bags. Recoveries of alpha-pinene and (Z)-jasmone were poor throughout. The former was shown to have a very low breakthrough volume on the Tenax TA adsorbent, and the latter may be strongly adsorbed on glass. All three materials were essentially transparent in the IR and visible (photosynthetic) range but with significantly different absorptions in the UV range. In a simulated dynamic entrainment in full sunlight, internal vessel temperatures were higher than ambient by up to 9.5 degrees C in the glass vessel and 7.5 degrees C in the polyester bag. Lower increases in temperature relative to ambient (<1 degrees C) were recorded when entrainments were conducted in the shade. In a field trial, the profiles of volatiles collected from an apple tree infested with rosy apple aphid using a glass vessel and a polyester bag were similar. Polyester bags are recommended as more convenient than glass vessels for the enclosure of plants during the collection of volatiles.

Suppression Behavior of Obstruction-Stabilized Pool Flames

The suppression phenomena of a nonpremixed flame stabilized by a recirculation zone behind an obstruction in a combustion tunnel have been studied because of their relation to fires in aircraft engine nacelles, dry bays, and shipboard and ground-vehicle compartments. The JP-8 fuel was supplied as a liquid fuel pool, or a gaseous (methane or ethane) fuel issued from a flat porous plate, downstream of a backward-facing step or J-shape flange. The OH planar laser-induced fluorescence revealed a narrow, wrinkled diffusion flame zone that was deeply folded into the recirculation zone in response to the dynamic air entrainment and back-flow. Both transient and steady-state fire suppression limits were determined; by impulsively injecting a gaseous fire-extinguishing agent (nitrogen, CF3Br, or C2HF5), or by continuously adding nitrogen, into the approaching airflow in the combustion tunnel. For high air velocities, the normalized critical agent mole fraction at suppression was a unique function of the agent injection period normalized by the effective mixing time in the recirculation zone, independent of types of fuels, agents, and obstacles. The extinction of the relatively low-strain-rate diffusion flame zone in the recirculation zone appears to determine the suppression limits of obstruction-stabilized flames.

A Representation of Cumulus-scale Effects in a Mesoscale-Convection-Resolving Model for Tropical Cyclones.

A new mesoscale-convection-resolving model (MCRM) for tropical cyclones (TCs) is proposed along a line of Yamasaki’s (1986) model in which mesoscale organized convection (MC) is resolved by the grid, but cumulus-scale convection (CC) is treated as the subgrid-scale. The most significant difference from Yamasaki’s model is that Kuo’s (1965) formulation is used to represent the CC-effects. Some important modifications from Kuo are made: (1) it is assumed that part of moisture converged in an air column is used for CC and that the ratio depends on low-level convergence and the degree of latent instability; (2) the ratio of moisture consumed for heating to moisture redistributed by CC is assumed to be significantly larger than that given by Kuo; (3) turbulent and dynamic entrainment and detrainment are taken into account so that the vertical profile of heating, which is crucial to MC, may be effectively controlled; (4) cloud water and rainwater of the subgrid-scale are treated with prognostic equations. Numerical experiments are performed with an axisymmetric model having a horizontal grid size of 10 km. The results are discussed compared with those from a 1 km grid model that can resolve CC. It is shown that the new model can simulate important features of MC and a TC, provided that the values of model parameters are specified properly. The CC-effects are made clear by comparison with a case that does not include them. It is shown that CC has two different effects, depending on the low-level relative humidity. One is to give realistic growth of MC through the upward transports of heat and moisture under a very humid condition, and the other is to enhance the formation and growth of MC when the air is not very humid. This study suggests that though Kuo’s parameterization was not proposed as that representing the CC-effects, a reasonable model can be developed when Kuo’s formulation is adopted in the framework of the MCRM. Important aspects of the model that contribute to realistic simulation of MC and a TC are discussed in comparison with those of Yamasaki’s model.