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With increasing computer power, explicit microphysics schemes are becoming increasingly important in atmospheric models. Many schemes have followed the approach of Kessler in which one moment of the hydrometeor size distribution, proportional to the mass content, is predicted. More recently, the two-moment method has been introduced in which both the mass and the total number concentration of the hydrometeor categories are independently predicted. In bulk schemes, the size spectrum of each hydrometeor category is often described by a three-parameter gamma distribution function, N(D) = N0Dαe−λD. Two-moment schemes generally treat N0 and λ as prognostic parameters while holding α constant. In this paper, the role of the spectral shape parameter, α, is investigated by examining its effects on sedimentation and microphysical growth rates. An approach is introduced for a two-moment scheme where α is allowed to vary diagnostically as a function of the mean-mass diameter. Comparisons are made between calculations using various bulk approaches—a one-moment, a two-moment, and a three-moment method—and an analytic bin model. It is found that the size-sorting mechanism, which exists in a bulk scheme when different fall velocities are applied to advect the different predicted moments, is significantly different amongst the schemes. The shape parameter plays an important role in determining the rate of size sorting. Likewise, instantaneous growth rates related to the moments are shown to be significantly affected by this parameter.

Many two-moment bulk schemes use a three-parameter gamma distribution of the form N(D) = N0Dαe−λD to describe the size spectrum of a given hydrometeor category. These schemes predict changes to the mass content and the total number concentration thereby allowing N0 and λ to vary as prognostic parameters while fixing the shape parameter, α. As was shown in Part I of this study, the shape parameter, which represents the relative dispersion of the hydrometeor size spectrum, plays an important role in the computation of sedimentation and instantaneous growth rates in bulk microphysics schemes. Significant improvement was shown by allowing α to vary as a diagnostic function of the predicted moments rather than using a fixed-value approach. Ideally, however, α should be an independent prognostic parameter. In this paper, a closure formulation is developed for calculating the source and sink terms of a third moment of the size distribution—the radar reflectivity. With predictive equations for the mass content, total number concentration, and radar reflectivity, α becomes a fully prognostic variable and a three-moment parameterization becomes feasible. A new bulk microphysics scheme is presented and described. The full version of the scheme predicts three moments for all precipitating hydrometeor categories. Simulations of an idealized hailstorm in the context of a 1D kinematic cloud model employing the one-moment, two-moment, and three-moment versions of the scheme are compared. The vertical distribution of the hydrometeor mass contents using the two-moment version with diagnostic-α relations are much closer to the three-moment than the one-moment simulation. However, the evolution of the surface precipitation rate is notably different between the three-moment and two-moment schemes.

This paper aims to investigate and quantify the turbulence effect on droplet collision efficiency and explore the broadening mechanism of the droplet size distribution (DSD) in cumulus clouds. The sophisticated model employed in this study individually traces droplet motions affected by gravity, droplet disturbance flows, and turbulence in a Lagrangian frame. Direct numerical simulation (DNS) techniques are implemented to resolve the small-scale turbulence. Collision statistics for cloud droplets of radii between 5 and 25 μm at five different turbulence dissipation rates (20–500 cm 2 s −3 ) are computed and compared with pure-gravity cases. The results show that the turbulence enhancement of collision efficiency highly depends on the r ratio (defined as the radius ratio of collected and collector droplets r/ R) but is less sensitive to the size of the collector droplet investigated in this study. Particularly, the enhancement is strongest among comparable-sized collisions, indicating that turbulence can significantly broaden the narrow DSD resulting from condensational growth. Finally, DNS experiments of droplet growth by collision–coalescence in turbulence are performed for the first time in the literature to further illustrate this hypothesis and to monitor the appearance of drizzle in the early rain-formation stage. By comparing the resulting DSDs at different turbulence intensities, it is found that broadening is most pronounced when turbulence is strongest and similar-sized collisions account for 21%–24% of total collisions in turbulent cases compared with only 9% in the gravitational case.

Idealized simulations of the 3 May 1999 Oklahoma tornadic supercell storms are conducted at various horizontal grid spacings ranging from 1 km to 250 m, using a sounding extracted from a prior 3-km grid spacing real-data simulation. A sophisticated multimoment bulk microphysics parameterization scheme capable of predicting up to three moments of the particle or drop size distribution (DSD) for several liquid and ice hydrometeor species is evaluated and compared with traditional single-moment schemes. The emphasis is placed on the impact of microphysics, specifically rain evaporation and size sorting, on cold pool strength and structure, and on the overall reflectivity structure of the simulated storms. It is shown through microphysics budget analyses and examination of specific processes within the low-level downdraft regions that the multimoment scheme has important advantages, which lead to a weaker and smaller cold pool and better reflectivity structure, particularly in the forward-flank region of the simulated supercells. Specifically, the improved treatment of evaporation and size sorting, and their effects on the predicted rain DSDs by the multimoment scheme helps to control the cold bias often found in the simulations using typical single-moment schemes. The multimoment results are more consistent with observed (from both fixed and mobile mesonet platforms) thermodynamic conditions within the cold pools of the discrete supercells of the 3 May 1999 outbreak.

The mean (ENM) of an ensemble of precipitation forecasts is generally more skillful than any of the members as verified against observations. A major reason is that the averaging filters out nonpredictable features on which the members disagree. Previous research showed that the nonpredictable features occur at small scales, in both numerical forecasts and Lagrangian persistence nowcasts. Hence, it is plausible that the unpredictable features filtered through ensemble averaging would also occur at small scales. In this study, the exact range of scales affected by averaging is determined by comparing the statistical properties of precipitation fields between the ENM and the individual members from a Storm-Scale Ensemble Forecasting (SSEF) system run during NOAA’s 2008 Hazardous Weather Testbed (HWT) Spring Experiment. The filtering effect of ensemble averaging results in a low-intensity bias for the ENM forecasts. It has been previously proposed to correct the ENM forecasts by recalibrating the intensities in the ENM using the probability density function (PDF) of rainfall values from the ensemble members. This procedure, probability matching (PM), leads to a new ensemble mean, the probability matched mean (PMM). Past studies have shown that the PMM appears more realistic and yields better skill as evaluated using traditional scores. However, the authors demonstrate here that despite the PMM having the same PDF of rainfall intensities as the ensemble members, the spectral structure and the spatial distribution of the precipitation field differs from that of the members. It is the lesser variability of the PMM fields at small scales that causes the better scores of the PMM relative to the ensemble members.

Background Dementia has been presenting an imminent public health challenge worldwide. Studies have shown a combination of cognitive and physical trainings may have synergistic value for improving cognitive functions. Daily functional tasks are innately cognitive demanding and involve components found in common exercise. Individuals with mild cognitive impairment may demonstrate difficulties with complex activities of daily living. Functional tasks could possibly be used as a means of combined cognitive and exercise training for improving cognitive functions. This pilot aims to validate the effects of functional tasks exercise on cognitive functions and functional status in older adults with mild cognitive impairment. Methods A four-arm, rater-blinded randomized controlled trial. Participants ( N  = 59) were randomized to either a functional task exercise group, a cognitive training group, an exercise training group, or a waitlist control group for 8 weeks. All outcome measures were undertaken at baseline and post-intervention using Neurobehavioral Cognitive Status Examination, Trail Making Test A and B, Chinese Version Verbal Learning Test, Lawton Instrumental Activities of Daily Living Scale, and Zarit Burden Interview. Results Results of the Kruskal-Wallis one-way ANOVA showed higher improvement in the functional task exercise group with significant between-group differences in memory ( p  = 0.009) compared to the exercise group and cognitive training group, functional status ( p  = 0.005) compared to the cognitive training group and waitlist control group, and caregiver burden ( p  = 0.037) compared to the exercise group and cognitive training group. Conclusion This pilot study showed that functional tasks exercise using simulated functional tasks as a means of combined cognitive and exercise program is feasible and beneficial in improving the memory and functional status of older adults with mild cognitive impairment as well as reducing the care-related burdens of their caregivers. The present findings warrant further well-designed longitudinal studies to examine the sustainability of effects and draw more definitive conclusions. Trial registration Australian New Zealand Clinical Trials Registry, ACTRN 12616001635459 . Registered on 25 November 2016.

Secondary eyewall formation and the ensuing eyewall replacement cycles may take place in mature tropical cyclones (TCs) during part of their lifetime. A better understanding of the underlying dynamics is beneficial to improving the prediction of TC intensity and structure. Previous studies suggested that the barotropic instability (BI) across the moat (aka type-2 BI) can make a substantial contribution to the inner-eyewall decay through the associated eddy radial transport of absolute angular momentum (AAM). Simultaneously, the type-2 BI can also increase the AAM of the outer eyewall. While the previous studies focused on the early stage of the type-2 BI, this paper explores the long-term effect of the type-2 BI and the underlying processes in forced and unforced shallow-water experiments. Under the long-term effect, it will be shown that the inner eyewalls repeatedly weaken and strengthen (while the order is reversed for the outer eyewalls). Sensitivity tests are conducted to examine the sensitivity of the long-term effect of the type-2 BI to different vortex parameters and the strength of the parameterized diabatic heating. Implication of the long-term effect for the intensity changes of the inner and outer eyewalls of real TCs are also discussed.

Radar imagery of some double-eyewall tropical cyclones shows that the inner eyewalls become elliptical prior to their dissipation. These elliptical features indicate that the barotropic instability (BI) across the moat (aka, type-2 BI) may play a role in the process. To investigate the mechanism for dissipation, a WRF simulation of Hurricane Wilma (2005) is performed. The results reveal an elliptical elongation of the inner eyewall and a change in the structure of the radial flow from wavenumber (WN) 1 to WN 2 at the lower levels. A linear stability analysis as well as idealized nonlinear experiments using a nondivergent barotropic vorticity model initialized with the vorticity fields before the change in the dominant wavenumber of the radial flow are presented with the results supporting the presence of a type-2 BI at the lower levels. The accompanying WN-2 radial flow is also found to dilute the vorticity within the inner eyewall and the eye. However, this dilution is not seen at higher levels as the type-2 BI becomes weak and short lived at the middle levels and reaches its weakest strength at the upper levels. This phenomenon is traced to the fact that a higher growth rate comes with a narrower moat for type-2 BI. As the outward slope of the outer eyewall is larger than that of the inner eyewall, the moat width increases with height so that the growth rate decreases with height. The results presented here thus highlight the potential role played by the barotropic instability across the moat in inner eyewall dissipation.

Radar imagery of some double-eyewall tropical cyclones shows that the inner eyewalls became elliptical prior to their dissipation during the eyewall replacement cycles, indicating that the barotropic instability (BI) across the moat (also known as type-2 BI) may play a role. To further examine the physics of inner eyewall decay and outer eyewall intensification under the influence of the type-2 instability, three-dimensional numerical experiments are performed. In the moist full-physics run, the simulated vortex exhibits the type-2 instability and the associated azimuthal wavenumber-2 radial flow pattern. The absolute angular momentum (AAM) budget calculation indicates, after the excitation of the type-2 instability, a significant intensification in the negative radial advection of AAM at the inner eyewall. It is further shown that the changes in radial AAM advection largely result from the eddy processes associated with the type-2 instability and contribute significantly to the inner eyewall decay. The budget calculation also suggests that the type-2 instability can accelerate the inner eyewall decay in concert with the boundary layer cutoff effect. Another dry no-physics idealized experiment is conducted and the result shows that the type-2 instability alone is able to weaken the inner eyewall and also strengthen the outer eyewall with nonnegligible effect.

Intense tropical cyclones (TCs) often experience secondary eyewall formations and the ensuing eyewall replacement cycles. Better understanding of the underlying dynamics is crucial to make improvements to the TC intensity and structure forecasting. Radar imagery of some double-eyewall TCs and a real-case simulation study indicated that the barotropic instability (BI) across the moat (aka type-2 BI) may play a role in inner eyewall decay. A three-dimensional numerical study accompanying this paper pointed out that type-2 BI is able to withdraw the inner eyewall absolute angular momentum (AAM) and increase the outer eyewall AAM through the eddy radial transport of eddy AAM. This paper explores the reason why the eddy radial transport of eddy AAM is intrinsically nonzero. Linear and nonlinear shallow water experiments are performed and they produce expected evolutions under type-2 BI. It will be shown that only nonlinear experiments have changes in AAM over the inner and outer eyewalls, and the changes solely originate from the eddy radial transport of eddy AAM. This result highlights the importance of nonlinearity of type-2 BI. Based on the distribution of vorticity perturbations and the balanced-waves arguments, it will be demonstrated that the nonzero eddy radial transport of eddy AAM is an essential outcome from the intrinsic interaction between the mutually growing vortex Rossby waves across the moat under type-2 BI. The analyses of the most unstable mode support the findings and will further attribute the inner eyewall decay and outer eyewall intensification to the divergence and convergence of the eddy angular momentum flux, respectively.