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J. A. Milbrandt and H. Morrison

Abstract

The predicted particle properties (P3) scheme introduced in Part I of this series represents all ice hydrometeors using a single “free” category, in which the bulk properties evolve smoothly through changes in the prognostic variables, allowing for the representation of any type of ice particle. In this study, P3 has been expanded to include multiple free ice-phase categories allowing particle populations with different sets of bulk properties to coexist, thereby reducing the detrimental effects of property dilution. The modified version of P3 is the first scheme to parameterize ice-phase microphysics using multiple free categories.

The multicategory P3 scheme is described and its overall behavior is illustrated. It is shown using an idealized 1D kinematic model that the overall simulation of total ice mass, reflectivity, and surface precipitation converges with additional categories. The correct treatment of the rime splintering process, which promotes multiple ice modes, is shown to require at least two categories in order to be included without introducing problems associated with property dilution. Squall-line simulations using a 3D dynamical model with one, two, and three ice categories produce reasonable reflectivity structures and precipitation rates compared to radar observations. In the multicategory simulations, ice hydrometeors from different categories and with different bulk properties are shown to coexist at the same points, with effects on reflectivity structure and precipitation. The new scheme thus appears to work reasonably in a full 3D model and is ready to be tested more widely for research and operational applications.

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I. Gultepe and J. A. Milbrandt

Abstract

This study analyzes the occurrence of the visibility (Vis) versus precipitation rates (PR) for rain and versus relative humidity (RH) from surface observations that were collected during the Fog Remote Sensing and Modeling (FRAM) field project, which was conducted near Toronto, Ontario, Canada, during the winter of 2005/06 and in Lunenburg, Nova Scotia, during the summers of 2006 and 2007. The main observations used in the analysis were PR and Vis for rain episodes from the Vaisala, Inc., FD12P present-weather sensor and RH and temperature from the Campbell Scientific Instruments, Inc., HMP45 sensor. The PR is compared with those from a total precipitation sensor to check the accuracy of the FD12P measurements. Vis parameterizations related to precipitation type have been previously studied by many other researchers and showed large variability in Vis (up to 1 order of magnitude) for a fixed PR. The results from the work presented here suggest that 1) significant differences exist among the various parameterizations of Vis (deterministic approach) and 2) statistical relationships obtained using fits applied to percentiles (probabilistic approach) can be a feasible alternative for model applications. Comparisons of previous parameterizations with the new Vis relationships suggest that simulated Vis values based on probabilistic approaches could be used in extreme-weather applications.

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J. A. Milbrandt, A. Glazer, and D. Jacob

Abstract

Bulk microphysics parameterizations play an increasingly important role for quantitative precipitation forecasting (QPF) in operational numerical weather prediction (NWP). For wintertime, numerical prediction of snowfall amounts is done by applying an estimated snow-to-liquid ratio to the liquid-equivalent QPF from the NWP model. A method has been developed to use prognostic fields from a detailed bulk scheme to predict the instantaneous snow-to-liquid ratio of precipitating snow. By exploiting aspects of the parameterization of the large crystal/aggregate (snow) category, which allow for a prediction of the mean particle size and a corresponding realistic bulk density, combined with pristine ice and graupel fields, the total volume flux of ice-phase precipitation (excluding hail) is computed, independently from the computation of the total solid mass flux. Ultimately, the accumulated unmelted solid precipitation quantity is thus predicted without having to estimate the average snow-to-liquid ratio for a given event, as is typically done for wintertime QPF.

The new technique has been implemented into the two-moment version of the Milbrandt–Yau microphysics scheme, which was used in a high-resolution (2.5 and 1 km) NWP modeling system over the Vancouver–Whistler region of Canada in support of forecasting for the Vancouver 2010 Olympic and Paralympic Games. Experimental fields were produced including the instantaneous snow-to-liquid ratio and the snowfall accumulation predicted directly from the scheme using the new approach. Subjective evaluation indicates that the model can discriminate between low-density and high-density snow for instantaneous precipitation. Comparison of the predicted snow-to-liquid ratio to observed climatologies indicates that the scheme produces a realistic probability distribution.

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J. A. Milbrandt and M. K. Yau

Abstract

A mesoscale simulation of the 19–21 July 1996 Saguenay flood cyclone was performed using the Canadian Mesoscale Compressible Community (MC2) model to study the processes leading to the explosive development and the large amount of precipitation. The performance of the simulation is verified by careful comparison with available observations with particular emphasis on the quantitative forecast of precipitation. It was shown that the model accurately simulates the wind, temperature, and humidity fields. Using the Kong and Yau microphysics scheme, the model performs quite well in the threat scores over a broad range of precipitation thresholds. Comparison of model precipitation against an objective analysis from rain gauge measurements and against the time evolution of accumulated precipitation at specific sites indicates generally good agreement except that the magnitude of the maxima is about 10% lower in the simulation.

Potential vorticity (PV) inversion and sensitivity experiments show that the rapid deepening of the cyclone results from a combination of upper-level forcing from two shortwave troughs that partially merge, an upper-level jet streak, latent heat release, and low-level thermal advection. Condensational heating was integral for the establishment of a phase lock between the surface cyclone and a strong, upper-level trough that steers the cyclone. The flow field associated with a weaker trough, located downstream of the stronger trough, acted to retard the progression of the stronger trough, ultimately causing the cyclone to be located in a favorable position to interact with orography. It was shown that in the middle of the explosive deepening period, the contributions to the 900-hPa geopotential height anomaly from the upper-level dry PV anomaly, the low-level moist PV anomaly, and the surface potential temperature anomaly were 47%, 41%, and 12%, respectively.

The contribution to the precipitation from orographic variation is quantified through sensitivity experiments in which aspects of the orography field are altered in the model conditions. It was found that orographic variation contributed to approximately 15% of the 48-h accumulated precipitation in the region of the flooding and up to over 25% in other local areas.

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J. A. Milbrandt and M. K. Yau

Abstract

With continuous increase in the resolution of operational numerical weather prediction models, grid-scale saturation schemes that model cloud microphysics are becoming increasingly important. In Parts I and II of this study, the importance of the relative dispersion of the hydrometeor size distribution in bulk microphysics parameterizations was demonstrated and a closure approach for a three-moment scheme was proposed. In this paper, the full three-moment version of the new multimoment scheme is tested in a 3D simulation of a severe hailstorm. The modeled microphysical fields are examined, with particular attention paid to the simulated hail fields including the maximum hail sizes at the ground.

A mesoscale model was initialized using synoptic analyses and successively nested to a resolution of 1 km. When compared to observations of the real storm from a nearby radar, the simulated storm reproduced several of the observed characteristics including the direction and speed of propagation, a bounded weak echo region, hook echo, mesocyclone, and a suspended overhang region. The magnitudes of radar reflectivity and surface precipitation are also well simulated.

The mass contents, total number concentrations, equivalent reflectivities, and mean mass diameters of each hydrometeor category in the model were examined. The spatial distributions of the various hydrometeors throughout the storm appeared realistic and their values were consistent with published observations from other storms. Using the three predicted parameters of the gamma size distribution for hail, a method was introduced to determine the maximum hail size simulated from a bulk scheme that is physically observable. The observed storm produced golf ball–sized hail while the simulation produced walnut-sized hail at approximately the same time and location. The results suggest that because of the additional information provided about the size distribution, there is added value in prognosing the relative dispersion parameter of a given hydrometeor category in a bulk scheme.

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J. A. Milbrandt and M. K. Yau

Abstract

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) = N 0 Dαe λD. Two-moment schemes generally treat N 0 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.

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J. A. Milbrandt and R. McTaggart-Cowan

Abstract

The computation of hydrometeor sedimentation in one-moment, two-moment, and three-moment bulk microphysics parameterizations is examined in the context of a 1D model, with no other microphysical processes active. The solution from an analytic bin model is used as a reference against which the bulk model simulations are compared. Errors in the computed (nonprognostic) moments from 0 to 7 from the bulk model runs are examined. In addition to the commonly used predicted variables (number concentration, mass, and reflectivity), bulk scheme configurations with alternative combinations of prognostic moments are considered.

While the extra degree of freedom in a two-moment scheme adds realism to the simulation of sedimentation over a one-moment scheme, the standard practice of imposing a constant relative dispersion in the particle size distribution results in considerable errors in some of the computed moments. The error can be shifted to different moments by selecting different prognostic moments. For three-moment schemes, the error is considerably reduced over a wide range of computed moments and there is much less sensitivity to the choice of prognostic variables.

Two alternative approaches are proposed for modifying the computation of sedimentation in two-moment schemes to reduce problems associated with excess size sorting. The first approach uses a diagnostic relative dispersion (shape) parameter, generalized for any pair of prognostic moments. The second involves progressively reducing the differential fall velocities between the moments and is therefore applicable for schemes that hold the shape parameter constant. Both approaches greatly reduce the errors in the computed moments, including those on which microphysical process rates depend, and are easily applied to existing two-moment schemes.

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J. A. Milbrandt and M. K. Yau

Abstract

Many two-moment bulk schemes use a three-parameter gamma distribution of the form N(D) = N 0 Dαe 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 N 0 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.

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J. A. Milbrandt and M. K. Yau

Abstract

This is the fourth in a series of papers exploring the effects of the number of predicted moments in bulk microphysics schemes. In Part III, the three-moment version of a new multimoment scheme was used to simulate a severe hailstorm. The model successfully reproduced many of the observed gross characteristics, including the reflectivity structure and the maximum hail sizes at the ground. In this paper, the authors compare a series of sensitivity experiments using various one- and two-moment versions of the scheme with the three-moment version to explore the effects of predicting additional moments on the simulated hydrometeor fields, precipitation, and storm dynamics.

Six sensitivity runs were performed. They varied in their ability to reproduce the precipitation pattern, storm structure, and peak values of microphysical fields of the control simulation. The two-moment simulations, which used diagnostic relations to prescribe the relative dispersion parameter, α, closely reproduced the spatial pattern, quantity, and phase of the precipitation at the surface as well as the overall storm structure, propagation speed, and peak values of several hydrometeor fields. The two-moment simulations, which used fixed values of α, on the other hand, differed more from the control. The runs using one-moment versions of the scheme were considerably different from each other and were poor at reproducing the control simulation.

The results suggest that there is a dramatic improvement in the simulation moving from one- to two-moment schemes. For the case studied, it was found that if maximum particle size is not of concern, a two-moment scheme with a diagnostic dispersion parameter can reproduce most of the important aspects in a hailstorm simulation with a three-moment scheme.

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J. A. Milbrandt, M. K. Yau, J. Mailhot, and S. Bélair

Abstract

This paper reports the first evaluation of the Milbrandt–Yau multimoment bulk microphysics scheme against in situ microphysical measurements. The full triple-moment version of the scheme was used to simulate a case of orographically enhanced precipitation with a 3D mesoscale model at high resolution (4- and 1-km grid spacings). The simulations described in this paper also serve as the control runs for the sensitivity experiments that will be examined in Part II of this series. The 13–14 December 2001 case of heavy orographically enhanced precipitation, which occurred over the Oregon Cascades, was selected since it was well observed during the second Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE-2) observational campaign. The simulated fields were compared with observed radar reflectivity, vertical velocity, precipitation quantities from rain gauges, and microphysical quantities measured in situ by two instrumented aircraft. The simulated reflectivity structure and values compared favorably to radar observations during the various precipitation stages of the event. The vertical motion field in the simulations corresponded reasonably well to the mountain-wave pattern obtained from in situ and dual-Doppler radar inferred measurements, indicating that biases in the simulations can be attributed in part to the microphysics scheme. The patterns of 18-h accumulated precipitation showed that the model correctly simulated the bulk of the precipitation to accumulate along the coastal mountains and along the windward slope of the Cascades, with reduced precipitation on the lee side of the crest. However, both the 4- and 1-km simulations exhibited a general overprediction of precipitation quantities. The model also exhibited a distinct bias toward overprediction of the snow mass concentration aloft and underprediction of the mass and vertical extent of the pockets of cloud liquid water on the windward side of the Cascades. Nevertheless, the overall spatial distribution of the hydrometeor fields was simulated realistically, including the mean-mass particle diameters for each category and the observed trend of larger snow sizes to be located at lower altitudes.

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