1. Introduction
The National Centers for Environmental Prediction (NCEP) North American Mesoscale Forecast System (NAM) contiguous United States (CONUS) nest is run at a horizontal grid spacing of 3 km (Rogers et al. 2017), the scale at which models are capable of resolving some circulations and physical processes associated with deep convective storms while also capturing convective mode with some degree of skill (e.g., Done et al. 2004; Kain et al. 2008). Correctly forecasting the mode of convection is important for predicting different types of severe weather. For example, Gallus et al. (2008) showed that quasi-linear mesoscale convective systems (MCSs) with trailing stratiform regions are most often associated with severe wind damage, and leading stratiform systems, while less common, are most often associated with hail and tornadoes. They also showed that tornadoes are most common in cellular systems within broken lines.
While the mode of a quasi-linear system can be initially governed by hydrometeor advection (Parker and Johnson 2000), microphysical processes can play an important role as well. The transport of buoyant air rearward from the convective region can result in further ascent in the stratiform region (Knupp and Cotton 1987) of trailing stratiform systems, with ascent being aided by condensation, freezing, and deposition (Houze 1982; Churchill and Houze 1984). Parker and Johnson (2004a,b) and Storm et al. (2007) showed that leading stratiform systems can be sustained by melting and evaporation, which can act to destabilize the atmosphere ahead of the convective line. Furthermore, microphysics impacts on supercells were shown in Gilmore et al. (2004), who illustrated the significance of assumed graupel density and intercept parameter on the areal coverage of rainfall in their idealized simulations. They found that slower-falling graupel particles, compared to faster-falling hail particles, remained suspended in the cloud for a longer period of time, allowing them to be advected outside of the updraft region and resulting in less total ground-accumulated rainfall. Initial near-surface downdrafts for the simulation with graupel particles were weaker, and outflow was warmer (compared to simulations using hail), as the slower-falling graupel particles took longer to reach the melting level and turn to rain, thus delaying the evaporation.
With forecasters regularly evaluating model-produced, storm-scale diagnostics, such as updraft helicity (Kain et al. 2008), hourly maximum 10-m winds (Kain et al. 2010), lightning (McCaul et al. 2009), and hail size (Adams-Selin and Ziegler 2016), forecasting the correct three-dimensional structure and mode of deep convective storms is critical. A motivation for developing the Ferrier–Aligo (FA) microphysics was in response to feedback from operational forecasters about the lack of structure and perceived realism in the NAM CONUS nest’s forecasts of deep convective storms, as seen from forecast reflectivity.1 This feedback, coupled with an ever-increasing focus on higher-resolution operational forecast model output (e.g., Clark et al. 2012), helped serve as motivation to begin taking an in-depth, careful look at the issue.
The FA scheme replaces previous versions of the Ferrier microphysics scheme (FER) (Ferrier et al. 2002, 2011) that had been run operationally in the NCEP operational NAM since 2001. Operational microphysical schemes outside the United States used in convection permitting model runs include the 3-ICE single-moment scheme used by Météo-France, with cloud ice, snow, and graupel being separated by the amount of riming (Seity et al. 2011). Nearly a dozen European countries use a variation of the 3-ICE scheme (Szintai et al. 2015; Bengtsson et al. 2017), while the Deutscher Wetterdienst (DWD; German Weather Service) uses a Lin et al. (1983)-type single-moment microphysics scheme (Baldauf et al. 2011). In the operational environment, computational efficiency is important, and the FA scheme continues to be a fast scheme, while more sophisticated microphysical schemes (double and triple moment) were too expensive to be implemented with the 2017 NAM upgrade. For example, Wolff et al. (2016) noted that Nonhydrostatic Multiscale Model on the B-grid (NMMB) runs with the Thompson scheme (Thompson et al. 2004, 2008), double moment in cloud ice and rain, take on average 50% more compute time than runs with the FA microphysics when using the operational NAM configuration. While the Thompson scheme could not be run operationally in the NAM, results from 3-km NMMB model runs using the Thompson scheme were used to develop the FA scheme.
Before the FA microphysics was implemented into the operational NAM, it underwent thorough pre-implementation testing spanning multiple seasons. The procedure for advancing this scheme into operations closely followed the steps described in Wolff et al. (2016), which included detailed case study analyses of some high-impact cases followed by extensive real-time testing, in combination with other model system changes. This paper describes and illustrates the modifications made to the FER scheme, based on microphysics sensitivity experiments that were carried out in the development of the FA scheme, to address concerns from various NCEP centers and NWS forecast offices.
While extensive evaluation of all cases described in Table 1 were used in development, in the interest of brevity, only illustrative results from a subset of representative cases are shown from the model microphysics sensitivity experiments, in addition to bias statistics summarizing the results over all of the cases. One of the cases shown in this paper includes the progressive derecho (Johns and Hirt 1987; Guastini and Bosart 2016) that affected an area from Iowa to Maryland on 29/30 June 2012. This progressive derecho produced widespread swaths of damage, resulted in numerous injuries and fatalities, and led to many indirect, heat-related fatalities following the event, when much of the affected region was without power during a heat wave (Vescio et al. 2013; Fierro et al. 2014; Guastini and Bosart 2016).
List of cases evaluated in NMMB runs with the initialization times and forecast length indicated. The first four cases were of cold-season events, and the last seven cases were of warm-season events. The cases with the superscripts a and b were of interest to SPC and WPC, respectively. The reports were provided by SPC and were refined based on the integration domain and forecast hours evaluated.
Section 2 describes the datasets that were used and the configuration of the model runs. Section 3 describes the general principles of the FA scheme and outlines the microphysics sensitivity experiments that were carried out in its development. Section 4 shows results of the microphysics sensitivity experiments and then provides a comparison between the FER and FA scheme results. A summary and conclusion can be found in section 5. The appendixes provide a detailed description of the FA microphysics, including definitions of microphysical scheme source and sink terms, as well as the extensive set of 12 lookup tables that are used, with modifications to the FER scheme clearly documented.
2. Data and methods
All model sensitivity runs were made with the Nonhydrostatic Multiscale Model on the B grid (Janjić 2005; Janjić and Black 2007; Janjić and Gall 2012) in full convection-allowing mode (i.e., no use of parameterized convection) at a horizontal grid spacing of 3 km using the following configuration: RRTMG radiation (Iacono et al. 2008), MYJ planetary boundary layer (Janjić 2001), MYJ surface layer (Janjić 1996), and Noah land surface model (Chen and Dudhia 2001; Ek et al. 2003). The cases evaluated with the NMMB are shown in Table 1 for both cool-season (first four) and warm-season (last seven) deep convection events. Some of the warm-season cases were of particular interest to the Storm Prediction Center (SPC) and the Weather Prediction Center (WPC) because they represented forecast failures of the operational 4-km NAM CONUS nest. The two 2015 cases in Table 1 were evaluated during the 2015 Flash Flood and Intense Rainfall Experiment (FFaIR; NOAA 2015) and identified by WPC as representative examples of the operational 4-km NAM CONUS nest’s high bias in heavy precipitation.
While the microphysics modifications went through vigorous pre-implementation testing in all seasons, the focus in this paper was on the deep convection events for which the modifications were intended. Not surprisingly, the microphysics modifications had only a minor impact on cold-season, nonconvection events due to the lack of supercooled liquid available for riming in the absence of intense updrafts (not shown). Components of the FA scheme that were modifications and additions to the FER scheme were activated only under more extreme conditions associated with warm-season deep convection. Eight of the cases in Table 1 used initial and lateral boundary conditions from the 12-km NAM interpolated to a 32-km grid, while the remaining three cases used an experimental, hourly updated version of the NAM run at grid spacing close to that of the operational NAM CONUS nest. One of the more unique aspects of this experimental system was its distinct data assimilation cycle for both the 12-km parent and CONUS nest domains. Initial NMMB runs of the 29 June 2012 derecho were initialized off of the 13-km Rapid Refresh version 2 (RAPv2) provided by the NOAA Earth System Research Laboratory (ESRL).
Precipitation histograms were constructed from 3-hourly model output and 3-hourly observations from the Climatology-Calibrated Precipitation Analysis (CCPA; Hou et al. 2014). Composite reflectivity histograms were constructed from hourly model output and hourly radar observations described in Liu et al. (2016). Both the precipitation and reflectivity data were interpolated onto a common 5-km grid using a neighbor interpolation option (Accadia et al. 2003).
3. The Ferrier–Aligo microphysics scheme
a. General principles
As with the FER scheme, the FA scheme is also a single-moment scheme that predicts the mixing ratios of cloud water (qc), rain (qr), cloud ice (qci), and snow–graupel (qs). A thorough description of the general microphysical scheme relationships is in appendix A, and a detailed description of the production terms is in appendix B. Also shared between the two schemes is the calculation of a diagnostic array called the “rime factor” (RF), which represents the degree of riming onto snow–graupel. The definition of the RF was changed to take into account the temperature of the ice particle, the impact velocity of the cloud droplet on the ice particle, and the size of the cloud droplet (see appendix C), and this was motivated by results that will be discussed in the subsections below. For all practical purposes, one can categorize precipitation ice as snow, graupel, or hail, similar to the ice species predicted in other microphysical schemes based on the value of the RF. For example, an RF = 1 represents unrimed snow; lightly rimed snow occurs when 1 < RF < 2; heavily rimed snow when 2 < RF ≤ 5; graupel when 5 < RF < 10; and frozen drops or hail when RF ≥ 10.2 In reality, the RF knows no arbitrary cutoff between different ice categories, and the categorizations above are somewhat subjective. Hereafter, we will also refer to mixing ratios of snow/graupel as precipitation ice. An advantage to having one precipitation ice category is the absence of an artificial boundary separating one precipitation ice species from another, which allows for a smoother evolution of particle properties (e.g., Morrison and Milbrandt 2015; Lin and Colle 2011). This approach is conceptually similar to that employed by Morrison and Milbrandt (2015), who used a single ice category and predicted its attributes, including rime volume and rime growth. Single-moment schemes that use a separate snow and graupel species include, but are not limited to, Weather Research and Forecasting (WRF) single-moment 6-class (WSM6; Hong et al. 2004; Hong and Lim 2006), which is used operationally in the NCEP High-Resolution Window (HIRESW) forecast system, and the Lin scheme (Lin et al. 1983).
Owing to operational computation constraints, the sedimentation process in both the FER and FA schemes does not use finite differencing of precipitation fluxes in the vertical in order to circumvent the requirement that small time steps be used in order to maintain numerical stability, particularly since the vertical resolution of the model increases dramatically near the ground. The algorithm is instead based upon a partitioning of precipitation already present in the grid box at the beginning of the time step and the precipitation entering the grid box from above at the end of the time step. A more detailed description of the sedimentation algorithm can be found in appendix D.
Throughout the rest of the model outside of the microphysics, the cloud ice (qci) and precipitation ice (qs) are combined into a total ice mixing ratio (qi = qci + qs). While there are no resolution restrictions to using the FA scheme, it is intended for convection-allowing resolutions where most of the benefits would more likely be noticed. The subsections below describe the components of the FA scheme developed through microphysical scheme sensitivity experiments that are modifications and additions to the FER scheme.
b. Modified ice nucleation
Number concentration of ice crystals formed from ice nucleation Nin (L−1) as a function of temperature (°C) showing the Fletcher, Meyers, and Cooper curves taken from Thompson et al. (2004) with some modifications. The red dashed line indicates the curve used in the FA scheme.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Number concentration of ice crystals formed from ice nucleation Nin (L−1) as a function of temperature (°C) showing the Fletcher, Meyers, and Cooper curves taken from Thompson et al. (2004) with some modifications. The red dashed line indicates the curve used in the FA scheme.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Number concentration of ice crystals formed from ice nucleation Nin (L−1) as a function of temperature (°C) showing the Fletcher, Meyers, and Cooper curves taken from Thompson et al. (2004) with some modifications. The red dashed line indicates the curve used in the FA scheme.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
c. Separate species and rime factor advection
d. Fall speeds of rimed ice
(a) Ice fall speed (m s−1) increase, VrimeF, as a function of RF (ordinate) and 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Ice fall speed (m s−1) increase, VrimeF, as a function of RF (ordinate) and
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Ice fall speed (m s−1) increase, VrimeF, as a function of RF (ordinate) and
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
e. Variable rain intercept parameter (Nor)
In response to concerns from both WPC and SPC over sharp gradients in precipitation associated with summertime deep convective storms, and a lack of reflectivity–rainfall at lower levels behind convective lines in 4-km operational NAM CONUS nest forecasts, respectively, a variable Nor was introduced to improve stratiform rainfall using results from 3-km NMMB runs with the Thompson microphysics. Because the Thompson scheme predicts the mixing ratios and number concentrations of rain drops (i.e., double moment in rain), Thompson scheme runs tended to have more robust stratiform rain regions with larger mean drop sizes (
(a) Schematic illustration of the drizzle parameterization for a single cloud layer in which drizzle forms from a low-level liquid water cloud at >0°C only when it is completely disconnected from rain formed from melting ice aloft. (b) The scatterplot from Westbrook et al. (2010) shows retrieved rain rate (R, mm h−1) vs the normalized rain intercept parameter (NL in m−4, where NL = Nor for exponential distributions) based on lidar observations of drizzle. The different values of Nor described in (7) are overlaid on the figure with the red line showing the variation of Nor as a function of rain rate for rain contents between 0.02 and 0.5 g m−3.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Schematic illustration of the drizzle parameterization for a single cloud layer in which drizzle forms from a low-level liquid water cloud at >0°C only when it is completely disconnected from rain formed from melting ice aloft. (b) The scatterplot from Westbrook et al. (2010) shows retrieved rain rate (R, mm h−1) vs the normalized rain intercept parameter (NL in m−4, where NL = Nor for exponential distributions) based on lidar observations of drizzle. The different values of Nor described in (7) are overlaid on the figure with the red line showing the variation of Nor as a function of rain rate for rain contents between 0.02 and 0.5 g m−3.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Schematic illustration of the drizzle parameterization for a single cloud layer in which drizzle forms from a low-level liquid water cloud at >0°C only when it is completely disconnected from rain formed from melting ice aloft. (b) The scatterplot from Westbrook et al. (2010) shows retrieved rain rate (R, mm h−1) vs the normalized rain intercept parameter (NL in m−4, where NL = Nor for exponential distributions) based on lidar observations of drizzle. The different values of Nor described in (7) are overlaid on the figure with the red line showing the variation of Nor as a function of rain rate for rain contents between 0.02 and 0.5 g m−3.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
f. Treatment of precipitation ice
This section describes the evolution of the size distribution assumptions from the FER scheme to the FA scheme, detailing the changes made to reduce high anvil reflectivity biases and the development of three RF regimes in order to improve convective region storm structure. The end of this section describes a diagnostic algorithm to increase reflectivity in the convective region under limited circumstances.
In either FER or FA, if Ns > Nsmax, then Ns = Nsmax, and new estimates for 
Reducing the rimed ice fall speeds tended to reduce the magnitude of reflectivity in the convective region, as more of the precipitation ice particles were able to advect rearward into the stratiform region. To recover the higher reflectivity, a diagnostic algorithm was employed in FA in areas with high graupel/hail contents (RF > 5) exceeding 2.5 g m−3, for which large subgrid-scale variability is assumed with the observed reflectivity being dominated by returns from the fewest, largest particles. The number concentrations of graupel/hail were assumed to decrease proportionally with mass content to a value of Ns = 1 L−1 at 5 g m−3. Values of Ns were assumed to decrease further to a minimum value of Ns = 0.2 L−1, when graupel–hail contents reached 10 g m−3 and were assumed to be fixed at Ns = 0.2 L−1 for larger graupel–hail contents. This algorithm produced reflectivities of 56 and 69.1 dBZ when the graupel–hail mass contents reached 5 and 10 g m−3, respectively. This algorithm does not modify process rates, and the thresholds above were determined through iterative case study analyses.
4. Results
a. RF advection
When the mass-weighted RF was advected, convective region reflectivity (i.e., ≥45 dBZ) was often higher, and these higher values were often seen at temperatures colder than −40°C. An example of this can be seen from a 9-h (09h) forecast of the progressive derecho event of 29 June 2012, valid at 0000 UTC 30 June 2012, where only scattered areas of >50-dBZ composite reflectivity were present without the RF advection (Fig. 4a), compared to a larger area predicted in the RF advection run (Fig. 4b). Without the RF advection, vertical cross sections indicated >50-dBZ values were limited to temperatures warmer than −20°C (Fig. 4c), but with the RF advection, >50-dBZ echoes extended to higher levels at temperatures colder than −40°C (Fig. 4d). Since the observed derecho was more progressive than in any of the NMMB runs, observed composite reflectivity and vertical cross-sections of reflectivity from earlier times (valid at 2100 and 2200 UTC 29 June 2012) are shown in Fig. 5 for comparison. Intense convective cores with >50-dBZ reflectivities extended higher than 10 km above ground level (AGL) at both times. In the FA cross sections shown, −40°C is at approximately 250 hPa, indicating the run with the RF advection more correctly forecasted the vertical depth of the 50-dBZ reflectivity.
NMMB 9-h forecast valid 0000 UTC 30 Jun 2012 of simulated maximum-in-column reflectivity (dBZ) (a) without and (b) with RF advection; and (c),(d) corresponding vertical cross-sections of reflectivity and temperature [°C, dashed (<0) and solid lines (≥0)] along line AB, respectively. Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
NMMB 9-h forecast valid 0000 UTC 30 Jun 2012 of simulated maximum-in-column reflectivity (dBZ) (a) without and (b) with RF advection; and (c),(d) corresponding vertical cross-sections of reflectivity and temperature [°C, dashed (<0) and solid lines (≥0)] along line AB, respectively. Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
NMMB 9-h forecast valid 0000 UTC 30 Jun 2012 of simulated maximum-in-column reflectivity (dBZ) (a) without and (b) with RF advection; and (c),(d) corresponding vertical cross-sections of reflectivity and temperature [°C, dashed (<0) and solid lines (≥0)] along line AB, respectively. Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a),(b) Maximum-in-column reflectivity and (c),(d) vertical cross-sections of reflectivity valid along line AB at (a),(c) 2100 and (b),(d) 2200 UTC 29 Jun 2012. Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a),(b) Maximum-in-column reflectivity and (c),(d) vertical cross-sections of reflectivity valid along line AB at (a),(c) 2100 and (b),(d) 2200 UTC 29 Jun 2012. Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a),(b) Maximum-in-column reflectivity and (c),(d) vertical cross-sections of reflectivity valid along line AB at (a),(c) 2100 and (b),(d) 2200 UTC 29 Jun 2012. Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Without the RF advection, most of the ice was in the form of cloud ice and snow (Fig. 6a), with only a small amount in the form of graupel (Fig. 6c), but with RF advection, cloud ice and snow mixing ratios were lower by a factor of 2 in the convective region (Figs. 6b,c), and graupel mixing ratios doubled in magnitude and extended to lower temperatures (Fig. 6d). From the reflectivity cross sections, it is clear the stratiform rain region suffered with the RF advection (Fig. 4d) as the result of higher RF values extending farther back into the stratiform region and to lower temperatures aloft (Figs. 6e,f). When RF increases, VrimeF and the resultant precipitation ice fall speeds (Fig. 2a) increase. With more precipitation ice in the form of faster-falling graupel, there was less of the lower-density, slower-falling snow that could be advected rearward into the stratiform region.
Vertical cross-sections of (a),(b) cloud ice + snow, and (c),(d) graupel in g kg−1 (color shaded), as well as (e),(f) RF for an NMMB run (left) without and (right) with RF advection. Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa. Snow and cloud ice are assumed to occur where RF ≤ 5 and graupel where RF > 5. The RF values are shown for mass contents ≥ 0.1 kg m−3.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Vertical cross-sections of (a),(b) cloud ice + snow, and (c),(d) graupel in g kg−1 (color shaded), as well as (e),(f) RF for an NMMB run (left) without and (right) with RF advection. Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa. Snow and cloud ice are assumed to occur where RF ≤ 5 and graupel where RF > 5. The RF values are shown for mass contents ≥ 0.1 kg m−3.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Vertical cross-sections of (a),(b) cloud ice + snow, and (c),(d) graupel in g kg−1 (color shaded), as well as (e),(f) RF for an NMMB run (left) without and (right) with RF advection. Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa. Snow and cloud ice are assumed to occur where RF ≤ 5 and graupel where RF > 5. The RF values are shown for mass contents ≥ 0.1 kg m−3.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Aggregating hourly composite reflectivity statistics over all 11 cases (Table 1) corroborated the subjective results that the RF advection reduced the size of the stratiform region, as seen by lower 15–40-dBZ reflectivity counts (Fig. 7a), and increased the instances of high (>45 dBZ) reflectivity (Fig. 7b). With the RF advection, there was a high bias in high reflectivity; however, without the RF advection, there was a low bias in the high reflectivity. A common complaint concerning the NAM CONUS nest prior to the implementation of the FA scheme in August 2014 was a low bias in high reflectivity, brought to our attention by SPC and NWS forecast offices; advecting the RF as is done currently in the operational NAM CONUS nest addressed those concerns. With the RF advection, instances of light precipitation (≤0.5 in.) were reduced (Fig. 7c), while instances of heavy precipitation (≥1 in.) were increased (Fig. 7d), compared to runs without the RF advection. This was not a surprising result, considering the partitioning of precipitation ice to be more in the form of higher-density ice when the RF is advected.
Histograms of hourly composite reflectivity (dBZ) aggregated over all 11 cases for reflectivity at 5-dBZ intervals starting with (a) 5 dBZ and (b) 45 dBZ. Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (c) starting with 0.01 in. and (d) starting with 1 in. Displayed in the figure are the observed counts (red) and counts from runs with the RF advection (blue) and without the RF advection (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Histograms of hourly composite reflectivity (dBZ) aggregated over all 11 cases for reflectivity at 5-dBZ intervals starting with (a) 5 dBZ and (b) 45 dBZ. Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (c) starting with 0.01 in. and (d) starting with 1 in. Displayed in the figure are the observed counts (red) and counts from runs with the RF advection (blue) and without the RF advection (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Histograms of hourly composite reflectivity (dBZ) aggregated over all 11 cases for reflectivity at 5-dBZ intervals starting with (a) 5 dBZ and (b) 45 dBZ. Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (c) starting with 0.01 in. and (d) starting with 1 in. Displayed in the figure are the observed counts (red) and counts from runs with the RF advection (blue) and without the RF advection (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
b. Fall speeds of rimed ice
Sensitivity experiments were made using different values of the tunable exponent (n) in (6) that controls the increase in the rimed ice fall speeds to reduce a high bias in heavy precipitation, which was a common complaint especially from WPC due to the RF advection. After an extensive evaluation using the cases in Table 1, it was determined that a value of n = 1 reduced the high precipitation biases while not degrading the reflectivity structure of MCSs. Figure 8 shows that the area of 20-dBZ composite reflectivity was too small in spatial extent with n = 2 (Fig. 8a) and in much better agreement with observations (Fig. 5) when n = 1 in the derecho case (Fig. 8b). Very little stratiform reflectivity/rainfall existed in the run with n = 2 (Fig. 8c), while a more robust stratiform region could be seen with n = 1 (Fig. 8d) that more closely matched observations (Fig. 5). When n = 2, the precipitation ice fall speeds in the convective region were as high as 15 m s−1 (Fig. 8e), but with n = 1, they generally did not exceed 7 m s−1 (Fig. 8f). Slowing the rimed ice fall speeds allowed more of the heavily rimed ice to be advected rearward, which resulted in a better-defined stratiform region reflectivity. Not surprisingly, the instances of light precipitation (≤0.5 in.) were higher with n = 1 (Fig. 9a), while the instances of heavy precipitation (≥1 in.) were lower, compared to the n = 2 runs (Fig. 9b). Although a high bias in precipitation amounts ≥2 in. might still be present with n = 1 (the current setting used in the operational NAM), it was an improvement over the higher biases when n = 2.
Maximum-in-column reflectivity (dBZ) for runs with (a) n = 2 and (b) n = 1, as well as corresponding vertical cross-sections of (c),(d) reflectivity and (e),(f) precipitation ice fall speeds (m s−1). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Maximum-in-column reflectivity (dBZ) for runs with (a) n = 2 and (b) n = 1, as well as corresponding vertical cross-sections of (c),(d) reflectivity and (e),(f) precipitation ice fall speeds (m s−1). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Maximum-in-column reflectivity (dBZ) for runs with (a) n = 2 and (b) n = 1, as well as corresponding vertical cross-sections of (c),(d) reflectivity and (e),(f) precipitation ice fall speeds (m s−1). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (a) starting with 0.01 in. and (b) starting with 1 in. Displayed in the figure are the observed counts (red), and counts from runs with n = 1 (blue) and with n = 2 (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (a) starting with 0.01 in. and (b) starting with 1 in. Displayed in the figure are the observed counts (red), and counts from runs with n = 1 (blue) and with n = 2 (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (a) starting with 0.01 in. and (b) starting with 1 in. Displayed in the figure are the observed counts (red), and counts from runs with n = 1 (blue) and with n = 2 (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
c. Variable Nor
Implementation of a variable Nor improved stratiform reflectivity and rainfall at low levels with forecasts more comparable to observations. For example, a comparison of observed hybrid scan radar reflectivity valid at 1500 UTC 1 July 2015 (Fig. 10a; Table 1) and 1-km AGL reflectivity for a 15-h forecast from a Thompson scheme run (Fig. 10b) indicates a larger stratiform rain region in the FA run using a variable Nor instead of a constant Nor (Figs. 10c,d), closer in spatial extent to what was observed and similar to what was seen in the Thompson run. Similar patterns were seen at other forecast times (not shown). While one should be careful making direct comparisons of 1-km AGL reflectivity from the model output to the hybrid scan reflectivity as different parts of the storm are being sampled, the areal coverage can be gleaned from the comparison.
Hybrid scan reflectivity (dBZ) and 1-km AGL reflectivity (dBZ) from (b) a Thompson run, (c) an FA run with a fixed rain intercept parameter Nor, and (d) an FA run with a variable Nor valid at 1500 UTC 1 Jul 2015 (forecast hour 15). The black solid line with the start and end points marked as A and B, respectively, represents the locations of vertical cross sections shown in Fig. 11.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Hybrid scan reflectivity (dBZ) and 1-km AGL reflectivity (dBZ) from (b) a Thompson run, (c) an FA run with a fixed rain intercept parameter Nor, and (d) an FA run with a variable Nor valid at 1500 UTC 1 Jul 2015 (forecast hour 15). The black solid line with the start and end points marked as A and B, respectively, represents the locations of vertical cross sections shown in Fig. 11.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Hybrid scan reflectivity (dBZ) and 1-km AGL reflectivity (dBZ) from (b) a Thompson run, (c) an FA run with a fixed rain intercept parameter Nor, and (d) an FA run with a variable Nor valid at 1500 UTC 1 Jul 2015 (forecast hour 15). The black solid line with the start and end points marked as A and B, respectively, represents the locations of vertical cross sections shown in Fig. 11.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
The more robust stratiform rain region in the Thompson microphysics run, also depicted in the vertical cross-sections of reflectivity (Fig. 11a), was associated with number-weighted mean drop sizes exceeding 400 μm, which remained nearly constant with height down to the surface (Fig. 11b). Stratiform region reflectivity from rain struggled to reach the surface in the FA run with a constant Nor (Fig. 11c), as drop sizes were often less than 250 μm (Fig. 11d) and decreased dramatically in size approaching the surface. Larger drops surviving to the surface were more evident in the stratiform region of the FA run with a variable Nor (Figs. 11e,f) and were a result of drop sizes assumed to be fixed with height below the melting layer, allowing the rain intercept parameter to vary with height.
Vertical cross-sections of (a) reflectivity (dBZ) and (b) number-weighted, mean drop sizes (μm) of rain for the Thompson run and corresponding cross-sections for FA runs; (c),(d) using a fixed Nor and (e),(f) using a variable Nor. Refer to Fig. 10 for the location of the cross sections. Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 1500 UTC 1 Jul 2015 (forecast hour 15). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Vertical cross-sections of (a) reflectivity (dBZ) and (b) number-weighted, mean drop sizes (μm) of rain for the Thompson run and corresponding cross-sections for FA runs; (c),(d) using a fixed Nor and (e),(f) using a variable Nor. Refer to Fig. 10 for the location of the cross sections. Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 1500 UTC 1 Jul 2015 (forecast hour 15). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Vertical cross-sections of (a) reflectivity (dBZ) and (b) number-weighted, mean drop sizes (μm) of rain for the Thompson run and corresponding cross-sections for FA runs; (c),(d) using a fixed Nor and (e),(f) using a variable Nor. Refer to Fig. 10 for the location of the cross sections. Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 1500 UTC 1 Jul 2015 (forecast hour 15). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Introducing a variable Nor also removed some of the spurious widespread light reflectivity often forecast in FER runs. At 1300 UTC 23 May 2003 (observations were not available at 1200 UTC), observations showed convection dissipating in Oklahoma (Fig. 12a), with a similar system forecast an hour earlier in the Thompson, FER, and FA runs (Figs. 12b–d). The FA run using a constant Nor had widespread scattered radar echoes <20 dBZ throughout central Texas, while the area and intensity of the scattered light reflectivity was reduced and agreed better with observations in the FA run using a variable Nor. These differences were present at other forecast times and in almost all of the cases were evaluated especially around sunrise (not shown).
(a) Observed composite reflectivity valid at 1300 UTC 24 May 2016 compared against 24-h forecasts from (b) a Thompson run, (c) an FA run using a fixed Nor, and (d) an FA run using a variable Nor valid at 1200 UTC 24 May 2016. No observations were available at 1200 UTC.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Observed composite reflectivity valid at 1300 UTC 24 May 2016 compared against 24-h forecasts from (b) a Thompson run, (c) an FA run using a fixed Nor, and (d) an FA run using a variable Nor valid at 1200 UTC 24 May 2016. No observations were available at 1200 UTC.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Observed composite reflectivity valid at 1300 UTC 24 May 2016 compared against 24-h forecasts from (b) a Thompson run, (c) an FA run using a fixed Nor, and (d) an FA run using a variable Nor valid at 1200 UTC 24 May 2016. No observations were available at 1200 UTC.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
d. FER versus FA
Several factors that contributed to improvements in storm structure in the FA scheme include the RF advection, the faster Thompson-based graupel fall speeds used for large RFs, the diagnostic enhancement of reflectivity, and the forcing of smaller Ns values in the convective region. Additionally, a high bias in anvil reflectivity, noted via the analysis of many vertical cross sections, was reduced when Nsmax was relaxed to be more consistent with results from Thompson scheme runs. The examples below highlight the differences between the FER and FA runs for two representative cases.
One of the features that stood out in the observed reflectivity of the 29 June 2012 derecho (Figs. 5c,d) was the narrow, nearly solid line of deep intense convection. Slightly less organized, but with similar intensity, the Thompson scheme run produced a well-defined, deep convective core with a robust stratiform region (Figs. 13a,b), as can be seen at 09 h, valid 0000 UTC 30 June 2012. However, the FER run had a more diffusive convective region (Fig. 13c), with composite reflectivity values that barely reached 50 dBZ and with the vertical extent of the 50-dBZ echoes restricted to below the melting level (Fig. 13d). The FA run was an improvement over the FER run, with higher convective region reflectivity (Figs. 13e,f), more intense echoes in the convective region, and 50-dBZ echoes extending to lower temperatures (below −40°C). None of the runs simulated the well-organized, solid line of convection that was observed (Figs. 5a,b).
(a) Composite reflectivity (dBZ) and (b) vertical cross-section of reflectivity for the Thompson run with the corresponding plots for the (c),(d) FER and (e),(f) FA runs valid at 0000 UTC 30 Jun 2012 (forecast hour 09). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Composite reflectivity (dBZ) and (b) vertical cross-section of reflectivity for the Thompson run with the corresponding plots for the (c),(d) FER and (e),(f) FA runs valid at 0000 UTC 30 Jun 2012 (forecast hour 09). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Composite reflectivity (dBZ) and (b) vertical cross-section of reflectivity for the Thompson run with the corresponding plots for the (c),(d) FER and (e),(f) FA runs valid at 0000 UTC 30 Jun 2012 (forecast hour 09). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 0000 UTC 30 Jun 2012 (forecast hour 09). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
The 09-h forecast reflectivity cross sections behind the convection from the Thompson scheme run (Fig. 13b) and from observations (Figs. 5c,d) indicated that the FER run produced anvil reflectivities that were too high by as much as 15 dBZ (Fig. 13d), compared with more reasonable values in the FA run (Fig. 13f). Anvil reflectivity at temperatures near −30°C approached 30 dBZ in the FER run versus 15 dBZ in the Thompson run and in the FA run. In the Thompson run, Ns values exceeded 250 L−1 at very cold temperatures (Fig. 14a) and were generally <30 L−1 in the FER run (Fig. 14b) and as high as 250 L−1 in the FA run (Fig. 14c).
Vertical cross-section of snow number concentration (Ns) for the (a) Thompson, (b) FER, and (c) FA run at the same time and cross sections described in Fig. 13. Units are L−1.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Vertical cross-section of snow number concentration (Ns) for the (a) Thompson, (b) FER, and (c) FA run at the same time and cross sections described in Fig. 13. Units are L−1.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Vertical cross-section of snow number concentration (Ns) for the (a) Thompson, (b) FER, and (c) FA run at the same time and cross sections described in Fig. 13. Units are L−1.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
The FER and FA schemes were also compared for the Moore, Oklahoma, tornado outbreak on 20 May 2013. At 2200 UTC 20 May 2013, large, isolated storms extended southwest to northeast across Oklahoma (Fig. 15a). A cross section through one of the convective storms showed a strong cell with 50-dBZ reflectivity extending up to 11 km AGL (Fig. 15b). A run with the FER microphysics produced two lines of storms that were oriented correctly, but with a mode that was too linear (Fig. 15c). A vertical cross section through the primary (strongest) line of storms showed reflectivity barely exceeding 45 dBZ (Fig. 15d). In the FA run, the mode of convection was more discrete and in better agreement with observations with higher reflectivity in the convective cores (Fig. 15e), a feature seen at other times and in other cases. A vertical cross section through one of the storms in the FA run showed the 50-dBZ reflectivity extended to temperatures near −40°C (~225 hPa), which was closer to the observed height of the 50-dBZ echo (Fig. 15f). As in the derecho case above, the anvil reflectivity in the FA run was in better agreement with observations than the anvil reflectivity in the FER run.
(a) Composite reflectivity (dBZ) and (b) vertical cross-section of reflectivity from observations with corresponding plots from (c),(d) an FER run, and (e),(f) an FA run, valid at 2200 UTC 20 May 2013 (forecast hour 22). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 2200 UTC 20 May 2013 (forecast hour 22). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Composite reflectivity (dBZ) and (b) vertical cross-section of reflectivity from observations with corresponding plots from (c),(d) an FER run, and (e),(f) an FA run, valid at 2200 UTC 20 May 2013 (forecast hour 22). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 2200 UTC 20 May 2013 (forecast hour 22). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
(a) Composite reflectivity (dBZ) and (b) vertical cross-section of reflectivity from observations with corresponding plots from (c),(d) an FER run, and (e),(f) an FA run, valid at 2200 UTC 20 May 2013 (forecast hour 22). Each cross section contains temperature [°C, dashed (<0) and solid lines (≥0)] with all fields valid along line AB and at 2200 UTC 20 May 2013 (forecast hour 22). Horizontal distance in km is plotted along the abscissa.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Aggregating the composite reflectivity statistics over all 11 cases indicated that for reflectivity ≤25 dBZ, a high bias existed in both the FER and FA runs; however, the high bias was reduced in the FA run, likely in areas associated with lower anvil reflectivity, and by representing rain as drizzle within shallow clouds that form at the top of moist PBLs (Fig. 16a). While a forecast high bias in the reflectivity ≤25 dBZ might exist, an underestimate of the observed counts at these lower thresholds is possible because the lowest 0.5° elevation angle used at most radar sites will not capture widespread light precipitation often seen at low levels (Zhang et al. 2005). Although a high bias can be seen in both the FER and FA schemes for the 45–50-dBZ reflectivity bin (Fig. 16b), there was a pronounced low bias in >55-dBZ reflectivity in the FER scheme that was eliminated with the FA scheme. Precipitation histograms were also aggregated over all 11 cases. The biases were reduced for precipitation amounts ≤0.5 in. (Fig. 16c), which was the result of the RF advection reducing the stratiform precipitation. The reduced bias was an improvement for the 0.01–0.1 in. precipitation bin, but resulted in a slight low bias in precipitation in the FA scheme for the 0.1–0.5 in. bins. For the 1 in.+ amounts (Fig. 16d), the FER scheme had a low bias, with 11% fewer counts than observed, while the FA scheme had a slight high bias, with 3% more counts than observed. The higher precipitation bias in the FA scheme is the result of having higher-density, faster-falling precipitation ice in the convective region.
Histograms of hourly composite reflectivity (dBZ) aggregated over all 11 cases for reflectivity at 5-dBZ intervals starting with (a) 5 and (b) 45 dBZ. Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (c) starting with 0.01 in. and (d) starting with 1 in. Displayed in the figure are the observed counts (red), and counts from FER runs (blue) and FA runs (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Histograms of hourly composite reflectivity (dBZ) aggregated over all 11 cases for reflectivity at 5-dBZ intervals starting with (a) 5 and (b) 45 dBZ. Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (c) starting with 0.01 in. and (d) starting with 1 in. Displayed in the figure are the observed counts (red), and counts from FER runs (blue) and FA runs (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Histograms of hourly composite reflectivity (dBZ) aggregated over all 11 cases for reflectivity at 5-dBZ intervals starting with (a) 5 and (b) 45 dBZ. Histograms of 3-hourly accumulated precipitation aggregated over all 11 cases for amounts (c) starting with 0.01 in. and (d) starting with 1 in. Displayed in the figure are the observed counts (red), and counts from FER runs (blue) and FA runs (green). Rounding of the counts above the bars was done to make the plot more legible.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
5. Summary and conclusions
The flagship microphysics of the NAM for more than a decade was updated with the FA microphysics scheme in order to improve the vertical structure of convective storms in the NAM CONUS nest. Running with a more sophisticated microphysics scheme like Thompson was not viable at the time; however, results from Thompson scheme runs proved useful in developing the fast FA scheme and addressing the concerns from forecast centers and NWS forecast offices. Notable components of the FA scheme include the advection of separate species in addition to the advection of the mass-weighted RF, which resulted in graupel reaching very cold temperatures. The RF advection, as well as the reduced number concentrations of precipitation ice (Ns) assumed in areas of convection, helped eliminate the low reflectivity biases seen in FER runs in areas associated with deep convection. The RF advection resulted in a high bias in heavy precipitation that was noted by WPC, and to counter this effect, the rimed ice fall speeds were reduced. The use of graupel fall speeds from the Thompson scheme in intense convection allowed for more coherent, narrow convective regions, while a diagnostic method was added to boost reflectivity in the most intense convection. A high reflectivity bias in the upper portions of stratiform anvils at temperatures colder than −10°C was reduced, allowing the number concentrations of snow to reach 250 L−1, which is more consistent with results seen in Thompson microphysics runs.
A variable rain intercept parameter was introduced into the FA scheme to address concerns regarding rainfall outside the convective region. Larger rain number concentrations and smaller drop sizes reduced or eliminated spurious, widespread radar echoes that developed in shallow liquid water clouds that form at the top of the PBL, as was often noted in the operational 4-km NAM CONUS nest. In areas associated with light-to-moderate precipitation rates away from areas of active convection, the mean drop diameter was conserved rather than the rain intercept, reducing the loss of rain by evaporation and allowing more rain produced from melting ice to reach lower levels, which reduced (improved) the low bias in light rainfall and low-level reflectivity.
Development of the FA scheme initially addressed concerns raised by SPC and NWS forecast offices regarding the proper representation of deep convective storms. Further modifications to the FA scheme addressed concerns from WPC regarding a high heavy precipitation bias and large gradients in forecast precipitation. Currently, the majority of modeling systems employing convection-permitting grid spacing exist primarily in the regional domain. However, in the coming years, it is likely that convection-permitting applications will extend to the global domain, where the challenges are vast and the impacts more far-reaching (e.g., tropical convection and the global circulation). Efficient yet sophisticated microphysics schemes, such as FA, will play a significant role in the development toward such a high-resolution, global modeling paradigm.
Acknowledgments
The authors thank SPC, particularly Steven Weiss and Israel Jirak. Matthew Pyle and Eric Rogers are thanked for technical support and valuable comments. The authors would also like to thank ESRL for providing RAPv2 grid data and Greg Thompson for incorporating his microphysics into the NMMB. Comments and suggestions from the anonymous reviewers led to substantial improvements to the original manuscript.
APPENDIX A
General Microphysics Relationships
a. Mass–diameter relationships
Values of ai and bi used in (A3) for bullet rosettes (i = 1), columns (i = 2), and plates (i = 3) from Heymsfield (1972) and Starr and Cox (1985), while those for aggregates of unrimed radiating assemblages of dendrites or dendrites (Agg1, i = 4), aggregates of unrimed radiating assemblages of plates, side planes, bullets, and columns (Agg2, i = 5), and aggregates of unrimed side planes (Agg3, i = 6) are from Locatelli and Hobbs (1974). The mass of the ice are in units of mg and the diameters are in mm, which are converted into mks units in the final lookup table calculations.
b. Fall speed relationships
Values of αi,j and β i,j used in (A8) for the same set of ice habits listed in Table A1, but for different size intervals. Ice fall speeds are in units of m s−1. The fall speed relationships for the first five size categories of ice crystals (j ≤ 5) are from Starr and Cox (1985) and Heymsfield (1972), in which the particle diameters are in units of μm. The fall speed relationships for the largest size category (j = 6), which involve different types of aggregates, are from Locatelli and Hobbs (1974).
c. Microphysics moments
APPENDIX B
FER and FA Microphysics Production Terms
Flowchart of the FA microphysical scheme production terms listed in Table B1.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Flowchart of the FA microphysical scheme production terms listed in Table B1.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
Flowchart of the FA microphysical scheme production terms listed in Table B1.
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-17-0277.1
List of microphysical processes, their description, and the equations in appendix B where they are defined. All processes are in units of kg kg−1.
List of symbols.
Each of the microphysical source sink terms referenced above will be discussed in more detail below.
a. Production terms for ice (DELI)
List of equations used to calculate venti1 and venti2, where the variable d represents the maximum ice-particle dimension in mm. For ice crystals <1.5 mm in length, the various relationships for bullets are from Heymsfield (1972, 1975), whereas for plates and columns, they are from Young (1993). For the larger aggregates whose maximum dimensions are >1.5 mm, the various relationships assume spherical particles. The fall speed relationships for the different ice habits listed in Table A2 are used to calculate Xagg and Xavg.
b. Production terms for cloud water (DELW)
The collection of cloud water by precipitation ice (PIACW) is given by (B26).
c. Production terms for rainwater (DELR)
APPENDIX C
New Rime Factor Calculation
APPENDIX D
Sedimentation
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