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  • View in gallery

    A comparison of the moments of interest for an IP size distribution of MXP with Γ size distributions (p = 1 and p = 2)

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    As in Fig. 1 but the Ryan–Platt IP size distribution. The dependence on temperature of the RP first moment is also depicted

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    (a) Sea level isobars superimposed with GOES-8 brightness temperature. (b) Satellite-derived cloud-top pressure. (c) National Climatic Data Center Next Generation Weather Radar mosaic reflectivity map. All valid at 1800 UTC 15 Jan 1998

  • View in gallery

    CFDE III research flight 1648–2133 UTC at 15 Jan 1998: (a) horizontal projection of aircraft trajectory showing cloud phases, (b) as in (a) but for the vertical projection, (c) time series of temperature (°C) observed during the flight, and (d) time series of observed LWC (g m−3) and IWC (×−1 g m−3)

  • View in gallery

    (a) Model CTP (mb) distribution. (b) Model surface precipitation rate (mm h−1). Both maps are 30-h forecasts valid at 1800 UTC 15 Jan 1998

  • View in gallery

    SLWP (kg m−2) maps valid at 1800 UTC 15 Jan 1998 for the three nested simulations. Outlines of the nested domains are also included for reference

  • View in gallery

    Time series of model LWC (g m−3) and IWC (×−1 g m−3) along the virtual aircraft trajectory for the three nested runs

  • View in gallery

    (a) Time series of aircraft and model temperature (°C) for the three nested runs. The instrument absolute error range (°C) has been incorporated into the aircraft time series. (b) As in (a) but for dewpoint

  • View in gallery

    CTP maps for (a) NEWC, (b) GAM2, and (c) RP

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    As in Fig. 9 but for RP-mod

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    As in Fig. 7 but for NEWC, GAM2, and RP-mod

  • View in gallery

    As in Fig. 11 but for RP-mod2 and MXP35-mod

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    As in Fig. 8 but for NEWC, GAM2, and RP-mod2

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Improvements of a Mixed-Phase Cloud Scheme Using Aircraft Observations

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  • 1 Cloud Physics Research Division, Meteorological Service of Canada, Dorval, Quebec, Canada
  • | 2 Recherche en Prévision Numérique, Meteorological Service of Canada, Dorval, Quebec, Canada
  • | 3 Cloud Physics Research Division, Meteorological Service of Canada, Dorval, Quebec, Canada
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Abstract

To improve the quality of forecasts of mixed-phase clouds in winter storms, some aspects of a cloud scheme are examined in detail. Modifications to the basic formalism and specification of selected parameters of the cloud model are studied, and simulation results are compared with aircraft observations and satellite data. In particular, a sensitivity study to the parameterization of the ice particle size distribution is presented. A special technique allowing the reconstruction of any model variable along a virtual aircraft trajectory is used to compare model results with aircraft observations. It has been possible from these comparisons to optimize the scheme and improve the quality of forecasts.

Corresponding author address: Dr. André Tremblay, Cloud Physics Research Division, Meteorological Service of Canada, 2121 Trans-Canada Hwy., Dorval, QC H9P 1J3, Canada. Email: andre.tremblay@ec.gc.ca

Abstract

To improve the quality of forecasts of mixed-phase clouds in winter storms, some aspects of a cloud scheme are examined in detail. Modifications to the basic formalism and specification of selected parameters of the cloud model are studied, and simulation results are compared with aircraft observations and satellite data. In particular, a sensitivity study to the parameterization of the ice particle size distribution is presented. A special technique allowing the reconstruction of any model variable along a virtual aircraft trajectory is used to compare model results with aircraft observations. It has been possible from these comparisons to optimize the scheme and improve the quality of forecasts.

Corresponding author address: Dr. André Tremblay, Cloud Physics Research Division, Meteorological Service of Canada, 2121 Trans-Canada Hwy., Dorval, QC H9P 1J3, Canada. Email: andre.tremblay@ec.gc.ca

1. Introduction

The production of realistic clouds and precipitation forecasts with detailed mesoscale models is a difficult task. Increasing the microphysics complexity implies the specification of a number of adjustable parameters and processes, which requires extensive research and numerical experimentation. Furthermore, a large number of predictive equations and microphysical processes significantly increase computational time and thus limit the use of complex cloud microphysics schemes in operational applications.

The mixed-phase cloud (MXP) scheme proposed by Tremblay et al. (1996) and described in Tremblay and Glazer (2000) was developed with the intention of incorporating cloud microphysics in the Canadian Meteorological Center (CMC) forecast models. In order to minimize uncertainties and the number of adjustable parameters associated with complex cloud microphysics formulations and to optimize computational efficiency, only the most important microphysical processes relevant to mesoscale systems were included in the scheme. The scheme has only one prognostic variable for the total water content and parameterizes the essential ingredients to allow mixed-phase clouds and freezing precipitation forecasts.

In a companion paper in this issue, Vaillancourt et al. (2003) perform a detailed comparison of MXP simulations with cloud microphysics aircraft observations collected during the First and Third Canadian Freezing Drizzle Experiments (hereafter referred to as CFDE I and III) described in Isaac et al. (1998, 2001). One of the conclusions of Vaillancourt et al. (2003) is that the MXP scheme has more facility at predicting ice rather than water clouds. It was also found that MXP underpredicts the presence and quantity of supercooled liquid water (SLW). Furthermore, in the simulated mixed-phase clouds the ice phase strongly dominates, which is not the case in the observations.

The research presented in this paper aims at improving the MXP forecasts, and in particular the aspects discussed above. The formulation of the original scheme and the setup of the model were examined in detail and numerical experiments have been designed to evaluate the impacts of various modifications and adjustments. In particular, given the dependence of the results on the ice particle size distribution, a sensitivity study to this parameterization has been conducted. The results of each of these experiments are compared with satellite data and aircraft measurements for two cases from CFDE III. The aircraft observations are compared to the model results following a procedure similar to that suggested in Tremblay et al. (1995), used by Guan et al. (2001), and subsequently refined in Vaillancourt et al. (2003). With this methodology, aircraft data are used to optimize the cloud model, which resulted in improved forecasts.

Some might argue that mixed-phase clouds are unstable and would not occur in nature very frequently. However, Cober et al. (2001a) and Korolev et al. (2002) show that mixed-phase stratiform clouds occur quite frequently in the mid- and high latitudes, accounting for approximately 40% of the in-cloud measurements at temperatures between −5° and −20°C. These results are in general agreement with previous observation studies in other geographical areas by Mazin et al. (1992) and Moss and Johnson (1994). Obviously better simulations of such clouds will lead to more accurate aircraft icing forecasts, as well as improved physical representation of the precipitation formation mechanisms.

This paper is organized as follows. In section 2, a summary of the basic MXP scheme formulation is given and some modifications to the physics of the scheme are proposed. Section 3 describes the selected case and the aircraft data used for the model evaluation. A brief description of the mesoscale model used and its configuration is given is section 4. The results of the various numerical experiments performed are discussed in section 5. Finally, a summary of the conclusions and findings of this investigation are presented in section 6.

2. Mixed-phase cloud scheme

In this section, the basic version of the mixed-phase cloud scheme is first summarized. Next, a minor modification to the physics of the scheme is described. Finally, several alternatives for ice particle (hereafter referred to as IP) size distributions are proposed.

a. The basic scheme

The MXP scheme has only one prognostic variable: the total water content (M or TWC), as shown in the following model equations:
i1520-0493-131-4-672-e1

For completeness, water vapor and thermodynamics equations are also shown. On the left-hand side, symbols Ax represent tendencies due to all other effects. The scheme has six explicit microphysical processes: condensation or evaporation of cloud droplets (C), evaporation of rain (E), ice nucleation (N), deposition or sublimation of ice particles (D), sedimentation of M (PM), and melting (χ). A detailed description of each of these processes is given in Tremblay and Glazer (2000). As discussed in Tremblay and Glazer (2000), the sedimentation term PM includes thresholds for both ice and liquid phases to model the onset of precipitation. These thresholds are analogous to the autoconversion thresholds currently used in Kessler-type parameterization schemes. In the basic version of MXP, the ice and liquid phase thresholds were chosen as ks = 0.01 g m−3 and kL = 0.1 g m−3, respectively. Only liquid or ice water contents in excess of their respective thresholds are allowed to sediment.

Equation (1) is easily solved for warm clouds (right hand side, rhs = CE + PL) or for glaciated clouds (rhs = N + D + PS). In conditions where mixed-phase clouds may exist or form (i.e., T < 0°C and saturated with respect to water), both liquid and ice microphysical processes are active. In this situation, the technique suggested by Tremblay et al. (1996) is used to partition the TWC between ice and liquid. This technique introduces a diagnostic equation for the fractional ice water content f (f = ice water content/total water content = IWC/TWC) within the saturated updraft in the cloud:
i1520-0493-131-4-672-e4
Both ice and liquid water contents can be calculated from MS = f · M and ML = (1 − f) M. The following definitions complete the formulation of the scheme:
i1520-0493-131-4-672-e5
where σi is the ratio of the saturation vapor pressure over water and ice, w > 0 the resolved-scale vertical velocity, fυ = 1 the ventilation coefficient, C3 the coefficient for units transformation, K the coefficient of thermal conductivity of air, esi the saturation vapor pressure over ice, Lυ (Ls) the latent heat of vaporization (sublimation), Rυ (Rd) the gas constant for water vapor (dry air), Δ the coefficient of diffusion of water vapor in air, ESC = 1 the collection efficiency of water droplets by ice particles, ρ (ρ0 = 1) the (reference) air density, υ0 = −5.1 m1−b s−1 the constant for ice phase fall speed, Γw the wet-adiabatic lapse rate, and g the acceleration of gravity; PL (PS) describes the sedimentation of liquid (ice) phase. The empirical constant b = 0.27 is the exponent in the power law that expresses the relationship between ice particles' fall speed and their diameter (Locatelli and Hobbs 1974). Similarly, c = −31.2 × 10−6d gd m1+3d s−1 and d = 0.125 are empirical constants related to the terminal fall speed of liquid droplets.

In Eq. (4) the first term is a sink of SLW, and f increases due to the scavenging of liquid water droplets by ice particles. The second term accounts for the deposition of water vapor onto ice crystals. This promotes the evaporation of liquid droplets and the subsequent deposition on ice crystals. The net effect is a reduction of the amount of SLW within the cloud. The first component of the last term represents the increase in saturation ratio due to adiabatic cooling resulting from a moist-adiabatic ascent. This contributes positively to the amount of SLW within a cloud volume. The second component of the last term is the net contribution of the differential sedimentation of the ice and liquid phases. The difference in fall speeds between ice and liquid particles changes locally the partition between SLW and ice particles. Depending on the sign of the vertical gradient of ML and MS this term can act as a source or sink of SLW. Except for unrealistically high values of the vertical gradient of MS and ML, the sedimentation term ξ is always confined to values |ξ| < 1. Considering the weak dependence of f on ξ within this range (Tremblay et al. 1996), the basic implementation of the scheme is for ξ = 0. This simplification saves unnecessary calculations.

It should be noted that in the calculation of microphysical process D used explicitly in (1)–(3) and implicitly in (4), crystals shape was assumed to be spherical. This is likely not the ideal assumption, and crystal habit should be parameterized. For example, dendritic or stellar crystals sweep out areas between 0.2 and 0.4 of that of a circle (A. Heymsfield 2002, personal communication).

The mass-moments coefficients α(x) and β(x) relate the xth moment of the IP distribution to its third moment (proportional to mass) following Zawadzki et al. (1993):
i1520-0493-131-4-672-e11
where D is the diameter of IP and N(D)dD is the number concentration of particles with diameters between D and D + dD. This technique allows the easy introduction of any arbitrary size distribution in the scheme. In the basic version of MXP, the exponential distribution of Lin et al. (1983) is used (N0 = 3 × 106 m−4).

b. A new formulation of closure assumption

In the original formulation of the MXP scheme, Tremblay et al. (1996) assumed as a closure assumption that mixed-phase clouds are saturated with respect to water. This implies an equilibrium in which supersaturation production is balanced by condensation on droplets and deposition on ice crystals. As an approximation for the production rate of supersaturation S, Tremblay et al. (1996) considered the generation of water vapor excess over saturation by moist-adiabatic cooling in a saturated updraft (S = wG). This assumption limits the occurrence of SLW to saturated updrafts while other potential sources of supersaturation, such as radiative cooling, advection, or surface evaporation, are not included. This assumption can be easily relaxed by considering in an atmospheric model:
Sqυqvstqυqvs
where qvs is the saturation density over water. Using (12) in (4) and setting ξ = 0 yields after some simplifications
cRM1+β(2+b)fβ(2+b)fcDMβ(1)fβ(1)fS
Mailhot et al. (2002) noted that this modification significantly improves the simulation of SLW boundary layer clouds associated with a polynya circulation over the Beaufort Sea.

c. Introduction of a Γ distribution for IP

Considering the influence of IP distributions in the calculation of SLW from (4) or (13), it is crucial to evaluate the sensitivity of MXP to this parameter. As concluded in Vaillancourt et al. (2003), MXP systematically underforecasts SLW amounts when compared to aircraft data. A possible cause may be the exponential IP distribution used in the basic version of MXP. Such a distribution tends to overestimate the number concentration of small IP, which may result in an overevaluation of vapor deposition on ice crystals.

A significant refinement can be easily obtained at low costs by introducing the more general three-parameter gamma distribution (Walko et al. 1995; Harringon et al. 1995; Ferrier et al. 1995):
NgDNogDpλgD
where p is a shape parameter that controls the concentration of small IP. Note that for p = 0, (14) reduces to an exponential distribution. Such a spectral form has also been used by Mitchell (1991, 1994), to model the evolution of snow and ice size spectra. A linear combination of distributions such as (14) can be used to the model bimodal distribution sometimes observed in clouds (Mitchell et al. 1996).
The parameters of this distribution, Nog, λg, and p, are arbitrary and change from case to case, but are independent of ice particle size D. The intercept parameter Nog was chosen so as to conserve the total number concentration (103 m−3) of the original MXP distribution. Thus, for p = 1, Nog = 1012 m−5, and for p = 2, Nog = 1016 m−6. The slope parameter λ can be expressed in term of Nog, p, and I(3), which is proportional to the prognostic variable MS:
i1520-0493-131-4-672-e15
Using (14) and (15) in (11), the following relationships are obtained:
i1520-0493-131-4-672-e16
where Γ(x) is the gamma function.

Figure 1 illustrates the effects of increasing the shape parameter on the moments involved in the MXP formulation (x = 1 for vapor deposition; x = 2 + b for riming and x = 3 + b for sedimentation of IP). The figure shows that increasing p significantly reduces moments 1 and 2 + b and slightly increases moment 3 + b. Thus, it is expected that the Γ distribution will increase both the production of SLW and the sedimentation of IP.

d. Introduction of the Ryan–Platt distribution for IP

Based on the work of Platt (1997) and Heymsfield and Platt (1984), Ryan (2000) suggested a bulk parameterization of the IP size distribution for implementation in atmospheric models. Ryan tested the parameterization in a simulation of a cold front and concluded that the results are consistent with microphysics observations and satellite-derived parameters from the International Satellite Cloud Climatology Project. Considering the scarcity of observations for IP size distributions and the relatively good results discussed by Ryan, it was decided to implement his parameterization in MXP and test it against aircraft measurements from the Canadian Freezing Drizzle Experiment (Cober et al. 2001b; Isaac et al. 2001).

The observations of Platt suggested that small IP in the 20–100-μm range (hereafter referred as HP particles—after Heymsfield and Platt, as in the Ryan's nomenclature) are size distributed according a power law of the form
NtDADb
The parameter A can be related to I(3) and b′ is an empirical function of temperature. Platt also concluded that large IPs in the 100–1400-μm (hereafter referred as MP particles—after Marshall and Palmer, as in the Ryan's nomenclature) are distributed according to an exponential law:
NsDNosλsD
In (18) λs is an empirical function of temperature, and the intercept parameter Nos is related to I(3) and λs as in (15). Ryan parameterized b′ in (17) for frontal clouds as a function of temperature T (K):
i1520-0493-131-4-672-e19
Ryan also assumed that HP particles are nonprecipitating and integrated (17) for the third moment assuming spherical shape. To ensure a meaningful comparison with microphysics measurements, Ryan used the limits of integration from D0 = 50 μm to Ds = 200 μm. He defined the critical ice content for the onset of precipitation similarly to the kS parameter discussed above and obtained
i1520-0493-131-4-672-e20
where kS is in kilograms per cubed meter. Introducing (17), (19), and (20) in (11), expressions for α and β for HP particles are derived:
i1520-0493-131-4-672-e21
In (21) ρi is the density of solid ice. Based on Platt's observation, Ryan has also parameterized the slope parameter λs for MP particles as
λsT−0.0245 · (T−273.16)
Proceeding as above with integration limits ranging from Ds to infinity, α and β for MP particles are derived:
i1520-0493-131-4-672-e23
In (23), Γ(x, y) is the incomplete gamma function.

The mass-moments coefficients of interest can be easily calculated for both HP and MP particles. A detailed comparison between HP and MP moments has shown that the contribution of HP particles is several orders of magnitude less than that of MP moments. Therefore, HP particles can be safely neglected in the calculation of the various microphysical processes discussed in section 2a.

A comparison between MXP and Ryan moments is depicted in Fig. 2. It is seen that the Ryan distribution decreases the first moment by several orders of magnitude as compared to MXP for low ice contents. This implies that vapor deposition on IP is reduced. For IWC < 0.5 gm−3, the x = 2 + b moment is also decreased and hence the contribution of the riming process is reduced. The net effect is that the production of SLW should be increased as for the Γ distribution discussed above. Finally, the moment x = 3 + b is increased, implying higher IP precipitation rates.

3. Selected case, field experiment, and aircraft data

In order to validate the modifications to the MXP scheme discussed above against observations, the case of 15 January 1998 was selected for numerical experimentations. On this particular day, the Canadian National Research Council Convair-580 research aircraft flew a 5-h cloud physics mission (1648–2133 UTC). This flight was 1 of 26 research flights conducted during CFDE III. This particular flight was selected because Vaillancourt et al. (2003) showed, with a numerical setup similar to that used for the control runs described below, that the basic meteorological situation was well simulated for that case. Furthermore, this case typifies well the general conclusions of Vaillancourt et al. (2003), namely that of a general underestimation of the supercooled liquid water content.

The instruments mounted on the research aircraft are discussed in Cober et al. (1995, 2001a,b). Temperature was measured with a Rosemount temperature probe and a reverse flow temperature probe. Dewpoint was measured with a Cambridge dewpoint hygrometer. Total and liquid water contents were measured with Nezorov and King hot-wire probes. Ice water contents were inferred from the measurements of LWC and TWC following Cober et al. (2001a).

Figure 3 illustrates the meteorological situation on 15 January 1998 at 1800 UTC. Key features are a deep system in the Pacific Ocean bringing clouds and precipitation over the west coast of the United States and a weaker system centered over the Canadian prairies and associated cloud cover the center of North America. On the eastern portion of the continent, a warm frontal trough extended from a low pressure system centered over Gulf of Mexico to the Great Lakes region. The major portion of the clouds [cloud-top pressure (CTP) is calculated here at the model resolution after Garand (1993)] and precipitation linked with this system is confined to the east coast of the United States. Over Lakes Erie and Ontario the cloud deck is shallower and the precipitation is less intense.

Aircraft data collected at low levels over Lake Erie indicate a well-defined freezing drizzle episode, and supercooled large drops were encountered in the clouds for a total duration of about 30 min (Cober et al. 2001b). Figure 4 summarizes some of the microphysics observations collected during the research flight. During this flight the temperature always remained below 0°C (see Fig. 4c) excluding freezing precipitation formed from the classical melting-ice mechanism (Huffman and Norman 1988). This flight provides a good test bed for the microphysics cloud scheme. The aircraft took off from Ottawa (point A) at 1648 UTC (see Fig. 4a) and encountered a deep ice cloud with embedded layers of SLW (see Fig. 4b). The aircraft exited the cloud at an altitude of 5000 m at point B just after crossing a mixed-phase area at a temperature of −20°C and started subsequently a descent to low level over Lake Erie (points C and D). At this point, an episode of freezing drizzle was detected at low level (z < 2000 m, T ≈ −5°C) and high values of SLWC (>0.2 g m−3) were observed. Near the end of the flight, while approaching Ottawa, a layer (2000–3500 m) of SLW with peak values >0.4 g m−3 was observed at point E. In summary, it can be said that except for the beginning of the flight (segment A–B), the clouds were mostly constituted of SLW (Fig. 4d).

4. Numerical experimentation setup

To evaluate the impacts of the proposed modifications to the basic MXP scheme, a number of numerical simulations were performed. The Canadian Mesoscale Compressible Community (MC2) model was used for these tests. The MC2 model originates from a regional hydrostatic model (Robert et al. 1985). It was generalized to the Euler system by Tanguay et al. (1990) and successfully applied to synoptic storm simulations. Subsequently, Robert (1993) used the model at finescale for bubble convection experiments and Tremblay (1994) simulated a squall line. These various applications illustrate the flexible nature of this dynamical framework. Recently, the MC2 model was used to provide the real-time forecast support during the Mesoscale Alpine Program field experiment (Benoit et al. 1999). Some characteristics of MC2 include variable vertical resolution, a modified Gal-Chen terrain-following scaled-height vertical coordinate, a limited-area one-way nesting strategy, and a complete physics package (Benoit et al. 1997).

Table 1 summarizes the various numerical experiments (including the names by which these experiments shall be referred to later) analyzed in the present investigation based on the discussion of section 2. Details are also given on resolution, grid size, and nesting strategy. Each of these simulations uses a 40-level vertical stretched grid with a resolution of 15 m near the surface increasing to about 1.5 km at model top (25 km). Additional tests were also done during the investigation to ensure that the present simulations results are meaningful. Thus, different numbers of vertical levels, horizontal domain sizes, and different initialization times were tested and the best configuration for convergence of numerical results has been established.

An important aspect of the present investigation is an evaluation of model performance from a point-by-point comparison of pertinent variables along real and virtual aircraft trajectories (Vaillancourt et al. 2003). During integration, the model is fed with aircraft trajectories in terms of latitude–longitude points. For each of these points, the closest grid point is calculated. During its execution the model outputs specified variables at all vertical levels and every time step for all such grid points. After model execution, the virtual aircraft trajectory is constructed by choosing, for every observed data point, the closest available model data point in terms of time, pressure level, and latitude–longitude position. To establish a meaningful comparison between model and aircraft (V = 100 m s−1) observations, a restriction on the time step (Δt ≤ Δx/V) was imposed to ensure that the aircraft remains within the same model tile during one model iteration.

5. Simulations evaluation

Figure 5 displays some results of the basic control run (MXP35). The figure shows the horizontal distribution of the modeled CTP and the surface precipitation rate, for a 30-h forecast valid at 1800 UTC 15 January 1998 (at that time the aircraft was located near point C in Fig. 4). The model CTP is calculated following a procedure described in Tremblay et al. (2001). Comparing to Fig. 3, it can be seen that the forecast is quite reasonable and that general features of both CTP and precipitation are well captured. As discussed in Tremblay et al. (2001) a comparison with Fig. 3b shows that the model tends to underforecast the overall cloud coverage and that upper-level clouds (<400 mb) are underestimated. An overestimation of midlevel clouds (700–400 mb) is also apparent. The low-level clouds (>700 mb) over the Pacific Ocean are not very well reproduced. The clouds over the Great Lakes seem slightly too low compared to the satellite retrieval of Fig. 3. The surface precipitation forecast seems acceptable and the systems on the west and east coasts of the United States, visible in the radar map (Fig. 3c), are reproduced. The model also captures the weak precipitation band over Lakes Erie and Ontario.

Since issuing SLW forecasts for aircraft icing and freezing precipitation is a major motivation for incorporating the MXP scheme in the Canadian NWP models, a detailed analysis of this variable is mandatory. In particular, it is imperative to determine the requested model resolution to optimally reproduce the location and intensity of SLW events. Figure 6 depicts the horizontal distribution of the supercooled liquid water path (SLWP) for MXP35, MXP10, and MXP03 runs. The nested domain outlines are also included in the figure for reference. It can be seen that, except for the narrow SLW band over Lake Ontario in the 10- and 3-km runs, there are no significant small-scale patterns appearing in the high-resolution runs. In particular, the intense SLW area located to the northwest of Pennsylvania remained unchanged for all tested resolutions. This suggests that the associated winter synoptic system is reasonably well resolved at coarse resolution (35 km) and that the numerical solution is convergent.

Furthermore, the time series of the virtual aircraft displayed in Fig. 7 confirms that increasing the horizontal resolution does not improve forecasts of SLW. A comparison with Fig. 4 indicates that all three simulations fail in reproducing the intensity of the SLW signal. The model systematically underforecasts the intensity of SLW and overforecasts IWC suggesting that some adjustments to the microphysics module are required. There is also a slight deterioration of the location of the cloud boundaries (sections B–C and C–E in Fig. 4) in the 10- and 3-km runs. Figure 8 compares observed and simulated time series of temperature and dewpoint for MXP35, MXP10, and MXP03. In the figure, observational uncertainty on the temperature (±1°C) and on dewpoint (±2°C) have been included in the aircraft time series. It can be seen that except for a small deterioration in the temperature and moisture fields at t = 500 in MXP03, the runs are roughly equivalent, suggesting again that this system is well resolved by MXP35 and no significant gain can be associated with high-resolution runs. A comparison between modeled and observed winds yields the same conclusion. The reader should note that these conclusions are not universal and only apply to winter storm synoptic systems like the present case. In fact, Bélair and Mailhot (2001) noted that high-resolution simulations greatly improve squall-line simulations and Mailhot et al. (2001) demonstrated the benefit of high-resolution models for simulation of SLW clouds in the Arctic.

Figures 9–13 summarize sensitivity tests discussed in section 2. It is clear from Fig. 9 that NEWC (see Table 1) is almost identical to MXP35 (Fig. 5a) implying that the new formulation of the closure assumption has virtually no effects on CTP distribution. As discussed in section 2b, NEWC is simply a reformulation of the SLW calculation and is inoperative in glaciated clouds where ice physics controls the distribution of cloud tops. A detailed examination (not shown) of model precipitation has not revealed any significant differences in quantitative precipitation forecasts (QPFs) between NEWC and the control run MXP35. The freezing precipitation event over the Great Lakes region is, however, significantly stronger in NEWC than in MXP35, but it is too localized to affect global CMC precipitation scores. A comparison of GAM2 and RP with Geostationary Operational Environmental Satellite-8 (GOES-8) CTP (Fig. 3) shows that the forecast quality has significantly decreased in these two runs. In particular, GAM2 significantly underestimates the extent of upper-level clouds and an overestimation of midlevel clouds is also apparent suggesting that this distribution is not appropriate as a forecast application. It is useful to mention that the GAM1 run has roughly an equivalent CTP distribution but underestimates SLW. The RP simulation systematically underestimates cloud cover (cf. with Fig. 3) and has a distribution of clouds in the vertical similar to the Canadian operational cloud scheme as discussed in Tremblay et al. (2001). In this paper, this behavior of the Canadian operational cloud scheme was attributed to the instantaneous removal of precipitation from the atmosphere by the scheme. This was the basic motivation for the additional test run RP-mod. The Ryan's critical ice content defined by (20) decreases steeply with temperature for T < 255.66 K implying that the sedimentation of cold clouds is increased, contributing to lower CTP. The RP-mod CTP map displayed in Fig. 10 shows that limiting kS for cold temperature greatly improves the CTP forecast compared to both RP and GAM2. There is also a definite resemblance between RP-mod and MXP, likely related to the selection of kS.

The virtual aircraft trajectories depicted in Fig. 11 demonstrate that the modifications to the basic MXP tend to significantly increase SLW amounts, particularly for the GAM2 and RP-mod simulations, the impact of NEWC being less important. It can be seen that RP-mod improves the forecast of the mixed-phase cloud observed along segment A–B compared to NEWC and GAM2. However, the position of the cloud boundaries is slightly deteriorated in the RP-mod run along segments B–C and D–E. In addition, both GAM2 and RP-mod provide an improved forecast of SLW over Lake Erie (segment C–D in Fig. 4) and the two peaks of SLW observed in the last portion of the flight are captured by these two runs. There is also an apparent saturation of the SLW signal in these two experiments. As discussed in Vaillancourt et al. (2003), this saturation is due to the chosen value of the kL parameter (=0.1 g m−3). An additional test run (RP-mod2) generated a SLW distribution in better agreement with aircraft observations (Fig. 4) as demonstrated in Fig. 12. It can be seen that increasing the value of kL to 0.5 g m−3, which in practice causes a delay in the initiation of precipitation, leads to the formation of intense peaks of SLW that better match aircraft observations. Even if sensitivity tests presented by Tremblay et al. (2001) have shown that surface precipitation is not dramatically affected by the choice of kL, it may be delicate to tune this parameter since the QPFs may be sensitive to this parameter. Thus a detailed study of QPFs involving many cases should be realized before recommending a definitive value for kL. Time series in Fig. 12 also show an improvement in the RP-mod2 run of the simulated IWC compared to the MXP35-mod run suggesting that RP-mod2 is a suitable substitute for the simple exponential IP distribution build into the basic MXP scheme. The sensitivity of cloud microphysics to adjustable parameters built into the model formulation suggests that alternatives to the simple Kessler-type warm rain parameterization (Kessler 1969) should be sought. The reader should note that this type of parameterization is not limited to the MXP scheme and can be found in several cloud models. The present context emphasizes that aircraft observations are powerful tools for the optimization of cloud microphysics models. For completeness, time series of temperature and dewpoint for aircraft observations and the NEWC, GAM2, and RP-mod2 runs are presented in Fig. 13. It can be seen from this figure that NEWC and RP-mod2 are roughly equivalent and generate acceptable forecasts. However, GAM2 produced large errors in dewpoint (≈20°C) at the end of the flight demonstrating once again problems with this distribution.

To generalize the results of the present investigation, a number of diagnostics have been calculated for the overall model three-dimensional domain. Specifically, the three-dimensional distribution of IWC, LWC, and CTP were analyzed in detail. The results of this additional investigation simply confirm the above discussion and show that RP-mod2 systematically forecast more SLWC and less IWC compared to the basic MXP scheme.

In order to provide further support for the conclusions discussed in the present paper, an additional CFDEIII case has been selected and all the numerical experiments discussed above have been repeated for this particular case. The case selected was the CFDEIII flight on 11 February 1998 at 1716–2213 UTC. This case was voluntarily selected because of its differences with the flight of 15 January. It was characterized by the presence of a predominant ice-phase cloud over the Great Lakes region. An analysis of these results identical to that discussed above has again confirmed that the RP-mod2 configuration produces better forecasts.

6. Summary and conclusions

In this paper, a methodology proposed initially by Tremblay et al. (1995) and subsequently refined by Vaillancourt et al. (2003) has been used in conjunction with aircraft data, collected during the First and Third Canadian Freezing Drizzle Experiments, to optimize a mixed-phase cloud microphysics scheme (MXP). The methodology consists of storing runtime model data at each time step, thus allowing the reconstruction of any model variable along a virtual aircraft trajectory that matches that of a given research flight in space and time. It has been demonstrated in this article that the proposed methodology is a powerful tool that allows the use of research aircraft observations to adjust unknown parameters and to evaluate alternatives in the formulation of the physics in a cloud model to obtain better forecasts of cloud microphysics properties.

From detailed comparisons between virtual and actual aircraft data, it has been possible to establish that increasing the model resolution from 35 to 3 km through a nesting strategy did not improve the accuracy of the cloud microphysics within one winter storm forecast. This suggests that for improvements in forecasts, the cloud model itself should be examined instead of attempting an increase in resolution. Although it was felt that the simulated winter storm system was resolved at a horizontal resolution of 35 km, no significant degradation of the forecast was found in the high-resolution simulations. This suggests that MXP can be run concurrently within a hierarchy of atmospheric models such as the new CMC Global Environmental Multiscale (GEM) GLOBAL-MESO (35 km) model and the next CMC GEM-REGIONAL (15 km) model.

As discussed in Vaillancourt et al. (2003), the original MXP scheme systematically underforecasts the supercooled liquid water content and overforecasts the ice water content. Several avenues have been explored to fix this problem. The formulation of the production rate of supersaturation in mixed-phase clouds has been generalized using the actual model supersaturation tendency instead of using the saturated updraft approximation built into the basic MXP scheme. A detailed comparison between model data and aircraft observations has revealed that this modification only weakly improves mixed-phase clouds simulations, implying that the original approximation used by Tremblay et al. (1996) was reasonable for winter storms situations and was not the main cause of the problems discussed above.

As discussed in sections 2c and 2d, the selected IP size distribution has a strong influence on the calculation of various ice-microphysics processes such as vapor deposition, riming, and sedimentation. Several test runs have been executed to choose a distribution that optimizes the quality of forecasts. In an attempt to replace the simple IP exponential size distribution used in the basic MXP scheme with a more realistic one, several numerical experiments have been done with Γ size distributions. These experiments have shown a deterioration of the CTP distribution compared to the basic MXP control run, suggesting that such a distribution is not suitable as a forecast application. On the positive side, it was noted that Γ distributions provided better SLW forecasts (with respect to the basic MXP scheme) when compared to the aircraft observations. This was attributed to a decrease in concentration of small-size particles compared to the exponential distribution used in the basic MXP scheme.

The empirically based bulk parameterization of IP size distribution of Ryan (2000) was also implemented in MXP for experimentation and testing. A first run has shown that the Ryan parameterization seriously underforecasts the overall cloud cover in the model domain. This run also indicated that the top of the clouds is too low, which is similar to the operational CMC cloud scheme (Tremblay et al. 2001). However, limiting the critical ice content [Eq. (20)] for temperatures colder than 255.66 K prevents the oversedimentation of upper-level clouds and gives a much better forecast. A detailed comparison of cloud properties along virtual and actual aircraft trajectories indicates a significant improvement of IWC forecast. However, just as for the Γ distribution, a saturation of the SLW signal was observed. This was attributed to a too low value of the liquid phase threshold and increasing this parameter has produced a forecast in reasonable agreement with aircraft observations. This suggests that under these conditions, the Ryan (2000) parameterization is a suitable alternative to the simple exponential distribution currently implemented in the MXP scheme.

Finally, it should be noted that the present study is only a first shy step toward optimizing clouds models with observations. Clearly, more studies with different and additional datasets are needed for other geographical locations and for a wide range of meteorological conditions.

Acknowledgments

The authors are grateful to the National Search and Rescue Secretariat of Canada for their financial assistance.

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Fig. 1.
Fig. 1.

A comparison of the moments of interest for an IP size distribution of MXP with Γ size distributions (p = 1 and p = 2)

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 2.
Fig. 2.

As in Fig. 1 but the Ryan–Platt IP size distribution. The dependence on temperature of the RP first moment is also depicted

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 3.
Fig. 3.

(a) Sea level isobars superimposed with GOES-8 brightness temperature. (b) Satellite-derived cloud-top pressure. (c) National Climatic Data Center Next Generation Weather Radar mosaic reflectivity map. All valid at 1800 UTC 15 Jan 1998

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 4.
Fig. 4.

CFDE III research flight 1648–2133 UTC at 15 Jan 1998: (a) horizontal projection of aircraft trajectory showing cloud phases, (b) as in (a) but for the vertical projection, (c) time series of temperature (°C) observed during the flight, and (d) time series of observed LWC (g m−3) and IWC (×−1 g m−3)

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 5.
Fig. 5.

(a) Model CTP (mb) distribution. (b) Model surface precipitation rate (mm h−1). Both maps are 30-h forecasts valid at 1800 UTC 15 Jan 1998

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 6.
Fig. 6.

SLWP (kg m−2) maps valid at 1800 UTC 15 Jan 1998 for the three nested simulations. Outlines of the nested domains are also included for reference

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 7.
Fig. 7.

Time series of model LWC (g m−3) and IWC (×−1 g m−3) along the virtual aircraft trajectory for the three nested runs

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 8.
Fig. 8.

(a) Time series of aircraft and model temperature (°C) for the three nested runs. The instrument absolute error range (°C) has been incorporated into the aircraft time series. (b) As in (a) but for dewpoint

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 9.
Fig. 9.

CTP maps for (a) NEWC, (b) GAM2, and (c) RP

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 10.
Fig. 10.

As in Fig. 9 but for RP-mod

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 11.
Fig. 11.

As in Fig. 7 but for NEWC, GAM2, and RP-mod

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 12.
Fig. 12.

As in Fig. 11 but for RP-mod2 and MXP35-mod

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Fig. 13.
Fig. 13.

As in Fig. 8 but for NEWC, GAM2, and RP-mod2

Citation: Monthly Weather Review 131, 4; 10.1175/1520-0493(2003)131<0672:IOAMPC>2.0.CO;2

Table 1.

Numerical experiments

Table 1.
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