## 1. Introduction

Initialization of finescale cloud-resolving models has always been a delicate task for nowcasting purposes, mostly because convective systems involve complex physical processes at different scales of time and space, such as large-scale convergence and microphysics. Lilly (1990) discussed a number of these difficulties and pointed out the need for initialization methods using observational data. As a matter of fact, simulated convective scale systems are classically initialized by superimposing arbitrary disturbances, such as warm or cold perturbations, to a horizontally homogeneous field derived from soundings. Even though this method often succeeds in simulating realistic features and sometimes in obtaining output close to the observations (Lafore et al. 1988; Trier et al. 1996; Montmerle et al. 2000), several drawbacks exist. For example, Montmerle et al. (2000) show that the interaction between ice processes and environmental wind shear involves a strong dependence of the evolution of convective organization on the orientation of its initial low-level forcing. Moreover, a common drawback is the spinup time of the model itself, which is inconsistent with numerical prediction, where the location and the timing of convective systems need to be predicted.

Another kind of initialization of cloud resolving models is by performing nested simulations from a large-scale analysis. In this case, as pointed out by Wilson et al. (1998), the model must be able to simulate the storm since the convective circulation was not described in the initial state. This initialization may be successful in the case where the convective system is strongly governed by large-scale forcing and by using appropriate convective parameterization schemes for the large-scale simulations. In most cases, this method involves too many processes for a short-term forecast of a convective system.

Simulations in which the explicit structure of thunderstorms is initialized have only been attempted recently. These studies are using Doppler radars that measure the three-dimensional distribution of reflectivity and radial velocity within the observed storm. In addition to the nowcasting interest of these methods, such an initialization permits to retrieve nonmeasurable physical parameters within the system, such as microphysical quantities. To have access to all the parameters that govern a given convective system allows the quantification of the effect of the latter on larger scales in terms of momentum, humidity, and latent heat release. Lin et al. (1993) and Bielli and Roux (1999) used multiple-Doppler-radar-derived fields to determine initial conditions from which a cloud-resolving model is started. Such a method requires retrieving, calculating, or estimating every prognostic variable of the model, that is to say, the dynamical, thermodynamic, and microphysical fields. Lin et al. (1993) established the feasibility of the method by performing a realistic simulation of a tornadic supercell storm during 30 min. However, their simulation evolves faster than the observations. Even if the cause of that feature was not discussed in their study we suspect the main reason to be the fact that their microphysical scheme did not contain cold processes. Besides, Bielli and Roux (1999) concluded that apart from the wind circulation, the initial moisture field was a key parameter for such a purpose.

Taking inspiration from large-scale numerical models, four-dimensional variational (4DVAR) data assimilation methods have been applied to convective scale models. Briefly, these methods consist of fitting a numerical model to a time series of Doppler radar observations. Sun and Crook (1997, 1998) used such a 4DVAR technique to retrieve the dynamical, buoyancy, and warm microphysical fields from single-Doppler observations of a Florida convective storm. These variational analyses permit generating unobserved fields at convective scales rather than forecasting the evolution of the observed fields.

The method presented in this paper uses some aspects of these two approaches. As in Lin et al. (1993), all the initial 3D physical fields corresponding to the model's prognostic variables are retrieved or estimated. The retrieval technique follows the previous works of Laroche and Zawadzki (1995, hereafter LZ95) and of Protat and Zawadzki (1999, hereafter PZ99) and Protat et al. (2001, hereafter P01), whose methods have been upgraded for numerical prediction purposes. This technique consists of a variational adjustment of the model variables to observations (coming from a bistatic Doppler radar network) under physical constraints that are the cloud-resolving model equations. The fields retrieved using this method are then considered as initial fields in the forthcoming simulations performed using the Canadian Mesoscale Compressible Community (MC2) cloud-resolving model (Laprise et al. 1997).

The goal of this paper rests on demonstrating the feasibility of such an initialization and its interest for nowcasting purposes. The most successful nowcasting method at the mesobeta scale is the “Lagrangian persistence” method (see Bellon and Austin 1978). Thus, our objective is to answer the following question: Can the forward simulation outperform the Lagrangian persistency in a 30-min period in terms of precipitation distribution? For this, we have chosen to simulate a midlatitude summer storm that passed over Montreal on 2 August 1997, which presents a great challenge for this purpose. Indeed, this case was composed of three different convective cells at different stage of development: one of the cells was in its mature stage, the second one was rapidly developing, and the final one was decaying.

This paper is organized as follows. Section 2 presents the observational data used in this study, coming from two different sources: one characterizing the precipitating areas and the other one the clear air environment. The formulation of the variational method that allow for the recovery of the various 3D physical fields from these datasets is described in section 3. Section 4 presents the initial states obtained from this method and used for the numerical experiments, the results of which are detailed in section 5 and compared to a simple Lagrangian persistency prediction in order to show the efficiency of the method.

## 2. The data

Doppler radar observations describe only the regions containing precipitation. For the model initialization, it is also necessary to fill regions void of data that correspond to precipitation-free areas or regions outside the dual- or triple-Doppler coverage area. The different fields that filled this unobserved region will be referred to as the *background fields* in what follows.

### a. The multiple-Doppler region

Reflectivity and radial velocities are sampled in the precipitating regions by the bistatic network operated by McGill University. This operational bistatic network consists of one S-band Doppler radar, located 30 km west of downtown Montreal, and of two passive bistatic receivers situated roughly south and northwest of Montreal Island (see Fig. 1). The locations of these two receivers allow for high-density triple-Doppler coverage over Dorval airport and dual-Doppler coverage in a more extensive area.

On 2 August 1997, a line of heavy convective storms passed over Montreal Island, propagating with an approximate advection speed of 10 m s^{−1} along a SEE direction. The monostatic radar and both bistatic receivers sampled three convective cells of the system during approximately 15 min, the more important of the three staying in the multiple-Doppler area for almost 45 min between 2200 and 2245 UTC.

Figure 2 displays a horizontal cross section of the monostatic radar reflectivity at 2.5 km performed at 2207 UTC and shows clearly this east–west-oriented line of heavy showers depicted by values greater than 50 dB*Z.* This figure also reveals the retrieval domain that corresponds to a region of 100 × 100 km^{2} within the area of bistatic coverage.

### b. The clear air environment

Since the chosen case is relatively isolated and does not depend on complex large-scale circulation, the background field is taken to be horizontally homogeneous. This background is defined by a composite sounding deduced from a regional analysis of the Canadian Meteorological Center (CMC) and from measurements performed by the McGill's UHF profiler located in downtown Montreal. The latter allows a more precise description of the boundary layer temperature, which is considered in our case to be a mixed layer. The analysis sounding is accordingly modified between the ground and the 925-hPa levels.

The large-scale environment is characterized by westerly winds that are increasing with altitude up to 12 km above ground level (AGL), where the ambient wind reaches a peak greater than 30 m s^{−1} (Fig. 3b). The east–west major axis of the entire convective system is aligned approximately parallel to the relatively constant wind shear. Furthermore, the atmosphere is moist in the lower troposphere (Fig. 3a). The lifting condensation level is at 0.8-km altitude, the level of free convection at 1.5 km, and the equilibrium temperature level at 12 km. The convective available potential energy value is approximately 540 J kg^{−1}, which corresponds to moderate instability.

## 3. Methodology

The basic principle of the retrieval method is to variationally adjust the model dynamical fields to the observations under physical constraints that compose the *constraining model.* As explained in LZ95, these physical constraints are combined into strong and weak constraints, depending, respectively, on whether they must be satisfied exactly or if a residual discrepancy between observations and model variables is allowed. The sum of the weak constraints (called the cost function) is then minimized in our case with the method of the conjugate gradients. The weak constraint formalism is particularly appropriate to allow for the observational errors or assumptions and approximations made in the equations (model errors).

PZ99 and P01 have developed the methodology to retrieve dynamic and thermodynamic fields in Cartesian coordinates from two successive volumetric scans of bistatic radar network data. In PZ99, the *control variables* (i.e., the variables to be retrieved by the method) were the two horizontal wind components *u* and *υ,* since *w* was obtained using weighted upward and downward integration of the anelastic continuity equation. The latter equation was used as a strong constraint, whereas the matching of the variables to the observations was written under a weak constraint formalism. In P01, the nondimensional pressure *π** and the “virtual cloud” potential temperature perturbation *θ*^{*}_{c}

In the present study, this variational method has been adapted for cloud model initialization purposes as explained in Caya et al. (1999). Indeed, the different dynamical fields must satisfy the physical equations of the MC2 model, as well as the numerical discretization, to avoid nonrealistic features during the integration of the model. Therefore, all the equations that compose the constraining model have been discretized on a Arakawa C grid type (Arakawa 1966), which is the staggered grid used in the model. Furthermore, as we will see in the following, we have chosen the same thermodynamic variables as those used as prognostic variables in MC2.

### a. Retrieval of the 3D air circulation

**V**

_{t},

**V**

_{P}, and

**V**

_{B}represent the analyzed radial velocities in space seen by the transmitter, the

*P*passive receivers, and the background, respectively. In the case of the background, vertical motion is assumed to be zero to avoid the development of nonobserved features. In contrast to PZ99, the two diagonal weighting matrices

**W**

_{t}and

**W**

_{P}that depend on the strength of the constraint do not have the same values in our case. De Elia and Zawadzki (2000) have shown that sidelobe contamination in bistatic radar systems can be an important source of error. Following their study, this contamination is quantified for grid points sampled by each of the two bistatic receivers. The variance of the Doppler measurements for each receiver, from which the two diagonal weighting matrices are deduced, is then computed according to this index of contamination. Finally, the diagonal matrix

**W**

_{B}is composed of unity or zero for points located in the background or in the radar coverage area, respectively, in order to avoid the contamination by the background of the area sampled by the bistatic network.

*k*= −∂(ln

*ρ*)/∂

*z*and

*ρ*is the air density. PZ99 proposed to integrate this equation by using a weighted average of both upward and downward integrations and their adjoints, starting from a lower boundary condition

*w*= 0 at ground and an upper level chosen one grid point above the echo top. Although their results seem consistent and realistic while using only radar data, this method leads to some nonrealistic features in the case where a background field is added. Some incoherence was appearing between vertical profiles of horizontal divergence and vertical velocity, and thus a nonnegligible residual of (2) was obtained at the border between the sampled domain and the background, which is not acceptable for the initialization of the cloud model. Here we modified the integration of the continuity equation by adding a new weak constraint in the retrieval process: we require that the discrepancies between the vertical velocities deduced from the upward integration and from the downward integration (denoted

**w**

_{↑}and

**w**

_{↓}, respectively) be minimized. This leads to a new additional cost function to be minimized:where

*xyz*is the entire retrieval domain,

**w**=

**w**

_{↑}, and

**W**

_{W}the weighting diagonal matrix.

### b. The smoothness constraint

*ψ*denotes a control variable and

*γ*is the associated weighting factor.

*J*

*J*

_{1}

*J*

_{2}

*J*

_{3}

This minimization is performed with the conjugate gradient method, which uses the gradient of the cost function to determine search directions.

It is desirable for the background field to influence the dual-Doppler area as little as possible. In other words, dynamical features of the background should not propagate through the precipitating areas via the smoothness constraint. Thus, as depicted in Fig. 4, the nine grid points that compose the smoothing operator contribute normally to *J*_{3}, but the gradients of *J*_{3} with respect to control variables are not taken into account for all points of the observed area located nearby a point that belongs to the background.

### c. Thermodynamic retrieval

*q*= ln(

*p*/

*p*

_{0}), where

*p*stands for pressure and

*p*

_{0}a constant, and the temperature

*T.*The nondimensional pressure is decomposed into a basic state

*q**(

*z*) corresponding to an hydrostatic isothermal atmosphere and a perturbation around this basic state

*q*′(

*x,*

*y,*

*z,*

*t*). The temperature is also decomposed but into an isothermal state

*T** and a deviation around this state. Thus,

*T*and

*q*are expressed as follows:The constant

*g*is the acceleration due to the gravity and

*R*is the gas constant for air. Following a method similar to Gal-Chen (1978), the fields of thermodynamic variables are deduced from the three momentum equations written in an Eulerian formulation:where

*κ*is the coefficient of eddy viscosity, ∇

^{2}is the three-dimensional Laplacian,

**ϵ**^{q}

_{m}

*q*

_{r}is the liquid rain mixing ratio (in g kg

^{−1}) deduced from the observed reflectivity

*Z*(dB

*Z*) using the empirical relationship from Hane and Ray (1985).

*q*

_{r}

^{(Z−43.1/17.5)}

*ρ.*

**Q**'s are diagonal model error covariance matrices, composed in our case of the identity matrix. In this part of the total cost function, only

*T*′(

*x,*

*y,*

*z,*

*t*) and

*q*′(

*x,*

*y,*

*z,*

*t*) are, respectively, allowed to vary around an initial guess

*T*′(

*z*) given by the sounding defined in section 2b and the hydrostatic profile

*q*′(

*z*) defined (for a nonprecipitating area) byThe uniqueness of the solutions is not guarantee, but the solution seems reasonable. The mean retrieved deviations from these initial states are indeed very close to zero.

To summarize, the retrieval is performed in two steps. First, the three components of the wind are analyzed in time and smoothed by minimizing (5). Then, *T*′ and *q*′ are retrieved by minimizing the additional cost function *J*_{4}, where they are the only control variables, from the initial dynamical state deduced from the previous minimization and the initial hydrostatic state given by the sounding defined in section 2b.

Thus, the three wind components *u,* *υ,* and *w*; the temperature perturbation *T*′; and the nondimensional pressure perturbation *q*′ are retrieved. The liquid rain *q*_{r} is also directly estimated from (13). Initial fields of the other prognostic variables of MC2 still needed to be estimated. These variables are the specific humidity *q*_{υ}, the liquid cloud *q*_{c}, the graupel *q*_{g}, and the ice cloud *q*_{i} mixing ratios.

### d. The humidity field

Previous studies, such as Lin et al. (1993) or Bielli and Roux (1999), have shown that an appropriate description of the humidity field is a key factor for the initialization of a cloud-resolving model by the explicit structure of the storm. Indeed, the saturated updrafts allow for the maintenance of ascending motions through latent heat release from condensation, and unsaturated areas permit the precipitation to evaporate and, therefore, the cooling of the concerned air mass. Since no observation of humidity is available, empirical formulations are commonly used. Lin et al. (1993) imposed saturation in the precipitating areas (i.e., observed by the radars) above the lifting condensation level, whereas clear air environment is characterized by a large-scale sounding. Ducrocq et al. (2000) extend these saturated regions to nonprecipitating but cloudy areas using satellite imagery. These studies show satisfactory results, but the unsaturated regions are not defined. An attempt to correct this has been made by Bielli and Roux (1999) by using a “production rate of precipitation,” which links the precipitating water content deduced from the reflectivity to their fall speed. Positive values show formation of precipitation, implying that the air is saturated, while negative values denote a precipitation sink, revealing evaporation in unsaturated air.

*w*are linked using a linear relationship. To derive this empirical formulation, we have performed a scatterplot of RH versus

*w*for some precipitating grid points of a simulation of a convective system. This system was a summer storm comparable to the 2 August 1997 case in terms of intensity and precipitation accumulation. This simulation was made using a 1-km horizontal grid resolution and was the result of two nested simulations from an initial large-scale analysis. The scatterplot performed after 3 h of integration is shown in Fig. 5. It indicates that the updrafts are almost always saturated (i.e., with a corresponding value of RH reaching 100%), while the downdrafts are related to the humidity in a less deterministic manner. By a linear fit to these points an empirical relation between RH and

*w*for downward motions is obtained:

*w*

*w*in meters per second. The humidity values are scattered around this line with a mean square root of 6.1%, which is acceptable. The specific humidity field

*q*

_{υ}is then deduced through the calculation of the specific humidity at saturation, following the relation

Finally, the humidity profile is determined elsewhere by the sounding plotted in Fig. 3.

### e. The hydrometeors

The liquid rain water mixing ratio *q*_{r} (g kg^{−1}) is derived from the reflectivity field *Z* using Eq. (13).

On the other hand, there is no reliable way to estimate the cloud water mixing ratio *q*_{c}. Since within well-developed precipitation the cloud water is usually much smaller than the rainwater counterpart, its contribution to the buoyancy evolution budget is relatively small. Thus, *q*_{c} is assumed to be zero at the initial time step. It has to be noted that experiments have been performed using different initial estimations of *q*_{c} [i.e. constant value for each precipitating grid points below the 0°C isotherm and above the LFC or using Kessler (1969) bulk microphysics] and that no improvement has been observed during the integration of the model. In the same manner, the initial values of the ice cloud *q*_{i} and the graupel *q*_{g} mixing ratios are equal to zero.

## 4. The initial field

Figure 6 displays horizontal cross sections at 2.25 km of reflectivity and absolute wind circulation, vertical motion, and thermodynamic variable fields at the initial time *t*_{0} of the integration. These fields are the result of the assimilation procedure applied on two successive 5-min volumetric scans performed at 2207 and 2211 UTC. Hence, *t*_{0} corresponds to the intermediate time between these two scans. The retrieval domain corresponds to the 100 × 100 km^{2} subdomain plotted in Fig. 2. The staggered grid has a resolution of 1 km horizontally and 500 m vertically.

These plots show one main large convective cell that includes two cores of heavy precipitation. This first cell, denoted C_{1}, is almost 30 km wide and is characterized by maximum reflectivity values above 45 dB*Z* and vertical motions reaching 4 m s^{−1} at 4.25-km altitude (Figs. 6a and 6b, respectively). Vertical cross sections taken across this cell show the important vertical extension of the associated cloud that reaches 11-km altitude (Fig. 7). In the eastern part of C_{1} are situated two smaller twin cells of strong precipitation. The southern one, denoted C_{2}, is characterized by a much stronger convective activity than its northern counterpart (referred to as C_{3}), with updrafts greater than 3 m s^{−1} around 5 km (Fig. 7a). The convective activity is less intense for C_{2} than for C_{1}, whose cores of maximum vertical velocity are located between 6 and 8 km. The area included between these two cells is characterized by stratiform precipitation (around 30 dB*Z*), coinciding with a dry pocket of downdrafts produced by the precipitation that is formed aloft (Fig. 7).

The horizontal cross section at 4.25 km of the retrieved temperature perturbation *T*′ displays positive values of 0.7 K in the cores of C_{1} and C_{2} (Fig. 6c). Since these positive deviations coincide with the areas of maximum convective activity, it is likely that they result from latent heat release within these updrafts. A positive value of *T*′ around 0.2 K is observed for C_{3}, denoting weaker diabatic heating consistent with the weaker updrafts. Negative perturbations reaching −0.4 K are also found around C_{1} and C_{2}. It results either from evaporative cooling or from dynamic interaction between the background and the storm, which is obviously the case in the eastern part of C_{2} located on the border of the bistatic coverage region. Between C_{1} and C_{2} an area of positive perturbation is located coincident with downdrafts, denoting downward motion of unsaturated air. In the background, a simplification of (12) considering the absence of vertical motions indicates that the south–north-oriented negative horizontal gradient of *T*′ is mainly due to the horizontal gradient of the vertical gradient of the pressure perturbation.

Negative horizontal gradients of pressure perturbations are pointing to the north-northeast at 4.25-km altitude for the whole retrieval domain (Fig. 6d). These perturbations are a deviation from the horizontal pressure deduced from the retrieved *q*′ and the pressure at ground given by the sounding. A pressure change of approximately 1.2 hPa for 100 km is observed and is due to the Coriolis terms in (10) and (11), except in the precipitating area where the contribution of temporal evolution of the horizontal wind is dominant.

From previous observations (not shown), C_{1} appears to be in its mature stage at time *t*_{0} while C_{2} seems to intensify progressively. On the other hand, C_{3} starts to dissipate, as characterized by a decrease of the intensity of the reflectivity and by the weakness of its convective activity at *t*_{0}. The nowcasting of this case seems challenging.

## 5. Forward simulation and comparisons with observations

Since the goal of this paper is to show the feasibility of the method presented in section 3, only one forecast is displayed herein. As discussed previously, this simulation uses the simpler assumptions: the background is deduced from a single sounding, relative humidity is deduced from the vertical velocity through a simple linear formulation, and initial solid hydrometeors are set to zero.

### a. Simulation methodology

The fields described in the previous section are then used as initial fields in the MC2 cloud-resolving model. This model uses a semi-implicit semi-Lagrangian algorithm (Tanguay et al. 1990) and a complete warm and cold microphysical parameterization (Kong and Yau 1997) that takes into account the liquid cloud *q*_{c} and liquid rain *q*_{r} mixing ratios, as well as the graupel *q*_{g} and ice crystal *q*_{i} mixing ratios.

The simulation domain is the same as the one used for the retrieval with a 100 × 100 km^{2} horizontal domain. The horizontal resolution is 1 km while in the vertical a stretched grid mesh is used. The model top lid is at 25-km altitude and a sponge layer is applied above 17 km. At the lateral boundary, the model variables are driven by large-scale values coming from the same CMC regional analysis that was used to define the clear air environment in section 2b. These large-scale values are nested progressively over a band of five-grid point width along the border. A time step of 10 s is used.

### b. Evolution of the reflectivity field

Horizontal cross sections at 2.5 km of the simulated and observed reflectivity are plotted in Fig. 8 at different times during the first 27 min, 30 s of integration. (The times of the outputs are chosen in the perspective of comparison with monostatic observations. Since the initial time step corresponds to the intermediate time between two volumetric scans that take 5 min to complete, the outputs are chosen after 7 min, 30 s; 17 min, 30 s; and 27 min, 30 s of simulation.) Since only observations performed in the bistatic area are taken into account for the simulation, a mask has been used to consider only the observations contained in a comparable area. This mask consists of the bistatic zone at *t*_{0} that is advected with respect to the time of each output.

These plots show, first, that the advection speed of the system is well reproduced by the model, which means that the environmental horizontal wind taken from the CMC regional analysis is coherent with the observations at the mesoscale and the vertical transport of horizontal momentum is well captured by the model. Furthermore, the model reproduces well the observed features of the three cells that compose the system. The first cell, C_{1}, evolves from a W–E to a NW–SE orientation during the 30 min of the simulation with the same timing as the observations. The merging during the first 10 min of the two cells of heavy precipitation that compose C_{1} is also well captured; in addition, the core of maximum reflectivity stays in its northern part during the second half of the simulation. However, the model produces a less extended stratiform precipitation than observed. After 17 min, 30 s of simulation, the reflectivity values that characterize the stratiform area, situated between C_{1} and C_{2}, are indeed reduced by a factor of 2 (Figs. 8a and 8c). The liquid rain, initially present at *t*_{0} in this region, falls almost instantaneously due to the absence of upward motion and because the lower troposphere is not saturated enough, which favors its evaporation. This aspect is directly linked to the fact that stratiform upward motions (of the order of a few cm s^{−1}) are not captured by the bistatic Doppler network. Therefore, in the absence of large-scale vertical motions, the regeneration of stratiform precipitation depends mostly on the melting of ice crystals aloft. Since these ice crystals are forming very slowly relative to the other hydrometeors (see Fig. 9), an appreciable regeneration of stratiform precipitation due to their melting takes place late in the forecast. At the end of the simulation, the solid hydrometeors generated by C_{1} are indeed advected following the high-level wind shear and are falling in its east-southeastern part. After 42 min, 30 s of integration, the formation of stratiform precipitation produced by the melting of these ice crystals induces the progressive shrinkage of the area between C_{1} and C_{2} (extent pattern, Fig. 10). However, the extent of this area is much smaller than the observed precipitation pattern. This result suggests that initial descriptions of stratiform vertical motions and of all hydrometeors' quantities, as well as a better approximation of the humidity field, are key factors in obtaining a realistic stratiform area.

Furthermore, the simulated second cell, C_{2}, develops with the same intensity and timing as indicated by the observations. It evolves from an initial small size to a more elongated band of strong precipitation that has the same NW–SE orientation as C_{1} after 27 min, 30 s of simulation (Fig. 8). The fact that C_{2} has been initially cut in an artificial manner to only keep the multiple-Doppler data regions does not seem to have a notable impact on its development. The initial convective cell is well reproduced by the model.

Finally, the decay of the third cell, C_{3}, is also well captured. The observed weak vertical motions (around 0.3 m s^{−1}) are not large enough to generate precipitation that compensates for the fall of the initial liquid rain (Fig. 6b). Nevertheless, weak precipitation is formed throughout the forecast because of the saturated conditions within these weak updrafts.

### c. Evolution of the radial velocity

The second simulated quantity, which is directly comparable to the monostatic data, is the radial velocity, *V*_{r}, displayed in Fig. 11. To compare only the areas sampled by the radar, the same mask is applied on both datasets. The latter consists in considering only regions where the observed monostatic reflectivity exceeds 10 dB*Z.*

At *t*_{0}, the differences are due to the use of the smoothness constraints in the retrieval process. Both C_{2} and C_{3} are characterized by a local enhancement of *V*_{r} of more than 2.5 m s^{−1}, while the maximum of reflectivity coincides with weaker velocity values within C_{1}. The observed pocket of stronger *V*_{r} is also present in the southern part of this last cell. After 7 min, 30 s, comparisons of the spatial distribution and the intensities of the velocity field remain good. However, the model does not reproduce the progressive weakening of *V*_{r} in the center of C_{1} and is still 2.5 m s^{−1} greater than the observations. After 17 min, 30 s discrepancies are appearing, but both outputs still demonstrate some common features. The simulated velocities are progressively shifted northward and the observed alternation of oblique strips of strong/weak *V*_{r} is less evident for the simulation.

### d. Evolution of the wind circulation

Since C_{2} and C_{3} were initially situated on the border of the bistatic area coverage and because of the advection of the whole system, no multiple-Doppler measurements are performed within these cells 10 min after *t*_{0}. Thus, only the observed and simulated fields of the main cell C_{1} are compared in this section.

After 10 min, the simulated wind circulation is very similar to the observations (Fig. 12). Both datasets display maximum velocity around 2 m s^{−1} at 2.25-km altitude in the core of C_{1} and downward motions area located in its eastern part. However, the shape of the simulated convective cell is more elongated in a NW–SE direction. Three kilometers higher, the regions of vertical motions are cellular in the two cases, albeit the observed maximum vertical velocity is almost two times greater than the simulated one (5 vs 2.6 m s^{−1}). The weakening of the simulated updraft at midlevel reflects the transition period between the instantaneous fall of the initial rain droplets and the formation of new precipitation. This transition is well captured by the time series plotted in Fig. 9, which shows that the relaxation time of the precipitation amount is about 5 min. The horizontal wind is also very similar at those two levels.

Ten minutes later, discrepancies appear at 2.25 km where the simulated convective cell coinciding with C_{1} becomes narrower and stronger (Fig. 13a). At the time of the simulation, the model has “forgotten” its initial convective circulation and the system is self-generating. The evaporation of the precipitation has reinforced the cold pool at low levels that produced convergence at its leading edge. This cold pool was present but rather weak initially, since the temperature perturbation was retrieved from the wind circulation that displays a front-to-rear circulation in that area. This convergence at low levels raises the ambient unstable moist air and strengthens the convective activity. This reinforcement of the convection in the simulation is also visible at 5.25 km, where the observed and the simulated convective cells are similar in shape (Figs. 13c and 13d).

### e. Microphysical retrieval

Besides the nowcasting aspect, initializing a mesoscale model with the explicit dynamical and thermodynamical structure of an observed storm allows the assessment of nonmeasurable parameters from the equations of the model. For instance, microphysical quantities can be retrieved as soon as they are formed within the model. The time series of the mean quantity of each of the hydrometeors plotted in Fig. 9 shows that cloud droplets appear very quickly from condensation of supersaturated vapor and that their amount reaches a stable value after 5 min of simulation. Since the water content of rain, *q*_{r}, is present at the initial time and since this quantity is produced mostly through fast, warm microphysical processes, a good description of the liquid precipitation is also obtained after few minutes. Figure 9 shows that the *Z*–*R* relationship (13) used in this study brought the amount of rain very close to the model compatible value. The precipitation amount maintains itself indeed within a reasonable value during the evacuation of the initial rain, which is underlined by a very shallow minimum of mean amount at the beginning of the simulation. Graupel, which is mostly produced from vapor deposition and collection of liquid cloud and rain, also reaches a stable amount very quickly. The short relaxation time of graupel and of liquid cloud seems to indicate that there is no strong motivation for assimilating their initial values. On the other hand, the specific content of ice crystals, *q*_{i}, is produced through slower processes, which explains that their amount grows slowly but regularly and reaches a stable value after 40 min of simulation.

Figure 14 displays vertical cross sections through C_{1} and C_{2} of those microphysical quantities after 17 min, 30 s of simulation. Condensation is active mostly in the convective ascent, producing cloud water from the cloud base to 400 hPa to feed the convective cells (Fig. 14a). Maximums up to 1.4 g kg^{−1} are found in both cells. Ice crystals are confined in a thin layer between 500 and 300 hPa within C_{1}, with contents up to 1.2 g kg^{−1} (Fig. 14b). Some of these ice crystals are collected by graupel and these nonprecipitating elements are almost not evacuated outside of the convective towers due to the weakness of the high-level wind shear. In the convective cells above the 0°C isotherm level the main hydrometeor is graupel with contents up to 0.8 and 0.4 g kg^{−1} for C_{1} and C_{2}, respectively (Fig. 14b). Their presence is due both to the cloud water that favors riming growth and to sedimentation. Rainwater is found under a horizontal uniform level at 650 hPa and results from melted graupel, and collection and cloud water autoconversion processes (Fig. 14a). Maximum amounts of 3 and 1.4 g kg^{−1} are found within C_{1} and C_{2}, respectively.

### f. Performance in terms of nowcasting

To evaluate the performance of this nowcasting method, we have performed comparisons with a Lagrangian persistency analysis. This has been made in an operational manner: to compute the advection speed of the whole system, we have chosen the variational technique developed by Laroche and Zawadzki (1994) using four successive volumetric scans performed before *t*_{0}. This method allows for the determination of the optimum moving frame of reference using the reflectivity echoes above 20 dB*Z* as a tracer. An advection speed of *c*_{x} = 10.4 m s^{−1} along the *x* axis and *c*_{y} = −4.3 m s^{−1} along the *y* axis has been retrieved. Then the Lagrangian persistency forecast (PER in the following) has been obtained by simply advecting the reflectivity field corresponding to *t*_{0} with this moving frame velocity, assuming stationarity.

Cross correlations between PER and the monostatic reflectivity have been performed for a given level and compared to cross correlations between the simulated reflectivity and the same observed reflectivity. At 2.25-km altitude, the results are, respectively, those displayed in Figs. 15 and 16. To take into account false alarms and nonsimulated precipitating areas, each scatter plot represents grid points where the reflectivity of the first dataset or the reflectivity of the second one is strictly greater than zero.

First the cross-correlation index, *r,* is not equal to unity at *t*_{0} because, in both cases, the correlations are performed between the reflectivity measured by the monostatic radar and the reflectivity deduced from the bistatic radar network, which also make use of the monostatic reflectivity, but with a finer resolution along its path (600 vs 1000 m). This leads to the observed discrepancies when the plan position indicators are interpolated on to a Cartesian grid. During the 30 min of simulation, the numerical forecast always gives better results than PER, with an improvement of 18% after 27 min, 30 s (0.42 vs 0.24; Figs. 15d and 16d). However, the model underestimates the intensity of precipitation after approximately 15 min of simulation.

## 6. Conclusions

An initialization method of a cloud-resolving model from observations of the explicit structure of a midlatitude summer storm is presented herein. The precipitating region of this storm is sampled by a bistatic radar network that allows for the retrieval of multiple-Doppler measurements and the clear air area is characterized by a sounding coming from a large-scale analysis. All the prognostic variables of the model are then retrieved or estimated using those observations, following the approach of Lin et al. (1993).

Following the previous work of LZ95, PZ99, and P01, a new variational method has been developed in the aim to retrieve the dynamical and thermodynamical fields of the storm and its environment. It consists of variationally adjusting a physical solution to the observations under physical constraints that are composed of the continuity equation, the momentum equations, and a smoothness constraint. This method has been adapted for initialization purposes: the control variables of the cost function correspond to the model variables, the different dynamical fields must satisfy the physical equations of MC2, and the discretization is done on the same staggered grid. Furthermore, the humidity field is determined using the environmental sounding and empirical saturation assumptions within the convective system. The liquid rain mixing ratio is deduced from the reflectivity field; the liquid cloud and all the cold microphysical quantities are taken to be equal to zero.

This assimilation method has been applied to a summer storm observed on 2 August 1997 over the Montreal region. All the retrieved fields were considered as the initial state of the atmosphere in the forward simulation performed with the Canadian mesoscale nonhydrostatic model, MC2. During the 30 min of the integration, the model succeeds in simulating the life cycle of the three convective cells that composed the part of the storm sampled by the bistatic radar network. The simulated shapes and intensities of the precipitation cells are of the same order as those observed. Some discrepancies in the wind circulation appear, however, at around 20 min of simulation, with a strengthening of the convective activity within the main cell in the boundary layer. The equations of the model also allow for the retrieval of a complete description of the nonmeasurable parameters after 15 min of integration. For instance, the model allows complete description of the warm and cold microphysical particles to be characterized. Results also seem to indicate that the need to assimilate liquid cloud and graupel may not be that critical since the time constant of the microphysical processes is short and the model produces a reasonable amount of the various hydrometeors very rapidly. The performances of the simulation in terms of nowcasting of the precipitating field has also been examined by performing cross correlations between the simulation, the Lagrangian persistency forecast, and the observations. An improvement in the forecast of more than 18% has been obtain after 30 min of simulation. Beyond that half-an-hour period the model solution diverges from the observations, mainly because of its inability to represent the stratiform part of the storm. Forecast errors are partly due to the different physical parametrizations used in the cloud model (for instance the microphysical and turbulence schemes). They are also probably due to errors in the representation of the background, to the incapacity of assessing the initial three dimensional distributions of all the microphysical quantities within the convective system, to the difficulty of retrieving stratiform vertical motions, and to the inadequacy of the humidity field description, notably in downdrafts.

Future works will be carried out in order to minimize these drawbacks. First, sensitivity experiments on a simulated case are currently under way to determine the relative significance in the forecast of each prognostic variable that has to be estimated. A refinement will be made by assimilating the refractivity index of ground targets (Fabry et al. 1997), which gives additional information about the crucial parameters, being the humidity and the temperature in the boundary layer. The recent implementation of the polarization on the McGill University S-band radar will allow a target classification to be obtained, as well as a detailed microphysical description within a precipitating system. This new information will allow for a better estimation of the fall speed for the different hydrometeors and eventually for the assimilation of these new microphysical quantities. Furthermore, some work is presently in progress to obtain a more realistic dynamical background using linear wind analysis as in Sun and Crook (1999). Briefly, this is approached using time series of scans describing the movement of a convective system with respect to the radar. The different viewing angles coupled with the frozen turbulence assumption allow for the retrieval of a linear wind that fits the complete circulation. This leads to a background in better agreement with the measurements within the precipitating cell as well as eventually leading to the obtaining of a large-scale convergence.

## Acknowledgments

This research was financially supported by Environment Canada. We would like to thank Dr. M. K. Yau and Dr. N. Badrinath for their help with MC2 and many fruitful comments, as well as A. Armstrong for her help in improving the writing of the manuscript.

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