a. Description of the rainfall dataset used for comparison

Vertically pointing profiling radar observations were collected during the TWP-ICE around Darwin, Australia, in January and February 2006. The experiment provided both remote sensing observations and aircraft in situ measurements within anvil clouds needed to verify the remote sensing microphysical properties needed to examine the life cycle of convective cloud systems from their initial forming stage to the decaying of thin, high-level cirrus. For this study, the Doppler velocity spectra collected by the collocated 50- and 920-MHz profiling radars were used to estimate the vertical air motion and the vertical profile of rain DSDs. The long wavelength 50-MHz profiler observations are used to estimate the ambient air motion and turbulent broadening in the finite radar beam as the precipitation passes directly over the profiler site. The shorter wavelength 920-MHz profiler observations are used to estimate the DSD. The two profilers, along with a JWD and two tipping-bucket rain gauges were deployed at the Bureau of Meteorology Research Center (BMRC) wind profiler site located at −12.44° and 130.96°.

The time–height cross sections of reflectivity, mean Doppler velocity, and spectral width of the precipitation event studied are shown in Fig. 1. After approximately 1930 UTC, the radar brightband signature can be seen in the reflectivity observations indicating stratiform rain. Another indicator of stratiform rain is the transition from snow and ice falling at 1–2 m s⁻¹ above h = 5 km into raindrops falling at 5–8 m s⁻¹ below h = 5 km. A third indicator of stratiform rain is the decrease in spectral width above the snow–rain transition altitude indicating that turbulent motions associated with convective and transitional precipitation processes have diminished at high altitudes directly over the profiler site. This rain event occurred during the active phase of the monsoon with strong low-level easterly winds transporting moisture off of the Timor Sea. The rain system consisted of large areas of stratiform rain with embedded convection. Two convective cells passed over the profiler site near 1550 and 1820 UTC, and can be identified by the enhanced reflectivity and increased spectral width between h = 3 km and h = 6 km.

Examples of observations made by the two profilers while precipitation was directly over the profiler site are shown in Fig. 2. Figure 2a was derived from the 50-MHz profiler and Fig. 2b was derived from the 920-MHz profiler. The 920-MHz profiler reflectivity is shown in the right-hand panel of Fig. 2b with units of dBZ = 10 log₁₀ mm⁶ m⁻³. The panels show the reflectivity-weighted Doppler velocity spectral density (often called just the “Doppler spectrum”) in units of 10 log₁₀ mm⁶ m⁻³ (m s⁻¹)⁻¹ at each range gate. The logarithmic scale is used to aid in visualizing the data that spans six orders of magnitude.

The advantage of using the 920-MHz operating frequency radar is that the radar is sensitive to backscattered energy from hard targets distributed throughout the radar pulse volume. Referring to Fig. 2b, the 920-MHz profiler Doppler spectra show particles with net downward motion below the freezing level, which is located around h = 4.5 km. The solid black lines in the panels indicate the air–density-corrected terminal fall speeds of raindrops with diameters of 1, 3, and 6 mm.

b. DSD retrieval procedure

Here we give a few elements on the retrieval procedure using VPR. For more details concerning the methodology, the reader is referred to Rajopadhyaya et al. (1999), Schafer et al. (2002), Williams (2002), Lucas et al. (2004), and Williams et al. (2007). Assuming a perfect radar with infinitesimal beamwidth and a static atmosphere with zero vertical air motion and zero turbulence, the observed reflectivity-weighted Doppler spectral density, S_hydrometeor(V), is uniquely related to the raindrop size distribution, N(d), through the relation (Atlas et al. 1973):

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where V and d(V) are the velocity and velocity resolution, respectively, of the Doppler spectrum (m s⁻¹); and d and d(d) are the diameter and diameter resolution corresponding to each V and d(V), respectively (mm). Of course, d has positive definite values and d and d(d) are valid only when V corresponds to downward air-density-corrected raindrop terminal fall speeds. Through laboratory studies, the transformation from velocity to diameter space in Eq. (5) is facilitated with a raindrop diameter to terminal fall speed relationship expressed as

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where ρ₀ and ρ represent the air densities at sea level (ρ₀ = 1.225 kg m⁻³) and at the level of the observation aloft, respectively (Gunn and Kinzer 1949; Atlas et al. 1973). The Doppler velocity reflectivity spectral density observed by a radar is not just the simple expression of Eq. (5), but is the reflectivity spectral density shifted by the ambient air motion and broadened by the turbulent motions and horizontal wind motions within the radar pulse volume. For the 920-MHz profiling radar, the observed reflectivity spectral density, S_model(V), can be expressed as

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where S_air(V − ω, σ_air) is the spectral-shift and spectral-broadening function corresponding to the vertical air motion ω and total spectral broadening σ_air and the asterisk refers to the convolution function (Wakasugi et al. 1986).

In Fig. 2a, the Doppler spectra show that the 50-MHz profiler is sensitive to the backscattered energy from distributed hard targets (as is the 920-MHz profiler) and it is also sensitive to the backscattered energy from changes in the turbulent refractive index (Gage and Gossard 2003). This second sensitivity is observed in the panel near zero velocity from near the surface to about h = 5 km. The asterisks and horizontal line at each range gate indicate the vertical air motion and spectral broadening determined by a best fit to a Gaussian function following the method of Gossard (1994).

Using the vertical air motion ω and spectral broadening σ_air estimated from the 50-MHz profiler Doppler velocity spectrum, the raindrop size distribution N(d) can be retrieved from the 920-MHz profiler Doppler velocity spectrum using Eqs. (5)–(7) and inverse modeling techniques that are dependent on the assumed raindrop size distribution. The raindrop size distribution N(d) is modeled using a normalized Gamma function DSD (Willis 1984; Illingworth and Blackman 2002; Bringi et al. 2004) as described in Williams and Gage (2008, manuscript submitted to Ann. Geophys.) where

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where N(d) (cm⁻⁴) is the raindrop size distribution, N_z (mm⁶ m⁻³) is the total reflectivity, μ is the shape factor, d₀ (mm) is the profiler retrieved median drop diameter, and f_z(d₀, μ) is given by

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One benefit of describing N(d) using Eq. (8) is that N_z represents the reflectivity of the observation and is independent of d₀ and μ, which determine the shape of the raindrop size distribution. The three parameters (N_z, μ, and d₀) describing the normalized Gamma DSD are determined by iteratively adjusting the parameters until minimizing the sum of the squared difference between the modeled spectrum described by Eq. (7) and the observed 920-MHz profiler Doppler velocity spectrum. Whereas N_z was held constant at the measured reflectivity, all values of d₀ between 0.25 and 3.5 mm at 0.01-mm steps and values of μ between −2 and 20 at unit steps were evaluated to find the global minimized solution. Estimates of N(d) are made at each vertical range gate of the radar independent of estimated obtained at other range gates. More specific details of inverse modeling techniques used to retrieve N(d) from profiling radar observations is given in Williams and Gage (2008, manuscript submitted to Ann. Geophys.).

c. Model incorporation of retrieved rainfall data

As pointed out earlier, the goal of this study is to achieve a dynamic simulation of a realistic warm rain event and compare the spatial and temporal evolution of integral parameters throughout the 1D rain shaft model with VPR measurements at different levels within the shaft. In previous studies, the unsteady behavior of rain was imposed by varying initial conditions at the top of the rain shaft generated synthetically using a sinusoidal DSD (LDS87), or single-pulse (LMF90) and multiple-pulse rain (MFL91) characteristics determined from ground-based disdrometer measurements. In this work, the 1-min time series average DSD retrieved from VPR measurements is imposed at the top of the rain shaft, and the evolution of the DSD spectra and related integral parameters are computed at each level throughout a 4-km rain shaft. In the stratiform rain event considered in this work (2000–2400 UTC), the bright band is clearly visible and located around h = 4.2–4.5 km as observed in Fig. 1. The selection of a 4-km rain shaft allows us to consider a rain event free of ice microphysics.

Figure 3 presents the evolution of the retrieved integral parameters below the freezing level (h = 4 km) for the 2000–0000 UTC period. Figure 3a displays the evolution of the radar reflectivity factor (Z). The period 1700–2000 UTC (not displayed here) is characterized by strong variations in the value of Z indicating strong convective activity with intense updrafts–downdrafts (respectively between ±5 m s⁻¹) as indicated by the retrieved mean air velocity with the 50-MHz profiler (not shown). For the stratiform period 2000–0000 UTC, the radar reflectivity presents smoother variations than for the period 1700–2000 UTC along with little or moderate updrafts–downdraft (respectively between 0.5 m s⁻¹; not shown). Other integral parameters of the DSD indicate a light/moderate rain event with rain rates between 0.7 and 7 mm h⁻¹, and liquid water content between 0.03 and 1 g m⁻³. In addition, the drop number concentration (M₀) computed from the retrieved DSD varies between 10⁻⁵ and 10⁻¹ drops per centimeter cubed for the period 2000–0000 UTC.

In Fig. 4, the transient evolution of the retrieved parameters of the normalized gamma DSD: the median drop diameter (d₀) and the shape parameter (μ) (parameter N_z not shown), indicates that the variability of the DSD decreases with time as a result from the transition from a convective to a stratiform rainfall regime. For this period, hourly averaged values of (d₀) increase from 0.12, 0.145, 0.16, to 0.165 cm, respectively, for 2000–2100, 2100–2200, 2200–2300, and 2300–0000 UTC. Simultaneously, the standard deviation decreases from 0.039 (2000–2100 UTC), 0.020 (2100–2200 UTC) to 0.015 (2200–2300 UTC), and finally increases up to 0.019 (2300–0000 UTC). The trend for the shape factor (μ) is more erratic with hourly averaged values (and standard deviation) of 1.7 (1.99), 0.36 (1.92), 1.5 (1.36), and 2.22 (1.57) for each hourly interval, respectively. A similar conclusion can be drawn when looking at the hourly evolution of the shape of the minute-by-minute retrieved DSD of the stratiform rainfall. While profiler DSD estimates are available every 20 s, the interval of 1 min was selected in order to obtain stable and representative averaged DSDs and remove noisy short-term perturbations due to radar measurement uncertainties. These minute-averaged retrieved DSDs, updated every minute and held constant during each time step of the simulation were imposed as the top boundary condition for the rain shaft (i.e., at h = 4 km). Except for the first time step (t = 0) when the entire column is initialized with the same DSD, each level of the shaft (z) is not constrained by any external condition and is thus let free to evolve during the simulation according to settling-microphysics (coalescence–breakup) processes only.

a. Model comparison with radar rainfall data

Figure 5 displays a comparison for the vertical profiles of integral parameters (Z, RNT, and LWC) of the DSD at three different times (2213, 2233, and 2253 UTC) during the stratiform rain event sequence from 2000 to 0000 UTC. The model tracks the evolution of the vertical profiles of integral parameters, and capture the temporal evolution of the retrieved reflectivity profile with an average residual between retrieved and simulated Z of about 5% for the reflectivity expressed in reflectivity decibels [about 20%–30% when expressed in linear scale (mm⁶ m⁻³)] once effects of the uniform initial condition have vanished (not shown). For the RNT and LWC, differences between model results and VPR retrieved data are significantly higher than for Z [when expressed in linear scale (mm⁶ m⁻³)] and remain in the range 20%–50%. Some of the largest differences can be explained by the differences in the fit of the DSD and the large uncertainty in the retrieved vertical velocity estimates. In addition please note that Fig. 5 is here to provide an instantaneous representation of the vertical range of differences between modeled and retrieved profiles at arbitrarily selected times. As we will discuss later, the average residuals for the integral parameters between modeled and VPR retrieved time series are found to be within the range of experimental uncertainties.

The transient evolution of reflectivity, rain rate, and liquid water content for selected fall distances (D_fall = 100, 500, 1500, 2500, and 3500 m) from 2000 to 0000 UTC is analyzed in Fig. 6. Besides measurement uncertainty, differences observed are due to the relatively simplified formulation of the homogeneous shaft model that does not take into account the local variation of the flow field around falling drops, shear, and horizontal wind effects. However, despite this simplification, the difference between modeling results and retrieved data for Z remains within 5% (dBZ scale) for all cases presented. Simulated evolutions for rain rate and liquid water at specific heights present average differences around 25% against VPR retrieved values, with a value significantly higher for the liquid water content than for the rain rate. In addition, we note that for fall distances greater than D_fall = 3000 m (i.e., h = 1000 m AGL), large differences are observed between model and experiments from 2000 to 2400 UTC. Those differences are due to the spatial resolution of the 50-MHz VPR (h = 1500 m) that does not permit reliable estimation of the magnitude of air motion below this limit (Williams 2002). For the air parcel located between h = 0–1500 m AGL, the mean velocity is assumed constant at the retrieved air velocity at h = 1500 m. Values of the correlation coefficient for integral parameters (Z, RNT, LWC) between modeling results and retrieved data time series (Table 1) indicate that differences increase with increasing fall distance (D_fall) from the h = 4-km level at which retrieved DSDs were imposed as boundary conditions. For instance, modeled and retrieved time series of the reflectivity (Z) present a degree of correlation ranging from 0.99 close to the top of the rain shaft (D_fall = 100 m) to 0.83 at the bottom of the rain shaft (at D_fall = 3000 m) giving an average correlation of 0.92 throughout the rain shaft. Closer to the ground level (D_fall = 3500 m), the correlation between the two times series decreases sharply (0.67) due to the presence of aforementioned artifacts. Comparatively, correlation coefficients obtained for RNT and LWC time series are lower than for Z with an average value of 0.83 and 0.78 for (RNT) and (LWC), respectively, throughout the column. Unlike reflectivity (Z), for which the coefficient correlation remains high throughout the shaft, the correlation for LWC decreases significantly closer to the top of the shaft with a strong variation between fall distances D_fall = 100 m (0.94) and D_fall = 200 m (0.80). Again, as pointed out for (Z) close to ground level (D_fall = 3500 m), the correlation coefficients for RNT (0.06) and LWC (0.07) time series are very low due to the difficulties for a correct measurement of the vertical air motion with the 50-MHz profiler. Also note that the radar reflectivity (Z) estimate is independent of vertical air motion and is more accurate than RNT and LWC below h = 1500 m.

Likewise, scatterplots of reflectivity, rain rate, and liquid water content for modeling results and radar retrievals at different fall distances (D_fall = 100, 500, 1500, and 2500 m) show an increase in dispersion with increasing fall distance (Fig. 7). The linear regression analysis performed for the reflectivity gives a coefficient of determination R² ranging from 0.93 (D_fall = 100 m) to 0.64 (D_fall = 3500 m: not shown). Results for the rain rate and the liquid water content are comparable with R² ranging from 0.86 (D_fall = 100 m) to 0.64 (D_fall = 3000 m) and from 0.82 (D_fall = 100 m) to 0.68 (D_fall = 3500 m), respectively.

Overall, the results suggest that the 1D homogenous shaft model captures closely the evolution of integral properties Z, RNT, and LWC. However, a true deterministic comparison as performed above, with retrieved boundary conditions sequentially imposed at the input of the shaft, is delicate. This approach, in which DSDs are updated each minute, does not take into account small time-scale variations and detailed flow fields and shear effects on the drop motion. From a modeling point of view, the model itself is not free of numerical uncertainties due to approximations introduced by a simplified space–time–bin discretization scheme for the resolution of the general advection–coalescence–breakup transport equation as indicated by the progressive decrease of correlation and determination coefficients with increasing fall distance from the level (h = 4 km) taken as a reference for modeled and retrieved integral properties.

Another possible explanation to the increasing differences between modeled and VPR retrieved vertical profiles with increasing fall distance relates to the model quasi-stochastic assumption that uses an average breakup function (kernel) to describe the drop population resulting from drop–drop interactions. A quasi-stochastic behavior is truly valid for significant rain-rate intensities (50 mm h⁻¹: McFarquhar 2004b), higher than those retrieved in the present study (0.7–7 mm h⁻¹). A complementary study (not shown) in order to determine the mean free path of drops (average distance for which a drop of diameter d will experience a collision with any other drops) as per McFarquhar (2004b), was performed for all DSDs imposed at the top of the shaft. Briefly, simulations show that drops of a given diameter can experience between 1 and 0 (i.e., average mean free path of 4–10 km for drops around d = 0.1–0.15 cm) and 1000–100 (average mean free path of 4–40 m for drops above d = 0.3 cm) collisions during their 4-km fall (for all DSDs retrieved during the period 2000–0000 UTC) for rain rates between 0.7 and 7 mm h⁻¹. Those results are comparable to those obtained by McFarquhar (2004b) for exponential [Eq. (10): Marshall and Palmer 1948, hereinafter MP48] and for normalized gamma (Willis 1984) DSDs. More importantly, this study (not shown) also indicated that the shape of the retrieved normalized gamma DSD (i.e., values of the parameters: N_z, μ, and d₀) was of prime importance as it concerns the value of the mean free path. The rain-rate intensity does not appear to be the key parameter governing drop–drop interaction statistics as it is the case for MP48 DSDs, with decreasing mean free path for increasing rain rates (McFarquhar 2004b).

From an experimental perspective the radar retrieval algorithm assumes a priori a normalized gamma distribution [Eqs. (8) and (9)] as the best fit for the retrieved DSD. The use of a normalized gamma distribution (Willis 1984; Illingworth and Blackman 2002; Bringi et al. 2004) requires the determination of three parameters (N_z, μ, and d₀) using the error minimization procedure described earlier, a challenge for occasional spectra when the inverse model converges to an unrealistic value of the shape factor μ. The use of other formulations such as the exponential [MP48; see Eq. (10)], gamma (Ulbrich 1983), and lognormal (Sauvageot and Lacaux 1995) distributions could address this problem in part as discussed in Williams and Gage (2008, manuscript submitted to Ann. Geophys.). By contrast, the model does not make assumptions concerning the shape of the DSD, and the evolution of the drop number concentration in each one of the 40-class category is controlled by exchanges between each class sizes from relative contributions of sedimentation–coalescence–breakup processes.

To assess the model sensitivity, ensemble simulations were performed using randomly generated DSDs from the statistical distribution derived from the reflectivity observations. Instead of specifying a normalized gamma DSD as the top boundary condition [Eqs. (8) and (9)], for simplicity we use a variable exponential DSD [Eq. (10)] that requires generating only one random variable (slope: Λ) for each exponential distribution rather than two (or three) nonlinearly related parameters in case of more complex formulations (i.e., gamma, or normalized gamma):

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For this exercise, 60 1-min exponential DSDs were randomly generated to be used as top of the model boundary conditions. Figure 8 displays the randomly generated exponential DSD slope parameters (Λ) bounded by the observed hourly upper (Λ_max) and lower (Λ_min) slope parameters that were determined from the retrieved normalized gamma DSD (Fig. 4). Values of the constant (N₀), similarly determined from retrieved normalized gamma DSD, were held equal to N₀ = 0.08 cm⁻⁴ (2000–2100 UTC), N₀ = 0.04 cm⁻⁴ (2100–2200 UTC), and N₀ = 0.02 cm⁻⁴ (2200–0000 UTC), respectively, for each hourly sequence.

Figure 9 displays retrieved and simulated vertical profiles of integral parameters of the DSD. For the reflectivity (Fig. 9a), the synthetic model vertical profiles are superposed by all the retrieved vertical profiles. The model profiles overlap the retrieved profiles with exceptions of erroneous artifacts of the retrieved reflectivity profile below h = 1000 m. Similarly, results for the rain rate (Fig. 9b) show the same overlapping behavior with profiles centered on 2 (2000 UTC), 4 (2100 UTC), 2 (2200 UTC), and 1.75 mm h⁻¹ (2300 UTC). The differences observed for the liquid water content (Fig. 9c) are due to the choice of an exponential DSD instead of a gamma DSD, and by the fact that the concentration of small drops is more important in the case of an exponential DSD. The liquid water content (i.e., equal to the first-order moment of the DSD) is more sensitive than the reflectivity (i.e., proportional to the second-order moment of the DSD) on the left-hand side of the DSD spectra. This sensitivity analysis emphasizes the fact that simplifications in the model’s description of the flow field (e.g., neglecting horizontal transport and the local influence of the turbulence) can explain differences observed between simulated and retrieved vertical profiles of the reflectivity, rain rate, and liquid water content. In addition, the assumed shape of the DSD (i.e., exponential for the sensitivity analysis versus normalized gamma for radar retrieved data) is found to play a significant role in the discrepancies observed between modeled and retrieved vertical profiles for the rain rate and the liquid water content.

b. Model comparison with ground-based rainfall data measured by the disdrometer

The results presented above show a good agreement between modeling results obtained with the 1D rain shaft model and estimates retrieved from the vertically pointing radar observations. However, the main limitation of vertically pointing radars is their lack of observations in the lower part of the atmospheric column. As a general rule, lower-frequency radars have larger low-altitude data gaps. Because of this lack of observations it is not possible to determine the value of the mean air velocity from the 50-MHz profiler, which handicaps the reliability of the retrieved DSD close to the ground. For this dataset, the retrieved DSDs at levels below h = 1500 m assume that the vertical air velocity is constant with altitude and equal to the air velocity measured at the lowest reliable gate. This assumption leads to some unrealistic results in the retrieval of integral parameters as can be seen in Fig. 6 for (h = 500 m).

One way in which the rain shaft model can aid VPR retrieval is by providing a physically based dynamical interpolator at low levels to infer the shape of the DSD and track the evolution of integral parameters. To evaluate this assertion, simulations were performed using a 1-km column. Boundary conditions are imposed at the top of the shaft (at h = 1 km) based on the DSDs retrieved from VPR at the same height. The choice of a 1-km column is because few measurement artifacts are observed at this level (h = 1 km) thus providing confidence in the retrieved shape of the DSDs. Next, the modeling results were compared at ground level with measurements performed using a JWD.

Figure 10 displays the integral parameters Z (Fig. 10a), RNT (Fig. 10b), and LWC (Fig. 10c) derived from the disdrometer observations and from model simulations at ground level (h = 0 m), that is at the bottom of the shaft. On average, the differences between the time series for the evolution of integral parameters (Z, RNT, and LWC) predicted by the model at ground level and observed by the disdrometer are on the order of 3% (dBZ scale) for the reflectivity and 20% for the rain rate and the liquid water content. Note that despite the application of postprocessing corrections (Tokay et al. 2003), the disdrometer is expected to undersample the actual DSD because it cannot detect very small raindrops. The model adequately captures the general trend of the temporal evolution of integral parameters (Z, RNT, and LWC), including the time shift between the time series of VPR retrieved (at h = 1000 m) and JWD observed (at h = 0 m) integral properties (Z, RNT, and LWC; not shown).

The residuals obtained for the integral properties (Z, RNT, and LWC) between modeled and JWD time series are smaller and of the same order of magnitude as those between modeled and VPR retrieved time series [residuals of about 5% for Z (dBZ, 20%–30% in linear scale), and about 20%–50%] for RNT and LWC between modeled and VPR retrieved time series. A like-minded comparison between VPR and JWD retrievals (not shown) indicates that the residuals are of the same order of magnitude as those reported for (model – VPR) and (model – JWD). These experimental VPR – JWD residuals are consistent with the VPR – JWD reflectivity time series analysis of Gage et al. (2004) indicating about 2.1- and 0.4-dBZ rms difference between 1-min JWD and VPR reflectivities, respectively, and thus provides a measure of the experimental uncertainties of the data presented in this work.

Table 2 summarizes the values of the correlation coefficient for the integral parameters (Z, RNT, and LWC) between model–VPR, model–JWD, and JWD–VPR time series at different levels throughout the 1-km shaft. A correlation coefficient equal to 1 between model and radar time series corresponds to the top of the rain shaft where boundary conditions are imposed. Despite the presence of artifacts, model and measured radar reflectivity time series exhibit a good degree of correlation. A similar behavior is observed between radar and disdrometer time series with maxima of 0.81, 0.76, and 0.72 obtained for Z, RNT, and LWC time series close to the top of the shaft. A comparison of model and disdrometer time series for Z, RNT, and LWC shows that the correlation coefficient increases with increasing fall distance (i.e., as we get closer to the ground) and tends to a value of about 0.84 for Z and 0.87 for RNT and LWC.

Model and disdrometer DSDs are compared at different times during the period 2000–0000 UTC in Fig. 11. For drop diameters greater than d = 0.1 cm, the shapes of modeled and JWD DSDs match closely for drop number concentrations between 5.10⁻⁵ and 10⁻⁴ cm⁻⁴. The major differences between model and disdrometer DSDs are observed in the left-hand side of the spectra for the small raindrops. The JW disdrometer detects drops impacting an aluminum surface of 50 cm², and an electric pulse resulting from the displacement of the sensor surface supporting device is measured. The electric pulse, proportional to a value between the force of the drops impacting the sensor and the mechanical momentum, is sorted into 20 class sizes equally spaced in terms of drop diameter (Sheppard 1990; McFarquhar and List 1993). To account for the instrument dead time, a mathematical correction (Sheppard and Joe 1994; Sauvageot and Lacaux 1995) is applied to increase the number of drops detected in the smallest size categories. Nevertheless, only drops above a certain threshold size (typically 0.03 cm in diameter) can be detected by the disdrometer. Furthermore, the threshold diameter is rain-rate dependent and can be up to d = 0.1 cm in case of heavy rain rate (McFarquhar et al. 1996). For the period considered 2000–0000 UTC, the threshold detection size for raindrops varies between 0.04 and 0.05 cm for light-to-moderate rain rate (<7 mm h⁻¹).

To help with assessing the impact of the disdrometer measurement threshold for small drop diameters, Fig. 12 displays the time evolution of model and disdrometer drop number concentrations (M₀). When computed over all the 40 bins (covering a diameter range from d = 0.01 to 0.7 cm), the temporal average of the difference between modeled and disdrometer integral parameters is on the order of 45% for M₀, 4% for LWC, 6% for RNT, and 2% for Z for the period 2000–2400 UTC. The difference M₀ varies widely in time from 45%, 90%, 27%, and 25% for hours 2000, 2100, 2200, and 2300 UTC, respectively. The larger errors occur at the beginning of the rain event when the concentration of small drops is larger and the errors decrease with time along with the concentration of small drops. If the model–JWD comparison is undertaken using exclusively the model bins that correspond to disdrometer channels that detect a drop, the difference in M₀ is greatly reduced to an average value of 15% for the 2000–0000 UTC rain event with hourly averages of 5%, 27%, 5%, and 1%. The results show that there is an improvement in the order of 90% in the estimation of rain rate and liquid water content using the model in the lower atmosphere h ≥ 500 m (Table 2).

This exercise shows that indeed there is great potential value in using a rain shaft model with detailed microphysics to complement the standard radar retrieval algorithms where radar retrieval is ambiguous, or excessively plagued by uncertainty. Furthermore, there is clearly great need to improve the measurement sensitivity of disdrometers for light rainfall. This simulation also provided insight into the possible consequences of using disdrometer data to calibrate or constrain radar retrieval algorithms, which can result in the introduction of inconsistent physics due to the lack of sensitivity of the disdrometer to measure accurately small drop population. Given the lack of ability to describe the dynamics of the very small raindrop populations in current parameterizations (Barros et al. 2008), this is an area where there is great need for fundamental experimental research both in terms of measurement technology as in terms of conceptual understanding.