The Impact of Evaporation on Polarimetric Characteristics of Rain: Theoretical Model and Practical Implications

a. Polarimetric variables

Following the nationwide upgrade of the WSR-88D radar network, meteorologists will have for their use a full slate of polarimetric variables in addition to the conventional radar reflectivity factor at horizontal polarization (Z_H), Doppler velocity (υ_r), and spectral width (σ_υ). These additional variables are the differential reflectivity (Z_DR), differential phase (Φ_DP) and specific differential phase (K_DP), and the copolar cross-correlation coefficient at zero lag (ρ_HV). Here, we will briefly describe the meaning of these measurands, but the reader is directed to more thorough descriptions in the literature (e.g., Herzegh and Jameson 1992; Doviak and Zrnić 1993; Zrnić and Ryzhkov 1999; Straka et al. 2000; Ryzhkov et al. 2005b).

Seliga and Bringi (1976) first proposed the use of the ratio of backscattered power at orthogonal polarizations for observations of rainfall. The so-called differential reflectivity Z_DR is the difference between reflectivity factors at horizontal and vertical polarizations. Differential reflectivity Z_DR is dependent on particle size, shape, orientation, and dielectric constant but is independent of concentration. Since raindrops become increasingly oblate with increasing diameter (e.g., Pruppacher and Beard 1970; Pruppacher and Pitter 1971), Z_DR is considered a good measure of the median drop size of a distribution. For spherical or randomly oriented hydrometeors, Z_DR is 0 dB.

The use of a differential propagation phase Φ_DP for rainfall measurements was introduced by Sachidananda and Zrnić (1986, 1987). Due to the oblateness of raindrops, the horizontally polarized wave lags progressively behind the vertically polarized wave in rain, resulting in a positive differential phase shift. The radar measures the cumulative phase shift along each radial. Because Φ_DP is immune to radar calibration, attenuation, and beam blockage (Zrnić and Ryzhkov 1999), and is not biased by noise, it is an attractive variable for quantitative precipitation estimation and attenuation correction.

A more convenient way of interpreting the path-integrated differential phase shift is its range derivative, the specific differential phase K_DP, which provides the phase shift per unit distance in the radial direction. Here, K_DP increases as the oblateness and dielectric constant of hydrometeors increase and is not affected by spherical or isotropic hydrometeors such as tumbling dry hail (Balakrishnan and Zrnić 1990). Sachidananda and Zrnić (1987) found that K_DP is almost linearly related to rainfall rate. In addition, K_DP is less sensitive to the particle diameter than radar reflectivity factor (Z_H ∼ D⁶ whereas K_DP ∼ D^4.24); thus, K_DP is more sensitive to the smaller drop sizes than Z_H and Z_DR, which are dominated by larger particles within the radar sampling volume.

The correlation coefficient between the horizontally and vertically polarized signals at zero lag ρ_HV is useful for discriminating between meteorological and nonmeteorological echoes such as biological scatterers (Zrnić and Ryzhkov 1999), chaff (Zrnić and Ryzhkov 2004), tornadic debris (Ryzhkov et al. 2005c), and smoke plumes (Melnikov et al. 2008). In pure rain at S band, ρ_HV generally does not fall below 0.98. Further decreases in the measured ρ_HV are due to the diversity of the particle sizes, orientations, shapes, and irregularities, and to the phase compositions within the radar sampling volume. For example, observations of rain mixed with melting hail will produce lower ρ_HV than pure rain or pure dry hail. Hydrometeors of the size at which resonance scattering effects occur will also contribute to substantially lower values of ρ_HV. Resonance scattering, or Mie scattering, occurs when the combined microwave radiation reflected from the near side of the particle and the radiation that penetrates the particle and is reflected from its back side interfere in such a way that the resulting backscattered wave is augmented or diminished.

b. Evaporation

Liquid drops in clouds can grow by the diffusion of water vapor from the ambient environment if the ambient vapor density is greater than the vapor density at the droplet’s surface. On the other hand, if the vapor density at the surface of the drop exceeds the vapor density in the ambient environment, vapor is diffused away from the drop (evaporation). The rate of mass diffusion from a falling drop can be written as

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where r is the radius of the drop, f_υ is the ventilation coefficient for the vapor diffusivity, D_υ is the molecular diffusion coefficient, and ρ_υ and ρ_υr are the vapor densities of the ambient environment and at the surface of the drop, respectively. Following Pruppacher and Klett (1978) and Rogers and Yau (1989), one can derive an approximate expression describing the rate of change of the drop radius:

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where S is the saturation ratio, and F_K and F_D are terms related to heat conduction and vapor diffusion, respectively, that include ventilation effects and are detailed in the appendix. For now, we simply focus on a qualitative interpretation of (2). For subsaturated environments (where S < 1), the drop radius will decrease, indicating decay through evaporation. Also note that dr/dt is inversely proportional to the drop radius, meaning that the radii of smaller drops will decrease more rapidly under evaporation than larger drops. This well-known fact is important when considering the impacts of evaporation on polarimetric variables.

Theoretically, the preferential depletion of smaller drops will result in a decrease in the observed Z_H and K_DP with an increase in the observed Z_DR. The observed decrease in Z_H has been well documented and is intuitive. Decreasing drop diameters across the spectrum and a decrease in the concentration of smaller drops (those that are totally evaporated) will result in a decreased magnitude of the backscattered signal. Recall that K_DP is less sensitive than Z_H to large drops, and as a corollary, more sensitive to changes in the lower end of the drop size spectrum. Therefore, one can expect evaporation to affect K_DP more substantially than Z_H.

The expected increase in Z_DR is less intuitive because all drops are losing mass (size). However, since Z_DR is a measure of the median drop size in a distribution, a preferential depletion of smaller drops (which generally have a large concentration) causes an increase in the median drop size of a given DSD. This effect is shown schematically in Fig. 1. At S band, the change in ρ_HV due to evaporation in pure rain is not expected to be significant for reasons discussed in a later section. The magnitude of the changes in all polarimetric variables should be dependent on the relative contributions of small drops and large drops and thus is strongly dependent on the DSD.

a. General description

In an effort to quantify the impacts of evaporation on the polarimetric variables under different conditions and assumptions, a simple numerical model is constructed. The idealized one-dimensional model explicitly computes the changes in size of raindrops falling through subsaturated air. The model domain is the subcloud layer, with 100-m vertical resolution. Eighty initial drop sizes are considered, ranging from 0.05 to 7.95 mm in 0.1-mm increments. Each drop size “bin” is tracked independently in order to isolate the effects of evaporation. Hence, no drop interactions such as collisions, coalescence, or breakup are taken into account. Note that coalescence and breakup significantly contribute to the evolution of the drop size spectrum, as found in the numerous theoretical and modeling studies mentioned in the introduction. These collisional processes become increasingly important in heavier rainfall. On the other hand, evaporation tends to only change the slope of the DSD slowly, instead mainly affecting the total water content (e.g., Srivastava 1978; HS). For rainfall estimation, evaporation is important since it is the only subcloud process that directly affects the total mass of rainwater reaching the ground. The relative contributions to the depletion of total water content from combinations of coalescence, breakup, and evaporation have been investigated previously (e.g., HS; Seifert 2008). HS found that the effects of coalescence and breakup tend to approximately balance. In their model, the total rainwater mass depletion in simulations that employed full microphysics (coalescence, breakup, and evaporation) was similar to that in which only evaporation was considered. Thus, only including evaporation in this model, although inherently limiting its applicability toward simulating the evolution of the DSD, is justifiable to improve the computational efficiency given our focus on the radar measurements and associated rainfall estimation.

At the top of the domain, or in the “cloud,” any DSD model can be prescribed. In the subcloud domain, any vertical profile of temperature and relative humidity can be administered. In our model, the feedback on the environmental thermodynamic profiles due to evaporation may be turned on or off. The feedback adjustment scheme is described below. Since the model is one-dimensional, no size sorting due to vertical shear (e.g., Kumjian and Ryzhkov 2009) is considered. At the initial time, drops begin to fall into the top of the domain, as in many rainshaft models. After numerous tests, the time step was selected to be 0.25 s, maximizing the computational efficiency while maintaining stable solutions.

b. Equations

We are interested in the vertical profiles of the polarimetric variables, so we convert (2) into an expression for the change in drop radius with height by dividing (2) by the fall speed of raindrops as a function of size. To simplify the ensuing integration, the empirical power law fall speed relation suggested by Atlas and Ulbrich (1977) is used for the terminal velocity of the raindrops:

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where α = 3.78 m s⁻¹ mm^−0.67, β = 0.67, and the equivalent spherical diameter D is given in millimeters. The multiplicative factor (ρ₀/ρ_a)^0.4 is a density correction, where ρ₀ is the surface reference density value following Foote and duToit (1969). Though (3) is less accurate for large drops than more recent empirical models (e.g., Brandes et al. 2002), it well represents the fall speeds of smaller drops (<5 mm) for which the evaporation effects are most significant. Thus, performing the change of variables in (2) and using the velocity relation (3) yields an analytic expression for the change in diameter of a raindrop with initial size D₀ as a function of height:

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where we have defined ξ as the right-hand side of (2). To numerically integrate this expression, ξ and ρ_a are assumed to be constant over each height step, Δh = h_i − h_i+1 (where h_i+1 < h_i), which should be relatively small (100 m is used in this study), resulting in

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In this way, the simple expression (5) is used to calculate what a given initial drop size should be at any height beneath the cloud base for given thermodynamic profiles, assuming the drops are falling at terminal velocity.

The mass concentration of raindrops n(m) in many of the aforementioned modeling studies is governed by the following equation:

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where the second term on the left-hand side is the change in drop concentration due to differential sedimentation. The third term describes the change in concentration of drops of mass m due to growth or decay by vapor diffusion, ṁ (i.e., dm/dt, which is the time rate of change of the drop mass due to condensation or evaporation). On the right-hand side, the terms B and C account for the collisional processes of breakup and coalescence, respectively; these will be ignored in this study. For the calculation of radar variables, it is more convenient to work in terms of diameter D. Thus, we seek an expression of (6) in terms of N(D), where N(D)dD is the number of raindrops of size D to D + dD. The concentrations n(m) and N(D) are related by

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Assuming spherical symmetry of the raindrops, m = (π/6)ρ_lD³, and thus

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where ρ_l is the density of liquid water. When computing the polarimetric radar variables, drop shape is important and must be dealt with appropriately. However, assuming a spherical shape of drops does not significantly impact the computation of evaporation (Straka and Gilmore 2006). Thus, the drop shape inconsistency will not affect the results of this study. The mass diffusion term must be written in terms of D:

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Thus, substituting (7)–(9) into (6), and making use of the change of variables,

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yields the governing equation in terms of drop diameter D:

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For the most general case in a 1D rainshaft model, the drop concentration is a function of diameter, height, and time, that is, N = N(D, z, t). For brevity, the functional dependence of N will herein be omitted. Thus, expanding the derivatives in (10) results in

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For drops falling at terminal velocity υ_t,

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So, (11) becomes

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which governs the time rate of change of the raindrop concentration. Using (3) for terminal velocity and noting that Ḋ = 4ξD⁻¹, we can write (12) in discrete form,

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for each time step i, height level j, and drop size bin k.

As raindrops begin to evaporate in subsaturated air, the thermodynamic properties of the air in the rainshaft are affected. Specifically, evaporation causes the shaft to gradually cool and moisten in time, thereby decreasing the subsaturations and limiting the amount of evaporation that occurs. The decrease in temperature and precipitation loading contributes to negative buoyancy relative to the surrounding precipitation-free air, which forces a localized downdraft. The downdraft also serves to limit the evaporation as it carries drops downward faster than their terminal velocities, decreasing the amount of time available for evaporation. Srivastava (1985, 1987) has showed how intense downdrafts can occur due to a combination of evaporation and melting of ice particles (both of which have a cooling effect on the local environment).

To simulate the local cooling and moistening effects, we utilize (1), as well as the equation governing heat conduction toward the drop:

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where f_h is the heat ventilation coefficient, K is the thermal conductivity of the air, and T_r is the temperature of the drop’s surface. For simplicity, we assume the raindrop temperatures to be in equilibrium at each level, neglecting the brief relaxation period toward their equilibrium temperature. Recently, Tardif and Rasmussen (2010) have investigated the validity of the equilibrium assumption and found that it may not hold if drops experience thermodynamic changes on time scales comparable to the equilibrium relaxation time. In our study, the height step (100 m) ensures that the drops remain within one grid box (in which thermodynamic conditions are constant) over the relaxation time scale, which tends to be on the order of 4–5 s for most drop sizes. Using the total amount of mass evaporated at each level, and assuming that all latent enthalpy from the environment contributes directly to cooling the drop’s surface (which immediately cools the surrounding air), the incremental change in the temperature of the air is calculated at each time step. Similarly, the entire mass of liquid water lost due to evaporation goes directly into vapor, increasing the vapor density in the air. Using the new temperature and vapor density, and the ideal gas law for water vapor, the new relative humidity can be calculated.

This environmental feedback scheme may be turned on or off in the model. Since the model is one-dimensional and is not tied to any dynamics, we have omitted the generation of a downdraft. The velocity relation (3) overestimates the fall speeds of the moderate and large drops already, which may partially account for the errors introduced when neglecting a downdraft. Also, to be realistic and dynamically consistent, the generation of a downdraft would require some parameterization of entrainment, a process that still has some uncertainty. Without this entrainment, the 1D column gradually moistens and cools until it becomes saturated, halting the evaporation.

The changes in diameter of the drop size bins at each height level and the calculated concentration of drops at each level are used to compute the vertical profiles of polarimetric variables according to the T-matrix method (e.g., Mishchenko 2000). For raindrop shapes, we assume the corrected relation suggested by Brandes et al. (2002):

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where D is in millimeters. See Brandes et al. (2002) for a discussion of the differences between this relation and others that are used frequently in the literature. Note that this relation produces slightly more spherical drops, especially in the range 1–4 mm. The polarimetric variables (especially Z_DR and ρ_HV) are more strongly affected by the larger drops, the shapes of which are similar to other relations. Thus, we expect only slight differences if other drop shape relations are used instead of (15). The raindrops are assumed to have a distribution of canting angles with mean 0° and standard deviation 20° with respect to the vertical. In general, 20° is too high for typical rainfall; a standard deviation of 10° is more appropriate (e.g., Ryzhkov 2001; Ryzhkov et al. 2002). However, the higher value was chosen to increase the effects of evaporation on ρ_HV. The impact of this wider distribution of canting angles is to dampen the effects of evaporation on the other variables very slightly. The wavelength of the radar will be discussed using convention, according to which “S band” refers to the 10.9-cm wavelength (as in the WSR-88D network) and “C band” refers to a wavelength of 5.3 cm.

The evaporation model calculations will be separated into two groups: sensitivity studies, which will focus on the exploration of parameter space, and simulations, which will model the vertical profiles of polarimetric variables using observed thermodynamic soundings from different climate regions. The sensitivity studies are designed to test the model sensitivity as well as the sensitivity of the polarimetric variables to different thermodynamic conditions, drop size distribution models, and rainfall rates. The simulations are intended to illustrate potential variations in vertical profiles of polarimetric variables in different regions of the United States that may be observed following the nationwide weather radar upgrade to polarization diversity. For the experiments, the gradual moistening and cooling feedback mechanism has been turned off in order to create “snapshots” of the profiles of polarimetric variables. For applied simulations, the mechanism should be turned on to avoid overaggressive evaporation.

a. Design

Because of the aforementioned differences in the drop size dependency for each of the polarimetric variables, sensitivity to selection of the DSD is expected. To address this, each model sensitivity experiment is repeated using different initial DSD models. The standard exponential and gamma models are used:

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and

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To conduct a fair comparison between the different DSD models, the rainfall rate for each has been fixed at the top of the domain. A Marshall–Palmer DSD (herein MP) is used for the exponential model. Note that the intercept parameter most often used with the MP distribution, N₀₀ = 8000 m⁻³ mm⁻¹, is calculated for use at sea level; since we are using fixed rainfall rates aloft, we must use N₀ = N₀₀[ρ(h₀)/ρ₀]^0.4. For the MP distribution, with the velocity relation (3), the slope parameter Λ is calculated using

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The gamma model has three parameters, though these are usually constrained and thus not entirely independent (e.g., Zhang et al. 2001, 2006; Brandes et al. 2004; Cao et al. 2008). For Oklahoma precipitation, Cao et al. (2008) found an empirical relation between the shape parameter μ and the slope parameter Λ:

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where the equation is applicable for 0 ≤ Λ ≤ 20. Constrained gamma models with μ varying between −1 and 5 are used in the calculations. These values encompass the bulk of the observations in Oklahoma rain (e.g., Cao et al. 2008). A slightly broader range of values of μ was found in rain in Florida (Zhang et al. 2001), so there is some dependence on climate region. Since Λ is determined from the preselected μ values using (19) and we have a fixed rainfall rate R,

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the intercept parameter can be determined by solving (20) for N₀ using (17) for N(D):

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where the height-density correction is included. Figure 2 displays each modeled DSD. It is evident that a variety of DSD shapes have been selected, covering a broad spectrum of precipitation regimes. Note that in the Oklahoma precipitation, the negative shape parameters are most often associated with convective precipitation events, so the relatively high concentration of larger drops makes sense. Also note the similarities between the MP DSD (corresponding to a shape parameter of 0) and the Γ, μ = 1 distribution, which nearly overlap for all drop sizes except at the small-drop end of the spectrum.

For each set of model runs the polarimetric variables are calculated for both S and C bands. In the first set of experiments, idealized isothermal layers 2 km deep are considered. The temperature is fixed at 20°C, and the relative humidity (RH) is set constant in height but varies from 10% to 95% in each experiment. Though not necessarily realistic, these experiments simply explore the parameter space of the model. In the second set of sensitivity runs, a dry-adiabatic lapse rate is prescribed with a surface temperature of 30°C. The RH profile is assumed to increase linearly from the given surface value to 100% at the cloud base (top of the domain, taken to be 3 km). The surface values are varied from 55% to 95% in 5% increments. These idealized well-mixed boundary layer cases apply to warm season precipitation events. Simulations using observed thermodynamic profiles, including both warm and cool season events, are explored in section 5. In these two sets of sensitivity tests, each of the DSD models is used. The final set of sensitivity tests varies R from 0.1 to 20 mm h⁻¹ using the MP DSD for a dry-adiabatic environment with a surface RH of 75% and a surface temperature of 30°C.

b. Transient differential sedimentation

At the onset of precipitation, a transient effect known as differential sedimentation occurs, where the largest raindrops fall to the ground before the smaller raindrops. The reason for this is simply the difference in the terminal velocity of the large drops versus the smaller drops; the large drops fall faster and thus reach the ground before the smaller drops. Once enough time has elapsed, all drops that do not evaporate reach the ground, and the visible effects of differential sedimentation disappear.

Recall that size sorting is an extremely important effect as observed by polarimetric radars (e.g., see a review by Kumjian and Ryzhkov 2008). With the largest, most oblate drops initially falling farther from the cloud than smaller drops, the polarimetric variables (especially Z_DR) are significantly enhanced beneath the cloud, with Z_DR increasing toward the ground. At S band, ρ_HV tends to change very little, only slightly decreasing toward the ground. This is because the resonance effects are still minimal even for the largest drops at S band. At C band, however, the large drops are within the band of sizes where resonance effects are quite strong. Thus, in addition to increased Z_DR toward the ground, C-band measurements will show a significant decrease in ρ_HV. Figure 3 shows an example of the impacts of differential sedimentation on the polarimetric variables. Note that this effect dominates any signal from evaporation, which produces more subtle changes in the vertical profiles of the polarimetric variables. Thus, for the remainder of the sensitivity studies and experiments where we quantify the effects of evaporation, the calculations are carried out for long times (equivalently, waiting for the profiles to attain steady-state solutions where the environmental feedback mechanism has been turned off).

c. Results of sensitivity tests

It is convenient to define the “evaporative change” in the polarimetric variables over the depth of the model domain, which is simply the value of the polarimetric variable at the ground minus its initial value aloft.¹ The evaporative change will be denoted as a Δ before the variable. As discussed above, evaporation will produce negative ΔZ_H and ΔK_DP (indicative of a decrease) and a positive ΔZ_DR (indicative of an increase). To make a more meaningful comparison between ΔZ_H and ΔK_DP, the evaporative change in K_DP will be converted into logarithmic units:

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Recall that the logarithmic differences for Z_H, Z_DR, and K_DP can be converted into relative changes (e.g., a 3-dB decrease corresponds to about a 50% reduction from its original value).

The results from the first set of experiments (considering isothermal layers) are summarized in Figs. 4 and 5 for S and C bands, respectively. It is clear that all of the variables are sensitive to the relative humidity in the layer, but perhaps more importantly the results are sensitive to the initial DSD model selected. The Γ, μ = 5 model exhibits much greater evaporative changes in Z_H and K_DP than do the other models (Figs. 4a,c and 5a,c). This is explained by two factors. First, the distribution contains a large concentration of small drops, which are preferentially evaporated, resulting in a substantial decrease in mass. Second, the Γ, μ = 5 has fewer large drops than any other distribution. These large drops, which do not evaporate as efficiently as smaller drops, tend to overwhelm the contribution to the observed Z_H (and, to a lesser extent, K_DP) for the other DSD models, which all exhibit lower magnitudes of ΔZ_H and ΔK_DP (dB).

Since Z_DR is more sensitive to drop size than Z_H, it follows that the large ΔZ_DR values occur for the DSDs with relatively large concentrations of big drops. However, also playing an important role in producing the significant ΔZ_DR values is a large concentration of small drops. The preferential evaporation of a significant portion of the spectrum will substantially increase the median drop size of the spectrum. This is why the MP model has the highest ΔZ_DR (Figs. 4b and 5b): it has the highest concentration of small drops and a comparatively large concentration of big drops. Also note that the ΔZ_DR at C band (Fig. 5b) is somewhat higher for the DSD models due to resonance scattering effects.

At S band, the Δρ_HV magnitudes are quite small (<0.002 even for extreme evaporation) for all DSD shapes, at least for the electromagnetic scattering model employed in this study (Fig. 4d). Such small changes are insignificant and likely within the uncertainty of the WSR-88D measurements, or about ±0.005–0.01. At C band, the evaporative changes in ρ_HV are slightly larger in magnitude and negative for all models (Fig. 5d). For modest evaporation rates, changes in ρ_HV at both radar wavelengths are insignificant and probably difficult to detect operationally.

Next, idealized 3-km-deep mixed layers are considered for the calculations. The results for S and C bands are summarized in Fig. 6. The resulting ΔZ_H and ΔK_DP are dependent on the surface RH and the DSD prescribed aloft, as expected. However, a feature of note is that ΔZ_H and ΔK_DP reverse sign for three of the DSD models (MP, Γ, μ = −1, and Γ, μ = 1) for high values of surface RH. This is because the relatively cool and moist conditions beneath the cloud base do cause enough evaporation to counteract the effects of “raindrop convergence,” a result of the drops encountering increasing air density with fall distance. In the absence of any evaporation, the concentration of drops increases slightly with decreasing height, which affects Z_H and K_DP, but not Z_DR or ρ_HV. Also of note is that the difference between the S- and C-band values of ΔZ_DR and Δρ_HV increases with higher concentrations of large drops, a result of the resonance scattering effects prevalent in big drops at C band.

The results of varying the rainfall rate R are provided in Fig. 7. For the higher rainfall rates considered, one should expect a greater change in K_DP for a given amount of evaporation than is observed in Z_H. At both S and C bands, Δρ_HV is insignificant for all rainfall rates with the MP model. For the S-band calculations, ΔZ_DR decreases with increasing rainfall rate whereas the ΔZ_DR at C band increases slightly. The difference in behavior may be attributable to the enhanced resonance scattering effects at C band.

The sensitivity experiments have shown, for given thermodynamic conditions, that the largest ΔZ_H and ΔK_DP occur for the Γ, μ = 5 DSD model, with the Γ, μ = −1 model having the smallest evaporative changes. Again, these results are directly related to the shape of the DSD: the smaller the concentration of large (>4 mm) drops, the greater the impacts of evaporation will be on Z_H and K_DP. The logarithmic changes in K_DP are slightly greater in magnitude than those of Z_H since K_DP is less dependent on drop diameter than Z_H; the preferential depletion of smaller drops has a greater relative impact on K_DP. Note that since Z_H typically is displayed in logarithmic units (dBZ), whereas K_DP generally is shown in degrees per kilometer, ΔK_DP may be more obvious to operational meteorologists. For example, an equivalent evaporative change of 3 dB for Z_H (e.g., 33–30 dBZ) “appears” to be less significant than a 3-dB relative change in K_DP (e.g., 1.0°–0.5° km⁻¹). However, it should be noted that for the relatively light rainfall rates considered in this study and at S band, K_DP can be noisy and difficult to estimate. At shorter radar wavelengths, the K_DP estimates will be less noisy as the K_DP values will be larger (since K_DP is inversely proportional to radar wavelength), possibly making such evaporative changes easier to detect operationally with C- and X-band polarimetric radars.

For given conditions, the largest values of ΔZ_DR occur for the MP model, with Γ, μ = −1 having the smallest values. The changes depend on the relative contributions from both the small- and large-drop ends of the spectrum. While having the largest concentration of big drops of any of the models used in this study, the Γ, μ = −1 model resulted in the smallest ΔZ_DR. This is because of the comparatively low concentration of small drops (<2 mm). With fewer small drops being depleted, there is a lesser shift in the median drop size of the spectrum. Coupled with this is the fact that the substantial concentrations of big drops, which are not as affected by evaporation, dominate the contribution to the backscattered signal.

a. Design

Once the model sensitivity is explored, it is informative to look at real cases in an attempt to see the types of variations in vertical profiles of the polarimetric variables that may be observed in different evaporation scenarios. To accomplish this, we have selected three soundings from different regions that display different thermodynamic characteristics. These observed temperature and relative humidity profiles are used to initialize the model.

The three soundings are shown in Fig. 8. The first sounding comes from Albuquerque, New Mexico, at 0000 UTC 16 August 2007 (Fig. 8a) and represents the summer season in the western United States with a deep, dry well-mixed layer. Light precipitation echoes were observed by the Albuquerque WSR-88D about the time of the sounding. Next is a spring sounding (Fig. 8b), taken from Norman, Oklahoma, at 1800 UTC 24 May 2008 and may be said to represent an atmosphere primed for severe weather: a cyclic tornadic supercell developed north of Oklahoma City, Oklahoma, in the afternoon, producing at least 10 tornadoes. The third sounding (Fig. 8c) comes from Wallops Island, Virginia, at 0000 UTC 7 October 2009 and represents a cool, moist boundary layer in which light rain was observed throughout the day. Note that the environmental feedback mechanism has been turned off for these simulations.

b. Results of simulations

The MP distribution with a 5 mm h⁻¹ rainfall rate aloft is used in the simulations. The MP model is employed because it is perhaps the most widely known DSD model and provides intermediate magnitudes of evaporative changes. As previously demonstrated, the choice of DSD model can have a significant impact on the evaporative changes of the polarimetric variables. This should be considered when interpreting the outcome of the simulations and the computed vertical profiles of the polarimetric variables presented herein. Nonetheless, the purpose of these simulations is to illustrate the potential variations in vertical profiles of polarimetric observables that may occur in different climate regions and seasons throughout the United States.

Figure 9 displays the vertical profiles of polarimetric variables for the Albuquerque sounding (Fig. 8a). For both radar wavelengths, ΔZ_H is less than −6 dB. The ΔZ_DR is nearly 0.3 dB at S band, which may be detectable by the WSR-88D, and greater than 0.3 dB at C band. The magnitude of the change in ρ_HV is negligible at S band. At C band, the Δρ_HV is about −0.003, which may be observable with very high quality radar systems. The evaporative changes in all polarimetric variables for each of the simulated soundings are summarized in Table 1.

Because of the uncertainty involved with the choice of the initial DSD, the same simulations are performed with the Γ, μ = −1 distribution as well as the Γ, μ = 5 model. These models were selected for comparison since they encompass the extremes for evaporative changes in the different polarimetric variables (Table 2). The Γ, μ = −1 distribution exhibits much smaller magnitudes of ΔZ_H and ΔK_DP than do the MP simulations. Also note that Δρ_HV changes sign with the Γ, μ = −1 model depending on the radar wavelength. In contrast, the Γ, μ = 5 model produces the most significant ΔZ_H and ΔK_DP values and very small changes in Z_DR and ρ_HV. These simulations can be viewed as the approximate quantitative bounds on the possible changes in polarimetric characteristics of light rain due to evaporation in differing environments.