# Dual-Polarization Radar Fingerprints of Precipitation Physics: A Review

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## Abstract

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## 1. Introduction

## 2. Qualitative Microphysical Fingerprints

_{H}), differential reflectivity (Z

_{DR}), specific differential phase shift (K

_{DP}), and the co-polar correlation coefficient (ρ

_{hv}). Z

_{H}is a measure of how much energy is scattered back to the radar, including from hydrometeors, insects, birds, etc. When these targets or particles are small compared to the radar wavelength, the amount of energy they scatter back to the radar is proportional to their horizontal dimension to the sixth power. The total Z

_{H}measured at a given location is the sum of this scattering from all particles within the radar pulse’s volume. As such, the total Z

_{H}is proportional to the number density of particles, as well. For a given particle size, those composed of liquid backscatter much greater power than those composed of ice; backscattered power from mixed-phase particles (i.e., those containing both liquid and ice) is somewhere between. Z

_{V}the radar reflectivity factor at vertical polarization, and is defined similarly, except it probes particles’ vertical dimensions. Z

_{DR}measures the difference between Z

_{H}and Z

_{V}(in logarithmic scale), and thus provides an indication of the particles’ shapes given that the particles are small compared to the radar wavelength. For example, an oblate raindrop with its maximum dimension oriented (on average) in the horizontal will backscatter more energy from the horizontally polarized radar signal than from the vertically polarized radar signal (i.e., Z

_{H}> Z

_{V}), leading to Z

_{DR}> 0 dB. Likewise, particles with more of their mass aligned in the vertical direction will have Z

_{V}> Z

_{H}, and thus Z

_{DR}< 0 dB. Spherical particles, or a collection of nonspherical particles that are randomly oriented, will scatter back energy equally at horizontal and vertical polarizations (Z

_{H}= Z

_{V}), resulting in Z

_{DR}= 0 dB. For a given non-spherical particle shape, those composed of liquid will produce larger magnitude Z

_{DR}values than those composed of ice, similar to the behavior of Z

_{H}. Z

_{DR}will be biased towards the particles in the radar sampling volume that dominate the backscattering because it is weighted by Z

_{H}and Z

_{V}.

_{H}and Z

_{DR}, K

_{DP}is a measure of phase shift: it is the difference between the phases of the horizontally polarized and vertically polarized waves as they propagate through precipitation. Such phase differences arise from nonspherical particles: those with more of their mass aligned in the horizontal direction will produce K

_{DP}> 0 deg km

^{−1}, and those with more of their mass aligned in the vertical direction will produce K

_{DP}< 0 deg km

^{−1}. The sensitivity of K

_{DP}to drop size D is less than that of Z

_{H}, closer to ~D

^{4}or ~D

^{5}compared to the ~D

^{6}dependence of Z

_{H}. K

_{DP}is also proportional to the number concentration of nonspherical particles. Unlike Z

_{H}and Z

_{DR}, K

_{DP}is insensitive to spherical particles; in a sense, it only “sees” the oriented nonspherical particles within the sampling volume. Finally, ρ

_{hv}is a measure of the diversity of particles’ intrinsic Z

_{DR}within the sampling volume. For spherical particles or non-spherical particles with very similar shapes and orientations (and thus similar Z

_{DR}), ρ

_{hv}is near unity. When there exists a variety of particle shapes and orientations in the sampling volume, ρ

_{hv}is reduced. For a more detailed overview of the physical meaning of these quantities, see the texts [1,2,7] and the review series [3,4,5].

_{H}and Z

_{DR}towards the ground). Use of multiple polarimetric radar variables provides additional degrees of freedom over conventional (i.e., Z

_{H}alone) observations, affording unique fingerprints for various microphysical processes. Such information provides an advantage over traditional techniques using Z

_{H}alone, such as contoured reflectivity by altitude diagrams (CFADs). These qualitative fingerprints are summarized in graphical form in [41], and reproduced with modifications in [7]. We will review these fingerprints associated with different microphysical processes here; their graphical depiction follows [42]. Figure 1 shows an example of how these fingerprints will be summarized graphically. The vertical axis represents height, and the abscissa indicates the value of the given polarimetric radar variable, each color coded and in individual subpanels. In the example shown, Z

_{H}, Z

_{DR}, and K

_{DP}all increase towards the ground.

#### 2.1. Rain Microphysical Processes

^{6}), which dominates over backscattering’s direct proportionality to number concentration (~N). Therefore, collision-coalescence is expected to increase Z

_{H}in the rainshaft towards the ground, because the increase in drop size resulting from the merging of two or more drops dominates the decrease in number concentration of these smaller drops. Similarly, Z

_{DR}and K

_{DP}are both expected to increase towards the ground owing to the production of these larger, more oblate drops (Figure 2a). Using a detailed bin microphysical model, Ref. [44] first quantified the expected collision-coalescence fingerprint, revealing increases in Z

_{H}of <4 dB, in Z

_{DR}of <0.5 dB, and in K

_{DP}< 0.5 deg km

^{−1}(at S band) over a 3-km, steady-state rain shaft.

_{H}, Z

_{DR}, and K

_{DP}towards the ground (Figure 2b). The modeling study of [44] showed much larger changes in the radar variables owing to collisional breakup compared to collision-coalescence: decreases in magnitudes up to 5 dB for Z

_{H}, 1.5 dB for Z

_{DR}, and 0.7 deg km

^{−1}for K

_{DP}(at S band) over the 3-km steady-state rain shaft. However, the authors noted that, based on comparisons to observations, the bin model’s accounting for collisional breakup may be “overaggressive,” leading to exaggerated vertical changes in the radar variables.

_{H}and K

_{DP}decrease towards the ground, but Z

_{DR}increases slightly (Figure 2c), as first pointed out by [52]. This occurs when the greater amount of mass lost from smaller drops relative to larger drops in a given DSD leads to a slight upward shift in the mean drop size. Using an idealized bin microphysics model, Ref. [53] showed that these increases in Z

_{DR}are quite small (<0.2 dB over a few-km-deep rainshaft) and likely within the measurement uncertainty of most polarimetric radars [54]. As such, careful averaging in space or time, or techniques such as quasi-vertical profiles [55] may be needed to observe this fingerprint robustly. In a follow-up study, Ref. [45] used a similar idealized model to demonstrate that the Z

_{DR}fingerprint can actually reverse, featuring Z

_{DR}decreasing towards the ground, in special cases of initial gamma DSDs (e.g., [56,57]) with large mean drop sizes (i.e., large Z

_{DR}at the top of the rain shaft) and large DSD breadth (Figure 3). However, Ref. [45] only considered evaporation, and ignored the collisional processes. Kumjian and Prat [44] showed that collisional breakup tends to dominate in rain shafts with such large initial Z

_{DR}; it is unclear if a pure evaporation signal could be observed given the propensity for such DSDs to undergo collisional breakup. The interplay between these processes requires detailed modeling; preliminary results of such modeling will be shown in a later section.

^{−1}. Use of polarimetric radar information to quantify thermodynamic changes in the environment is an exciting research frontier, and one that could lead to significant improvements in numerical models through, for example, data assimilation (e.g., [58]).

_{DR}and Z

_{H}(and/or K

_{DP}); an iconic example is the “Z

_{DR}arc” feature offset from the precipitation core in supercell storms (e.g., [64,65,66,67]). For a rain shaft, the transient effect of size sorting is observed as a strong increase in Z

_{DR}towards the ground paired with decreases in Z

_{H}and K

_{DP}(Figure 2d; [44,61]). Although the fingerprint is qualitatively consistent with that of evaporation (cf. Figure 2c,d), the magnitude of the Z

_{DR}increase is far more significant for size sorting than for evaporation. Thus, in situations where size sorting and evaporation are both ongoing, it is expected that size sorting dominates the observed fingerprint.

_{H}and Z

_{DR}towards the ground in the example shown in Figure 4) allows easy classification of the ongoing microphysical process. This rain microphysical fingerprint framework has found uses in the hydrometeorological literature, including classifying rainfall for quantitative precipitation estimation [68,69,70], and has recently been extended to similar work with satellite observations [71].

_{H}, revealing consistently moderate to heavy rain, with some times experiencing > 40 dBz at the lowest levels. Figure 5b is a similar presentation, but for Z

_{DR}. We note that, despite the larger Z

_{H}values, Z

_{DR}remains < 1 dB for much of the event, indicative of smaller drops (and expected based on the tropical nature of the precipitation).

_{H}and Z

_{DR}at each time and applied a 5-gate (~220-m) moving average filter to smooth the data. Then, a least-squares linear fit was computed for each data segment along a 15-gate (~660-m) moving window; the slope of these best-fit lines indicates the vertical gradients of Z

_{H}and Z

_{DR}. Next, these computed Z

_{H}and Z

_{DR}vertical gradients were used to assess the qualitative microphysical fingerprint. To avoid false classifications based on noise present in the data, we applied minimum thresholds of dZ

_{H}/dz > 0.002 dB km

^{−1}and dZ

_{DR}/dz > 0.0001 dB km

^{−1}(based on measurement uncertainties of 1–2 dB in Z

_{H}and 0.1–0.2 dB in Z

_{DR}cited in [54]).

_{DR}after 19 UTC are small in magnitude. Recall that during this time, Hurricane Matthew was ingesting drier air from the west. Thus, this signal of increased prevalence of the evaporation fingerprint throughout this period is at least broadly consistent with the observed storm evolution.

_{H}and Z

_{DR}and greater collisional breakup. As we will see later in Section 3, there is now some evidence that these fingerprints can be used for quantitative process rate information, which could substantially advance evaluation of numerical model microphysics schemes.

#### 2.2. Snow and Ice Microphysical Processes

_{H}. The aspect ratio’s growing departure from unity would suggest an increase in Z

_{DR}, because small, pristine ice crystals align themselves with maximum dimension in the horizontal, regardless of whether they take on oblate (e.g., plate-like) or prolate (e.g., needle-like) shapes [1,2,3,4,5,6,7]. However, ice crystal growth can be complicated by factors such as branching or hollowing (e.g., [74]). Such complicating factors may reduce the compactness of ice molecules in the particle, sometimes referred to as reducing the particle’s effective density, thereby contributing to a decrease in Z

_{DR}(see [75]). Which effect wins out? There is some observational evidence that pure vapor depositional growth for dendrites leads to approximately no change in Z

_{DR}, at least at X band (e.g., [76,77]). The lack of an observable sharp increase in Z

_{DR}during the very early growth from frozen droplets or other ice nuclei may be because the particle sizes were too small for the radar wavelength used. We speculate that, given a shorter radar wavelength sensitive to cloud-particle sizes, early growth should reflect a rapidly decreasing aspect ratio and thus increase in Z

_{DR}concurrent with an increase in Z

_{H}. For precipitation radar wavelengths (S, C, and X bands), this early growth likely is unobservable. K

_{DP}may respond similarly to Z

_{DR}, with the exception that a sufficiently large quantity of snow crystals would be necessary to obtain a strong enough signal to make a reliable estimate of K

_{DP}, particularly at longer wavelengths [76], given the much weaker scattering of ice particles compared to liquid and the inverse wavelength dependence of K

_{DP}[1,2]. Enhancements of K

_{DP}in the planar crystal growth region near −15 °C have been identified as a signal of vigorous vapor depositional growth (e.g., [78,79,80,81,82,83,84]). In contrast, others have argued that K

_{DP}enhancements represent the onset of aggregation (e.g., [85]). Some emerging evidence (Dunnavan et al., in preparation) suggests that primary nucleation and growth of large concentrations of ice crystals may be responsible for the observed K

_{DP}signal, consistent with the arguments put forth by [79]. Studies simulating the vapor depositional growth of ice crystals using reduced-density spheroids (e.g., [86,87]) are unable to capture the effects of snow crystal shape on electromagnetic scattering (e.g., [75]), and thus likely do not produce accurate fingerprints of vapor growth from Z

_{DR}and K

_{DP}. In summary, with considerable uncertainty, we suggest the fingerprint of vapor growth as increases in Z

_{H}, steady Z

_{DR}, and an increase in K

_{DP}accounting for primary nucleation and subsequent vapor growth of large concentrations of ice crystals (Figure 6a).

_{H}. Contrary to arguments that snow aggregates are well modeled by oblate spheroids (e.g., [89,90]), measurements of snow aggregate shapes reveal that they are highly irregular (e.g., [91,92]). However, their complicated and often chaotic orientations, paired with lower effective density, lead to Z

_{DR}values near 0 dB. Thus, the transition from pristine monomer ice crystals (particularly planar or columnar crystals) to well-developed aggregates comprising substantial numbers of monomer crystals (in other words, the snow aggregates often experienced in midlatitude snow storms that usually contain very large numbers of monomer ice crystals) is marked by a substantial decrease in Z

_{DR}. Note that, at temperatures below about −20 °C, ice crystal habits are complicated and not well understood [93]. These polycrystals, rosettes, and other irregular shapes have less extreme aspect ratios, and thus only moderate Z

_{DR}; for these cases, the aggregation fingerprint would be a more modest decrease in Z

_{DR}towards 0 dB (as seen in some cases from, e.g., [83]). In cases of very light aggregation (e.g., [76]), the resulting early aggregates with fewer constituent monomers may lead to positive Z

_{DR}values. Thus, the Z

_{DR}fingerprint of such light aggregation is still a decrease towards the ground, though this decrease may be less in magnitude than is typical in, for example, midlatitude snowstorms. Aggregation signatures for K

_{DP}are still subject to some debate in the scientific literature. As mentioned above, although some have argued the enhancement of K

_{DP}in the planar crystal growth region, constrained to temperatures near −15 °C, is a signal of the onset of aggregation [85], others have attributed this signature to vapor growth and/or nucleation. For the same reasons that well-developed snow aggregates produce near-zero Z

_{DR}values, K

_{DP}in snow aggregates also is near 0 deg km

^{−1}. Thus, any initial enhancement of K

_{DP}will decrease towards zero during ongoing aggregation. These are summarized in Figure 6b.

_{H}is expected to increase (though perhaps less substantially than aggregation, given the comparatively much smaller sizes of the collected cloud droplets). Evidence presented in [94] shows that Z

_{DR}could either increase or decrease as ice crystals become rimed, and that this ambiguous behavior may depend on the initial size (and, perhaps, the initial shape) of the crystals undergoing riming. However, the end result of heavy riming from a pristine crystal to a lump graupel particle is much like that of aggregation: increases in Z

_{H}and decreases in Z

_{DR}and K

_{DP}(Figure 6c). Riming can be complicated by other ongoing processes—for example, Hallett-Mossop rime splintering [95], which occurs at temperatures between about −3 and −8 °C and can lead to rapid vapor growth of columnar ice crystals in the same radar sampling volumes as the ongoing riming. In these cases, although Z

_{H}and Z

_{DR}tend to be dominated by the rimed particles (i.e., rimed aggregates or graupel), the large concentration of columnar ice crystals may lead to observable enhancements in K

_{DP}(Figure 6d), as shown in [83,96,97,98]. Kumjian et al. [97] argued that riming also leads to observable local decreases in the melting layer height, which they called “saggy bright bands”. However, subsequent modeling work by [99] suggested that heavier precipitation falling into the melting layer and associated increased cooling (owing to the enthalpy of melting) can lead to the development of an isothermal layer that is responsible for the sagging bright band (see the next subsection).

_{H}and slightly reduced Z

_{DR}(usually no more than a few tenths of a dB, and likely often within the radar system’s noise) within sublimating, aggregated snow (Figure 6e). Intriguingly, they also found K

_{DP}enhancements at the bottom of the column, which they interpreted as sublimational fragmentation, a form of secondary ice production [100,101]. This represents another potential use of enhanced K

_{DP}to identify secondary ice production processes in clouds. Indeed, K

_{DP}is particularly well-suited for identifying secondary ice production given its strong sensitivity to the number concentration of highly anisotropic particles, and relatively low sensitivity to the larger particles that tend to dominate backscatter (e.g., snow aggregates, graupel).

_{H}, Z

_{DR}, and K

_{DP}. However, a local increase in Z

_{DR}(i.e., a local maximum) was observed within a broader layer of Z

_{H}decreasing towards the surface (Figure 6f). Kumjian et al. [102] proposed that preferential freezing of smaller drops led to the signature by increasing the relative contribution to Z

_{H}(and thus to Z

_{DR}) of the larger, unfrozen drops, analogous to evaporation and size sorting. They presented simple scattering calculations that supported this hypothesis. In contrast, Ref. [104] suggested that ice pellets acquired more exaggerated shapes owing to deformation during freezing (although no supporting calculations were provided). However, follow-up work by [105] using fully polarimetric Ka-band radar observations and modeling with scattering calculations by [106] have suggested that asymmetric freezing is the likely explanation for increasing Z

_{DR}. As a falling drop freezes, the upwind (downward-facing side) experiences much greater thermal energy transfer owing to the ventilation (e.g., [107]), and thus faster freezing. This asymmetry in ice shell thickness between the top and bottom of a freezing drop leads to an exaggerated aspect ratio for the inner, unfrozen liquid portion of the particle, increasing Z

_{DR}. A subtle increase in K

_{DP}is sometimes observed within the refreezing layer, and can also be explained by asymmetric freezing [106]. However, the presence of anisotropic crystals generated in the refreezing layer, which have been observed in at least some cases (e.g., [105,108]), could also lead to an increase in K

_{DP}as observed. Given the exaggerated particle shapes in the refreezing layer, as well as any additional particle shape deformations or other irregularities (e.g., [104]), ρ

_{hv}also tends to decrease in the refreezing layer (not shown). Recently, Ref. [109] have suggested that refreezing of partially melted hydrometeors presents a different fingerprint, in which Z

_{H}, Z

_{DR}, and K

_{DP}all decrease towards the surface (indicated in Figure 6f by dashed lines). This is in part because a partially melted hydrometeor—one that contains ice—may start freezing immediately from the existing ice, rather than forming an ice shell that grows inward asymmetrically. This difference in geometries of the unfrozen liquid portion is argued to be responsible for the difference in observed fingerprints [109].

#### 2.3. Melting of Snow and Ice

_{H}increases and any polarization contrasts owing to nonspherical particle shapes become exaggerated. This can lead, for example, to large increases in Z

_{DR}and K

_{DP}, and decreases in ρ

_{hv}(Figure 6g). The decreases in ρ

_{hv}can be so dramatic that we have added a panel to Figure 6g to emphasize the importance in ρ

_{hv}for identifying melting.

^{2}> 0.9) between the maximum K

_{DP}in the melting layer and the cooling rate.

_{H}and more exaggerated polarimetric contrasts. Several studies have coupled a microphysical model of melting hail by [117] with scattering calculations to produce expected melting hail signatures in terms of vertical profiles of the polarimetric radar variables (e.g., [118,119,120,121]). In particular, smaller (<2 cm) hailstones tend to acquire a “torus” of liquid meltwater that accumulates about their equator, stabilizing fall behaviors and leading to larger Z

_{DR}. In contrast, larger hail (>2 cm) tends to shed much of its meltwater. The lack of stabilization during fall leads to lower Z

_{DR}, on average, given the diversity of shapes found in natural hailstones [122]. This feature was exploited for an operational hail size discrimination algorithm ([121]) that classifies hail into three categories: sub-severe, severe, and significantly severe (<2.5 cm; 2.5 to 5.0 cm; and >5.0 cm, respectively; see [123] for proposed hail size naming conventions). However, none of this work has exploited the radar data for quantitative use in understanding hail processes; undoubtedly, interpretation is complicated by the myriad of natural hailstone shapes [122] as well as the significant uncertainty in fall behavior [124].

## 3. Emerging Research with Microphysical Fingerprints

_{H}and Z

_{DR}, along with vertically pointing Ka-band radar observations of mean Doppler velocity, taken during an Arctic mixed-phase cloud that produced pristine dendrites (a case analyzed by [76]). The resulting MCMC-constrained growth parameters produced values of differential growth rates along the “a” and “c” axes (along the basal and prism faces, respectively), equal to a temperature-dependent inherent growth ratio, Γ, times the ratio of the ice crystal c and a axis lengths, shown by purple dots in Figure 7. Detailed laboratory measurements and numerical simulations by [129] suggested that ice crystal facets grow at a rate equal to the ratio α

_{c}/α

_{a}, where α

_{c}and α

_{a}are the deposition coefficients along the a and c axes. Figure 7 also shows this ratio’s dependence on temperature and the associated uncertainty, extracted from wind tunnel measurements. The excellent correspondence between the radar-retrieved growth rates and wind tunnel measurements seen in Figure 7 demonstrates the quantitative microphysical information contained in dual-polarization radar fingerprints.

_{DR}values were produced when the inherent growth ratio was larger, leading to crystals with less extreme aspect ratios and larger fall speeds ([77]). The authors made use of a probabilistic forward operator by [130] to better capture the natural variability of planar crystal shapes. Incredibly, the radar observations were informative to uncertain parameters in this probabilistic forward operator, as well: Z

_{DR}observations provided some constraint on the subbranch fractional coverage (a parameter determining the thickness of the dendritic ice crystal sub-branches).

^{−3}mm

^{−1}, and shape parameters ranging from −1 to 10, encompassing rainfall rates up to 500 mm hr

^{−1}. In all, this database comprises 9922 simulations featuring a wide parameter space of initial DSDs and rainfall rates (e.g., see [42,132] for additional details). As in [44], the dual-polarization radar variables were computed from the output of these bin model simulations, taking the final output time (t = 60 min) to obtain “steady state” rainshaft profiles. Vertical gradients in the polarimetric radar variables were computed at 299 height levels (corresponding to every 10 m in the vertical) in the domain, displayed in units of dB km

^{−1}for ease of interpretation. Data points for which Z

_{H}≥ 50 dBz were discarded as being unrealistically heavy rain. At each height level, the instantaneous process rates are obtained for the 0th and 6th DSD moments, hereafter M0 and M6, respectively, physically representing the total raindrop number concentration and radar reflectivity factor (in the small-particle scattering approximation). Given the clear relationship between M6 and the radar variables (e.g., see [134] for how each DSD moment is related to the dual-polarization radar variables), we will focus here on M6 process rates. Note that the results are sensitive to the bin model’s treatment of complex microphysical processes such as collisional breakup. Even though the bin model uses the state-of-the-art parameterizations of these processes, considerable uncertainty still exists e.g., [48,49,50,51,133]. Indeed, [44] suggested that the collisional breakup of drops in the bin model may be too aggressive, leading to more extreme collisional breakup fingerprint magnitudes than typically observed in rain. We therefore cautiously proceed with the analysis, given that the bin model and forward operator are the best available tools to quantitatively link process rate magnitudes and dual-polarization radar observables.

_{H}at S band), negative values indicate breakup is dominating changes in M6, and values near zero indicate a balance between these two processes. We can see that, in general, the breakup-dominated cases (negative values, purple dots) do fall within the “breakup” quadrant of the [44] parameter space, as expected. Likewise, the coalescence-dominated cases (green dots, positive values) are found mainly within the coalescence quadrant. Further, there is a tendency for stronger magnitudes of these processes to fall deeper within their respective quadrants, implying that the magnitudes of the radar fingerprints are related to the magnitudes of the process rates.

_{H}). The M6 evaporation rates exhibit large magnitudes in the “evaporation” quadrant, as well as the “breakup” quadrant. Interestingly, there is a clear shift of increasing magnitudes moving towards the top left within the cloud of points—in other words, even for points in the “breakup” quadrant, those closer to the evaporation quadrant of the [44] parameter space have larger M6 evaporation rate magnitudes. Further, the larger the breakup process rate magnitude, the larger the evaporation process rate magnitude, presumably because both scale with M6 and/or precipitation rate. Thus, even when evaporation does not dominate the observed changes in the dual-polarization radar fingerprints, information about the magnitude of evaporation is contained in the proximity to the evaporation quadrant, when displayed in the [44] parameter space diagram.

_{H}(and thus M6). For the majority of cases in which evaporation and coalescence are the dominant processes, Z

_{DR}tends to increase for both.

## 4. Concluding Remarks

_{hv}) was neglected in most of the fingerprints discussed herein. In part, this is because the fingerprint work was originally developed for rain processes and using S-band radars, at which wavelength ρ

_{hv}values tend to be very high (>0.98) for pure rain [3,7]. However, work [135] shows how some information may be gleaned from ρ

_{hv}about the DSD shape (or “dispersion”) parameter, which controls the DSD breadth. Such information could potentially provide additional constraint for process rates that was not used for our BOSS work [125,126] Section 3. Linking this information about DSD breadth to generalized DSD moments, rather than to a specific parameter in an assumed underlying DSD functional form, may be particularly informative while simultaneously removing a major source of uncertainty [125,126,134]. Extracting this type of information from ρ

_{hv}requires very high-quality measurements, however, and is likely only a capability of research-grade radars. Snow and ice processes are more challenging given the complexities of shapes. However, advances in scattering calculations [136] and microphysics schemes [40] should allow better realism in the representation of other processes for the coupled approach demonstrated above for rain and vapor depositional growth of ice. Incorporating ρ

_{hv}into analyses of ice processes in a manner similar to [135] may also be valuable, particularly for aggregation and riming e.g., [84]. In this sense, the realm of ice microphysical processes guarantees fruitful advances. We advocate for Bayesian inference frameworks such as those used in [78,125,126] to consider all potential sources of uncertainty carefully and robustly. Doing so is crucial for critical evaluation of, and, ultimately, improvement of microphysics parameterizations in models of varying scales.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Graphical representation of microphysical “fingerprints” in vertical profiles of dual-polarization radar variables. Height is on the vertical axis, increasing upwards, whereas the value of each polarimetric radar variable increases from left to right along the abscissa. Each radar variable is shown in a subpanel, color-coded as follows: goldenrod for Z

_{H}on the left, cyan for Z

_{DR}in the middle, and magenta for K

_{DP}on the right. In this example, all three radar variables are seen to increase towards the ground.

**Figure 2.**Different microphysical fingerprints for liquid precipitation, including (

**a**) coalescence, (

**b**) breakup, (

**c**) evaporation, and (

**d**) size sorting. In panel (

**c**), the lighter cyan shading indicates a range of possible fingerprints for Z

_{DR}, based on work by [45].

**Figure 3.**Adapted from [45]: color shading shows Z

_{DR}at top of rainshaft (dB according to outset scale); labeled solid contours show change in Z

_{DR}(in dB) over the 3 km rainshaft (positive indicates increase towards ground, negative indicates decrease towards ground) as follows: gray is zero change, blue contours are +0.2 and +0.3 dB; purple dashed lines are −0.15 and −0.3 dB. Results are shown as a function of initial gamma DSD (i.e., at the top of the domain) shape parameter $\mu $ on the abscissa and mean volume diameter D

_{0}on the ordinate. Computations were performed for X band.

**Figure 4.**Fingerprint parameter space of [44]; shows dominant processes (colored text in each quadrant) inferred from vertical gradients in Z

_{H}and Z

_{DR}($\Delta $, with changes towards ground). For example, coalescence is inferred from vertical profiles of Z

_{H}and Z

_{DR}that increase towards the ground (i.e., $\Delta $Z

_{H}> 0 dB and $\Delta $Z

_{DR}> 0 dB).

**Figure 5.**The evolution of vertical profiles of precipitation during Hurricane Matthew on 8 October 2016, observed by the WSR-88D radar near Raleigh, North Carolina (KRAX). (

**a**) Time series of quasi-vertical profiles of Z

_{H}(in dBz, shaded according to scale); (

**b**) time series of quasi-vertical profiles of Z

_{DR}(in dB, shaded according to scale); (

**c**) retrieval of the dominant microphysical fingerprint in rain (see text for details), where light blue indicates coalescence, dark green indicates breakup, light green indicates the coalescence-breakup balance, and dark blue indicates evaporation or size sorting.

**Figure 6.**As in Figure 2, but for ice microphysical processes including (

**a**) vapor depositional growth of ice crystals, (

**b**) aggregation, (

**c**) riming, (

**d**) riming with the Hallett-Mossop rime splintering process occurring, (

**e**) sublimation (including a range of possible increases in K

_{DP}owing to sublimational fragmentation identified by [88]), (

**f**) refreezing (with dashed lines showing the refreezing of partially melted hydrometeors, and solid lines indicating the refreezing of fully melted hydrometeors), and (

**g**) melting. Note in (

**g**) the additional panel showing the reduction in $\rho $

_{hv}associated with melting, given its importance for identifying this process.

**Figure 7.**The green line shows the ratio of deposition coefficients for the ice crystal c and a axes as a function of temperature, with the green shading indicating the uncertainty, extracted from wind tunnel measurements (from [129]). The purple dots show the inherent growth ratio ($\mathsf{\Gamma}$) times the ice crystal axis ratio obtained from Markov chain Monte Carlo simulations and X-band polarimetric radar observations (plotted with reduced data density, for clarity). Reprinted/adapted with permission from [77]. 2021, American Meteorological Society.

**Figure 8.**Normalized M6 process rates owing to collisional processes of breakup and coalescence. Positive values (green colors) indicate increases in M6 owing to collision-coalescence of raindrops. Negative values (purple colors) indicate decreases in M6 owing to collisional breakup.

**Figure 9.**As in Figure 7, but normalized M6 evaporation rate is shown.

**Figure 10.**The [44] parameter space showing the observational fingerprint quadrants. In each, histograms show the difference in the actual process rates: collisional processes—evaporation. If evaporation dominates changes to M6, the resulting difference is negative (

**left**of vertical gray line). If collisional processes dominate over evaporation, the result is positive (

**right**of vertical gray line). Magenta dotted shows distributions of all cases that fit into those quadrants. These are subdivided into those for which coalescence dominates the collisional process rates (blue), breakup dominates the collisional process rates (red), or they are balanced (goldenrod); these are annotated in the top left quadrant. Number of data points included in each quadrant as follows: coalescence n = 1,087,210; evaporation/size sorting n = 765,021; breakup n = 1,016,795; balance n = 97,652.

**Table 1.**Summary of the changes in the polarimetric radar variables towards the ground for different microphysical processes. A positive sign + indicates an increase in that radar variable between the top and bottom of the profile, whereas a negative sign indicates a decrease. The presence of a second sign in brackets [] indicates the possible variation.

Microphysical Processes | $\mathbf{\Delta}{\mathbf{Z}}_{\mathbf{H}}$ | $\mathbf{\Delta}{\mathbf{Z}}_{\mathbf{D}\mathbf{R}}$ | $\mathbf{\Delta}{\mathbf{K}}_{\mathbf{D}\mathbf{P}}$ |
---|---|---|---|

Collision-Coalescence | + | + | + |

Breakup | $-$ | $-$ | $-$ |

Evaporation | $-$ | $+[-]$ | − |

Size Sorting | $-$ | $-$ | + |

Vapor Deposition | + | + | + |

Aggregation | + | $-$ | $-$ |

Riming | + | $-$ | $-$ |

Riming with ice splintering | + | $-$ | + |

Sublimation | $-$ | $-$ | $-$ |

Sublimation with fragmentation | $-$ | $-$ | + |

Refreezing | $-$ | $+[-]$ | $+[-]$ |

Melting * | + | + | + |

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**MDPI and ACS Style**

Kumjian, M.R.; Prat, O.P.; Reimel, K.J.; van Lier-Walqui, M.; Morrison, H.C.
Dual-Polarization Radar Fingerprints of Precipitation Physics: A Review. *Remote Sens.* **2022**, *14*, 3706.
https://doi.org/10.3390/rs14153706

**AMA Style**

Kumjian MR, Prat OP, Reimel KJ, van Lier-Walqui M, Morrison HC.
Dual-Polarization Radar Fingerprints of Precipitation Physics: A Review. *Remote Sensing*. 2022; 14(15):3706.
https://doi.org/10.3390/rs14153706

**Chicago/Turabian Style**

Kumjian, Matthew R., Olivier P. Prat, Karly J. Reimel, Marcus van Lier-Walqui, and Hughbert C. Morrison.
2022. "Dual-Polarization Radar Fingerprints of Precipitation Physics: A Review" *Remote Sensing* 14, no. 15: 3706.
https://doi.org/10.3390/rs14153706