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**Atmospheric Measurement Techniques**
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**Research article**
10 Jul 2020

**Research article** | 10 Jul 2020

Preliminary investigation of the relationship between differential phase shift and path-integrated attenuation at the X band frequency in an Alpine environment

^{1}Institut des Géosciences de l'Environnement (IGE, UMR 5001, Université Grenoble Alpes, CNRS, IRD), Grenoble, France^{2}Centre de Météorologie Radar, Direction des Systèmes d'Observation, Météo-France, Toulouse, France

^{1}Institut des Géosciences de l'Environnement (IGE, UMR 5001, Université Grenoble Alpes, CNRS, IRD), Grenoble, France^{2}Centre de Météorologie Radar, Direction des Systèmes d'Observation, Météo-France, Toulouse, France

**Correspondence**: Guy Delrieu (guy.delrieu@univ-grenoble-alpes.fr)

**Correspondence**: Guy Delrieu (guy.delrieu@univ-grenoble-alpes.fr)

Abstract

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The RadAlp experiment aims at developing advanced methods for
rainfall and snowfall estimation using weather radar remote sensing
techniques in high mountain regions for improved water resource assessment
and hydrological risk mitigation. A unique observation system has been
deployed since 2016 in the Grenoble region of France. It is composed of an
X-band radar operated by Météo-France on top of the Moucherotte mountain
(1901 m above sea level; hereinafter MOUC radar). In the Grenoble valley (220 m above sea level; hereinafter a.s.l.), we
operate a research X-band radar called XPORT and in situ sensors (weather station, rain gauge and disdrometer). In this paper we present a methodology for
studying the relationship between the differential phase shift due to
propagation in precipitation (Φ_{dp}) and path-integrated
attenuation (PIA) at X band. This relationship is critical for
quantitative precipitation estimation (QPE) based on polarimetry due to
severe attenuation effects in rain at the considered frequency. Furthermore,
this relationship is still poorly documented in the melting layer (ML) due
to the complexity of the hydrometeors' distributions in terms of size, shape
and density. The available observation system offers promising features to
improve this understanding and to subsequently better process the radar
observations in the ML. We use the mountain reference technique (MRT) for direct
PIA estimations associated with the decrease in returns from mountain
targets during precipitation events. The polarimetric PIA estimations are
based on the regularization of the profiles of the total differential phase
shift (Ψ_{dp}) from which the profiles of the specific differential phase
shift on propagation (*K*_{dp}) are derived. This is followed by
the application of relationships between the specific attenuation (*k*) and the
specific differential phase shift. Such *k*–*K*_{dp} relationships are
estimated for rain by using drop size distribution (DSD)
measurements available at ground level. Two sets of precipitation events are
considered in this preliminary study, namely (i) nine convective cases with high
rain rates which allow us to study the *ϕ*_{dp}–PIA relationship in
rain, and (ii) a stratiform case with moderate rain rates, for which the melting
layer (ML) rose up from about 1000 up to 2500 m a.s.l., where we were
able to perform a horizontal scanning of the ML with the MOUC radar and a
detailed analysis of the *ϕ*_{dp}–PIA relationship in the various layers
of the ML. A common methodology was developed for the two configurations
with some specific parameterizations. The various sources of error affecting
the two PIA estimators are discussed, namely the stability of the dry weather mountain
reference targets, radome attenuation, noise of the total differential phase shift profiles, contamination due to the differential phase shift on
backscatter and relevance of the *k*–*K*_{dp} relationship derived from DSD
measurements, etc. In the end, the rain case study indicates that the
relationship between MRT-derived PIAs and polarimetry-derived PIAs presents
an overall coherence but quite a considerable dispersion (explained variance
of 0.77). Interestingly, the nonlinear *k*–*K*_{dp} relationship derived
from independent DSD measurements yields almost unbiased PIA estimates. For
the stratiform case, clear signatures of the MRT-derived PIAs, the
corresponding *ϕ*_{dp} value and their ratio are evidenced within the
ML. In particular, the averaged PIA∕*ϕ*_{dp} ratio, a proxy for the
slope of a linear *k*–*K*_{dp} relationship in the ML, peaks at the level
of the copolar correlation coefficient (*ρ*_{hv}) peak, just below the
reflectivity peak, with a value of about 0.42 dB per degree. Its value in
rain below the ML is 0.33 dB per degree, which is in rather good agreement with
the slope of the linear *k*–*K*_{dp} relationship derived from DSD
measurements at ground level. The PIA∕*ϕ*_{dp} ratio remains quite high
in the upper part of the ML, between 0.32 and 0.38 dB per degree, before
tending towards 0 above the ML.

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Delrieu, G., Khanal, A. K., Yu, N., Cazenave, F., Boudevillain, B., and Gaussiat, N.: Preliminary investigation of the relationship between differential phase shift and path-integrated attenuation at the X band frequency in an Alpine environment, Atmos. Meas. Tech., 13, 3731–3749, https://doi.org/10.5194/amt-13-3731-2020, 2020.

1 Introduction

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Estimation of atmospheric precipitation (solid/liquid) is important in a
high mountain region such as the Alps for the assessment and management of
water and snow resources for drinking water, hydropower production,
agriculture and tourism characterized by high seasonal variability. One of
the most critical applications concerns the prediction of natural hazards
associated with intense precipitation and melting of snowpacks, i.e.,
inundations, floods, flash floods and gravitational movements, which
requires a high-resolution observation, namely spatial resolution ≤1 km^{2} and temporal resolution ≤1 h. While this can hardly be achieved
over extended areas with traditional in situ rain gauge networks, the use of radar
remote sensing has a high potential that needs to be exploited but also a
number of limitations that need to be surpassed. Quantitative precipitation
estimation (QPE) with radar remote sensing in a complex terrain such as the
Alps is made challenging by the topography and the space–time structure and the dynamics of precipitation systems. Radar coverage of the mountain regions
brings the following dilemma. On the one hand, installing radar at the top
of a mountain allows for a 360^{∘} panoramic view and therefore the
ability to detect precipitation systems over a long range at the regional
scale. This is particularly relevant for localized and heavy convective
systems in warm seasons. But the precipitation is likely to undergo a
significant change between detection and arrival at ground level,
including a phase change when the 0 ^{∘}C isotherm is located
at the level of or lower than the radar beam altitude. Such situations are
likely to be frequent during cold periods, with a strong impact on QPE
quality at ground level. On the other hand, installing a radar at the bottom
of the valley provides high-resolution and quality data required for
vulnerable and densely populated Alpine valleys, but the QPEs are limited in
the latter due to beam blockage by surrounding mountains.

In Europe, MeteoSwiss has the longest-standing experience in operating
radars in mountainous regions. The Swiss C-band radar network in the Alps
(Joss and Lee, 1995; Germann et al., 2006) is one of the highest in the world
and is coping with the associated altitude dilemma by using a large number
of plan-position indicator (PPI) scans (including negative elevation ones) aimed at determining high-resolution vertical profiles of reflectivity. Sophisticated radar–rain gauge
merging techniques and echo-tracking techniques, as well as numerical
prediction models outputs (Sideris et al., 2014; Foresti et al., 2018) are
implemented to better understand and quantify the complexity of
precipitation distribution in such a rugged environment. More recently,
Météo-France has chosen to complement the coverage of its
operational radar network of Application Radar à la
Météorologie Infra-Synoptique (ARAMIS) in the Alps by means of X-band
polarimetric radars. A first set of three radars was installed in the southern
Alps within the Risques Hydrométéorologiques en
Territoires de Montagnes et Méditerranéens (RHyTMME) project in the period 2008–2013
at Montagne de Maurel (1770 m above sea level; hereinafter a.s.l.), Mont Colombis (1740 m a.s.l.) and Vars Mayt (2400 m a.s.l.; Westrelin et al., 2012). This effort was continued in 2014–2015 with the installation of an additional X-band
radar system (hereinafter MOUC radar) on top of the Moucherotte mountain (1920 m) that dominates the valley of Grenoble, the biggest city in the French
Alps with about 500 000 inhabitants. The choice of the X-band frequency is
challenging due to its sensitivity to attenuation (e.g., Delrieu et al.,
2000). In the past, the Institute of Environmental Geosciences (IGE) radar team has proposed the so-called mountain reference technique (MRT; Delrieu et al., 1997; Serrar et al., 2000;
Bouilloud et al., 2009) to take advantage of this drawback for both
correcting the gate-to-gate attenuation and performing a self-calibration of
the radar. The idea was to estimate the path-integrated attenuations (PIAs) in
some specific directions from the decrease in mountain returns during rainy
periods. Such PIA estimates were then used as constraints for backward or
forward attenuation correction algorithms (Marzoug and Amayenc, 1994) with
optimization of an effective radar calibration error, given a drop size
distribution (DSD) parameterization. The development of polarimetric radar
techniques (e.g., Bringi and Chandrasekar, 2001; Ryzhkov et al., 2005) has
allowed a scientific breakthrough for quantitative precipitation estimation
(QPE) at X band by exploiting the relationship which exists between the
specific differential phase shift on propagation
(*K*_{dp}, in ${}^{\circ}\phantom{\rule{0.125em}{0ex}}{\mathrm{km}}^{-\mathrm{1}}$) and the specific
attenuation *k* (dB km^{−1}). As with the MRT, the differential
propagation phase Φ_{dp}(*r*_{2})−Φ_{dp}(*r*_{1}) over a given path
(*r*_{1},*r*_{2}) can
be used to estimate PIA(*r*_{1},*r*_{2}), which can constrain a backward attenuation
correction algorithm and allow a self-calibration of the radar and/or an
adjustment of the DSD parameterization (Testud et al., 2000; Ryzhkov et al.,
2014). Two major advantages of the polarimetric technique over the MRT can
be formulated, namely (1) the availability of PIA constraints for any direction
with significant precipitation and (2) the subsequent possibility of using a
backward attenuation correction algorithm, which is known to be stable, while
the forward formulation is inherently unstable. Accounting for their
respective potential in different rain regimes (moderate to heavy), some
combined algorithms making use of various polarimetric observables
(reflectivity, differential reflectivity and specific differential phase
shift on propagation) have also been proposed for the X-band frequency (e.g.,
Matrosov and Clark, 2002; Matrosov et al., 2005; Koffi et al., 2014). Although
the polarimetric QPE methodology is now quite well established and validated
for rainy precipitation (Matrosov et al., 2005; Anagnostou et al., 2004; Diss
et al., 2009), Yu et al. (2018) have shown, in their first performance
assessment of the RHyTMME radar network, the limitations associated with the
use of polarimetric X-band radars in mountainous regions. They have pointed out (i) the need to better understand and quantify attenuation effects in the
melting layer (ML), (ii) the importance of nonuniform beam filling (NUBF)
effects at medium-to-long ranges in such a high-mountain context, and
(iii) the stronger impact of radome attenuation at X band compared to S or C band. Yu et al. (2018) also had a first attempt at studying the
relationship between the specific differential phase shift on propagation
and the specific attenuation in the melting later by using the collocated
measurements of two X-band radars, one situated well below and the other one situated
well above the 0 ^{∘}C isotherm, and by considering the attenuation
uniform within the ML.

Since 2016, we have had the opportunity to operate a research X-band
polarimetric radar system (hereinafter XPORT radar) at IGE at the bottom of
the Grenoble valley. This unique facility, consisting of two radar systems
11 km apart and operating on an altitudinal gradient of about 1700 m, should
enable us to make progress on how to deal with the altitude dilemma and the
potential/issues associated with the choice of the X-band operating
frequency. Following a first article based on the RadAlp experiment about
the characterization of the melting layer (Khanal et al., 2019), we
concentrate hereinafter on the relationship between total differential phase
shift (*ϕ*_{dp}) derived from polarimetry and PIAs
derived from the MRT. In Sect. 2, we present the observation system
available and contrast rainy events considered in this study as follows: (i) a set of nine convective events with high rain rates, for which the melting
layer was well above the detection domain of the XPORT radar, allows us to
study the *ϕ*_{dp}−PIA relationship in rain; and
(ii) a stratiform case with moderate rain rates, for which the melting layer
rose up from about 1000 to 2500 m a.s.l., allows us to perform a
horizontal scanning of the ML with the MOUC radar and a preliminary analysis
of the *ϕ*_{dp}−PIA relationship in the
various layers of the ML. We present and illustrate, in Sect. 3, the
methodology used for the PIA and *ϕ*_{dp} estimation.
We also investigate the relationship between the specific differential phase
shift on propagation (*K*_{dp}) and the specific
attenuation (*k*) thanks to drop size distribution (DSD)
measurements collected in the Grenoble valley during the two sets of events.
The results concerning the *ϕ*_{dp}–PIA
relationship in rain and in the ML are presented and discussed in Sect. 4,
while conclusions and perspectives are drawn in Sect. 5.

2 Observation system and datasets

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Grenoble is a y-shaped alluvial valley in the French Alps, with a mean altitude of about 220 m a.s.l. and surrounded by three mountain ranges, namely the Chartreuse (culminating at 2083 m a.s.l.) to the north, the Belledonne (2977 m) to the southeast and the Vercors (2307 m) to the west. Figure 1 shows the topography of the area and the positions of the Météo-France radar system on top of the Moucherotte mountain and the IGE experimental site at the bottom of the valley.

Among other devices, the IGE experimental site includes the following: (i) the IGE XPORT
research radar (Koffi et al., 2014; see Table 1 for the list of its main
parameters); (ii) one Micro Rain Radar (MRR; not used in the current study);
(iii) one meteorological station including pressure, temperature, humidity,
wind probes and several rain gauges; and (iv) one Parsivel^{2} disdrometer. The
characteristics of the MOUC radar are listed in Table 1. XPORT radar was
built in the laboratory in the 2000s. It was operated during more than 10
years in western Africa within the African Monsoon Multidisciplinary Analysis (AMMA) and Megha-Tropiques calibration/validation
campaigns. Since its return to France in 2016, a maintenance and updating
program has been underway to improve its functionalities, notably with respect to
the real-time data processing and the antenna control program. One
noticeable feature of XPORT radar is the range bin size of 34.2 m
(which actually corresponds to an oversampling since, for a pulse width of 1 µs, the theoretical bin size is 150 m), which is an interesting figure
for the close-range and volumetric measurements considered in this study.
Note that while the MOUC radar is operated 24 h per day and its data are
integrated in the Météo-France mosaic radar products, the XPORT
radar is operated with alerts only on for significant precipitation events.

Table 2 shows the main characteristics of the nine convective events considered
for the study of the *ϕ*_{dp}–PIA relationship in rain, by using the
XPORT radar data. A stratiform event, which occurred on 3–4 January 2018,
is also considered for a preliminary study of the *ϕ*_{dp}–PIA
relationship in the ML, with both the MOUC and the XPORT radar data. Figure 2 presents a time series of one of the most intense convective event (21 July 2017) and the stratiform event. In both cases, the total rain amount
observed at the IGE site was about 35 mm, but in 3 h, with two peak
rain rates of about 40 mm h^{−1} for the 21 July 2017 convective event,
while the 3–4 January 2018 stratiform event lasted more than 12 h with
an average rain rate of about 3 mm h^{−1}. The two events also differ in
their vertical structure. The bottom graphs of Fig. 2 display the time
series of the altitudes of the tops, peaks and bottoms of the horizontal
reflectivity (*Z*_{h}) and copolar correlation coefficient (*ρ*_{hv})
signatures of the ML, obtained with the automatic detection algorithm
described in Khanal et al. (2019). The quasi-vertical profiles (QVP; Ryzhkov
et al., 2016) derived from the XPORT 25^{∘} PPIs are considered in
the ML detection. For the convective case, the ML extends from 3000 to
4000 m a.s.l. and more, i.e., well above the altitudes of the two radars. Table 2 indicates that this is also the case for the other convective events – at least
for the XPORT radar. For the stratiform event, the ML extends between 800
and 1500 m a.s.l. during the first part of the event (between 3 January, 20:00 UTC, and 4 January, 01:30 UTC) and then rises in about 2 h to stabilize at
an altitude range of about 2200–2800 m a.s.l. after 04:00 UTC, passing
progressively at the level of the MOUC radar in the meantime.

As an additional illustration of the dataset, Fig. 3 gives two examples of
XPORT PPIs at 7.5^{∘} elevation angle for moderate (left) and intense
(right) rain during the 21 July 2017 event. As a clear feature, one can see
that, for this elevation angle, the radar beam is fully blocked by the
Chartreuse mountain range in the northern sector. Also visible in the
northeastern sector and, to a lesser extent, in the southwestern sector are
partial beam blockages associated with tall trees in the vicinity of the
XPORT radar on the Grenoble campus. This figure is also intended to draw
the attention of the reader to the decrease in the Chamrousse and
Moucherotte mountains returns (within red circles) during the intense rain
time step, compared to their values in moderate rain, as a first illustration
of the MRT principle.

3 Methodology

Back to toptop
Our aim is to study the relationship between two radar observables of
propagation effects at X band, namely path-integrated attenuation and differential
propagation phase due to precipitation occurring along the radar path. We
describe, in the following two subsections, the estimation methods that were
implemented. In Sect. 3.3, we complement the methodology description
with the presentation of DSD-derived *k*–*K*_{dp} relationships.

Let us express the PIAs (in dB) at a given range *r* (km) as follows:

$$\begin{array}{}\text{(1)}& \text{PIA}\left(r\right)=\text{PIA}\left({r}_{\mathrm{0}}\right)+\mathrm{2}\underset{{r}_{\mathrm{0}}}{\overset{r}{\int}}k\left(s\right)\mathrm{d}s,\end{array}$$

where *k*(*s*) (dB km^{−1}) is the specific attenuation due to rain at range
*s* (km). *r*_{0} is the range where the measurements start to become
exploitable, i.e., the range where measurements are free of ground clutter
associated with side lobe effects. The term PIA(*r*_{0})
represents the so-called on-site attenuation resulting from radome
attenuation and range attenuation at range closer than *r*_{0}. Note that
PIAs can be obtained from Eq. (1) for both the horizontal and the vertical
polarizations. In the present article, we will restrict ourselves to the
horizontal polarization, as the study of differential attenuation is a
possible topic for a future study. Delrieu et al. (1999) have proposed an
assessment of the quality of PIA estimates from mountain returns by
implementing a receiving antenna in the Belledonne mountain range in
conjunction with an X-band radar operated on the Grenoble campus. They found good agreement between the two PIA estimates for PIAs exceeding the
natural variability of the mountain reference target during dry weather.
They recommended using strong mountain returns (greater than, e.g., 50 dBZ
during dry weather) so as to minimize the impact of precipitation falling
over the reference target itself. They also point out that this approach is
not able to separate the effects of on-site and range attenuation. They
verified, however, by implementing the receiving antenna close to the radar
(at a range of about 200 m), that the on-site attenuation was negligible for
a radomeless radar, which is the case for the XPORT radar but not for the
MOUC radar. Another interesting feature of the MRT PIA estimator is its
independence with respect to eventual radar calibration errors.

In the current study, we used the following procedure to determine the mountain reference targets for the XPORT radar.

A large series of raw reflectivity data, observed during widespread rainfall
with no ML contamination, was accumulated and averaged in order to
characterize the detection domain of the XPORT radar at the 7.5^{∘}
elevation angle. This allowed us to determine the mountain returns, the full beam blockages due to mountains, the partial beam blockages due to tall
trees and spurious detections due to side lobes in the vicinity of
the radar. A manual selection of the mountain reference targets was then
performed based on the map of the apparent reflectivity above 45 dBZ. The
targets, made up of mountain returns from successive radials (up to 9) with a
limited range extent (less than 2.0 km), are described in Table 3. Based on
the radar equation and the receiver characteristics, care was taken to
discard targets eventually subject to saturation at close range. The
selected targets are located at a mean range between 4.1 and 17.1 km and have sizes between 0.06 and 0.94 km^{2}. For each rain
event, dry weather data before and/or after the event were used to
characterize the mean target reflectivity and its time variability. Note
that the mean reflectivity for each target and each time step was computed
as the average of the dBZ values of each radial gate comprising the target.
This is justified by the fact that we aim at estimating PIAs in dB. Table 3 lists
the mean, standard deviation and 10 % and 90 % quantiles of the time series of
the dry weather apparent reflectivity of the reference targets for the first
and last event of the considered series. One can notice the good stability
of the mean reflectivity values between the two events, which is an indication of
both the radar calibration stability during the period and the moderate impact
of the mountain surface conditions already evidenced in previous studies (Delrieu et al., 1999; Serrar et al., 2000). The standard deviations of the reflectivity time series range
between 0.2 and 0.9 dBZ, and the mean 10 %–90 % interquantile range is equal
to 1.03 dBZ.

Due to limited data availability, a simpler approach was implemented for the
selection of the MOUC mountain reference targets. Here again, the raw
reflectivity data were accumulated and averaged, but only over the period of
3 January 2018, 19:00–23:55 UTC, preceding the rise of the ML at
the level of the MOUC radar. It was snowing during this period at the MOUC
radar site. So, we are implicitly making the assumption of negligible
attenuation during snowfall (supported by the literature; e.g., Matrosov et
al., 2009) in the considered case study. Table 4 displays the geometrical
characteristics of the targets, as well as the mean, standard deviation and
10 % and 90 % quantiles of their apparent reflectivity time series.
Targets are located at greater distances than those of the XPORT radar, i.e.,
between 19.9 and 44.9 km. In spite of having larger sizes (between 0.7 and
4.0 km^{2}), this range effect probably explains why their standard
deviations are higher, namely between 0.75 and 1.44 dBZ. The 10 %–90 %
interquantile ranges are subsequently higher as well, with a mean value of
2.6 dBZ.

The top graphs of Fig. 4 give two examples of apparent reflectivity profiles for a radial of a given target during the 21 July 2017 rain event. The example on the left-hand side corresponds to a moderate PIA (5.4 dB, when considering all the gates of the radials comprising the target) and the right-hand side example corresponds to one of the highest PIA value observed (27.6 dB) in our dataset. We tried to limit, as far as possible, the radial extent of targets (less than 2000 m) and/or multipeaks targets, such as the one shown in the left-hand side example, in order to limit positive bias on MRT PIA estimates. The top graphs of Fig. 5 give two examples of apparent reflectivity time series during the events of 21 July 2017 and 20 July 2018, together with the mean, 10 % and 90 % quantiles of the dry weather apparent reflectivity. For both cases, the XPORT data acquisition started a bit after the actual beginning of the storm. Therefore, the dry weather reference values were estimated with data collected after the event, i.e., between 19:00 and 22:00 UTC for the 21 July 2017 event and between 00:00 and 06:00 UTC on the day after for the 20 July 2018 event. For these convective events, one can note the erratic nature of the apparent reflectivity time series at the XPORT radar acquisition period used at that time (about 7 min). The MRT PIA estimates are simply calculated as the difference between the mean values of the target apparent reflectivity during dry weather and at each time step of the rain event (blue lines in the bottom graphs of Fig. 5).

Let us express the total differential phase shift between copolar (HH and VV) received signals as follows:

$$\begin{array}{}\text{(2)}& {\mathit{\psi}}_{\mathrm{dp}}\left(r\right)=\mathrm{2}\underset{{r}_{\mathrm{0}}}{\overset{r}{\int}}{K}_{\mathrm{dp}}\left(s\right)\mathrm{d}s+{\mathit{\delta}}_{\mathrm{hv}}\left(r\right),\end{array}$$

where *K*_{dp}(s) is the specific differential phase shift on
propagation (^{∘} km^{−1}) related to precipitation at any range
*s* between *r*_{0} and *r*, and *δ*_{hv}(*r*) is the differential
phase shift on backscatter (^{∘}) at range *r*.

The quantity of interest, i.e., the differential propagation phase associated with precipitation along the path, is denoted as follows:

$$\begin{array}{}\text{(3)}& {\mathit{\varphi}}_{\mathrm{dp}}\left(r\right)=\mathrm{2}\underset{{r}_{\mathrm{0}}}{\overset{r}{\int}}{K}_{\mathrm{dp}}\left(s\right)\mathrm{d}s={\mathit{\psi}}_{\mathrm{dp}}\left(r\right)-{\mathit{\delta}}_{\mathrm{hv}}\left(r\right).\end{array}$$

As with the on-site attenuation for the MRT, we have a
problem here with the possible influence of the differential phase shift on
backscatter *δ*_{hv}(*r*) that may introduce a positive bias on the
estimation of the differential phase shift associated with precipitation
along the path. In the literature (e.g., Otto and Russchenberg, 2011;
Schneebeli and Berne, 2012) we find power law relationships between *δ*_{hv} and *Z*_{dr} at X band in rain, giving values for the differential phase shift
on backscatter in the ranges of [0.6–1.0^{∘}] and
[2.1–3.5^{∘}] for the differential reflectivity of 1 and 2 dB, respectively. Scattering simulations based on disdrometer data
(Trömel et al., 2013) indicate that quite a large scatter may exist
with respect to such power law models, and there is an important influence from the
considered hydrometeor temperature. From simulations based on radar data at
various frequencies, the same authors quantify *δ*_{hv}(*r*) values as
high as 4^{∘} in the ML at X band and mention that strong *δ*_{hv}(*r*) values may be associated with both large dry hailstones and wet
hailstones, especially at X band. Let us note that no hail was reported for
the convective cases considered in the present study. Keeping the related
orders of magnitude in mind, and the fact that significant *δ*_{hv}
effects are associated with bumps in the *ψ*_{dp} profiles, hereafter
we will carefully discuss the possibility of assuming *δ*_{hv}
to be negligible, or not, with respect to *ϕ*_{dp}.

In this study, the following method was implemented for the processing of
the *ψ*_{dp} profiles and the subsequent estimation of
*ϕ*_{dp} values near the mountain targets for the XPORT radar
(rain case based on convective events).

We first determined so-called rainy range gates along the path by using
the *ρ*_{hv} profiles. The raw *ψ*_{dp}(r) values, for which *ρ*_{hv}(r) was less than 0.95
(empirical threshold with limited impact in the [0.95–0.97] range), were set
to missing values. In addition, we defined the beginning of the rainy range
by determining the first series of 10 successive gates (again, an empirical
choice corresponding to a range extent of 342 m) overpassing this
threshold. The *r*_{0} value was set to the minimum range value of this
series. Similarly, we defined the end of the rainy range by determining the
last series of 10 successive range gates overpassing this threshold close to
the mountain target. A maximum rainy range, denoted as *r*_{M}, was defined as
the maximum range value of this series. It is noteworthy to mention that
rain likely occurs in the ranges less than *r*_{0} and greater than *r*_{M}
and in the intermediate ranges for which the *ψ*_{dp}(r) values were set to missing values. It is, however,
critical to discard such gates that may be prone to clutter due to side
lobes close to the radar or mountain returns close to the mountain
target. Although the intermediate missing values will not impact the
*ϕ*_{dp} estimation, we have to mention that both the initial
and final missing values may result in a negative bias on the PIA estimation
based on *ϕ*_{dp}(*r*_{M}).

In the current version of the procedure, every single radial was processed
separately. First, an unfolding was applied by adding 360^{∘} to
negative *ψ*_{dp}(r) values. The system
differential phase shift was estimated as the median of the *ψ*_{dp}(*r*) values corresponding to the beginning of the rainy range. This
value was subtracted from the raw *ψ*_{dp}(*r*) profiles, and
eventual negative values were set to 0. Regarding the *ψ*_{dp}
measurement noise processing, we have implemented and improved a
regularization procedure initially proposed by Yu and Gaussiat (2018). This
procedure consists of defining an upper envelope curve, starting from
*r*_{0}, and a lower envelope curve, starting from *r*_{M}, by considering a
maximum jump, denoted as *diffmax*, authorized between two successive gates. The
calculation was performed for a series of *diffmax* values in the range of 0.5–10^{∘}. The regularized *ψ*_{dp} profiles (increasing
monotonous curves) were estimated by taking the average of the upper and
lower envelope curves. Note that the values for the missing gates between
*r*_{0} and *r*_{M} were simply interpolated with the adjacent values of the
regularized profile. A mean absolute difference (MAD) criterion between the
raw and regularized profiles over a series of 30 gates with nonmissing
values near the mountain target (an empirical choice corresponding to a range
extent of about 1 km) was used to determine the optimal *diffmax* value and the
associated profile. The optimal profile was finally selected if the MAD
criterion was less than 50 %, otherwise we considered the
polarimetry-derived PIAs to be missing for the considered radial. Finally,
the *ϕ*_{dp}(*r*_{M}) value for the target was
estimated as a weighted average of the *ϕ*_{dp}(*r*_{M}) values of all the nonmissing radials composing the target, with the
weights being the number of reference gates of each radial. The bottom
graphs of Fig. 4 present the raw and regularized profiles, and the
envelope curves, for the examples already commented on above. For the
right-side hand example corresponding to one of the strongest PIAs (27.6 dB)
observed, one can note that the noise of the raw *ψ*_{dp}
profile is low, especially in the range with the highest gradients between 7
and 13 km. There is no apparent bump on the raw profile that could signal
a *δ*_{hv} contamination so that one might be tempted to consider
the regularized profile as a good estimator of the *ϕ*_{dp}
profile in that case. The left-hand side example, corresponding to a
moderate MRT-derived PIA of 5.4 dB, is more complex. As already noted, the
mountain target itself is noisy with significant mountain return
contamination before range *r*_{M}, as evidenced by the *ρ*_{hv}
profile. In addition, one can note a nonmonotonic behavior of the raw
*ψ*_{dp} profile, with a plateau of about 17.5^{∘} for
ranges greater than 4 km, following an increase in the raw profile (with
moderate noise) up to 22^{∘} at a 4 km range. One might assume that there is a
*δ*_{hv} contamination in that case. Interestingly, the
regularization procedure is shown to provide a good filtering of the
bump, and here again we are tempted to consider the regularized profile
as a good estimator of the *ϕ*_{dp} profile. The middle graphs
in Fig. 5 display the time series of the *ϕ*_{dp}(*r*_{M}) values associated with the apparent reflectivity of the mountain
returns discussed above. One can note good consistency in the two time
series for the highest peaks, while discrepancies can be evidenced for the
moderate and small values.

Basically, the same methodology was implemented for the MOUC radar case
study, with some alterations to be described hereafter. Figure 6 provides
the time series of the apparent reflectivity of a given mountain target, the
resulting PIA estimates and the *ϕ*_{dp}(*r*_{M}) estimates for the 0^{∘} PPI of the MOUC radar during the stratiform
event of 3–4 January 2018. The time period considered in the figure
ranges from 00:00 to 06:00 UTC on 4 January 2018 in order to
focus on the rising of the ML between 02:00 and 04:00 UTC. The target is
located at a distance of 19.9 km from the radar. The bottom graph of Fig. 6
displays the results of the ML detection algorithm (Khanal et al., 2019) in
terms of the altitudes of the top, peak and bottom of the *Z*_{h} (blue) and
the *ρ*_{hv} (orange) ML signatures. The altitude of the *Z*_{h} top
inflexion point is assumed to correspond to the 0 ^{∘}C isotherm
altitude, while the *ρ*_{hv} bottom inflexion point corresponds well with
the bottom of the ML according to Khanal et al. (2019). We therefore define
the ML width as the altitude difference between *Z*_{h} top and *ρ*_{hv}
bottom. Before 02:00 UTC, the ML is well below the altitude of the MOUC
radar. MOUC radar measurements at the 0^{∘} elevation angle are
therefore made in snow/ice precipitation during this period. Based on the ML
detection results, the passage of the ML at the altitude of the MOUC radar
begins at about 02:20 UTC and ends at 04:10 UTC. After this time, MOUC radar
measurements are therefore made in rainfall.

As representative examples, Fig. 7 illustrates the range profiles taken by the
MOUC radar during the snowfall (left) and the ML (right) periods. As
expected, the *ρ*_{hv} profiles are very different in the two cases,
with *ρ*_{hv} values close to 1 in snow, indicating precipitation
homogeneity while *ρ*_{hv} presents a high variability in the ML.
During the ML period, we therefore had to adapt the *ρ*_{hv} threshold
used to detect gates with precipitation. Based on the *ρ*_{hv} peak
statistics presented by Khanal et al. (2019), we have chosen a value of 0.8.
As it can be seen in Fig. 7, such a threshold may prevent the detection of the
mountain reference return itself. Subsequently, we had to adapt the
determination of ranges *r*_{0} and *r*_{M} with respect to the XPORT radar
case, firstly, by considering two successive gates corresponding to a range
extent of 480 m (instead of 10 gates corresponding to 342 m) and, secondly,
by making sure that the calculated *r*_{M} value was less than the range of
the first mountain reference gate. Regarding the regularization of the *ψ*_{dp} profiles (bottom graphs of Fig. 7), it was found that the raw
profiles were noisier compared to the XPORT case study. Well-structured
bumps were not evidenced in the ML profiles, maybe as a result of the
lower-range resolution of the MOUC radar, and the regularization procedure
was found to work satisfactorily. It remains, however, difficult to assume
that there is no *δ*_{hv} contamination during the ML period.

Coming back to Fig. 6, one can note the mean value of *ϕ*_{dp}(*r*_{M}) to be equal to 11.2^{∘} during the
snowfall period, resulting in a specific differential phase shift on a
propagation of 0.28^{∘} km^{−1} if the differential phase shift on
backscatter is neglected. Such values indicate a significant heterogeneity
in the horizontal and vertical dimensions of the snow/ice hydrometeors.
During the rainy period between 04:10 and 06:00 UTC, there is good
coherence between the specific attenuations derived from the MRT PIA (0.078 dB km^{−1} at around 04:00 UTC–0.035 dB km^{−1} at 06:00 UTC) and
those derived from the polarimetry (0.076–0.046 dB km^{−1} at the same
time steps) using the *k*–*K*_{dp} relationship established for this event and
by using the DSD measurements available from the IGE site (see Sect. 3.3
below).

Our main objective with the 3–4 January 2018 event is to study the
*ϕ*_{dp}–PIA relationship within the ML. Figure 6 indicates that both
variables take, as expected, higher values during that period compared to
during the snowfall and rainfall periods. The maximum values reached are
14.2 dB for PIAs and 25.6^{∘} for *ϕ*_{dp}(*r*_{M}). Figure 6b and c also show that the cofluctuation of the two time
series is not that good during the ML period, with a *ϕ*_{dp}(*r*_{M}) signal having a trapezoidal shape with maximum
values between 02:35 and 03:15 UTC, while the MRT PIA signal is more
triangular and peaks at 03:15 UTC. We note that the two signals compare well
after the peak, and that they both peak down at 03:55 UTC when measurements
are made in the lowest part of the ML. These features are quite systematic
for all of the 13 targets considered for the MOUC radar for this event,
giving the impression that the *ϕ*_{dp}–PIA relationship depends on the
position within the ML and, as such, on the physical processes occurring
during the melting. This will be further illustrated and discussed in
Sect. 4.2. However, we have to mention the following three points here that may
limit the validity of such inferences for the MOUC radar configuration
compared to the XPORT one: (i) the MRT PIA estimates may be positively
biased by radome attenuation, (ii) the polarimetry-derived PIA estimates
may be affected by *δ*_{hv} contamination in the ML, and (iii) nonuniform beam filling effects probably become significant for the 20–40 km range considered, leading to a smoothing of the radar signatures. There
is no evidence so far of the first two points in the available dataset; this
may be due to the moderate intensity of this precipitation event.

Before presenting the analysis of the *ϕ*_{dp}–PIA relationship in rain
and in the melting layer based on the estimates for all the mountain targets
and time steps available for the two sets of events, we study in this
subsection the *k*–*K*_{dp} relationships that we were able to derive from
the DSD measurements collected at ground level at the IGE site. For all the
events, precipitation was in the form of rainfall at this altitude. As for
the scattering model, we used the CANTMAT version 1.2 software program
that was developed at Colorado State University by Chenxiang Tang and Viswanathan N. Bringi.
The raw Parsivel^{2} DSD measurements have a time resolution of 1 min. The
volumetric concentrations were computed with a 5 min resolution and binned
into 32 diameter classes with increasing sizes from 0.125 mm up to 6 mm. The
CANTMAT software uses the T-matrix formulation to compute radar observables
such as horizontal reflectivity, vertical reflectivity, differential
reflectivity, copolar cross-correlation, specific attenuation, specific
phase shift, etc., as a function of the DSD, the radar frequency, air
temperature, oblateness models (e.g., Beard and Chuang, 1987; Andsager et al.,
1999; Thurai and Bringi, 2005), and canting models for the rain drops and the incidence angle of the electromagnetic waves. Figure 8 displays the
empirical *k*–*K*_{dp} pairs of points obtained for the convective events
(left) and the stratiform one (right) as well as the fits of least square
linear models and power law nonlinear regressions.

Based on the literature review mentioning an almost linear relationship
between *k* and *K*_{dp} at X band (Bringi and Chandrasekar, 2001; Testud
et al., 2000; Schneebeli and Berne, 2012), we have first tested a linear
regression with an intercept forced to be equal to 0 (red lines in Fig. 8).
This simple model provides a rather good fit to the data, especially
for the convective events. Due to the observed bending of the scatterplots,
we have also tested a nonlinear regression to a power law model (blue
curve) which significantly improves the fittings. A sensitivity analysis was
performed in order to test the influence of the raindrop temperature, the
raindrop oblateness model, the standard deviation of the canting angle
distribution and the incidence angle. For reasonable ranges of the variation of
these parameters, the DSD itself appears to be the most influential factor on
the values of the regression coefficients. We note that the slopes of our
zero-forced linear models are significantly higher than the values proposed in the
literature (0.233 in Bringi and Chandrasekar, 2001; 0.205–0.245 in
Scheebeli and Berne, 2012). The exponents of the fitted power law models
are also significantly higher than 1.0. The fits in Fig. 8 correspond to the
most likely parameterization of the scattering model in terms of temperature
and incidence angles for the two events, i.e., 20 ^{∘}C and
7.5^{∘}, respectively, for the convective cases and 0 ^{∘}C and
0^{∘} for the stratiform case. The Beard and Chuang (1987)
formulation was used as the raindrop oblateness model. The DSD-derived
linear and nonlinear *k*–*K*_{dp} relationships were used to process
the regularized *ϕ*_{dp}(*r*) profiles which were first simply derived to obtain the *K*_{dp}(*r*) profiles prior to the application of the two *k*–*K*_{dp} relationships. The bottom graphs of Fig. 5 show examples of the
resulting polarimetry-derived PIAs.

4 Results

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Figure 9 displays the scatterplot of the *ϕ*_{dp}–PIA values obtained
for the nine convective events (Table 2) with the XPORT 7.5^{∘} PPI
data, following the methodology described in Sect. 3.1 and 3.2. The data
from the 16 mountain targets (Table 3) were considered. For a given
event, targets with maximum MRT-derived PIAs less than 5 dB were discarded
in order to limit the weight of small PIA estimates in the global analysis.
Since we consider the two variables to be on an equal footing, we preferred to
calculate the least rectangles regression (blue straight line) between the
two variables rather than the least squares regression of one variable over
the other one. One can notice the rather large dispersion of the
scatterplot with an explained variance of 77 %. We note the regression slope
(0.41) to be higher than the slope of the *k*–*K*_{dp} linear relationship
(0.336), which is reported as the red straight line in Fig. 9.

To go further, Fig. 10 presents the comparison of the MRT-derived PIAs with
the polarimetry-derived PIAs. The linear *k*–*K*_{dp} relationship leads to
a significant positive bias for the polarimetry-derived PIAs with a
least rectangles slope of 1.24. The nonlinear *k*–*K*_{dp} relationship
does a good job of reducing this bias (least rectangles slope of
1.03). This result may be surprising given the *k*–*K*_{dp} relationships
displayed in Fig. 8. One has to realize that the range of *K*_{dp} values is
much smaller for the 5 min DSD estimations than for the *K*_{dp}(*r*) profiles
discretized with a 34.2 m resolution. Considering that the 1 min DSDs allowed us
to confirm the validity of the linear and nonlinear *k*–*K*_{dp} models
for a wider *K*_{dp} range (not shown here for the sake of conciseness), we
are therefore confident in the relevance of the results presented in Fig. 10.

Figure 11 displays the scatterplot of the *ϕ*_{dp}–PIA values obtained
in the ML for the 4 January 2018 stratiform event with the MOUC
0^{∘} PPI data, following the methodology described in Sect. 3.1
and 3.2. The results obtained for the 13 targets (Table 4) are
considered in this analysis, with no target censoring based, for instance, on
the minimum PIA observed for a given target as for the XPORT case study. One
can see that the correlation between the two variables is severely degraded
compared to the rain case with an explained variance of 41 % and a
least rectangle slope of 0.51 dB per degree. The red line recalls the
*k*–*K*_{dp} linear regression determined with the DSDs observed at ground
level for this event. Clearly, the *ϕ*_{dp}–PIA relationship is
different in rain and in the ML and, as suggested when commenting on Fig. 6, it
likely depends on the physical processes occurring during the melting.

To investigate this point, *ϕ*_{dp}(*r*_{M}) and PIA(*r*_{M}) values
estimated during the rising of the ML at the level of the MOUC radar are
represented in Fig. 12 as a function of their position within the ML. As
already noted, we define the ML width as the difference between the *Z*_{h} top
altitude and the *ρ*_{hv} bottom altitude (Khanal et al., 2019). Since
the ML width significantly varies during the considered period (from 630 to
1020 m; see Fig. 8), we found it necessary to scale the altitudes by the ML
width. This was achieved by considering the following linear transformation
of the altitudes:

$$\begin{array}{}\text{(4)}& H\left(t\right)=({h}_{\mathrm{M}}-{h}_{\mathit{\rho}\mathrm{hvB}}(t\left)\right)/\text{ML}w\left(t\right),\end{array}$$

where *h*_{M} is the altitude (m a.s.l.) of the MOUC radar, *h*_{ρhvB}(*t*)
is the altitude of the ML bottom and ML*w*(*t*) is the ML thickness at a
given time *t*. The scaled altitude *H*(*t*) [–] subsequently takes the value 0 at ML bottom and the value 1 at ML top (orange and blue thick horizontal
lines, respectively, in Fig. 12). Furthermore, in order to locate more
precisely the position of the *Z*_{h} and *ρ*_{hv} peaks within the ML, we
computed their scaled altitudes at each time step, *H*_{zhP}(t)
and *H*_{ρhvP}(t), respectively, as follows:

$$\begin{array}{}\text{(5)}& {H}_{\mathrm{zhP}}\left(t\right)=\left({h}_{\mathrm{zhP}}\right(t)-{h}_{\mathit{\rho}\mathrm{hvB}}(t\left)\right)/\text{ML}w\left(t\right)\end{array}$$

and

$$\begin{array}{}\text{(6)}& {H}_{\mathit{\rho}\mathrm{hvP}}\left(t\right)=\left({h}_{\mathit{\rho}\mathrm{hvP}}\right(t)-{h}_{\mathit{\rho}\mathrm{hvB}}(t\left)\right)/\text{ML}w\left(t\right),\end{array}$$

where *h*_{zhP}(*t*) and *h*_{ρhvP}(t) are the altitudes of
*Z*_{h} peak and *ρ*_{hv} peak at time *t*. The broken horizontal lines in
Fig. 12 represent the 10 % and 90 % quantiles of the time series of the
scaled altitudes of *Z*_{h} peak (broken blue lines) and *ρ*_{hv} peak
(broken orange lines). We can observe a shift between the *Z*_{h} and *ρ*_{hv} characteristic altitudes, consistent with the ML climatology
established by Khanal et al. (2019) who reported a shift of about 100 m in
average between the two peaks. We note in Fig. 8 that this shift is visible
during the snowfall period and at the beginning of the ML rising but that it
is less pronounced after 03:00 UTC and during the rainfall period. In order
to better evidence their vertical trends, the MRT PIA(*r*_{M}) and *ϕ*_{dp}(*r*_{M}) values are presented in Fig. 12 as
a function of the scaled altitudes in the form of boxplots with a scaled
altitude class of size 0.1. The number of counts in each class is indicated
on the right of the graphs; it is a multiple of the number of MRT targets
(13 here) depending on the time occurrence of estimates in a given altitude
class. The vertical sampling is not very rich, with missing classes within
the ML. However, there is a clear signature for the two variables in the ML.
The trends already evoked when commenting on Fig. 8 are confirmed as follows: (i) the MRT PIAs peak when measurements are made at the level of the *Z*_{h} and *ρ*_{hv}
peaks – more precisely, the PIA peak is observed for the altitude class
containing the *ρ*_{hv} peaks (scaled altitude class centered at 0.3);
(ii) the region with maximum values is somewhat thicker for *ϕ*_{dp},
encompassing a significant part of the upper ML, between the 0.3 and 0.8
scaled altitude classes; (iii) *ϕ*_{dp} tends towards almost similar
values on average in rain (ML bottom) and snow (ML top); and (iv) the PIA tends
towards its value in rain below the ML and towards 0 above the ML. One would
have expected a more pronounced return towards 0 of the PIAs on top of the
ML. This lower-than-expected decrease could sign a radome attenuation;
however, the rainfall intensity is low for the considered event, and the
radome is equipped with a heating system so that accumulated snow is
unlikely. It may also result from a smoothing effect related to nonuniform
beam filling. With its 3 dB beamwidth of 1.28^{∘}, the angular
resolution of the measurements of the MOUC radar is 447 and 1005 m at
distances of 20 and 45 km, respectively, which correspond to the minimum
and maximum ranges of the considered mountain targets.

Finally, Fig. 13 displays the evolution of the ratio of the mean of the
MRT PIA(*r*_{M}) values over the mean of *ϕ*_{dp}(*r*_{M})
values as a function of the scaled altitudes. The value of the ratio below
the ML (0.33) is in rather good agreement with the slope of the linear model
established between the specific attenuation *k* and the specific
differential phase shift *K*_{dp} using the DSD measurements in rain
available for this event (0.29; see Fig. 9). Near the *ρ*_{hv} peak, the
ratio value is equal to 0.42. For the three classes of scaled altitude 0.7,
0.8 and 0.9, the ratio is between 0.32 and 0.38, with an apparent secondary
maximum for the altitude class 0.8. Data with increased vertical resolution
would be necessary to confirm, or not, this observation, which is also visible
on the PIA profile and on several *ϕ*_{dp} and PIA time series like
the ones displayed in Fig. 8. Above the ML, the ratio progressively tends
toward 0 at about 300 to 400 m.

5 Summary and conclusions

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In this work we developed a methodology for studying the relationship
between total differential phase shift (*ϕ*_{dp}) and path-integrated
attenuation (PIA) at X band. Knowledge of this relationship is critical
for the implementation of attenuation corrections based on polarimetry. We
used the mountain reference technique (MRT) for direct PIA estimations associated
with the decrease in strong mountain returns during precipitation events.
The MRT sensitivity depends on the time variability of the dry weather
mountain returns. The MRT PIAs may be positively biased by on-site
attenuation related in particular to radome attenuation and negatively
biased by the effect of precipitation falling over the reference targets.
The polarimetry PIA estimation is based on the regularization of the raw
*ψ*_{dp} profiles, and their derivation in terms of specific differential
phase shift (*K*_{dp}) profiles, followed by the application of a power law
relationship between the specific attenuation and the specific differential
phase shift. Such *k*–*K*_{dp} relationships were evaluated for rain with a
scattering model by using DSD measurements and an oblateness model for
raindrops. The noise of the raw *ψ*_{dp} profiles, the possible
contamination of the signal by differential shift on backscatter and the
adequacy of the *k*–*K*_{dp} relationship is the main factor that determines the quality of the
polarimetry-derived PIAs. Nonuniform beam filling (NUBF) effects may also
play a role. A point to emphasize is that both PIA estimators are not
sensitive to an eventual radar miscalibration.

We presented first a rain case study based on nine convective events
observed with the XPORT radar located in the Grenoble valley. A total of 16
mountain targets were considered with the dry weather mean apparent reflectivity
greater than 45 dBZ. The stability of the apparent reflectivity of the
mountain targets was shown to be very good, which is an indication of good radar
calibration stability during the considered period. The time variability of
the reference returns during dry weather preceding or succeeding the rain
events was also found to be very small with standard deviations in the range
of [0.2–0.9 dBZ], enabling a MRT PIA sensitivity better than 1 dB. Since
the XPORT radar is radomeless, on-site attenuation effects are most likely
negligible. The impact of rain falling over the mountain targets may also be
very limited due to the high reflectivity threshold considered (45 dBZ). The
development of the regularization procedure of the raw *ψ*_{dp} profiles
required a significant effort, and we are confident in its ability to deal
with the measurement noise, especially for heavy precipitation. We carefully
examined many raw and regularized profiles, looking for possible evidence of
*δ*_{hv} contamination during the considered convective events. We
found some profiles with rather well organized bumps that could signal
such contaminations. The regularization procedure was adapted in order to
filter such effects, with a satisfactory performance when they occur at some
distance (some kilometers) from the mountain target. In addition, we remind
the reader that the observed *ψ*_{dp}(*r*_{M}) values extend up to
80^{∘}, while the theoretical *δ*_{hv} range is 0–4 dB. The
*δ*_{hv} effect may therefore impact the results obtained only at the
margin in the considered case study. NUBF effects may constitute an
additional source of error which, although the rain events were convective,
should remain limited due to the short ranges considered. In the end, the
scatterplot of the MRT PIAs as a function of the *ϕ*_{dp}(*r*_{M}) values
for all the nine convective events presents a good coherence overall with,
however, a significant dispersion (explained variance of 77 %). It is
interesting to note that the nonlinear *k*–*K*_{dp} relationship derived
from independent DSD measurements taken during the events of interest at
ground level allows for a satisfactory transformation of the XPORT *ϕ*_{dp}(*r*_{M}) values into almost unbiased (although dispersed) PIA
estimates. Both estimation methods are prone to specific errors and, even if
the MRT PIA estimator is more directly related to power attenuation, it is
a priori difficult to say which estimator is the best. An assessment exercise of
attenuation correction algorithms, making use of both PIA estimators, with
respect to an independent data source (e.g., rain gauge measurements), is
desirable to distinguish the two PIA estimators. From this perspective, a
specific experiment is being designed within the RadAlp project and it will
be implemented in the near future.

The melting layer (ML) case study of 3–4 January 2018 was made possible by
the unique configuration of the observation system available. The study of
the *k*–*K*_{dp} relationship within the ML is desirable to better quantify the
attenuation effects in the ML with polarimetry; and one has to recognize
that such a relationship can still be very difficult to characterize
theoretically given that scattering models and particle size distributions need to be
collected in the ML. The XPORT radar located at the bottom of the valley
allowed for a detailed temporal tracking of the ML from below using
quasi-vertical profiles derived from 25^{∘} PPIs. The MOUC radar
provided horizontal scans at an altitude of 1917 m a.s.l. in the direction of
several mountain targets during the rising of the ML in about 2 h. From
this dataset, it was possible to derive the evolution of PIA(*r*_{M}) and *ϕ*_{dp}(*r*_{M}) values as a function of the altitude within
the ML. The evolution with the altitude of the ratio of the mean value of
PIA(*r*_{M}) over the mean value of *ϕ*_{dp}(*r*_{M}), as a proxy for the slope of a linear *k*–*K*_{dp} relationship
within the ML, was also considered. Since the ML width varied during the ML
rising, we found it necessary to scale the altitudes with respect to the ML
width. The three variables considered present a clear signature as a
function of the scaled altitude. In particular, the PIA∕*ϕ*_{dp} ratio
peaks at the level of the *ρ*_{hv} peak (somewhat lower than the *Z*_{h}
peak), with a value of 0.42 dB per degree, while its value in rain just
below the ML is 0.33 dB per degree. The latter value is consistent with
the slope of the linear *k*–*K*_{dp} relationship (0.29) established from
concomitant DSD measurements at ground level. The PIA∕*ϕ*_{dp} ratio
remains quite strong in the upper part of the ML, between 0.32 and 0.38 dB per
degree, before tending towards 0 above the ML. One would have
expected a more pronounced return towards 0 of the PIAs on top of the ML.
This lower-than-expected decrease could signal on-site attenuation occurring
at the beginning of the ML rise due to the melting of the snow eventually
accumulated over the radome; this effect is probably low for the considered
event since the snowfall intensity was small and since the radome is heated.
It may also result from a smoothing effect related to nonuniform beam
filling (angular resolution of 447 and 1005 m for the range of mountain
target distances). The *δ*_{hv} effect is likely to be strong in the
ML (up to 4^{∘}), and its relative importance may be quite high in
our case study since the PIA range is significantly lower compared to the
rain case study, with maximum PIAs of about 15 dB (note also that the
sensitivity of the MRT is less than for the XPORT case study since the
dry weather variability of the mountain returns is higher with
standard deviations in the range [0.62–1.44]). However, we did not find
evidence of *δ*_{hv} signatures in the raw *ψ*_{dp}(r) profiles, and we are confident in the ability of the regularization
procedure to filter them in a rather satisfactory way if they eventually
occur. Although the experimental configuration for the study of attenuation
in the ML presents some limitations (e.g., possible radome attenuation and NUBF
effects), the preliminary results presented here will be deepened by
processing a dataset of about 30 stratiform events with the presence of
the ML at the level of the MOUC radar.

Data availability

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Data availability.

Data can be made available by the first author upon request.

Author contributions

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Author contributions.

GD developed the concept of the article, realized the codes and performed the data processing; GD also wrote the article and handled the review process. AKK was involved in the development of the codes (ML identification, Phidp processing, etc.); NY shared his experience of the RHytMME radars and provided the MOUC radar data and the preliminary version of the Phidp regularization procedure. FC is a research engineer who has built the XPORT radar and is now responsible for the current updating program and the data acquisition. BB and NG contributed to the article through scientific discussions and amendments to the paper.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

We are grateful to Patrick N. Gatlin (NASA Marshall Space Flight Center, Huntsville, Alabama, USA) for providing the CANTMAT version 1.2 software developed at Colorado State University by Chenxiang Tang and Viswanathan N. Bringi, whom we also thank. The RadAlp experiment is cofunded by the LabEX OSUG@2020 of the Observatoire des Sciences de l'Univers de Grenoble, the Service Central Hydrométéorologique et d'Appui à la Prévision des Inondations (SCHAPI) and Electricité de France/Division Technique Générale (EDF/DTG).

Review statement

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Review statement.

This paper was edited by Gianfranco Vulpiani and reviewed by three anonymous referees.

References

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Anagnostou, E. N., Anagnostou, M. N., Krajewski, W. F., Kruger, A., and Miriovsky, B. J.: High-Resolution Rainfall Estimation from X-Band Polarimetric Radar Measurements, J. Hydrometeor., 5, 110–128, https://doi.org/10.1175/1525-7541(2004)005<0110:HREFXP>2.0.CO;2, 2004.

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Delrieu, G., Serrar, S., Guardo, E., and Creutin, J. D.: Rain Measurement in Hilly Terrain with X-Band Weather Radar Systems: Accuracy of Path-Integrated Attenuation Estimates Derived from Mountain Returns, J. Atmos. Ocean. Tech., 16, 405–416, https://doi.org/10.1175/1520-0426(1999)016<0405:RMIHTW>2.0.CO;2, 1999.

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Matrosov, S. Y. and Clark, K. A.: X-Band Polarimetric Radar Measurements of Rainfall, J. Appl. Meteor., 41, 941–952, https://doi.org/10.1175/1520-0450(2002)041{%}3C0941:XBPRMO{%}3E2.0.CO;2, 2002.

Matrosov, S. Y., Kingsmill, D. E., Martner, B. E., and Ralph, F. M.: The Utility of X-Band Polarimetric Radar for Quantitative Estimates of Rainfall Parameters, J. Hydrometeor., 6, 248–262, https://doi.org/10.1175/JHM424.1, 2005.

Matrosov, S. Y., Campbell, C., Kingsmill, D. E., and Sukovich, E.: Assessing Snowfall Rates from X-Band Radar Re?ectivity Measurements, J. Atmos. Ocean. Tech., 26, 2324–2339, https://doi.org/10.1175/2009JTECHA1238.1, 2009.

Otto, T. and Russchenberg, H. W. J.: Estimation of Specific Differential Phase and Differential Backscatter Phase From Polarimetric Weather Radar Measurements of Rain, IEEE Geosci. Remote S., 8, 988–992, https://doi.org/10.1109/LGRS.2011.2145354, 2011.

Ryzhkov, A. V., Giangrande, S. E., and Schuur, T. J.: Rainfall estimation with a polarimetric prototype of WSR-88D, J. Appl. Meteor., 44, 502–515, https://doi.org/10.1175/JAM2213.1, 2005.

Ryzhkov, A. V., Diederich, M., Zhang, P., and Simmer, C.: Potential utilization of specific attenuation for rainfall estimation, mitigation of partial beam blockage and radar networking, J. Atmos. Ocean. Tech., 31, 599–619, https://doi.org/10.1175/JTECH-D-13-00038.1, 2014.

Ryzhkov, A., Zhang, P., Reeves, H., Kumjian, M., Tschallener, T., Trömel, S., and Simmer, C.: Quasi-Vertical Profiles – A new way to look at polarimetric radar data, J. Atmos. Ocean. Tech., 33, 551–562, https://doi.org/10.1175/JTECH-D-15-0020.1, 2016.

Schneebeli, M. and Berne, A.: An Extended Kalman Filter Framework for Polarimetric X-Band Weather Radar Data Processing, J. Atmos. Ocean. Tech., 29, 711–730, https://doi.org/10.1175/JTECH-D-10-05053.1, 2012.

Serrar, S., Delrieu, G., Creutin, J. D., and Uijlenhoet, R.: Mountain Reference Technique: Use of mountain returns to calibrate weather radars operating at attenuating wavelengths, J. Geophys. Res.-Atmos., 105, 2281–2290, https://doi.org/10.1029/1999JD901025, 2000.

Sideris, I. V., Gabella, M., Erdin, R., and Germann, U.: Real-time radar–raingauge merging using spatio-temporal co-kriging with external drift in the alpine terrain of Switzerland, Q. J. Roy. Meteor. Soc., 140, 1097–1111, https://doi.org/10.1002/qj.2188, 2014.

Testud, J., Le Bouar, E., Obligis, E., and Ali-Mehenni, M.: The Rain Profiling Algorithm Applied to Polarimetric Weather Radar, J. Atmos. Ocean. Tech., 17, 332–356, https://doi.org/10.1175/1520-0426(2000)017{%}3C0332:TRPAAT{%}3E2.0.CO;2, 2000.

Thurai, M. and Bringi, V. N.: Drop axis ratios from 2D video disdrometer, J. Atmos. Ocean. Tech., 22, 963–975, https://doi.org/10.1175/JTECH1767.1, 2005.

Trömel, S., Kumjian, M. R., Ryzhkov, A. V., Simmer, C., and Diederich, M.: Backscatter differential phase – estimation and variability, J. Appl. Meteor. Climatol., 52, 2529–2548, https://doi.org/10.1175/JAMC-D-13-0124.1, 2013.

Westrelin, S., Meriaux, P., Tabary, P., and Aubert, Y.: Hydrometeorological risks in Mediterranean mountainous areas – RHYTMME Project: Risk Management based on a Radar Network. ERAD 2012 7th European Conference on Radar in Meteorology and Hydrology, June 2012, Toulouse, France. 6 p., hal-01511157, 2012.

Yu, N. and Gaussiat, N.: A monotonic algorithm for estimation of the specific differential phase. Poster presentation during the 10th European Conference on Radar in Meteorology and Hydrology (ERAD 2018), 1–6 July 2018, Ede-Wageningen, the Netherlands, 2018.

Yu, N., Gaussiat, N., and Tabary, P.: Polarimetric X-band weather radars for quantitative precipitation estimation in mountainous regions, Q. J. Roy. Meteor. Soc., 144, 2603–2619, https://doi.org/10.1002/qj.3366, 2018.

Atmospheric Measurement Techniques

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