Preliminary investigation of the relationship between differential phase shift and path-integrated attenuation at the X band frequency in an Alpine environment
Authors: Delrieu Guy , Khanal Anil Kumar , Yu Nan , Cazenave Frédéric , Boudevillain Brice , Gaussiat Nicolas 
Published: July 2020

Abstract. 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 (Φdp) 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 (Ψdp) from which the profiles of the specific differential phase
shift on propagation (Kdp) are derived. This is followed by
the application of relationships between the specific attenuation (k) and the
specific differential phase shift. Such k–Kdp 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 ϕdp–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 ϕdp–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–Kdp 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–Kdp relationship derived
from independent DSD measurements yields almost unbiased PIA estimates. For
the stratiform case, clear signatures of the MRT-derived PIAs, the
corresponding ϕdp value and their ratio are evidenced within the
ML. In particular, the averaged PIA∕ϕdp ratio, a proxy for the
slope of a linear k–Kdp relationship in the ML, peaks at the level
of the copolar correlation coefficient (ρhv) 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–Kdp relationship derived from DSD
measurements at ground level. The PIA∕ϕdp 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.