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The RadAlp experiment aims at developing advanced methods for rain and snow 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, France. It is composed of a X-band radar operated by Météo-France on top of the Mt Moucherotte (1970 m asl; MOUC radar hereinafter). In the Grenoble valley (220 m asl), we operate a research X-band radar called XPORT and in situ sensors (weather station, rain gauge, disdrometer). We present in this article a methodology for studying the relationship between the total differential phase (ψdp) and path-integrated attenuation (PIA) at X-Band, a relationship critical for the implementation of attenuation corrections based on polarimetry. We use the Mountain Reference Technique for direct PIA estimations associated with the decrease of returns from mountain targets during precipitation events. The polarimetric PIA estimations are based on the regularization of the ψdp radial profiles and their derivation in terms of specific differential phase (Kdp) profiles, followed by the application of relationships between the specific attenuation and the specific differential phase. Such k - Kdp relationships are estimated for rain by using available DSD measurements, empirical oblateness models for raindrops and a scattering model. Two contrasted precipitation events are considered in this preliminary study: (i) a convective case with strong rainrates allows us to study the Φdp-PIA relationship in rain; (ii) during a stratiform case with moderate rainrates, for which the melting layer (ML) rose up from about 1000 m asl up to 2500 m asl, 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 parts of the ML. The rain case study indicates that the relationship between MRT-derived PIAs and polarimetry-derived PIAs presents a considerable dispersion (explained variance of 0.72) in rain. Interestingly, the non-linear k - Kdp relationship derived from independent DSD measurements allows obtaining almost unbiased PIA estimates. For the stratiform case, the averaged PIA/ψdp ratio peaks within the melting layer at the level of the co-polar correlation coefficient (ρhv) peak, just below the reflectivity peak, with a value of about 0.4 dB°-1. Its value in rain below the ML is 0.27 dB°-1, in very good agreement with the slope of the linear k - Kdp relationship derived from DSD measurements at ground level. The PIA/ψdp ratio remains quite strong in the upper part of the ML, between 0.32 and 0.38 dB°-1, before tending towards 0 above the ML. [ABSTRACT FROM AUTHOR]