Quantitative Analysis of the Performance of Spatial Interpolation Methods for Rainfall Estimation Using Commercial Microwave Links

Abstract

Using signal level measurements from commercial microwave links (CMLs) has proven to be a valuable tool for near-ground 2-D rain mapping. Such mapping is commonly based on spatial interpolation methods, where each CML is considered as a point measurement instrument located at its center. The validity of the resulted maps is tested against radar observations. However, since radar has limitations, accuracy of CML-based reconstructed rain maps remains unclear. Here we provide a quantitative comparison of the performance of CML-based spatial interpolation methods for rain mapping by conducting a systematic analysis: first by quantifying the performance of maps generated from semi-synthetic CML data, and thereafter turning to real-data analysis of the same rain events. A radar product of the GermanWeather Service, serves as ground truth for generating semi-synthetic data, in which several temporal aggregations of the radar rainfall fields are used to create different decorrelation distances. The study was done over an area of 225X245 km2 in southern Germany, with 808 CMLs. We compare the performance of two spatial interpolation methods - Inverse Distance Weighting and Ordinary Kriging - in two cases: where each CML is represented as a single point, and where three points are used. The points’ measurements values in the latter are determined using an iterative algorithm. The analysis of both cases is based on a 48 hour rain event. The results re-confirm the validity of CML-based rain retrieval, showing a slight systematic performance improvement when an iterative algorithm is applied so each CML is represented by more than a single point, independent of the interpolation method.

Rain Field Retrieval by Ground-Level Sensors of Various Types

“…Here, the differences between the two cases were noticeable, but they were less significant than for the simplified Gaussian-shaped rain cells. In Eshel et al (2021), however, the Kriging technique (spatial covariance-based interpolation) was also applied, showing similar results. A potential point of failure in GMZ as implemented in Eshel et al (2021) was suggested for specific scenarios, where the redistribution of rain intensities between the VRGs on a given CML is more detrimental than assuming a single point in the center.…”

“…A similar approach was used on real rainfall patterns, obtained from a radar product of the German Weather Service, for different aggregation intervals (Eshel et al, 2021), where the attenuation of an actual 808-CML network was simulated (referred to as a "semi-real" study). Here, the differences between the two cases were noticeable, but they were less significant than for the simplified Gaussian-shaped rain cells.…”

“…These two questions were partially studied in our research group under different models, assumptions, and conditions. In particular, Question #1 was studied by simulations using synthetic scenarios with CMLs and RGs, as well as with semireal data and an actual CML network (Eshel et al, 2020;Eshel et al, 2021;Zheng et al, 2022). Question #2 was studied using theoretical performance bounds, assuming parametric (Gat and Messer, 2019) or nonparametric (Sagiv and Messer, 2022) models for the rain field.…”

A Review on Rainfall Measurement Based on Commercial Microwave Links in Wireless Cellular Networks

“…However, OK has its own limitations and needs to make some assumptions, such as isotropy and statistical stationarity. Eshel et al [71] compared the performance of the IDW and OK algorithms, and the results show that the performance improves with the increase in decorrelation distance (i.e., less intermittent field). The OK interpolation technique uses more prior/auxiliary information and correlates slightly better with ground truth than IDW, and the performance of OK and IDW-based algorithms with multiple points representing a CML is slightly better than that with only one point representing a CML.…”

Hydrological response of a peri-urban catchment exploiting conventional and unconventional rainfall observations: the case study of Lambro catchment

“…In the past, various methodologies have been tested and applied for spatial interpolation of CML retrieved rainfall measurements, considering different spatial scales (e.g., Fencl et al, 2013;Overeem et al, 2013;D'Amico et al, 2016;Haese et al, 2017;Chwala and Kunstmann, 2019;Graf et al, 2020;Eshel et al, 2021). Here, we exploited the simple and robust IDW method (Shepard, 1968) for both RG and CML measurements.…”