Figure 1: A comic illustrating microwave link towers.
Radar-based rainfall retrievals are subject to uncertainties. These uncertainties have different sources. Two major sources are the variability of drop size distributions (DSD) of rain and attenuation effects. Another problem is the comparability of precipitation measurements, i.e. adjustments of radar measurements to rain gauges should be performed on larger time scales, because radar volume measurements can not be directly compared to point measurement like rain gauges or distrometers.
Commercial microwave backhaul links (figure 1) operate at Ku-, or Ka-band (between 12 GHz and 40 GHz). Both, radar and microwave links provide attenuation measurements, i.e. the path-integrated attenuation (PIA) measured along the links can be compared to radar measurements.
There are two possibilities to compare these measurements which depend on the orientation of the microwave link path with respect to the radar. If the microwave link is oriented arbitrarily,the comparison of radar-based PIA estimates with the microwave link measurements can „only“ be used to adapt and optimize the intercept of rainfall relations (like R(KDP) or R(A)) in order to account for DSD variability.
The best benefit arises if the microwave links are orientated along radar radials. In this case, the synergistic measurements can also be exploited to improve the attenuation coefficient alpha=A/KDP. This coefficient is influenced by the frequency, temperature, DSD and many more but for a lot of operational applications assumed used as a constant parameter. The PIA of the microwave link is directly proportional to the span of the differential phase shift measured by the radar along the link.
Two microwave links around the Bonn region are roughly located within a radar beam and can be compared towards the Bonn X-band radar (BoXPol):
The idea now is to compare the differentail phase shift measured by the radar with the PIA measured by the microwave link. The differentail phase shift is directly proportional to the PIA measured by the link and can be recalculated to an equivalent PIA at the same frequency as the microwave link.
Figure 2: Measurements by the radar and the microwave links in the Bonn region on the 9th June, 2014. (left) Based in the ZPHI-Method attenuation corrected horizontal radar reflectivity with standard α=0.32. Black solid line indicates the position of the shorter microwave link, black dashed line indicates the position of the of the longer microwave link. (right panels) Developement of the PIAs measured by the microwave links (blue lines) and the calculated equivalent PIAs for the radar at the respective link frequencies for α=0.32. The green line indicates the timestep refering to the left panel with the radar measurement at the related black lines, upper right pannel with the solid black line, lower right pannel with the dashed black line. (lower right panel) The dotted blue line between 18:55 UTC and 19:10 UTC covers interpolated microwave link data, as the microwave link signal was not measurable within this period.
Figure 3: Uncorrected horizontal reflectivity for BoXPol. Black solid line indicates the position of the shorter microwave link, black dashed line indicates the position of the of the longer microwave link.
The animation in figure 2 demonstrates the development of the radar refelctivity (Z) during the very strong Pentecost event on the 9th June, 2014 in the Bonn region. The standard attenuation coefficient α for an X-Band radar is set to 0.32. With this attenuation coefficient the ZPHI-method can correct the measured horizontal reflectivity (figure 2, left) and the equivalent PIA of the radar for the long and the short microwave link measurement at the different frequencies (figure 2, right).
The animation in figure 3 shows the uncorrected reflectivity of the BoXPol radar. The difference of the attenuation corrected radar measurements (figure 2) and the not corrected measurements (figure 3) reflect the need of attenuation correction especialy during strong precipitation events even with a standard attenuation coefficient α.
The two different timelines of the PIA developement in figure 2 on the right give us a first idea of the PIA developement. The green and the red line show the same shape during the event, but the amplitudes have obvious differences. For the shorter microwave link (figure 2, top right) the PIA reaches a maximum value of 22.5 dB but the equivalent PIA of the radar only reaches 15 dB. For the longer microwave link the developement of the PIA does not show these large differences in the amplitude, but there is a gap in the mesurements due to attenuation of the microwave link signal. The equvalent PIA developement of the radar and the measured PIA of the microwave link still shows some differences at the side of the peak. Both timelines reflect an higher PIA of the microwave link and a lower equiv. PIA of the radar, which indicates a too low α for both measurements.
Figure 4: Correlation of the differential phase shift and PIA of the microwave link measurement for both microwave links. (left) Correlation of the differential phase shift and PIA for the shorter microwave link. Blue crosses indicate the measurements, red line indicates the correlation for standard α and the green line indicate correlation with recalculated α=0.48. (right) Correlation of the differential phase shift and PIA for the longer microwave link. Blue crosses indicate the measurements, red line indicates the correlation for standard α and the green line indicate correlation with recalculated α=0.41.
The timelines from figure 2 show the discrepancies of PIA from the microwave link and the radar. These discrepancies need to be corrected, which can be done by an α correction. The correlation in figure 4 shows this correction. The correlation indicated by the standard α for the PIA of th microwave links with the differential phase shift makes it clear that a change in the attenuation coefficient leeds to a better correlation of both measurements.
Figure 5: Measurements by the radar and the microwave links in the Bonn region on the 9th June, 2014. (left panels) Based in the ZPHI-Method attenuation corrected horizontal radar reflectivity, upper panels with α=0.41 and lower panels with α=0.48. Black solid lines indicate the position of the shorter microwave link, black dashed lines indicate the position of the of the longer microwave link.(right panels) Developement of the PIAs measured by the microwave links (blue lines) and the calculated equivalent PIAs for the radar at the respective link frequencies for α=0.41 (upper panels) and α=0.48 (lower panels). The green lines indicate the timestep refering to the left panels with the radar measurement at the related black lines, first and third right pannel with the solid black lines, second and fourth right pannel with the dashed black lines. The dotted blue line between 18:55 UTC and 19:10 UTC in the second and fourth right panels covers interpolated microwave link data, as the microwave link signal was not measurable within this period.
In figure 5 we see the used α for the longer and the shorter microwave link. The left panel reaches higher values in the reflectivity the higher α is. The right panel shows the impact of α on the amplitude of the PIA developement. The upper panel reflects the lower α=0.41. The Amplitude of the timeline from the longer link (right, second) is covered better now, but in the first right panel there is still a difference in the amplitudes of the PIAs.
The lower panels reflect the impact if we use th higher α=0.48. The amplitude of the microwave link measured PIA andt equivalent PIA of the radar is only covered if we use the high coefficient.
The attenuation coefficient is set as constant during this event although it is dependant on the dropsize distribution. The dependence of α on the DSD can be seen in the difference of the values of α for the different microwave links. the shorter microwave link seems to be in higher refelctivities, which is coupled with larger raindrops, as the longer microwave link, which measures through lower reflectivities.
Note that reliable attenuation correction for this supercell is challenging due to melting hail resulting in large differences between the appropriate α compared to average values often applied in operational applications.
Trömel, S., M. Ziegert, A. Ryzhkov, C. Chwala, C. Simmer (2014): Using microwave backhaul links to optimize the performance of algorithms for rainfall estimation and attenuation correction. J. Atm. Ocean Tech., 31(8), 1748-1760.