Importance of Effective Isotropic Radiative Power (EIRP) for GNSS-R Lake Ice Remote Sensing

GNSS-R applications for lake ice remote sensing is still under study, and there are many vague points in this subject, especially for those like me who are “encore vert” in this topic. Among various corrections and calibrations must be made on GNSS-R data, EIRP looks decisive; however, a genius solution has been recently proposed for that: dynamic calibration.

Postdoctoral researcher with the University of Michigan Tianlin Wang, who is known with his insightful research items on microwave instrumentation of GNSS-R systems, has recently published a paper expanding the concept and application of the dynamic calibration of EIRP for GNSS-R remote sensing. This research item, which has been conducted in co-authorship with a number of GNSS-R giants, such as Dr. Chris Ruf and Dr. Scott Gleason, is in the following of a conference paper that had been presented at IGARSS 2019. In this research, authors have discussed the necessity of various calibrations should be applied to normalized bistatic radar cross section (NBRCS) measurements as it is a key to obtain physical insights into the mechanism of GNSS-R scattering from reflective surfaces. Among those calibrations, the one applied to EIRP has been discussed as one of the most challenging as it has to overcome multiple major challenges including variations in the transmit power, inaccuracies in antenna gain measurements, and the flex transmit power. Being mentioned as the most important motivation of this research, the latter challenge, i.e., flex transmit power, will cause changes in CYGNSS level-1 NBRCS values, which may limit the mission’s potential by flagging out up to 37% of observations. In this dynamic calibration method, direct GPS signals are used to estimate the EIRP in the direction of specular reflection point, and by implication, calibrate the NRBCS.

It is my understanding that this correction is crucial specially for CYGNSS as it is classified among conventional GNSS-R approaches (vs. interferometric GNSS-R), in which the narrower bandwidth of the public codes (for more information on iGNSS-R and cGNSS-R, and their application in ice altimetry, see this paper). Moreover, the calibration quality of NBRCS could be extremely decisive as the roughness of the reflective surface increases. Roughness can be really challenging in lake ice GNSS-R remote sensing as I have mentioned here and here. Moreover, under this LinkedIn post, which was about the same topic, two GNSS-R researchers (Ben and Lucy) discussed various sources of uncertainty in CYGNSS remote sensing specifically for lake ice studies. Tianlin’s paper seems to open a new way to improve CYGNSS ability in lake ice remote sensing.

CYGNSS and Spatial Interpolation; a Review

“Why talk to others when you can talk to yourself?” This is how Clara Chew captioned her fantastic YouTube video in LinkedIn to start suggesting a spatial interpolation method for CYGNSS data.

First of all, I should say what a great idea form one of my most inspiring and favorite researchers. Establishing a YouTube channel to talk to ourselves about GNSS reflectometry is what we’d need, and to be honest, that’s the main encouragement for myself to kick off this website. Although I am currently the only writer here, but this platform is going to become an online magazine for GNSS-R researchers to freely read and write others’ opinions. It’s yet to be widely advertised, but the core idea is the same: let’s just talk to ourselves : )

About the video, let’s start from the end; this method is not going to be used for every application. “If you are trying to do some sort of analysis where you need exact knowledge of reflectivity at a certain point,” Clara clarifies “you might not want to use this method”. It sounds very true for my current research focusing on Qinghai Lake, Tibet Plateau, where I restricted Fresnel Zones to only the central region of the lake to make sure that I am not receiving reflections from the surrounding lands or even the shore lines. So, no interpolation is required at any level. But aside from the Qinghai’s research, it’s been a few months that I’ve been thinking about expanding my CYGNSS explorations to a wider region, say central desert of Iran, and meanwhile, one of my greatest concerns has been how to do data interpolation over a large area. Clara has also mentioned it somewhere in her video that “trust me, it won’t be too frustrating”, but it is for me :)) because I haven’t started yet.

But when I’m saying my concern is on how to do it, I wouldn’t say that choosing the interpolation method is not a big concern, as it really is, but it is not the biggest issue for me, because I had practiced a method years ago. The story took place in 2013-2015, when I was working on geodynamics of the Earth, and my specific research at that time was calculating strain tensors. I found out that routine methods for interpolating crustal movement values, e.g. IDW and Spline, are way off the road. I spent couple of months on that, and realized that “deterministic interpolation methods” do not perfectly work for those problems which require “geo-statistical interpolation methods”, such as Kriging. That was the point.

In short, despite deterministic methods which only consider distance as the effective parameter in weighting procedure, geo-statistical interpolation methods also take the correlation into account as a weighting function. This is exactly what Clara suggested: “correlation coefficients“. In Kriging, for example, a covariance matrix is created among node points based on statistical constraints, and then, that matrix plays a key role in establishing the weighting function. The same idea can be seen in another powerful interpolation method called Least-Square Collocation, which is widely used in geoid problems and potential field anomaly interpolations.

I employed Ordinary and Universal Kriging interpolation techniques for estimating strain matrix components, and improved the accuracy up to 70%. As Clara has remained the discussion open at the end of her video, I would invite her to a collaboration in order to explore the ability of geo-statistical methods of interpolation in CYGNSS cases.