GIRAS; a GNSS-IR Analysis Software

Recently, a GNSS-IR analysis software has been published online offering a handy graphical user interface, which tends to become a popular alternative to existing software packages and tools. This MATLAB-based open-source software package is GIRAS.

GNSS-IR has become a robust method to extract the characteristic environmental features of reflected surfaces, in which, fluctuations in the strength of the signal received by the GNSS receiver are analyzed. A short video was created and posted here showing how fluctuations in reflected SNR relates to altimetric applications. Frequency, amplitude, and phase values that provide the most appropriate model of the changes in signal strength are used as GNSS-IR metrics. Although there are several different software packages currently available to find these metrics, they may be insufficient in some cases.

Newly, a MATLAB-based, open-source GNSS-IR analysis software (GIRAS), developed by Cemali Altuntas and Nursu Tunalioglu from Yildiz Technical University, Turkey, has been published online in GPS Solutions. With its graphical user interface and capabilities, GIRAS is a good alternative to existing software packages and tools. GIRAS has three main modules and five sub-modules. The first main module is “Read & convert files”. This module reads raw GNSS data and stores the necessary observations in the MATLAB environment. RINEX version 2 and RINEX version 3 observation files are supported. Both broadcast ephemeris and precise ephemeris (sp3) files can be used. Multi-GNSS (GPS, GLONASS, Galileo, Beidou) sp3 files are supported.

The second main module is “Pre-analysis” which has three submodules: (1) SNR & dSNR data, (2) Sky view, (3) FFZ. Here, the user can plot the SNR and dSNR data for different polynomial degrees for each satellite and signal type. The sky view can be plotted as including the selected satellite systems. The first Fresnel zones (FFZs) can be displayed on the plot screen and Google Earth. The user also can export all graphs as MATLAB figures.

The third main module is “Analysis”, and it has two submodules: (1) Make estimations, (2) Improve estimations. Here, GNSS-IR metrics can be estimated using several options included. In addition, filtering and outlier analysis of the results can be performed. Analysis results can be saved in both TXT and MAT formats.

GIRAS enables the selection of azimuthal and elevation angle masks with multiple range selections for either short-term or long-term GNSS data collected, which may help to predict future models for climatological studies. The software is also suitable for multi-GNSS analysis. The quality-control modules are in a way of multiple choice, in where the researchers can apply options for their aims of use. The output files are well-designed for users in a defined format for further computations.

GIRAS seems to be widely used in future GNSS-IR work, thanks to its functional GUI and many options included.

Improving GNSS-R ability in mean sea level measurement; a new paper on Turkish Mediterranean coast

GNSS antennas are designed to suppress the reflected signal before it reaches the antenna. However, some of the reflected signals interfere with the direct signal, leading to a multipath effect in the GNSS observations. Reflected signals are used in many remote sensing applications. The determination of sea level variations is also included in these applications.

Cansu Beşel, a researcher from Karadeniz Technical University, Department of Geomatics Engineering, Turkey, has recently published a paper determining the sea level variations along the Turkish Mediterranean coast using GNSS-R. For this purpose, the monitoring sea level was assessed by using the MERS station located in Erdemli, Mersin, on the Mediterranean coast of Turkey. In this paper, the dominant multipath frequency in the SNR data is derived with two methods presented: the Lomb-Scargle periodogram (LSP) and the LSP with the Moving Average (MA) filtering.

Time series of the sea level heights derived from LSP analysis can contain irregular variations. Thus, reasonable results cannot be generated for sea level heights. This study uses the moving average filtering method to eliminate these irregular variations. First, GNSS-R sea level heights were retrieved using the LSP method. Then, these results were used as input data in the MA filtering method and reconstruct the sea level heights. The GNSS-derived sea level observations were computed by the LSP and LSP with MA method and were compared with nearby tide gauge records. Figure below shows the comparison of GNSS-R retrievals and tide gauge records using LSP and LSP with MA method.

Sea level at MERS station estimated from GNSS-R and sea level recorded by Erdemli tide gauge. GPS- L1 signal is shown in the top, GPS-L5 signal is shown in the bottom.

LSP with MA method indicated improvement in GNSS-R derived sea level, decreasing the RMSE and standard deviation. The results of the LSP and the LSP with MA method are presented in the table below. The GNSS-R-derived sea level observations and sea level records from a nearby tide gauge show similar trends. It should be noted that the performance of the SNR data at the MERS site could be improved with a higher sampling rate and different quality control metrics.

How to Make Earth Observation More Efficient; a Short Interview with GeoOptics’ Founder.

Milton Friedman’s “If you put the federal government in charge of the Sahara Desert, in five years there’d be a shortage of sand” alludes to the fact that how it would become more efficient and agile if government-run projects were fully operated by privately-run teams. This liberal attitude has become a motivation for me to ask Thomas Yunck, the founder of GeoOptics, one of the pioneer companies in the Earth Observation business (founded in 2006 based in Pasadena, California), for a friendly chat on their achievements and prospects.

As one of the first and few privately-run businesses in the modern industry of earth observation (EO), how do you describe the comparative advantage of your services?

The fast-growing number of missions and applications developed in EO research and industry calls for more rapid innovations to be done at lower costs. Commercial solution is exactly what we provide at GeoOptics; undertaking ground-breaking missions, such as GNSS Radio Occultation (GNSS-RO), at a fraction of the costs that government-based organizations have been spending. As a long-time technical manager at NASA, I’ve been keeping the track of relentless costs of many NASA and NOAA missions, e.g., GRACE, and it’s obvious that they cannot keep up with those soaring costs. The commercial solution can provide an opportunity to dwindle those expenses to a fifth or a tenth and make projects much more efficient in terms of timing and also output distribution. This strategy may then help government labs to become more competitive and, by implications, more efficient and agile. This public-private model we developed in our business encourages governments to outsource their missions to privately-run enterprises.

Who are your partners? Are you still in collaboration with JPL?

JPL and Tyvak Nano-Satellite Systems are the main partners we collaborate with. I was at NASA for almost 30 years, where we developed the GNSS-RO technique which uses GNSS signals passing through the atmosphere and ionosphere to sense their properties in fine detail. We can now benefit from the professional relationships established during that time to put GNSS-RO into commercial practice. In partnership with JPL and Tyvak, we’ve lunched our own constellation, CICERO, for atmospheric radio occultation. CICERO delivers data for operational weather forecasting, climate research, and space weather monitoring. The products include high-accuracy profiles of atmospheric density, pressure, temperature, and moisture as well as 3D maps of the electron distribution in the ionosphere.

Such a coincidence! You named your constellation CICERO after a Roman statesman and philosopher, Marcus Tullius Cicero, who was one of the first icons in history theorizing free market. How did you come with the word CICERO?

Yes, that’s correct. However, I learnt about the great Roman statesman/philosopher after we named our constellation as it stands for “Community Initiative for Continuing Earth Radio Occultation”. The constellation, especially our next-generation satellites, offer an improved version of GNSS-RO with a much higher data capacity.

Let’s get back to the mission. Among the products you listed for CICERO, most of them are related to the Earth’s atmosphere, which makes a perfect sense for a GNSS-RO mission. However, ocean and ice property have been also mentioned among the prospects of this mission. I wonder how GNSS-RO is capable of ocean and ice remote sensing.

Ocean and ice remote sensing are not going to be done through GNSS-RO, but they’re among our upcoming plan which is be on GNSS-Reflectometry (GNSS-R). CICERO will start receiving reflected GNSS signals from the ocean soon to monitor the ice volume, ice age (i.e., FYI, MYI, etc.), and ice/water recognition as well as ocean surface winds and soil moisture. The advantages of CICERO, compared to other LEO micro-satellite constellations, such as CYGNSS, will be a higher radar accuracy, wider coverage area including sub-polar regions, shorter revisit time around few hours, and near real-time data distribution. We are currently expanding technical team by hiring engineers and scientists.

What challenges you face while running your enterprise?

The main challenge is familiarizing commercial providers and agencies with this win-win opportunity, which allows both sides to be more efficient. Government agencies, such as NASA, NOAA, and the Air Force are our main clients; they pay the major part of the system cost. So, They appreciate the value of this sort of collaboration and plan to expand such arrangements for future data procurements. We need to tap our professional connections to highlight the importance of commercial solutions in making EO more cost- and time-efficient.

Your closing statement would be welcome.

We are a business, and we must cover our costs, but I have been a scientist as well; I know how scientific affairs and knowledge are decisive in preserving our environment. GeoOptics was founded by a team of scientists to serve the world’s citizens. That’s why we’ve pledged ourselves to provide all CICERO data free of charge to researchers. Although we are still in the middle of transition, we have a strong business model as well as a hard-working team of scientists dedicating themselves to meeting our commitment to society. So, If you are a researcher interested in using our data, please get in touch. We’d love to hear from you.

Tom Yunck is Founder and Chief Technical Officer of GeoOptics, Inc., a startup dedicated to advancing Earth remote sensing with constellations of small satellites.  For 25 years he over­saw the develop­ment of flight instruments and information systems for Earth science at NASA’s Jet Propulsion Laboratory.  At JPL, Tom developed the first proposals for the GRACE gravity mission and for GPS radio occultation sounding of the atmosphere, which are brought together, and advanced, in GeoOptics’ Earth Gravitational Observatory – Crosslink Occultation (EGO-XO) project, which has received several development grants from NASA.  Tom has been PI on many NASA projects, including the General Earth Science Investigation Suite (GENESIS), the Active Tropospheric Ozone and Moisture Sounder (ATOMS), and the Climate Virtual Observatory (CVO).  He was chief inventor of the “state space” precise real time GPS positioning technique used in the Federal Aviation Administration’s Wide Area Augmentation System.  In 2004, Dr. Yunck was inducted into the Space Foundation’s Space Technology Hall of Fame.

GNSS-Scatterometry Challenges in Lake Ice Remote Sensing

Delay-Doppler Maps (DDMs) have already shown promising potentials in the sea ice remote sensing, including ice recognition and sea ice thickness estimation. However, this kind of products is yet to be tested for lake ice remote sensing, which looks more challenging than that of sea ice, especially for mid-latitude ones.

Generally speaking, two main approaches have been established so far for GNSS-R remote sensing: altimetric and scatterometric approaches. Although these two approaches are somehow connected to each other, the methodologies can be way apart. Accordingly, ice remote sensing using GNSS-R can be, and has been, conducted in both ways.

Among many scatterometric-based research items for ice remote sensing, Qingyun Yan has successfully carried out and published several papers on sea ice remote sensing by analyzing DDMs obtained from TechDemoSat-1 (TDS-1) satellite over northern regions. He has also introduced the feasibility of sea ice thickness measurement by extracting brightness temperature values from DDMs reflectivity observations. However, no GNSS scatterometry experiments have been yet done over lake ice to examine the GNSS-R capability of lake ice remote sensing by means of DDMs.

As part of an experiment that I’m currently involved in regarding the DDMs potential of lake ice remote sensing, I started exploring challenges that one may face in lake ice remote sensing using scatterometric data. Lake ice covers, especially mid-latitude ones, as discussed in some previous posts of this blog (e.g., this one), are, in general, highly influenced by mid-winter warmings and melt/refreeze events, which significantly change the reflectivity properties of the lake ice reflective layer(s). Therefore, I came up with two main challenges as follows.

Firstly, in GNSS scatterometry, it’s usually assumed that we’re dealing with a single scattering regime, i.e., only one surface contributes to the reflection. This assumption in mid-latitude frozen lakes is improper because, as mentioned above as well as in my master’s thesis, mid-winter warming events leads to the appearance of some wet layers inside and over the ice column causing interferences in reflections. In other words, depending on the water content of each contributing layer, which controls the dielectric permittivity of overlaying layers, these layers may cause a multi-reflection regime, which differs the scenario from what has been defined in the GNSS-R tutorial.

secondly, melt/refreeze events during the freezing season change the ice-water interface roughness significantly, which may change the amount of the reflected power received by the satellites. In the literature, some theoretical models, such as Kirchhoff Approximation and Integral Equation Method, are applied to simplify assumptions regarding model the roughness of reflective surfaces. However, ice-water interfaces at frozen lakes are less likely to be adopted with those models; therefore, non-specular reflections are very likely to happen from lake ice towards GNSS-R receivers.

Furthermore, topography and EIRP effects have been discussed here an here, respectively; however, we’re actively exploring for other potential sources of inconsistencies. Feel free to reach us out and contribute if you have ideas on that.

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.

How GNSS SNR Values Are Connected to Antenna Heights; the Geometry of SNR-Based GNSS Interferometric Reflectometry

You may know what formula I am talking about; one of the most famous formulas in GNSS reflectometry that magically links the reflected SNR values, satellite elevation angle, and the signal wavelength to the antenna height. I have created a short animated video to explain where this formula comes from.

In October 19, 2020, at 11:00 a.m., when I was defending my master’s thesis, which was on the applications of GNSS interferometric reflectometry, both my committee members asked questions about the origin of this formula. First, Dr. Richard Kelly, asked me how we can geometrically connect the SNR to the antenna height, and I referred to some basic trigonometric equations to clarify the geometry of SNR-based GNSS-Reflectometry. Afterwards, Dr. Grant Gunn, asked how bending effect and penetration delay can be ignored in this technique; so, I refered to its geometry and mentioned that this technique is classified as a “phase altimetry” method, in which the delay and bending effects are significantly reduced compared to those method categorized as “range altimetry”.

Although I successfully passed my defense, I felt that the origin of this formula might be unclear for researchers whose main fields of interest are not GNSS reflectometry. Therefore, I decided to create this short video to simply explain how the antenna height can be retrieved from SNR values. This video is a part of my i-poster submitted to the Global Water Future 4th Annual Open Science Meeting (GWF2021) in where a large number of researchers and scientists present their recent findings on Canada’s water future. As I guess that many of them are not super expert in GNSS reflectometry, I decided to create this short video and put it in my poster. The link to my poster will be shared when it becomes available.

How to Fund Smartphone-Based GNSS-R Observations for Lake Ice Remote Sensing; Cryptocurrencies may Help!

I got surprised to see this post, which was about smartphones potential for lake ice thickness measurement, has been circulated a lot and gained many views from different countries around the world. However, talking about this ideas through one-to-one discussions with my colleagues and friends, a question cropped up, which made me to write this post: “How would we encourage non-specialist individuals to dedicate their phones, even for a short period of time they’re spending over lake ice, for our GNSS-Reflectometry goal regarding lake ice thickness measurement?”

I have heard a lot from people inside academia saying that environmental issues are somehow apart from financial affairs. In their point of view, when we get through environmental issues/crises, it doesn’t make sense if one talks about costs and economic feasibility, but instead, people should sincerely dedicate what they have, or even don’t, to tackle the issues. Dead Wrong! A commercialized business plan should be, I believe, the first step for turning any research\academic solutions into a practical subject.

I came up with this challenge too, when I was thinking about the idea I proposed in the previous post. In our scenario, individuals go over lake ice covers to spend their leisure time or even to do their routine jobs by, for instance, ice fishing. Now, we’d like to ask them to put their smartphones on the ice surface in a certain short distance off themselves and leave their smartphones there for couple of hours to measure the ice thickness by running our proposed app. How would we make it beneficial for them?

I know that education is a very important and effective way to raise public awareness about harms caused by the downward trends of lake ice duration, which are obviously shown by multiple environmental studies. But I believe that public awareness could not be enough to encourage individuals to devote their smartphones for this purpose; a stronger inspiration would be required.

This figure was used in my master’s thesis, without any technical analyses; originally derived from CLIMo, a lake ice model developed by Dr. Claude Duguay

Cryptocurrencies have already become a very hot topic in financial affairs, and a fast-growing number of businesses and concepts are being defined or re-developed using blockchain technologies. Aside from businesses, scientific activities have also shown potentials to be benefited and funded by endowments placed on the blockchain. Moreover, cryptocurrencies have suggested an opportunity to better protect the integrity and provenance of scientific data. In addition, ENV Finance has introduced itself as a cryptocurrency project aiming to bring environment and finance together; you can read about their project here. Seemingly, we’re not the pioneers of the “cryptoscience” (such an odd word), but we have some examples to refer.

As a result, people who are helping the environment by their smartphones equipped with a GNSS-R app may be awarded by tokens assigned by sponsors. Furthermore, a very recent cryptocurrency has been developed by a group of Stanford’s scientists enabling smartphones to mine blocks. This cryptocurrency, which is called Pi Network, may give us hints on how to encourage smartphone users to measure ice thickness and mine coins at the same time.

I am not a blockchain specialist; but even if I were, any comments, guides, and critiques would still be welcome.

GNSS Reflectometry Using Smartphones; A Potential for Lake Ice Thickness Monitoring

SNR-based GNSS-Reflectometry has shown an enormous potential for ground-based altimetry purposes as the frequency of SNR oscillations is directly connected to antenna height from the reflective surface. This technique, which is usually called in the literature as GNSS Interferometric Reflectometry, has been already tested for retrieving snow depth, monitoring water level changes, and measuring lake ice thickness. The considerable advantage of this technique can be listed as the low costs of equipment since a simple standard GNSS receiver would be enough for running a GNSS-IR experiment.

Recently, Cemali Altuntaş, a researcher from Yildiz Technical University, Turkey, has evaluated the potential of android smartphones for the GNSS-IR experiment and antenna height measurement. This well-structured research, which is going to be published in a couple of weeks by Digital Sensor Processing, Elsevier, analyzed the SNR-based retrieved heights obtained from a single-frequency GNSS receiver embbeded in a Xiaomi Mi 8 Lite smartphone, compared with those recorded by a Trimble NetR9 geodetic receiver, and then validated with in-situ measurements. Results show a stunning performance by the smartphone unit compared to the geodetic receiver in terms of height residuals.

As I am not an electrical specialist, I have no clue on why a low-cost GNSS receiver designed for daily routine jobs shows better results in comparison with a standard geodetic receiver, which has been always used for highly professional geodetic observations. Although the positioning precision of Xiaomi Mi 8 Lite has been tested and shown to get close and be comparable to geodetic receivers, but in terms of SNR-based reflectometry, I would be grateful if a specialist could make it a bit clear whether it is related to the noise amount, antenna gain, or any other possible reasons.

Considering the advantageous potentials of smartphone GNSS receivers for reflectometry purposes, one may expand the mobile-based GNSS-IR to a wider range of remote sensing applications, especially those requireing massive data, which can be collected by non-specialists individuals. As an example, GNSS-IR has shown a promising potential for the freshwater ice thickness measurement using a single geodetic receiver. In a study, we placed a GNSS antenna on the ice surface allowing it to receive reflected GNSS signals from the ice-water interface to measure lake ice thickness. Lake ice is known as a very common place for many people who live in cold regions, such as Canada, to spend hours over for, for instance, ice fishing. Therefore, smartphone-based GNSS-IR may offer a new opportunity for individuals allowing them to just leave their smartphones in a short distance away from themselves on the ice surface during their on-ice activities in order to collect reflected GNSS signals from the lake ice. This contribution may be aggregated by a central server to provide a wide coverage of lake ice thickness data with a demonstrated accuracy in our paper.

Can Small Changes in Water Surface Topography be Detected by GNSS Reflectometry?

Precipitation detection over ocean using various radar remote sensing techniques have been fully understood and tested for several decades. But in terms of GNSS Reflectometry, researchers had been skeptical about its potential as a rain detector. Recently, a groundbreaking paper has been published by Dr. Milad Asgarimehr and his colleagues addressing this question cropping up in another paper published three years ago.

Having done his Ph.D. with Technische Universität Berlin, Berlin, Germany, Milad is currently doing his postdoctoral research on improving GNSS-R observations with AI at the German Research Centre for Geosciences (GFZ). Although the GNSS-R capability of rain detection had been doubted at the beginning, Milad’s recent study suggested that precipitation affects the power of reflected GNSS signals, which can be critical in GNSS-R experiments as we prefer to seek for unaffected data.

Regardless of microwave remote sensing, the effect of rain on ocean waves and currents has been simulated in laboratory experiments. As an example, this study designed a circulating wind-wave tank to simulate rain drops effects on ocean surface waves showing that ring waves caused by rain drops can amplify the surface roughness at centimetre scales although it can attenuate gravity waves over ocean surfaces. However, these laboratory studies could not fully explain the mechanism of rain effects on ocean surfaces in real environment.

In this recent study, Milad tested the rain effect by analyzing polarimetric GNSS observation at a GFZ coastal GNSS-R station at Onsala Space Observatory in Sweden equipped with two side-looking antennas at two different polarizations (RHCP and LHCP). Among multiple results obtained from this experiment, including sea surface salinity changes due to rain events, the key one was discerning rain drops in the power of RHCP and LHCP reflections over a calm sea. Analyzing the I/Q components of the reflected signals, authors has shown that the received signal power at a low-wind-speed condition (<5 m/s) is reduced due to the diffuse scattering caused by rain-drop-made ring-waves over sea surface.

Reviewing this paper, I came up with this question if we could study ice bottom roughness using GNSS-R tools as either a ground-based or a satellite payload sensor. As discussed in a previous post, mid-winter warm temperature may cause changes in ice roughness, and this variation can be significant enough to be discerned by reflected GNSS signals. In addition, the water underneath the ice is so calm that satisfies the weak diffuse scattering regime condition, similar to the low-wind-speed condition Milad suggested in his paper. To see if GNSS-R has the potential to be used as a roughness indicator, the same steps can be taken as Milad has; however, a very big challenge is ahead of us in lake ice remote sensing: multi-layer scattering! In most GNSS-R studies, the reflection is assumed to be from a single reflective layer, e.g, sea water surface, but in lake ice, as shown in my master’s thesis, there are usually multiple reflective layers unless we experience consecutive days with a cold temperature so we can neglect undesired L-band reflections from layers rather than the ice-water interface.

To be specific, our Haliburton experience, which has been explained in Chapter 4 of my master’s thesis, clearly reflects the temperature effect in the power retrieval process (see this post). But aside from the temperature effect, Milad’s paper shows that GNSS-R is able to detect topography changes in small amplitudes. In other words, if the temperature is cold enough to avoid wet layers, ice bottom roughness may change the power of reflected signals as GNSS-R has well shown the potential to discern the rain-caused roughness in the order of ~5 to 50 mm. However, the other big challenge we may face is ancillary data about real ice bottom roughness, which seemingly necessitates another lengthy fieldwork. Dr. Grant Gunn has recently conducted a research on freshwater ice roughness and capacity (will be bulished by Jun 2021) summerizing multiple methods of ice roughness retrieval and explaining in-situ measurements they have done for this purpose in the Straits of Mackinac region of the Great Lakes between Michigan’s upper and lower peninsulas.

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.