Automated outlier detection with machine learning in GRACE and GRACE-FO post-fit residuals - Scientific contribution

Sep 17, 2026

Uploaded by Finn

Automated outlier detection is applied to GRACE/GRACE-FO inter-satellite K-band range-rate observations used for monthly Earth gravity field solutions. Because range-rates depend on Earth mass distribution as well as satellite relative motion, orientation, and attitude handling, observation screening is challenging. The work uses unsupervised isolation forests on high-dimensional post-fit residuals and geographic location, then refines anomaly selection with mutual information to separate true anomalies from effects of imperfect model fit. Results are discussed for May 2019 and for GRACE single-orbit processing.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages1

Reading Time3 min

AccessFree to download

Problem

Isolation forest for outlier detection

GRACE-FO outliers based on isolation forest

Isolation forest + Mutual information

Remaining outliers

Mutual information

Comparison between correlation and MI

Outliers based on sequences of single orbits

Conclusions

Automated outlier detection with machine learning in GRACE and GRACE-FO post-fit residuals Jonas Zbinden, Martin Lasser, Ulrich Meyer, Brandon Panos, Daniel Arnold, Adrian Jäggi Problem GRACE/GRACE-FO inter-satellite K-band range-rates are the main observable for the determination of monthly solutions of the Earth’s gravity field. The rangerates are sensitive not only to the mass distribution of the Earth, and as a consequence, the relative motion of both GRACE and GRACE-FO satellites respectively, but also to the relative orientation of the satellites and consequently to the attitude handling. Therefore, an efficient screening of the range-rate observations isnot trivial. In this contribution, we apply machine learning to flag outliers in an unsupervised and fully automated way. Isolation forest for outlier detection For outlier or anomaly detection isolation forests offer a fast and easy way to detect outliers within a high-dimensional dataset. The data is split along each dimension randomly. The easier it is to isolate a point, the higher its anomaly score . Image: [https://en.wikipedia. org/wiki/](https://en.wikipedia. org/wiki/)[ ](https://en.wikipedia. org/wiki/)Isolation_forest The anomaly score 􀀡 (􀀣) of a point 􀀣 ! is measured with the number of random cuts ℎ(􀀣!) to isolate it. The score 􀀡 (􀀣) is given by 􀀡 􀀣 ∝ −2()(*($ )), where Ε (ℎ(􀀣)) is the expectation value of the path length of all trees to isolate the point 􀀣 . A score 􀀡 􀀣 close to −1 . The minus is a convention from the Python library scikit-learn . GRACE-FO outliers based on isolation forest We applied the isolation forest algorithm to the combination of the post-fit residuals and the geographic location of the satellite at this time to find outliers independent of the geographic location . As an example, we show the post-fit residuals (left) and the outliers found with isolation forest (right) from May 2019 . Over the Amazon basin both maps exhibit some geographical pattern . To distinguish between true anomalies, and unfitted gravity signal we make use of mutual information to find any ( cor )relations between the geographical position and the post-fit residuals . Isolation forest + Mutual information Mutual information 􀀩􀀪 can show more complex relations and dependencies between the geographic position and the post-fit residuals . If there is any geographically ( cor )related signal in the post-fit residuals, then 􀀩􀀪 ≠ 0 . Therefore, we strive to find true outliers flagged by isolation forest which have 􀀩􀀪 = 0 . remaining outliers We can see the same pattern over the Amazon basin in MI (left) . Based on the combination of isolation forest + MI we can isolate the true outliers (right), not affected by a bad model fit. Mutual information Mutual information 􀀩􀀪 captures the dependency between two random variables and their probability distributions . Two variables 􀀯, 􀀱 are independent if and only if 􀀲 􀀣 , 􀀳 = 􀀲 􀀣 􀀲 (􀀳) . To capture the dependency between 􀀣 and 􀀳 we compute the pointwise-mutual information measure 􀀴􀀩􀀪 (􀀣! , 􀀳 !): 􀀴􀀩􀀪 􀀣 ! , 􀀳 ! ≜ log ""($!~~ ~~!",&(&!~~ ~~)!) . The 􀀴􀀩􀀪 can be calculated by training a neural network 􀀺 at capturing the dependencies between 􀀯 and 􀀱 for instance through sampling the marginal probabilities P(􀀯), P (􀀱) () by sampling signals from different pixels in animage and the joint probability distribution by sampling signals from the same pixel P(􀀯, 􀀱),() maximizing the difference || - || . Comparison between correlation (left) and MI (right), the MI also captures non-linear dependencies . Image: [https://www.science.org/doi/10.1126/science.1205438](https://www.science.org/doi/10.1126/science.1205438) With our trained neural network 􀀺 we can then estimate the 􀀴􀀩􀀪 􀀣 ! , 􀀳 ! on e . g. the position on Earth and the post-fit residuals for a single timestep. Outliers based on sequences of single orbits Due to the lower global coverage by GRACE in 2004 (repeat cycles) compare

FAQs

Why is screening GRACE/GRACE-FO range-rate observations difficult?

Range-rates are sensitive not only to Earth’s mass distribution and satellite relative motion, but also to relative orientation and attitude handling, making reliable detection non-trivial.

How does isolation forest produce an anomaly score in this approach?

Isolation forest randomly splits data along dimensions; the easier it is to isolate a point, the higher its anomaly score, measured via expected path length across trees.

How does mutual information help distinguish true anomalies from model-fit errors?

Mutual information between geographic position and post-fit residuals identifies geographically correlated signals; the method aims to keep isolation-forest outliers where mutual information indicates no correlation (MI = 0).

What was learned from applying orbit-by-orbit outlier detection for GRACE?

Removing outliers on an orbit-by-orbit basis improved gravity field uncertainty estimation compared with manual visual removal, but isolation forest + mutual information was not applicable to the 2004 GRACE dataset due to inhomogeneous coverage.

Sep 17, 2026

Uploaded by Finn