Assessment of the Earth orientation parameter accuracy from concurrent VLBI observations

Here is an explanation of the paper, translated from complex geodesy jargon into everyday language using analogies.

The Big Picture: Measuring the Earth's Wobble

Imagine the Earth is a giant spinning top. Sometimes it spins perfectly straight, but often it wobbles, tilts, and speeds up or slows down slightly. Scientists call these movements Earth Orientation Parameters (EOP). Knowing exactly how the Earth is wobbling is crucial for GPS, satellite navigation, and even for knowing exactly where "North" is.

The authors of this paper are like master detectives trying to measure this wobble with extreme precision. They use a technique called VLBI (Very Long Baseline Interferometry). Think of VLBI as a giant, planet-sized camera made of radio telescopes scattered across the globe. Instead of taking a photo of a face, these telescopes "listen" to radio waves from distant, ancient galaxies (quasars) to triangulate exactly where the Earth is pointing.

The Problem: The "Official" Numbers Were Wrong

For decades, scientists calculated the "error bars" (how much they might be wrong) on their measurements using a standard math formula. They assumed that the "noise" in their data (static, like radio interference) was random and unconnected, like raindrops hitting a roof independently.

The Paper's Discovery: The authors found that this assumption was wrong. The noise isn't random rain; it's more like a wind gust. If the wind blows hard for a minute, it affects the whole measurement for that minute. Because the noise is "correlated" (connected over time), the standard math formulas underestimated the errors by a huge margin. The "official" error bars were like saying a ruler is accurate to the millimeter when it's actually only accurate to the centimeter.

The Experiment: The "Twin Race"

To find the real accuracy, the authors didn't trust the math formulas. Instead, they set up a race.

They looked at times when two different teams of telescopes were watching the Earth at the exact same time (concurrent observations).

Team A might be running a 24-hour marathon session.
Team B might be running a quick 1-hour sprint.

If both teams are looking at the same spinning Earth at the same time, their results should be identical. Any difference between Team A and Team B is the "real error." By comparing these twins, they could measure the true accuracy without relying on the faulty math formulas.

Key Findings (The "Aha!" Moments)

1. The Weather is the Boss

The biggest source of error isn't the telescopes; it's the atmosphere.

Analogy: Imagine trying to measure the distance to a lighthouse through a foggy window. If the fog is thick and moving (turbulence), your measurement is off.
The Seasonal Twist: The authors found that measurements are much better in Winter than in Summer. Why? In summer, the atmosphere is hotter and more turbulent (like a hot summer day with rising heat waves), making the "fog" worse. In winter, the air is calmer, and the measurements are sharper.
The Limit: They found that no matter how clever the scheduling of the telescopes is, you can't perfectly fix the atmospheric "fog" just by looking at the radio waves. There is a hard limit to how well we can correct for the weather using these tools.

2. The "Diminishing Returns" of Time

You might think that watching the Earth for 24 hours would give you a result 24 times better than watching for 1 hour.

The Reality: It's not that simple. The authors found that accuracy improves quickly at first (like the first few hours of a marathon), but then it hits a "speed bump."
The Analogy: Imagine trying to hear a whisper in a noisy room. Listening for 1 hour helps you tune out the noise. Listening for 2 hours helps a bit more. But listening for 24 hours doesn't help you much more because the "noise" (the atmospheric turbulence) is changing in a pattern that you can't average out.
The Result: Extending a session from 4 hours to 24 hours costs a lot of money and resources but only gives a tiny improvement in accuracy. The authors suggest we might be wasting resources by running 24-hour sessions when shorter ones might be just as good for certain measurements.

3. The "Source Structure" Myth

Some scientists worried that the "shape" of the distant galaxies (the quasars) might be changing, which would mess up the measurements.

The Verdict: The authors did the math and found that while the galaxies do have structure, it's a tiny problem. It's like worrying about a speck of dust on a camera lens while trying to take a photo of a mountain. The atmosphere is the mountain-sized problem; the galaxy shape is just a speck of dust.

The Takeaway for the Future

This paper is a wake-up call for the scientific community:

Stop trusting the old math: The standard formulas for calculating error are broken because they ignore the "windy" nature of the atmosphere.
Rethink the schedule: We don't need to run 24-hour marathons as often. Shorter, more frequent sprints might give us better data for less money.
Focus on the weather: The biggest hurdle to better Earth measurements isn't better telescopes; it's better ways to model the atmosphere.

In short: The Earth's wobble is harder to measure than we thought because the air above us is messier than we admitted. By comparing "twin" observations, the authors found the real accuracy, which is lower than we hoped, but now we know exactly why and how to fix our methods.

Here is a detailed technical summary of the paper "Assessment of the Earth orientation parameter accuracy from concurrent VLBI observations" by Petrov, Plötz, and Schartner.

1. Problem Statement

The primary challenge addressed in this study is the difficulty in accurately assessing the accuracy of Earth Orientation Parameters (EOP) derived from Very Long Baseline Interferometry (VLBI).

Limitation of Formal Errors: Traditional error estimates ("formal errors") rely on the assumption that noise in observables (group delays) is uncorrelated and white. The authors demonstrate that these formal errors systematically underestimate true uncertainties by a factor of 1.2 to 10 because they fail to account for correlated noise, particularly from atmospheric turbulence.
Lack of Ground Truth: Since no other technique measures Earth's spin angle more precisely than VLBI, EOP accuracy cannot be validated against an external "ground truth."
Need for Robust Metrics: There is a need for a robust metric to evaluate EOP accuracy that does not rely on flawed covariance assumptions or external smoothed time series (like IERS C04) which may introduce their own biases.

2. Methodology

The authors employed a concurrent observation approach, analyzing the differences between EOP estimates derived from independent VLBI experiments running simultaneously at different networks.

Data Sources:
- 24-hour Multi-baseline Campaigns: Analyzed data from 1997–2000 (CORE-A/NEOS-RAPID/IVS-R1/R4) and 2019–2024 (VGOS-OPS/TEST/RD, IVS-R1/R4).
- 1-hour Single-baseline Campaigns: Analyzed intensive sessions (e.g., IVS-INT, VGOS-INT) and a specific 22-hour campaign (s22) consisting of 22 consecutive 1-hour blocks on the Mg-Ws baseline.
- Total Dataset: 7,818 experiments spanning 1980–2025, totaling ~19.8 million ionosphere-free group delay observables.
Analysis Technique:
- Concurrent Comparison: For every target experiment, a reference solution was generated using concurrent background and reference experiments. The difference between the target and reference EOP estimates served as the accuracy metric.
- Statistical Correction: Since both target and reference estimates contain errors, the Root Mean Square (RMS) of differences was divided by $\sqrt{2}$ to isolate the accuracy of a single solution (assuming uncorrelated errors between the two independent networks).
- Segmentation Analysis: 24-hour sessions were artificially split into shorter blocks (1 to 23 hours) to study how EOP accuracy scales with observation duration.
- Noise Injection: To test the nature of the noise, uncorrelated Gaussian noise was injected into the data to see if the scaling behavior would revert to the theoretical expectation for uncorrelated noise.
- Three-Corner Hat Method: Used to compare VLBI results against GNSS (IGS Final) and other VLBI campaigns to derive individual variances.

3. Key Contributions

Validation of Concurrent Differences: Established that the RMS of differences between concurrent independent VLBI solutions is a reliable, robust metric for EOP accuracy, superior to formal errors.
Discovery of Correlated Noise: Provided empirical evidence that atmospheric noise in VLBI is highly correlated, violating the Gauss-Markov theorem assumptions used in standard least-squares analysis.
Scaling Law of Accuracy: Determined that EOP error scaling with session duration follows a broken power law:
- For durations < 2–4 hours: Accuracy improves rapidly (exponent $\approx -0.4$ to $-0.5$ ).
- For durations > 2–4 hours: Accuracy improves slowly (exponent $\approx -0.3$ ), indicating diminishing returns due to correlated atmospheric noise.
Seasonal Variability: Quantified a strong seasonal dependence in EOP accuracy, with summer errors being significantly larger than winter errors (up to 1.8x variance increase).
Source Structure Impact: Quantified the impact of unmodeled source structure on EOP, finding it to be negligible ( $\sim 0.1$ nrad) compared to atmospheric errors.

4. Key Results

A. Accuracy Metrics

24-hour Sessions: The accuracy of EOP estimates (E1, E2, E3) from concurrent 24-hour sessions is approximately 0.4–0.6 nrad (nanoradians).
1-hour Sessions: Accuracy degrades to 1.3–1.6 nrad for 1-hour intensive sessions.
Formal vs. Real Errors: Formal errors significantly underestimate the true uncertainty. For example, formal errors suggested a 2.1x improvement in accuracy with new VGOS hardware, while actual concurrent comparisons showed only a 15% improvement.

B. Seasonal Effects

Winter vs. Summer: EOP accuracy is significantly better in winter.
- For the KkWz baseline, summer adds 0.73 nrad of variance compared to winter.
- For the K2Ws baseline, summer adds 0.89 nrad.
Cause: The authors attribute this to residual atmospheric path delays. While zenith path delays are modeled, the unmodeled, turbulent components of the atmosphere are more active in summer, and the mapping functions used to scale zenith delays to slant paths are inadequate at short time scales.

C. Session Duration and Power Law

Broken Power Law: The relationship between session duration ( $t$ $t$ ) and error ( $\sigma$ $σ$ ) is $\sigma \propto t^{\beta}$ $σ \propto t^{β}$ .
- $\beta \approx -0.43$ to $-0.46$ for $t < 2-4$ hours.
- $\beta \approx -0.28$ to $-0.30$ for $t > 2-4$ hours.
Interpretation: The deviation from the theoretical $-0.5$ (expected for uncorrelated white noise) confirms the presence of correlated noise. The authors identify this as residual atmospheric path delay that cannot be fully resolved by the observation geometry or scheduling.
Implication: Extending sessions beyond 4 hours yields diminishing returns. A 24-hour session is not 6 times more accurate than a 4-hour session, but only ~1.7 times more accurate.

D. Scheduling Strategies

Advanced Scheduling: The study tested "Strategy B" for the s22 campaign, which optimized for rapid elevation angle changes to better solve for atmospheric delays.
Result: No measurable improvement in EOP accuracy was found compared to traditional scheduling (Strategy A). This suggests a fundamental limit in solving for atmospheric path delay using microwave observations alone within short timeframes.

E. Source Structure

The impact of unmodeled source structure on EOP was estimated at ~0.1 nrad.
This is an order of magnitude smaller than the seasonal variance caused by atmospheric errors, indicating that source structure is not the dominant error source for EOP determination.

5. Significance and Outlook

Redefining VLBI Optimization: The findings challenge the current operational strategy of running 24-hour sessions with large networks. The authors suggest that for EOP determination, running shorter sessions (2–4 hours) more frequently might be more resource-efficient, as extending duration yields diminishing returns due to correlated atmospheric noise.
Data Analysis Reform: The study highlights that the standard practice of using diagonal weight matrices (assuming uncorrelated noise) is anachronistic. Future analysis must incorporate full covariance matrices to account for correlated atmospheric noise to produce realistic uncertainty estimates.
Generalizability: Since atmospheric noise affects all microwave observations, these findings regarding correlated noise and scaling laws are likely applicable to GNSS and other geodetic techniques.
Future Work: The authors call for the development of algorithms that can predict EOP accuracy within tens of percent by modeling the correlated noise structure, rather than relying on formal errors.

In summary, this paper provides a rigorous, data-driven re-evaluation of VLBI EOP accuracy, shifting the focus from formal statistical assumptions to empirical metrics derived from concurrent observations, and identifying atmospheric turbulence as the primary, correlated limiting factor.