[Paper Review] Modeling of path delay in the neutral atmosphere: a paradigm shift

Leonid Petrov|arXiv (Cornell University)|Feb 24, 2015

GNSS positioning and interference3 references3 citations

TL;DR

This paper proposes a paradigm shift in modeling atmospheric path delay for radio astronomy by leveraging high-accuracy numerical weather model outputs (GEOS and MERRA) to compute path delay and extinction a priori with 45 ps * cosec(elevation) accuracy. The method enables routine, real-time computation of propagation effects—comparable to updating star positions—demonstrating 0.5% accuracy for total path delay and 10% for wet component, rendering traditional calibration methods like tipping curves obsolete.

ABSTRACT

Computation of propagation effects in the neutral atmosphere, namely path delay, extinction, and bending angle is a trivial task provided the 4D state of the atmosphere is known. Unfortunately, the mixing ratio of water vapor is highly variable and it cannot be deduced from surface measurements. That fact led to a paradigm that considers path delay and extinction in the atmosphere as a~priori unknown quantities that have to be evaluated from the radio astronomy data themselves. Development of our ability to model the atmosphere and to digest humongous outputs of these models that took place over the course of the 21st century changed the game. Using the publicly available output of operational numerical weather model GEOS run by NASA, we are in a position to compute path delay through the neutral atmosphere for any station and for any epoch from 1979 through now with accuracy of 45 ps * cosec elevation. We are in a position to compute extinction with accuracy better than 10 pro cents. We are in a position to do it routinely, in a similar way how we update apparent star positions for precession and nutation. Moreover, we are in a position to do it now. As a demonstration of current capabilities, I have computed time series of path delays for all radiotelecopes that I was aware of (220 sites) since 1979 with a step 3-6 hours. Results of the validation tests are presented. A new paradigm of data analysis assumes that we know the atmosphere propagation effects a priori with the accuracy higher that one could deduce them from radio astronomy observations.

Motivation & Objective

• To replace traditional data-driven modeling of atmospheric path delay with a physics-based, a priori computation using numerical weather model outputs.
• To demonstrate that path delay and extinction can now be computed routinely and accurately for any station and epoch since 1979.
• To validate the accuracy of a priori path delay computation against baseline length repeatability and zenith delay residuals.
• To show that legacy calibration techniques like tipping curves and geodetic blocks are no longer necessary due to superior model-based corrections.
• To enable real-time, high-accuracy atmospheric correction in radio astronomy, comparable to precession and nutation updates.

Proposed method

• Utilizes publicly available 4D atmospheric state outputs from NASA's GEOS and MERRA numerical weather models (1979–present) for temperature, pressure, and water vapor partial pressure.
• Applies Fermat's principle and solves the variational problem for ray trajectory using a 4th-order nonlinear system of differential equations derived from refractivity gradients.
• Represents refractivity as a 4D tensor product of B-spline functions (degree m) to enable continuous, differentiable modeling of refractivity over height, longitude, latitude, and time.
• Computes path delay integrals over azimuth-elevation grids using B-spline expansions, storing coefficients for efficient retrieval and application.
• Validates results via baseline length repeatability tests using weighted RMS deviations and extrapolates to Earth's diameter to estimate vertical position errors.
• Computes atmosphere brightness temperature and attenuation by calibrating fringe amplitudes with e^(-a) factors and isolating receiver temperature from system temperature using model-based atmospheric contributions.

Experimental results

Research questions

• RQ1 Can atmospheric path delay be computed a priori with sufficient accuracy to replace data-driven calibration in radio astronomy?
• RQ2 What is the achievable accuracy of a priori path delay and extinction modeling using modern numerical weather models?
• RQ3 How does the accuracy of a priori modeling compare to traditional methods like tipping curves and geodetic blocks?
• RQ4 To what extent can system temperature anomalies be corrected by separating receiver and atmospheric contributions using model-based brightness temperature?
• RQ5 Can the new paradigm enable real-time, routine correction of propagation effects in the same way as precession and nutation updates?

Key findings

• Path delay can be computed with an accuracy of 45 ps * cosec(elevation), equivalent to 0.5% relative accuracy for total path delay.
• The wet component of path delay is computed with 10% accuracy, corresponding to a 37 ps uncertainty in zenith wet delay on average.
• Baseline length repeatability extrapolated to Earth's diameter shows an additional 1.45 cm (48 ps) variance in vertical station positions due to errors in a priori path delay models.
• Zenith wet path delay residuals vary from 0.6 cm (37 ps) at polar stations to 2.2 cm (66 ps) at tropical stations, with a mean of 1.25 cm (37 ps).
• Atmosphere brightness temperature and attenuation can be computed with uncertainty close to that of wet path delay, suggesting 10% accuracy in the water vapor-dominated frequency range.
• Legacy calibration techniques such as tipping curves and geodetic blocks are no longer necessary, as model-based corrections now exceed their accuracy.