| 19 Dec 2025
A New Approach to Inversion of Multi-spectral Data with Applications to FUV Remote Sensing
Abstract. Many atmospheric measurement techniques involve inversion of photon counts detected by multi-spectral sensors spanning the X-ray to microwave regions of the electromagnetic spectrum. Although photon counts follow Poisson statistics, commonly used inversion techniques often rely on statistical assumptions that disregard the Poisson nature of the sensor data, limiting the scientific utility of datasets. Motivated to overcome this limiting assumption, this study focuses on retrieval techniques that involve the ratio of counts received in different sub-bands and introduces a new computationally efficient and robust approach to this type of inverse problem that respects the underlying count statistics. The method assumes that the received photon counts in each channel are a realization of a binned point process, allowing the ratio of the channel intensities to be modeled within a hierarchical Bayesian framework. This allows us to directly incorporate correlation between the bins via the prior that is modeled using a permanental process. It further enables more accurate uncertainty quantification without costly sampling procedures common in Bayesian inversion methods. The method is verified and validated on thermospheric neutral temperature retrievals from simulated top-of-atmosphere far-ultraviolet (FUV) disk emission data corresponding to 2–8 November 2018, which includes a minor geomagnetic storm. It is also demonstrated on calibrated photon counts data from the NASA Global-scale Observations of the Limb and Disk (GOLD) mission from the same time period and from 11 May 2024 during a severe geomagnetic storm. The study demonstrates the method's ability to accurately recover neutral temperature in a variety of geomagnetic conditions, attesting to its potential to extend the fidelity of neutral temperature retrievals over broader solar zenith angles than currently possible with existing techniques.
Summary comments:
As a physicist my comments focus on the physics and the data interpretation, rather than the math used.
The approach presented is interesting and may be useful, but the more information on the context for the present work is needed. For example, the relationship of the errors and uncertainties in the present and previous approaches is not sufficiently clear. While some of the figures suggest much smaller errors (apparently 10K) than in the current GOLD data products (30-40K near solar max) the temperatures retrieved for the May 2024 storm deviate dramatically from the released data which show unambiguous consistency between the temperature and composition fields, an indication that the temperature structure is real but is not apparent when the approach described in the paper is applied. The geophysically interesting structure observed during the storm seems to be obscured by the approach presented, possibly indicating biases inherent in the proposed approach when analyzing rare, atypical observations.
As noted by the authors, the approach presented may be useful for data with low signal to noise. The assumption of a normal distribution in GOLD’s current temperature retrieval, while appropriate for most of the dayside where the difference between normal and Poisson statistics are negligible, is not appropriate for all solar zenith angles. However, the authors mischaracterize the current solar zenith angle restrictions in the GOLD data products. Retrievals are possible with lower signal to noise data, but the current retrieval introduces a cold bias (as discussed by Evans et al. 2024). While the figures presented by the authors show that the proposed approach also becomes subject to biases at the larger solar zenith angles where signal to noise is lower (Figure 3), it may be productive to explore the use of Poisson statistics for data with low signal to noise. The use of data at large solar zenith angles is further complicated by the increases in peak emission altitude that occur at large SZA (as discussed in Evans et al. 2024).
The paper has multiple assumptions in the work presented and in comments on previous work that need to be clarified or corrected. An example is the comment in line 98 that a fully calibrated instrument model. Such a model is unnecessary for any of the approached that researchers have used, but a relative calibration is necessary for all the approaches, especially when using multiple emission bands. Other cases are noted in the annotated .pdf file.
A related issue is the possible geophysical implications of assumptions made, e.g., cap harmonics, by the authors. There is an underlying asymmetry in the morning versus evening or the northern latitudes versus the southern latitudes distorted by the symmetry within the harmonics. Another example is the significance of being dependent on the posterior distribution, e.g., in the May 2024 storm results.
The limitations of the Cantrall are noted very late in the paper (line 312?), after the extensive discussions that are likely to be unfamiliar to most readers. Seems to deflate the significance of the work. If introduced earlier, could you compare the present results with the previous Cantrall Matsuo results and include some discussion of the role of Poisson statistics in the differences? That could clarify the significance and possible limitations of each new fundamental assumption in your retrieval, Poisson statistics and Bayesian probability.