| 31 Jul 2026
Spectral analysis of GNSS zenith wet delay and microwave radiometer precipitable water during FESSTVaL Lindenberg 2021: a multi-scale observational test of horizontal heterogeneity sensitivity
Abstract. Every Global Navigation Satellite System (GNSS) station estimates a zenith wet delay (ZWD), a direct measure of the water vapour integrated above it. The ZWD is a standard product of GNSS meteorology, yet its small-scale temporal structure is conventionally treated as noise. We ask whether the temporal spectrum of the ZWD reveals horizontal water vapour heterogeneity near the boundary layer top that a vertical sounding cannot see. Using FESSTVaL observations at Lindenberg in summer 2021, we compare the GNSS ZWD with the precipitable water from a microwave radiometer over 28 days. Both are described by a Matérn spectrum whose scale and amplitude are tracked on sliding windows. The radiometer scale follows the boundary layer height in calm conditions and shifts to a wind-driven, advective behaviour when the atmosphere becomes unstable, confirmed by tower turbulence. The GNSS scale stays stable across all conditions, because its oblique geometry ties it to horizontal structure at the boundary layer top, unchanged by the shifts in vertical stability. The strength of the GNSS signal grows with the horizontal heterogeneity measured independently at two scales (ρ = +0.433 and +0.525), while the vertical radiometer shows none and a scintillometer rules out a surface contribution. Accessible from any positioning solution, the GNSS scale measures horizontal coherence at the boundary layer top that is far more stable than the ERA5 boundary layer height (coefficient of variation 0.32 against 0.90) and persists through the night.
General Comments
The work assess the possibility to study the horizontal hetrogeneity in the atmosphere by using the short term variations in the atmospheric signal delay caused by water vapour. They are estimated from a ground-based GNSS receiver station in Lindenberg, Germany. In total. there are 28 days in June-July 2021 with GNSS estimates which are supported by and compared to observations by microwave radiometers and several other instruments.
Although the temporal resolution of the ZWD estimates is 30 s, I assume that there are constraints in the estimation process (often used is a random walk model with a corresponding constraint specified as a standard deviation). I have no hands on experience from using PRIDE but from what I understand the atmospheric estimates are obtained in a similar way as in the GIPSYX software package, also using PPP. Adjacent values are not independent estimates. The model and the constraint are of fundamental importance and shall be motivated and presented (see, e.g. Young et al., 2024). Furthermore, because the constraints used in the GNSS processing have a significant impact on the resulting variability it is also necessary to determine how significant it is. This is especially true in this case because the variability is the fundamental observable in the whole study. A possible method is to carry out a number of GNSS processings using different constraints. Given that it is only one station and 28 days of observations this is a quick task. If the constraint used so far has a reasonable value, given the expected atmospheric variability at Lindenberg, it will make sense to make solutions using say half of this value and the double value. Thereafter, the main question is if and how much these three time series will affect the results in the rest of the manuscript.
Another general observation is that it is not clear how observations during rain are used, if they are used at all. The microwave radiometer produce more or less useless data during rain. This is not discussed, see below.
When the above question about the impact of constraints used in the GSS processing is resolved the manuscript would benefit from a discussion on the overall context for future applications using this type of analysis. For example, will it have a real-time application for forecasting. The IGS networks is mentioned but not the E-GVAP, run by EUMETNET, including several thousands of GNSS ground stations in Europe (see https://egvap.dmi.dk/).
Young, Z.M., Blewitt, G., and Kreemer, C.: Improved GPS tropospheric path delay estimation using variable
random walk process noise, J. Geod., 98:89, https://doi.org/10.1007/s00190-024-01898-3, 2024.
Specific comments
Lines (L) 2-3: The statement " ... yet its small-scale temporal structure is conventionally treated as noise." does not agree with my experiences from the GNSS meteorology community (although it may be true in the geodetic community. focusing on daily estimates of 3D positions). This text can be deleted in order not to upset readers that are eager to improve the true temporal resolution in GNSS meteorology.
L 70+: In addition to the general comment above more information about the GNSS observations and processing is needed. Are all four GNSS used? What is the elevation cutoff angle? It determines the diameter vs. height of the sensed cone-shaped volume of air. One expects that a higher cutoff angle will increase the variations in the time series of the estimated zenith wet delay. Although the zenith total delay product from IGS does not have the high temporal resolution it would be a quick task to compare it with your time series for validation? For the future it may be a good idea to present the estimates time series from GNSS both those from using different constraints and the official IGS product.
L 77: Here you may want a citation to support the statement.
L82: Why use the Bevis coefficients (which were derived from stations in North America) when the RPG instrument provides the zenith wet delay directly? Most likely the RPG has optimized these algorithms for the Lindenberg site, depending on if it was stated at the time of placing the order.
L 149: You write "... used to filter out windows with non-turbulent rain contamination in the GNSS PPP." I do not understand this. GNSS estimates are more or less insensitive to rain unless it is an extrem rain intensity. In the introduction you refer to GNSS as a technique that " ... deliver, in all weather ...". There is a need for clarification.
L173-175: My experience is that the MWR noise in general exceeds the noise in the estimates based on GNSS data. Of course that depends on the constraint used in the GNSS process (discussed above). In any case it will be informative to state the percentage of data when the MWR noise exceeds the GNSS noise.
Technical Corrections
General: The word "cadence" is often used. It reminds me of music but I assume that the meaning is "temporal resolution". If so, why not use this well established term?
L 10: Define \rho (later in the manuscript it seems to represent both density and correlation coefficient)
L 84: Define all the symbols in Eq. (1)
L 114: "data sets" change to "datasets"
L148: Do not begin a sentence with "18"
Figure 5: Labels are not in the correct positions
Figure 6: The volume of air sensed by the MWR seems to be presented as a cylinder indicating that this part of the atmosphere is in the near field of the antenna. I think the half-power beam width at K-band of these RPG radiometers are around 4° and the aperture is around 20 cm, meaning that the near field ends at around 6 m. So the sensed air volume is a cone with a half-power diameter of some 140 m at the height of 2 km. It may not have an influence on your analyses but it would be nice with a figure that reflects reality. Additionally, also the elevation cutoff angle used in the GNSS processing could be included in the figure.
Reference list: The AMT guidelines are to use the full journal name when the abbreviation is not known. In this case I think most of the journals are found in the list published by "Web of Science: https://wos-help.webofscience.com/WOKRS535R111/help/WOS/A_abrvjt.html