| 04 Feb 2026
TED: A global temperature-driven thermoelastic displacement dataset for GNSS reference stations (2000–2023)
Abstract. The nonlinear signals in global GNSS station height time series reflects both non-tidal mass loading (atmospheric, oceanic, and hydrological) and temperature-driven thermoelastic deformation (TED). However, a globally consistent and reproducible TED data product has long been lacking. Here we present a global dataset of vertical TED for ~15,000 GNSS stations spanning 2000–2023, generated using a full-spectrum, layered finite-element model. The model is driven by hourly ERA5 soil-temperature profiles and parameterized with depth-dependent thermophysical properties from the SoilGrids dataset, enabling consistent quantification of TED from semi-diurnal/diurnal variability through seasonal to interannual timescales. Compared with an identical homogeneous-medium benchmark, subsurface stratification typically changes annual amplitudes by ~0.3 mm and shifts the timing of the annual maximum by ~1 month, yielding regionally coherent and smoothly varying spatial patterns. At stations with independent site characterization, the site-constrained solutions agree closely with SoilGrids-based solutions, with annual-amplitude differences of 0.01–0.03 mm and annual-phase differences mostly within 1–3°. Sensitivity tests using ±10% perturbations in thermal expansion, thermal diffusivity, and Young’s modulus indicate that annual-cycle amplitude and phase are robust. Globally, annual TED amplitudes are typically 1–2 mm, exceed 2–3 mm at some stations, and reach peak-to-peak values up to ~5 mm, with the largest signals concentrated in arid inland and continental climate regions. When TED corrections are applied together with non-tidal mass-loading corrections, the residual vertical dispersion decreases at most stations, with vertical scatter reduced by up to ~70 % at selected sites. The dataset is publicly available for direct use in GNSS coordinate time series correction and related geophysical applications: https://doi.org/10.5281/zenodo.18256342 (Lu et al., 2026).
The authors present a unique and important new dataset of Earth thermoelastic vertical displacement at 15000 GPS stations globally. This is an important source of GPS signal, especially at annual and semi-annual periods, and yet there is no operational or even non-operational widely available product for users to apply to GPS bedrock time series in order to reduce noise and signal. The methods look solid and robust in the main. The work builds on previous work published with some methodological advances. The dataset and quality control is well described. I expect this will be a widely used dataset, although note there is no statement on if the dataset will be kept up to date - something that will terminate its usefulness as GPS time series get longer. Likewise, the decision to commence in 2000 may cut off the greatest value. During the sparsely observed (by GPS) 1990-2000 period the effects of signals like this will be even greater in some studies due to asymmetry of the global netowrk. it also leaves users wondering what to do with older data.
I have three major concerns and some other suggestions and points.
First, as with all previous studies of global thermoelastic deformation, the authors mishandle areas of the planet that are permanently and seasonally ice- or snow-covered. Take Antarctica for example. The permanent ice cover there insulates the sub-ice region from experiencing any annual thermal effects. This presumably affects the deformation of sites located next to the ice sheet or on rock outcrops through the ice sheet. This will include Greenland, and the many small glacier regions globally. As such, I suspect the modelling is unreliable in these regions and should be removed from the dataset until the model is revised. To investigate this, I looked at two Antarctic sites CRDI and MAW1, which are adjacent to the Antarctic Ice Sheet, on small (~100x100m outcropping bedrock). The modelled series (see in the PDF) show significant annual signal and, in the case of CRDI, an apparent offset in 2010. My initial reaction is that these are likely not robust signals. However, maybe the thermal effect is of such small scale that even 100mx100m outcrops are enough to experience these thermal deformations (although presumably the very cold ice to the side of the sites also regulates the bedrock temperature considerably). I suspect the CRDI offset is not caught by the QC as there are few sites in Antarctica. But I also presume this is driven by an ERA5 temperature artefact. Also, there does not appear to be any data in the SoilsGrid paper under the permanent ice, so it is not clear how these regions are modelled anyhow.
Seasonal snow cover is more complex. This would be available in ERA5 I guess, in addition to temperature. Again, snow will insulate the soil/bedrock from air temperatures.
Second, I was not sure how ocean and lake areas are considered and what resolution any mask has. There are many coastal GPS sites and presumably this will matter.
Third, the data itself has no version control. I would expect there will be revisions and hence the dataset should be versioned. The data instructions are not clear that the trend component is not to be trusted.
Finally, it is a shame that the authors only released the vertical components. It would have been interesting to see the horizontals. Also, it would be useful in some cases to consider subdaily corrections for thermal expansion, and hence, the 6h series would have been useful, not just the daily ones. Maybe that will be a focus of future work, including validating the subdaily signals. Given that they are discussed here, it would be appropriate to include a map of subdaily amplitudes and phases, although I guess these are also seasonally modulated.
Minor comments
L15 I am not sure the current TED is reproducible. That would require code and workflows. I think you can say comprehensive.
L24 add how many stations had independent site characterisations
L32 please express what % of stations not just vague 'most'. Here and later, the authors merge the effect of TED into the combined effect with loading products. The authors should stick to just the TED effect here in the abstract. it is no more than +-10% at most sites. That is ok.
L49 obscure *other* subtle
L66 this is an important point. you could say a little more. there is no CM movement in this case, even if there is CF and CE movement.
L69 This tidal aliasing type effect could reference Penna and Stewart 2003 GRL as an e.g.
L103 this is where I would like to see versioning
L114 in this section it would be good to say what is not modelled. Buildings and monuments above ground, such as pillars. These may cause significant effects, and the authors could cite such works.
L149 gives the horizontal resolution of ERA5 forcing
L189 give the horizontal resolution of the FEM
L230-233 I didn't understand this sufficiently well to be able to reproduce it. Why not just take daily averages?
Results. consider adding a map of the trends. I think more is required in terms of discussing hte correlation with ERA5 trends or where else trends are coming from. A map of trends of the two (forcing and response) would be helpful to know if these may be real or a modelling artefact of kinds.
L367 this paragraph, please explicitly cite the panels of Fig 6 as relevant
Fig 6 caption. explain all panels explicitly
L388 'weak' downplays it without showing us the trends. Delete weak and let the reader decide that. change long-term to trend-like.
L437 I did not see Neff defined.
L438 I think a new subheader is appropriate here.
Section 3,3 As also noted for the abstract, the merging of the TED product with surface loading products, some with much larger importance, is not satisfactory. Please commence with the TED effect on WRMS. You could reasonabl remove first the other signals from the series.
Figure 14 labels the y-axis as %. Note the different colour scale for NTAL and HYDL
L646 new para at 'in practical'. Give TED only results not the merged results with NTAL etc.
L657 add also above-ground pillars.
L662 new paragraph
L668 new paragraph
Matt King, March 6 2026