| 08 Jan 2026
Fiber-Optic Distributed Temperature Sensing to quantify turbulence over space and time: A feasibility study
Abstract. Turbulence is essential for land atmosphere interactions; however, it is difficult to quantify due to its statistical and three dimensional nature. Typically, turbulence is determined using time series data to obtain turbulent data over a length scale (through Taylor's hypothesis). Ideally, turbulence is measured directly over multiple spatial dimensions as well as time, at high frequency. Currently turbulence measurements are limited to either time series (e.g., sonic anemometers) or integrated spatial measurements (e.g., scintillometers). However, direct spatiotemporal measurements of turbulence are lacking. In this study we aim to quantify turbulence over both time and space using fiber-optic distributed temperature sensing (DTS) using the structure parameter of temperature CT2. We conducted an experiment in the northeast of Spain in July 2021, where we measured temperature over a 70 m horizontal extent at a height of 2 m using a thin 0.5 mm fiber optic cable. The DTS experiment had a response time of 1.3 s and a response length of 0.35 m. We determined CT2 both spatially and temporally, through its definition as well as through the temperature turbulent spectrum, resulting in 4 results for CT2 from the DTS for each 30 minutes. Several (spectral) correction steps were applied to compensate for limited response rates, spatial averaging and noise. The CT2 values were compared with reference values from a sonic anemometer and a pair of scintillometers. For wind regimes with crosswind lower than 1.9 ms-1 and mean absolute wind speed higher than 1.5 ms-1, a correlation of R between 0.86 and 0.92 was found. The spectral DTS underestimates by a factor 3-4 in comparison to the sonic and by a factor 6 for the scintillometer. Similar results are found for the definition method and include a persistent offset of 0.04 for CT2. Hence, DTS correlates well with conventional reference instruments within the current limitations of DTS and it provides a direct and independent spatial measurement of turbulence. This opens the door to the use of DTS as a relative and spatial turbulence instrument to be used alongside an absolute reference instrument. The used setup and methodology can be scaled up to enable direct spatial measurements of turbulence at the km scale while keeping a spatial resolution in the order of meters.
This manuscript evaluates DTS derived temperature structure functions relative to baseline observations from sonic anemometers and a scintillometer. The authors present four ways of calculating the structure function which are equivalent when the assumption of ergodicity is valid and for the inertial scales: one spatially-explicit, one temporal using ergodicity, and two using spectra along space and time dimensions. The methods are evaluated over a flat experimental site using a harp of DTS observations along a 70 m transect. The authors find that the DTS-derived structure functions are biased relative to the baselines, but evaluates well enough to be used as a sensor for small-scale turbulence. The methods are robust and well-presented and I am happy to see someone attempting to get relevant turbulent quantities out of DTS data. The approach is interesting!
However, it is not well justified why we care to investigate such small-scale turbulence using a device like DTS, and thus it is not clear that deriving the temperature structure function is a useful step. One of the major benefits of DTS is that we are not limited by temporal sparsity (e.g., LIDARs) or spatial sparsity (e.g. point observations) all at a relatively high spatiotemporal resolution. Thus, we do not need to invoke Taylor’s Hypothesis. Structure functions, and similar statistics, are what I will refer to as a “uni-scale” approaches: they collapse higher-dimensional and multi-scale information. Uni-scale approaches aggregate over scales and ignore the simultaneous information in space and time. This collapsing of dimensions is an unfortunate necessity when we have sparse observations but not for the highly multi-scale information from DTS.
This is not to say that deriving the structure function is not without value, but in my humble opinion we should not seek to cram DTS observations into the uni-scale approach necessary for traditional statistics and theory and instead embrace the multi-scale nature of the data we get from DTS. The authors thus need to address two issues. (1) What is the value and meaning of a baseline that is only valid when classical assumptions are met? (2) What is the value and meaning of uni-scale methodologies for high-dimensional data?
Choice of baseline:
The citation the authors use of Cheng et al., 2017 explicitly uses DTS to question the validity of Taylor’s hypothesis in the inertial subrange and thus undermines the choice of baseline. At larger spatiotemporal scales the data (e.g., Figure 3) clearly show that Taylor’s hypothesis would not be valid for the entire period, even if it is valid for the sub-period. Thus, what is the value of the baseline evaluations that invoke Taylor’s hypothesis? I encourage the authors to consider the possible drawbacks from invoking a questionably valid hypothesis as the baseline.
The authors need to better motivate what additional value the evaluation of the structure function offers over the existing evaluations they mention. Most of the issues in the error of the structure function seem to be regarding the smallest resolvable scales and under-sampling, all of which were already known. What makes the structure function evaluation distinct and necessary?
Imposing uni-scale assumptions:
I question the value of deriving a measure of small-scale turbulence in a spatially-explicit fashion that is only valid in the limit of existing theory. We, as a field, like to focus strongly on representing the smallest scale turbulent fluctuations because that is where our assumptions are most valid. I argue that the novel value of DTS is that it gives us information that are missed by traditional observational platforms, explicitly at the scales excluded in Figure 9, without the need to invoke questionable assumptions. The major, open questions in turbulence are related to multi-scale interactions (Jimenez 2018, Stiperski et al., 2025), in particular at larger scales at which similarity theory is less valid. These scales are uniquely observable with DTS.
I suggest the authors examine approaches like from Zeeman 2021 in which a method that is not uni-scale is presented. The results from that study also place a limit on the smaller scale eddies that are resolvable but then push into the rich information contained in DTS that is missing in something like a sonic anemometer.
The existing DTS studies largely evaluate DTS observations at a point or over very short spatial distances. This is an fantastically interesting gap in the literature that could be filled by considering larger separation distances! If Taylor’s hypothesis is not valid at certain wind speeds and you have a definition of turbulence intensity that does not need to invoke it and you have continuously varying separation distances, you can explore something that could not be measured before!
In essence, I challenge the authors to transform their paper from a simple methodological evaluation that invokes questionable assumptions to one that challenges the limitations of traditional approaches. The disagreement between the structure function from the traditional observation platforms are potentially the most interesting aspects of this study and one which could help transform the use of DTS.
Technical Issues:
Section 5.4: I think every point mentioned has already been discussed in other manuscripts and thus does not bear repeating here. I know it is frustrating that we all seem to rediscover that same issues with each DTS experiment.
References
Stiperski, I. et al. Open questions in atmospheric turbulence: A synthesis from the centenary workshop “100 years of turbulence: Innsbruck 1922 -2022”. Journal of the European Meteorological Society 3, 100022 (2025).
Jiménez, J. Coherent structures in wall-bounded turbulence. Journal of Fluid Mechanics 842, P1 (2018).
Zeeman, M. Use of thermal signal for the investigation of near-surface turbulence. Atmospheric Measurement Techniques 14, 7475–7493 (2021).