In recent years, the spatial resolution of fiber-optic distributed
temperature sensing (DTS) has been enhanced in various studies by helically
coiling the fiber around a support structure. While solid polyvinyl chloride
tubes are an appropriate support structure under water, they can produce
considerable errors in aerial deployments due to the radiative heating or
cooling. We used meshed reinforcing fabric as a novel support structure to
measure high-resolution vertical temperature profiles with a height of
several meters above a meadow and
within and above a small lake. This study aimed at quantifying the radiation
error for the coiled DTS system and the contribution caused by the novel
support structure via heat conduction. A quantitative and comprehensive
energy balance model is proposed and tested, which includes the shortwave
radiative, longwave radiative, convective, and conductive heat transfers and
allows for modeling fiber temperatures as well as quantifying the radiation
error. The sensitivity of the energy balance model to the conduction error
caused by the reinforcing fabric is discussed in terms of its albedo,
emissivity, and thermal conductivity. Modeled radiation errors amounted to
Distributed temperature sensing (DTS) allows for sampling temperatures at
thousands of points along a fiber-optic cable with one single instrument.
Over the past 10 years, Raman scattering DTS has been used in hydrology to
monitor water temperatures over both long and short distances
Studying small-scale processes may require a higher spatial resolution than
can be achieved with a straightly aligned fiber-optic cable, which is
limited by the along-fiber resolution of the DTS instrument to several tens
of centimeters. To overcome this issue, several studies have used a support
structure for helically coiling the fiber-optic cable and thus enhancing the
spatial resolution up to the millimeter scale in one dimension
In our application, precise vertical temperature profiles with a
height of several meters in the near-surface air layer
were desired. For this purpose, the coiled-fiber-optic approach was deployed.
Previous studies have pointed out two important issues for this approach.
Firstly, coiling the fiber cable around a support structure with a very small
diameter (
The radiation error for a coiled DTS system includes both the direct effect
of radiative transfer to and off the fiber cable and the indirect effect of
the support structure via heat conduction (here referred to as conduction
error). The direct effect of radiation also applies to a straightly aligned
fiber cable in open air or water. For fiber cables under water, this effect
is only relevant at shallow depths in clear and low-velocity water during
peak solar radiation
The conduction error results from differences in the radiative energy
exchange of the fiber-optic cable and the support structure. For temperature
profiles under water or at the water–air interface, polyvinyl chloride (PVC)
tubes have been used as a support structure.
To date, a comprehensive and quantitative analysis of the conduction error
for coiled DTS systems is lacking. For a perforated PVC tube,
In order to avoid the large conduction errors found for a solid PVC tube,
Schematic setup of the meadow column
The overarching objective of our study was to quantify the radiation error for this novel setup of the aerial DTS deployment by means of a comprehensive and quantitative energy balance model. The three specific objectives were to (1) quantify and if possible correct for the radiation error of the aerial coiled DTS deployment by means of a full energy balance model validated with measurements, (2) estimate artifacts caused by the novel support structure via conduction, and (3) visualize the utility of coiled-fiber deployments for observing high-resolution air temperature profiles near the surface ground.
The DTS technique allows simultaneous measurements at thousands of points in
space by injecting laser pulses into a fiber-optic cable. Raman scattering
systems measure the intensities of non-elastic backscatter having slightly
lower (Stokes signal) or higher (anti-Stokes signal) frequencies than the
original laser light
In our experiment the instrument-specific along-fiber averaging was limited
to 1
We used a tightly buffered and bend-insensitive fiber cable with an outer
diameter of 0.9
The reinforcing fabric was formed into a column by hot glueing with an
approximately 12
Laboratory experiment:
The high-resolution profile measurements were part of the Cold Air Drainage
Experiment (CADEX), conducted from 13 March 2015 to 29 April 2015 in the
Ecological Botanical Gardens of the University of Bayreuth, Bayreuth, Germany
(44
The meadow column was located on a gentle slope within a few meters of a
long-term weather and climate station, which provided the reference
observations for direct and total incoming shortwave irradiance (pyranometer
SDE, type 9.1, UTK – EcoSens GmbH, Zeitz, ST, Germany), incoming and
outgoing longwave irradiance (pyrgeometer CG2, Kipp & Zonen B.V., Delft,
ZH, the Netherlands), dry bulb temperature at 2
The lake column was horizontally separated from the meadow column by
87
The fiber-optic cable was attached to the DTS instrument in a double-ended
configuration, but the instrument was operated in single-ended mode; i.e.,
measurements of the two directions were stored separately. The along-fiber
averaging was 1
Artifacts in the measured temperature profiles:
Two coiled-fiber sections of approximately 50
The temperature output of the DTS instrument was calibrated based on two
thermally insulated baths with heated and ice-cooled water. Approximately
50
The post-processing also included the transformation of the measurement
positions from length along the fiber into height above surface. For this
purpose, cold packs were attached to individual sections of the fiber at
known heights, while the heights in between were inferred by means of the
column proportions. The computed heights were cross-checked against the
counted number of fiber coils. This cross-check indicated an accuracy of the
computed heights of approximately
The acrylic glass rings of the support structure caused obvious artifacts due
to solar heating for daytime and radiative cooling at night, especially at
lower heights and with weak winds (Fig.
As the signal-to-noise ratio decreases with length along the fiber
For the averaged temperature profiles, some random scatter remained. This
uncertainty can be quantified as the spatial standard deviation of DTS
measurements in the calibration baths with a mean error of 0.12
Radiation errors for the coiled DTS system were quantified by modeling the
fiber temperature via an energy balance approach. The model included the
contribution of heat conduction from the support structure to the radiation
error and can be applied to a wide range of meteorologic conditions or
material properties. Since the DTS measurements were averaged over one
fiber-optic winding, the energy balance model was proposed for the same
spatial extent. The sum
The energy flux from conduction
Since
We adopted the temporal resolution of the input data from the long-term
weather station of 10
Combining Eqs. (
Properties of dry air at atmospheric pressure
The convective heat transfer coefficient
Material properties used in the energy balance model. For brevity, a
fiber cable coil and a reinforcing fabric skein are called fiber and fabric,
respectively. Numbers in brackets express the range used for sensitivity
analysis.
Sources (accessed on 3 July 2016):
Material properties used to model the fiber's energy balance are listed in
Table
The energy balance model can be used to correct for the radiation error of
the coiled DTS system even if reference air temperatures have not been measured.
In this case, the DTS temperature
Validation of modeled temperatures by comparing with measured
temperatures at 2 and 2.13
Prior to analyzing the radiation error, the energy balance model was
validated by comparing its estimates with the temperature measurements in the
5-day period from 6 to 10 April 2015. Daily maximum incoming shortwave
irradiance ranged from 677 to 839 J s
The RMSE for the modeled and measured temperatures
was insensitive to the choice of including or excluding the conduction term
(Table
Comparison of measured and modeled temperatures (10 min averages)
from 8 to 10 April 2015 (mostly clear sky) at 2.00 and 2.13
Correcting DTS temperatures for the radiation error reduced the RMSE between
DTS and reference temperature above the meadow by 41 % from 0.71 to
0.42
The temporal course of temperatures, radiation error, and uncertainties of
selected model versions from 8 to 10 April are presented in Fig.
The modeled radiation error ranged between
Radiation error
Sensitivity of the conduction error
Example of DTS temperature profiles:
The sensitivity of the conduction error to differences in albedo and
emissivity between fiber cable and reinforcing fabric was investigated for
2
To illustrate the utility of the coiled-fiber deployment for observing
high-resolution vertical temperature profiles close to the ground, we
selected a night with clear skies (Fig.
In this study, we quantified the radiation error for a helically coiled fiber-optic cable around a novel support structure observed using distributed temperature sensing by proposing a comprehensive energy balance model, which includes terms for shortwave radiative, longwave radiative, convective, and conductive heat transfers. With regard to the three objectives defined in the introduction, we arrive at the following conclusions.
In the investigated period, the modeled radiation error ranged from
The reinforcing fabric is an excellent support structure for aerial DTS deployments since its artifacts on the observed fiber temperature via conduction are very small or negligible. The model results suggest that the conduction term can be neglected in the fiber's energy balance as long as the thermal conductivity of the material is small and the difference in albedos between the fiber and the fabric is negligible. In the worst possible case, the conduction error increases to 13 % proportional to the total radiation error. The structures supporting the reinforcing fabric, which in our case was done via acrylic glass rings spaced at 1 m intervals, caused significant conduction errors where the ring touched the fabric of up to 2.5 K. Therefore the number and dimensions of these rings should be reduced to a minimum.
For a clear night with weak winds, the measured temperature profiles showed
sharp vertical gradients, varied strongly in time, and revealed vertical
temperature differences of up to
Data used in the analysis will be provided on request. Please contact the authors.
The authors declare that they have no conflict of interest.
This research was partially supported by the US National Science Foundation CAREER award AGS 0955444. The fiber-optic instrument was provided by the Center for Transformative Environmental Monitoring Programs (CTEMPS), funded by the US National Science Foundation, award EAR 0930061. We thank John Selker for technical support and Wolfgang Babel and Johannes Olesch for technical assistance in the field experiment. We also thank Gregor Aas, who placed the measurement site in the Ecological Botanical Gardens at our disposal. Edited by: S. Malinowski Reviewed by: N. van de Giesen and two anonymous referees