Abstract
Distributed temperature sensing (DTS) systems can be used to estimate the temperature along optic fibers of several kilometers at a sub-meter interval. DTS systems function by shooting laser pulses through a fiber and measuring its backscatter intensity at two distinct wavelengths in the Raman spectrum. The scattering-loss coefficients for these wavelengths are temperature-dependent, so that the temperature along the fiber can be estimated using calibration to fiber sections with a known temperature. A new calibration approach is developed that allows for an estimate of the uncertainty of the estimated temperature, which varies along the fiber and with time. The uncertainty is a result of the noise from the detectors and the uncertainty in the calibrated parameters that relate the backscatter intensity to temperature. Estimation of the confidence interval of the temperature requires an estimate of the distribution of the noise from the detectors and an estimate of the multi-variate distribution of the parameters. Both distributions are propagated with Monte Carlo sampling to approximate the probability density function of the estimated temperature, which is different at each point along the fiber and varies over time. Various summarizing statistics are computed from the approximate probability density function, such as the confidence intervals and the standard uncertainty (the estimated standard deviation) of the estimated temperature. An example is presented to demonstrate the approach and to assess the reasonableness of the estimated confidence intervals. The approach is implemented in the open-source Python package “dtscalibration”.
Highlights
Temperatures can be measured with distributed temperature sensing (DTS) along optical fibers that may extend to several kilometers with a sub-meter resolution [1,2]
The probability density functions are propagated through the model using a Monte Carlo sampling procedure following the steps from JCGM [26,27]. This procedure results in an approximation of the probability density function for the estimated temperature, which is different at each location and varies over time
The uncertainty in the estimated temperature is caused by the noise from the Stokes and anti-Stokes detectors, and the uncertainty in the calibrated parameters that relate the Stokes and anti-Stokes intensity measurements to temperature
Summary
Temperatures can be measured with distributed temperature sensing (DTS) along optical fibers that may extend to several kilometers with a sub-meter resolution [1,2]. The application of DTS is of great value to characterize thermal dynamics at a scale that corresponds to, for example, many geophysical processes. Heat tracer tests with DTS have been used to estimate wind speed [3,4], evaporation [5,6], soil moisture [7], groundwater-surface water interaction [1,8], and groundwater flow [9,10]. The specification sheets of DTS measurement systems list the uncertainty in the temperature estimated under ideal conditions. The uncertainty in the temperature estimate varies along the fiber, is different for each setup, and is temperature-dependent. The uncertainty in the temperature estimate should be estimated separately for every DTS measurement
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