Impacts of temporal resolution and timing of streambed temperature measurements on heat tracing of vertical flux

Paper No. H11D-1228

INTRODUCTION• 1D heat transport modeling can be used to obtain accurate, continuous

measurements of flux across the streambed interface over time. • Long-term deployment of temperature sensors, particularly in remote

locations, may be used to monitor streambed flux continuously over extended periods of time.

• Data loggers are limited in capacity for storage, so users must weigh the temporal resolution of their recorded temperature time series with the length of deployment possible.

• Here, impact of temporal resolution of temperature time series, as well as the timing of temperature measurements, on estimates of vertical flux was explored using results from controlled laboratory experiments.

METHODS• Column experiments1 were used to generate 1D flow of water and heat

through saturated sand with a sinusoidal temperature oscillation at the upstream boundary (Fig 1).

• Measured flux rates were compared to modeled flux rates derived using the VFLUX2 computer model and the amplitude ratio between filtered temperature records from two depths in the column.

• 1-minute temperature time series from the column experiments were resampled at increasingly coarse temporal resolutions (e.g. every 5 min, 10 min, 15 min, etc) and from different starting minutes (e.g. minute 1, 2, 3, etc).

• Resampled time series were used to derive flux to assess how temporal resolution and timing impact modeled flux rates.

References Cited1 Lautz, LK. 2012. Observing temporal patterns of vertical flux through streambed sediments using time-series analysis of temperature records. Journal of Hydrology, 464-465:199-215, doi:10.1016/j.jhydrol.2012.07.006.2 Gordon, RP, LK Lautz, MA Briggs, JM McKenzie. 2012. Automated calculation of vertical pore-water flux from field temperature time series using the VFLUX method and computer program. Journal of Hydrology, 420-421:142-158.

RESULTS• At the original, very high temporal resolution (360 observations per temperature

oscillation), the normalized root mean square error (nRMSE) was between 10 and 14%, depending on the starting minute (Fig 1).

• At very low temporal resolution (e.g. 3.43 observations per temperature oscillation, Fig 2A), reasonably accurate estimates of vertical flux are possible using 1D heat transport modeling, with a nRMSE of ~14-22% for the experiment.

• At low temporal resolution (e.g. 4 samples per cycle or less), the timing of observations can be critically important (Fig 2B), as variable start times will have varied success capturing the daily maximum and minimum temperatures (Fig 3).

• Temperature observations at time intervals corresponding to the signal harmonics, such as every 6 hrs in a 24 hr cycle, result in strong fluctuations in model error, depending on the timing of the observations (Fig 4).

• Not surprisingly, the accuracy of flux estimates derived using the heat transport model increases with the temporal resolution of the observed temperature time series (Fig 4).

Laura K. Lautz, Earth Sciences, Syracuse University, Syracuse, NY 13244, lklautz@syr.edu

CONCLUSIONS• For long-term deployment of temperature data loggers to make

continuous measurements of streambed flux, users should select data logger time steps that do not correspond to signal harmonics, such that they are sampling different points on the sinusoidal curve each day.

• Under such conditions, even temperature time series with relatively coarse temporal resolution can yield accurate information about streambed flux over time.

Fig 1: Column experiments were used to generate variable vertical flux rates over time from a water reservoir with an oscillating temperature. Temperature was observed every 1 minute at multiple column depths and then used to derive flux rates. Modeled and measured flux rates were nearly equivalent.

Fig 2: (A) Results using a sampling interval of 105 minutes, or 3.43 observations per cycle, which is analogous to a sampling interval of 7 hrs for a 24-hr temperature oscillation. This interval samples different parts of the sinusoidal oscillation each day, allowing filtering methods to correctly isolate the true periodic signal. (B) Results using a sampling interval of 90 minutes, or 4 observations per cycle, which is analogous to a sampling interval of 6 hrs for a 24-hr temperature oscillation. This interval is a harmonic of the signal of interest and samples the same part of the sinusoidal oscillation each day. For this reason, filtering methods fail to capture the true periodic signal, depending on the points in the signal that are sampled (see Fig 3).

Fig 3: (center) For sampling rates that correspond to harmonics of the signal of interest (e.g. every 6 hrs of a 24-hr signal), the start time of the time series strongly influences the accuracy of the modeled flux rates over time (see also Fig 2B). The start time controls which points on the curve are recorded in the raw data. (left) Some start times result in the approximate times of the maximum and minimum daily temperatures being sampled. (right) Other start times cause the raw data to miss the timing of the maximum and minimum temperature throughout the time series.

A B

B CA

Fig 4: A surface showing the n-RMSE of model flux rates as a function of the sampling interval and the start time of the temperature time series used for the modeling. At sampling intervals shorter than 60 min, or more than 6 samples per cycle, nRMSE values are less than 20%. Very coarse sampling intervals can yield accurate flux time series if they do not correspond to a harmonic of the periodic signal of interest (harmonics are indicated with horizontal black lines).

RESULTS (con’t)