U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2020–5005

Prepared in cooperation with the Lac du Flambeau Band of Lake Superior Chippewa Indians

A Distributed Temperature Sensing Investigation 

of Groundwater Discharge to Haskell Lake, 

Lac du Flambeau Reservation, Wisconsin, 

July 27–August 1, 2016
Cover. Photograph showing Haskell Lake looking south from the north end of the distributed 

temperature sensing survey area. Photograph by Andrew Leaf, U.S. Geological Survey.

Back cover Photograph showing the distributed temperature sensing instrument housing. 

Photograph by Andrew Leaf, U.S. Geological Survey.
A Distributed Temperature Sensing 

Investigation of Groundwater Discharge 

to Haskell Lake, Lac du Flambeau 

Reservation, Wisconsin, 

July 27–August 1, 2016

By Andrew T. Leaf

Prepared in cooperation with the Lac du Flambeau Band of Lake Superior 

Chippewa Indians

Scientific Investigations Report 2020–5005

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2020

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Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

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Suggested citation:

Leaf, A.T., 2020, A distributed temperature sensing investigation of groundwater discharge to Haskell Lake, Lac du 

Flambeau Reservation, Wisconsin, July 27–August 1, 2016: U.S. Geological Survey Scientific Investigations Report 

2020–5005, 17 p., https://doi.org/10.3133/sir20205005.

Associated data release for this publication: 

Leaf, A.T., 2020, Distributed lakebed temperature data, Haskell Lake, Lac du Flambeau Reservation, Wisconsin, July 

27–August 1, 2016: U.S. Geological Survey data release, https://doi. org/10.5066/P9X2OHNX.

ISSN 2328-0328 (online)
iii

Acknowledgments

Funding was provided by the Lac du Flambeau Band of the Lake Superior Chippewa Indians, 

through a Water Resources grant from the U.S. Bureau of Indian Affairs and from U.S. Geological Survey Cooperative Water Program funds.

The author acknowledges the following external assistance: Kristen Hanson (Environmental 

Response Program Coordinator, Lac du Flambeau Band of Lake Superior Chippewa Indians) for 

being the local project coordinator, Justin Brown (Student Volunteer, University of WisconsinMadison) for field support, Professor Jean Bahr (University of Wisconsin-Madison Department 

of Geoscience) for providing the fiber optic cable, and David J. Hart (Wisconsin Geological and 

Natural History Survey) for doing a technical review.

The author also acknowledges the following internal assistance from U.S. Geological Survey 

colleagues: Brent Olson, Dan Baumann, and Paul Reneau for field support; the Office of Groundwater, Branch of Geophysics for providing the oryx distributed temperature sensing unit; Martin 

A. Briggs for doing a technical review; Brent Trickett and Valerie Dressler for technical editing; 

Julia Prokopec for the groundwater specialist review; and Janet M. Carter (Bureau Approving 

Official) for the Bureau-level review and approval. 

v

Contents

Acknowledgements......................................................................................................................................iii

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Distributed Temperature Sensing Principles ............................................................................................3

Field Methods.................................................................................................................................................3

Data Analysis..................................................................................................................................................5

Instrument Noise...................................................................................................................................5

Temperature Calibration......................................................................................................................6

Cable Location.......................................................................................................................................7

Distribution of Groundwater Discharge.....................................................................................................8

Summary and Conclusions.........................................................................................................................16

References Cited..........................................................................................................................................16

Figures

1. Map showing Haskell Lake location..........................................................................................2

2. Photograph showing cable retrieval on August 3, 2016.........................................................4

3. Graphs showing comparison of temperatures measured in the calibration baths...........5

4. Graphs showing spurious peaks in the distributed temperature sensing data .................7

5. Graphs showing error in calibrated distributed temperature sensing temperatures 

in the calibration baths ................................................................................................................8

6. Map showing interpreted cable location .................................................................................9

7. Graph showing the time-distance image of the complete distributed temperature 

sensing dataset...........................................................................................................................10

8. Graph showing air temperatures recorded by the section of fiber between the 

ice bath and lake compared to temperatures recorded at Lakeland Airport ..................11

9. Graphs showing daily temperature range .............................................................................12

10. Graphs showing daily standard deviation in temperatures recorded by the 

the distributed temperature sensing fiber..............................................................................13

11. Graphs showing daily minimum temperatures recorded by the distributed 

temperature sensing ..................................................................................................................14

12. Map showing average temperatures between 6 and 7 a.m................................................15
vi

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2)

acre 0.404685 hectare (ha)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows: 

°F = (1.8 × °C) + 32.

Datum

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Abbreviations

DGPS differential global positioning system

DTS distributed temperature sensing

GIS geographic information system

RMSE root mean squared error

RTD resistance temperature detector

USGS U.S. Geological Survey
A Distributed Temperature Sensing Investigation of 

Groundwater Discharge to Haskell Lake, Lac du Flambeau 

Reservation, Wisconsin, July 27–August 1, 2016

By Andrew T. Leaf

Abstract

Haskell Lake is a shallow, 89-acre drainage lake in the 

headwaters of the Squirrel River, on the Lac du Flambeau 

Reservation in northern Wisconsin. Historically, this lake was 

an important producer of wild rice for the Lac du Flambeau 

Band of Lake Superior Chippewa Indians (LDF Tribe); but, 

beginning in the late 1970s, the rice began to diminish and 

by the late 1990s, the lake no longer had harvestable stands. 

Restoring wild rice to Haskell Lake is a long-term priority for 

the LDF Tribe. A first step towards that effort is the cleanup 

of a petroleum-contamination plume in the shallow aquifer 

upgradient of the northern end of the lake. Knowledge of the 

downgradient extent of the plume and the locations where 

contaminated water is discharging to the lake is needed to 

inform cleanup efforts.

A cooperative study between the U.S. Geological Survey 

and the LDF Tribe was initiated to characterize the distribution 

of groundwater discharge to Haskell Lake in the areas downgradient of the contamination plume. A fiber optic distributed 

temperature sensing system was used to monitor temperatures 

at the sediment-water interface for a 7-day period in July and 

August 2016. Challenges during the investigation included 

data storage and power supply limitations, maintenance of 

calibration baths, accurate location of the cable in space, 

cable placement in weeds and soft sediment, the confounding 

effects of solar radiation, and contamination of the data by 

multiple sources of instrument noise. The problem of instrument noise was overcome by solving the fiber optic distributed 

temperature sensing calibration equation for two parameters 

that describe temporal variation in the source laser and the 

photon detectors that observe the backscatter. Early morning 

temperatures, when the influence of solar radiation via direct 

warming of the sediment-water interface is minimized, were 

used to evaluate groundwater discharge, similar to other studies. The results indicate a persistent, horizontal variation in 

temperature of as much as 5.5 degrees Celsius across the study 

area, with cooler temperatures interpreted to indicate spatially 

discrete preferential groundwater discharge. Results of the 

study can be used to determine locations for collecting lakebed 

pore water samples to better define the extent of contamination 

discharging to the lake.

Introduction

Haskell Lake is an 89-acre drainage lake in the headwaters 

of the Squirrel River, on the Lac du Flambeau Reservation in 

northern Wisconsin (fig. 1). Historically, this lake was an important producer of wild rice for the Lac du Flambeau Band of 

Lake Superior Chippewa Indians (LDF Tribe); but, beginning in 

the late 1970s, the rice began to diminish and by the late 1990s, 

the lake no longer had harvestable stands. Restoring wild rice to 

Haskell Lake is a long-term priority for the LDF Tribe. A first 

step towards that effort is the cleanup of a petroleum-contamination plume in the shallow aquifer upgradient of the northern 

end of the lake. Knowledge of the downgradient extent of the 

plume and the locations where contaminated water is discharging to the lake is needed to inform cleanup efforts.

The surrounding area is characterized by irregular 

topography and a nascent drainage network that reflect the 

recent retreat of the Laurentide Ice sheet only 10,000 years 

ago. Numerous lakes and wetlands dot the land surface, filling 

kettle depressions left by the melt out of stagnant ice. Subsurface lithology consists of as much as 280 feet (ft) of glacial 

deposits; primarily outwash sands and gravels, with intermittent silt-rich debris flow sediments of supraglacial origin; and 

areally extensive but relatively thin till units that also contain 

appreciable silt (Attig, 1985). Haskell Lake occupies a kettle 

depression in collapsed glacial outwash sediments and probably some debris flow deposits (Leaf and Haserodt, 2020). 

The substrate beneath Haskell Lake is primarily a dark brown, 

diatomaceous sapropel (about 40–60 percent organic matter) 

that has a high-water content in the upper 6 ft and ranges in 

thickness from absent near shore to more than 30 ft thick away 

from shore. The bottom interface of the sapropel with the 

underlying hard mineral sediments drops off steeply, making 
2 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

mad19-1901_fig01

Lakeland Airport/

Noble Lee 

Memorial Field

COUNTY HIGHWAY H

U.S. HIGHWAY 51

STATE HIGHWAY 70

COUNTY HWY D

STATE HIGHWAY 70

COUNTY 

HIGHWAY F

STATE HIGHWAY 47

COUNTY HIGHWAY 47

HIGHWAY 47

STATE 

Manitowish Manitowish Waters

Lac du Flambeau

Woodruff

Minocqua

Hazelhurst

Lake Tomahawk

Little Trout 

Lake

Bear River

Allequash 

Lake Trout 

Lake

Sparkling

Lake

Fence 

Lake

Ike Walton 

Lake

White Sand 

Lake

Pokegama 

Lake

Flambeau 

Lake

Crawling 

Stone Lake

Squaw 

Lake

Buckskin 

Lake

Booth 

Lake Squirrel 

Lake

Shishebogama 

Lake

Kawaguesaga 

Lake

Minocqua 

Lake

Tomahawk 

Lake

Tower 

Creek Haskell

Lake

Tomahawk River

Squirrel River

Squirrel River Basin

Lac du Flambeau Reservation 

boundary

EXPLANATION

[DTS, distributed temperature sensing]

Rivers and lakes from WDNR, 2015, 1:24,000 

Major roads from U.S. Department of Commerce, 2014 

Cities modified from USGS, 2004 

Airports modified from Wisconsin Department 

of Transportation, 2015 

State boundaries from National Atlas 

of the United States, 2014, 1:1,000,000 

Reservation boundary from U.S. Department of Commerce 

and U.S. Census Bureau, 2017, 1:500,000 

Hillshade base map modified from USGS, 2013

0 2 4 KILOMETERS

0 2 4 MILES

!

Study area

WISCONSIN

90°3' 90°0' 89°57' 89°54' 89°51' 89°48' 89°45' 89°42' 89°39' 89°36'

46°9'

46°6'

46°3'

46°0'

45°57'

45°54'

45°51'

45°48'

DTS 

survey site

Figure 1. Haskell Lake location (modified from Leaf and Haserodt, 2020).

wading generally infeasible more than a few feet away from 

shore (Leaf and Haserodt, 2020).

A key challenge in characterizing groundwater-lake 

interactions in glacial settings is that aquifer heterogeneity 

can produce spatially preferential discharge patterns that differ substantially from the exponential decay of seepage away 

from shore predicted for a homogenous aquifer (McBride and 

Pfannkuch, 1975). For example, Krabbenhoft and Anderson 

(1986) identified an offshore area of high seepage in a similar 

setting at nearby Trout Lake (fig. 1), which was caused by a 

subsurface lens of coarse-grained material intersecting the 

lake. In another heterogeneous glacial setting in Denmark, 
Field Methods 3

Sebok and others (2013) observed groundwater discharge 

originating from the opposite side of a lake, as well as large 

variations in groundwater seepage rate at scales of less than 

1 meter, and seasonal changes in discharge patterns driven by 

changes in head gradients.

In Haskell Lake, the locations and magnitude of 

groundwater discharge downgradient of the petroleumcontamination plume are of interest for locating pore water 

sampling to define the plume extent and contaminant flux 

to the lake. However, most available field techniques for 

characterizing groundwater discharge to surface water (for 

example, seepage meters and vertical temperature profilers) 

only observe a single point along the interface, making collection of data from many points prohibitively labor intensive (Rosenberry and others, 2008; appendix 6 in Leaf and 

Haserodt, 2020).

Fiber optic distributed temperature sensing (DTS) allows 

for the continuous observation of temperature at the meter 

scale along a fiber optic cable, at regular intervals through 

time. Temperatures near the sediment-water interface can be 

used to identify groundwater discharge to surface water when 

a thermal contrast exists between groundwater and surface 

water (Conant, 2004) or when discharging groundwater 

reduces daily variations in temperature (Lowry and others, 

2007). DTS has been used to study groundwater and surfacewater interactions for more than a decade; one of the earliest 

applications investigated groundwater discharge to nearby 

Allequash Creek in central Vilas County, Wisconsin (near 

Allequash Lake in fig. 1; Lowry and others, 2007).

A cooperative study between the U.S. Geological Survey 

(USGS) and the LDF Tribe was initiated to investigate the 

distribution of groundwater discharge to Haskell Lake in the 

areas downgradient of the petroleum-contamination plume. 

DTS was used to monitor temperatures at the sediment-water 

interface between July 27 and August 3, 2016, when the 

thermal contrast between the lake and groundwater was close 

to its annual maximum. This report documents the DTS study, 

including the field deployment, data processing methods, and 

key findings.

Distributed Temperature Sensing 

Principles

In DTS, a laser pulse is emitted down a fiber optic cable, 

and the backscattered light is monitored through time. Inelastic collisions between the emitted photons and crystalline 

structures in the fiber produce red-shifted (Stokes) and blueshifted (anti-Stokes) components in the backscatter; the ratio 

of the Stokes and anti-Stokes amplitudes varies as a function 

of temperature (Hausner and others, 2011). The temperature 

at a given point (z) and time (t) along the cable is determined 

by using an equation from van de Giesen and others (2012) 

as follows:

T z t

P z t

P z t

C t a z dz s

aS

z ( , )

ln( ,

, ) ( ) ( )

  

      





0

(1)

where

γ is hΩ/k;

h is Planck’s constant;

k is Boltzmann’s constant;

Ω is the frequency shift between the 

backscattered Stokes radiation and incident 

laser; s

aS

P

P is the Stokes/anti-Stokes ratio;

C is a dimensionless calibration parameter that 

accounts for the relative efficiencies of 

the Stokes and anti-Stokes measurements 

made by the instrument, which can be 

affected by operating conditions such as 

instrument temperature, humidity, and 

fluctuations in the power supply; and

∆α	 is the differential attenuation of the Stokes/

anti-Stokes backscatter along the cable.

Equation 1 indicates that to determine temperature, 

the differential attenuation and parameters C and γ must be 

accounted for. In theory the parameter Ω is constant for a 

given DTS laser system. However, in practice Ω has been 

known to be affected by instrument temperature and power 

supply (Hausner and others, 2011). The values of C and γ can 

be solved for using independent measurements of temperature 

at different points along the cable; the differential attenuation 

term can be directly computed using DTS measurements from 

both ends of the fiber. Previously documented DTS calibrations have included γ as a time-varying parameter (Hausner 

and others, 2011) or assumed a single, fixed value (van de 

Giesen and others, 2012; McDaniel and others, 2018), with the 

latter two studies reporting little effect on calibration quality. 

Both the variable and single-value γ approaches to calibration 

were tested in the study. A more thorough description of the 

DTS method and applications to hydrology can be found in 

Tyler and others (2009). Detailed descriptions of methods for 

estimating the C, γ, and ∆α terms can be found in Hausner and 

others (2011) and van de Giesen and others (2012).

Field Methods

A 2004-model Oryx DTS interrogator (Sensornet Ltd) 

was obtained from the USGS Office of Groundwater Branch 

of Geophysics, and a 1,130-meter (3,700-ft), 2008-model 

BRUsteel armored cable (Brugg Cables) with two optical 

fibers, each terminated by a connection port on either end (four 

ports total) was provided by Professor Jean Bahr (University 

of Wisconsin Madison Department of Geoscience). The cable 
4 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

was doubled back on itself (duplexed), so that the four connection ports were collocated (all going into the DTS interrogator), with the cable midpoint making up the opposite (distal) 

end. This duplexed configuration left 1,850 ft of doubled cable 

available for measurements, allowing for locations along the 

doubled cable to be measured from two different directions 

and differential attenuation to be directly calculated.

Approximately 1,400 ft of the armored cable were 

deployed on July 27, 2016, using a small rowboat. The cable 

was allowed to settle into the soft substrate under its own 

weight. No additional weighting was used because of concern 

that the cable might sink unevenly into the soft sediments 

near the locations of any weights. Observation of the cable on 

retrieval indicated that it had mostly settled evenly into the 

top few inches of sapropel sediment below the sediment-water 

interface. In a few areas of dense aquatic vegetation, however, 

downward trends in temperatures throughout the deployment 

indicated that the cable may have initially rested on submerged vegetation, then slowly sunk towards the sedimentwater interface.

Distances along the cable were marked every 20 ft. 

Location of the cable was recorded on retrieval of the cable 

(August 3, 2016) by mounting a differential global positioning system (DGPS) receiver, sampling at a rate of 1 hertz on 

the stern of the rowboat (fig. 2), and then noting the times of 

retrieval for distances along the cable at an interval of approximately 100 ft or less.

Two calibration baths, each containing approximately 

66 ft (20 meters) of coiled fiber optic cable placed in insulated 

coolers filled with water, were installed in a shaded location 

on shore near the DTS interrogator unit. One bath consisted 

of an ice-water mixture that was maintained throughout the 

deployment; the second bath was left at ambient temperature. 

In both baths, the cable coils were kept off the bottoms of the 

Figure 2. Cable retrieval on August 3, 2016. Photograph by Bob Egan, U.S. Environmental Protection Agency, used with permission.
Data Analysis 5

coolers using foam tubing, and coiled tight enough to minimize contact with the cooler sides. External reference resistance temperature detector (RTD) thermometers connected to 

the Oryx unit, and independent temperature loggers (Solinst 

Leveloggers; accuracy of 0.1 degree Celsius [°C]; resolution 

of 0.1 °C) were both attached to the fiber optic cable coils 

using zip ties, and set to record temperature every 5 minutes. 

The accuracy and precision of both Leveloggers was verified 

prior to the DTS deployment, using an ice bath assumed to be 

about 0.07 °C (Tyler and others, 2009). Continuous circulation 

was maintained in each cooler with two small, submersible 

electric pumps.

The Oryx interrogator unit was installed on shore 

in weatherproof housing similar to that used for USGS 

streamgages. Power for the Oryx unit and cooler circulation pumps was provided by two 100-watt solar panels and 

a 100-amp-hour battery. Following a rough field calibration 

using the Oryx control software, the instrument was set to 

acquire temperature profile measurements every 30 seconds 

and average (stack) every 10 measurements to improve precision, resulting in a 5-minute measurement interval. A spatial 

sampling interval of 1.01 meters was used (each data point 

represents an average for that length of cable). Measurements 

were made in both fibers, in the forward and reverse directions, resulting in a 20-minute cycle between measurements 

in the same channel and direction. USGS staff visited the site 

every 2 days to download collected data from the Oryx to a 

laptop and refresh the ice bath.

Data Analysis

The temperature data collected for this study are available in a companion data release (Leaf, 2020). The field data 

were processed to estimate temperatures along the cable and 

the physical location of the cable in space. This section of 

the report describes analysis of instrument noise, temperature 

calibration, and cable location, which presented challenges 

during this study.

Instrument Noise

Inspection of the apparent temperatures recorded by the 

Oryx control software (Sensornet, 2007) revealed several 

issues with the field calibration. A negative bias in the apparent temperatures of approximately 7 °C appeared to be caused 

by the field calibration being completed before the temperature 

coil in the ice bath had equilibrated (the cable in the ice bath 

was actually warmer than 0 °C but was incorrectly assumed 

to be at 0 °C). Further inspection revealed instrument noise of 

several degrees Celsius, which seems to be present in the temperatures reported for the fiber optic cable and the reference 

RTD thermometers connected to the Oryx instrument.

Figure 3 compares apparent temperatures for the calibration baths recorded by the DTS fiber, reference (RTD) 

Figure 3. Comparison of temperatures measured in the 

calibration baths. A, ice bath and B, ambient temperature bath. 

The apparent distributed temperature sensing temperatures are 

a spatial average of the coil immersed in the calibration bath. The 

Solinst Levelogger temperatures are assumed to be accurate to 

within plus or minus 0.1 degree Celsius. The apparent distributed 

temperature sensing temperatures recorded by the Oryx software, 

and the reference resistance temperature detector thermometers 

show instrument noise of several degrees Celsius or more, 

possibly related to changes in the instrument power supply or 

operating temperature, or both. 

Apparent DTS temperatures

Reference RTD thermometer

Solinst Levelogger

EXPLANATION

[DTS, distributed temperature sensing; RTD, resistance temperature detector]

–6

–4

–2

0

2

4

6

A. Ice bath

Date

07−28−2016

07−29−2016

07−30−2016

07−31−2016

08−01−2016

14

16

18

20

22

24

26

B. Ambient temperature bath

mad19-1901_fig03 Measured temperature, in degrees Celsius
6 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

thermometers, and Leveloggers. The instrument noise is nonrandom and appears to follow a diurnal pattern. Increasing spikes in 

the apparent fiber temperatures towards the end of the deployment are most likely explained by diurnal variations in the ambient temperature experienced by the Oryx unit, which could affect the C and γ parameters. The weather during the deployment 

was initially cloudy, with increasing sun and eventually clear skies by July 31, 2016, consistent with increasingly severe positive 

and negative deviations in the apparent temperatures, which may have been additionally enhanced by direct solar radiation on 

the instrument enclosure. The cause of the noise pattern in the reference RTD thermometers, which is diurnal but offset in phase 

between the two calibration baths, is unclear. The noise in the reference RTD thermometers precludes calibration of the DTS 

data with the Oryx software and underscores the importance of external reference temperatures that are completely independent 

of the DTS instrument.

Temperature Calibration

Two approaches to estimating the C and γ parameters (to get DTS temperatures) were investigated. The first approach 

involved optimization of C and γ to minimize the squared error between the DTS calibration bath temperatures and external 

temperature measurements made by the Leveloggers (for example, van de Giesen and others, 2012). The second approach 

involved explicitly solving equation 1 for C and γ simultaneously, using the DTS temperatures in both calibration baths (similar 

to Hausner and others, 2011). All computations were done in a Jupyter Notebook (http://jupyter.org/) available in the companion 

data release (Leaf, 2020).

In both approaches, differential attenuation for a section of fiber was determined by comparing DTS measurements taken 

from opposite ends (forward and reverse) as follows:

( ) ( ) ( ) ( ) ln( ) ln( ) ln( ) ln( ) ( ) ( ) ( ) ( ) ( ) 2

s s ss

z z forward forward reverse reverse

aS aS aS aS

z

Pz z Pz Pz Pz z

Pz z Pz Pz Pz z a z dz

+∆

+ ∆ + ∆

− +−

+ ∆ + ∆ ∆ = ′ ′ ∫ (2)

Equation 2 can then be summed for successive increments of cable to get the cumulative effect of differential attenuation 

between a measurement point and the DTS transmitter/receiver (the differential attenuation term in eq. 1).

Because the DTS cable was duplexed, four sections of cable were available for calibration (two instances of each bath). In 

the optimization approach, the sum of residuals across all four cable sections in the baths was minimized using the minimize 

function in SciPy (Jones and others, 2001). Optimization was completed with C and γ together and C only, with γ fixed at the 

mean value from the combined optimization.

The explicit calibration approach involved rearranging equation 3 in Hausner and others (2011), substituting the computed 

differential attenuation terms (eq. 2) at the locations of the calibration baths (where temperatures T1 and T2 were independently 

measured) as follows:

1

2

1

1

1 1 0

2 2

2

2 0

( ) ln ( )

1 ( )

1 ( ) ln ( ) ( )

z

a

aS

z

a

aS

P z T a z dz

T P z

T C P z T a z dz

P z



        − ∆ ′ ′

  −       =      −     − ∆ ′ ′      

∫

∫

(3)

In this case, only the near cable section in the ice bath and distal cable section in the ambient bath were used; the remaining two 

cable sections were used for validation.

C and γ (when not fixed) were determined for each measurement time, and temperatures along the cable were computed 

using equation 1. Although the results were generally acceptable for the goals of the study (detecting groundwater-related 

anomalies on the order of a few degrees Celsius), none of the calibration methods were able to completely remove spurious 

peaks in the temperature data that are on the order of a few tenths of a degree Celsius. Although optimization of C and γ together 

resulted in the lowest error at the calibration baths, optimization of just C was ultimately selected because it appeared to reduce 

the magnitude of the peaks somewhat, which are visible as horizontal bands in the time-distance plane (fig. 4A). The explicit calculation method produced similar overall results to optimization of C and γ (fig. 4B), but resulted in a less favorable balance of 

error among the calibration coils, because only two of the four coils were used in the parameter estimation (error was negligible 

in the coils used and somewhat higher than the combined optimization in the remaining two baths).
Data Analysis 7

The cause of the peaks is unclear; however, they may be 

related to sun shining on instrument housing and solar panel 

assembly during the same period each morning (through a gap 

in the tree canopy). The peaks all occur around 11 a.m. and 

coincide with spikes in the internal reference temperature of 

the DTS instrument.

Figure 5 shows error in the spatial mean of the calibrated DTS temperatures for the calibration baths. Root mean 

squared error (RMSE) of the DTS temperatures varies up 

to approximately plus or minus 0.3 °C through time, with 

average RMSE values ranging from 0.07 to 0.10 °C for the 

four coils. The pattern in the noise is nonrandom, with peaks 

corresponding to the false peaks observed in the temperature 

data, except that the anomalies are positive in the ice baths and 

negative in the ambient temperature baths. Adjustment of γ in 

addition to C reduces these peaks in the calibration baths but 

increases the magnitude of false peaks elsewhere in the dataset 

(figs. 4A–B).

Cable Location

Accurate location of the cable in space was also challenging because the boat stern, where the DGPS receiver 

was located, did not always coincide with the cable during 

retrieval. Obstacles such as logs and emergent vegetation 

made control of boat position difficult. This issue was partially 

addressed by recording the retrieval times of known distances 

along the cable when the distance markings were close to 

Figure 4. Spurious peaks in the distributed temperature sensing data, A, as seen in the timedistance plane and B, with individual temperature traces at the 600-foot cable distance compared 

to the internal reference temperature of the distributed temperature sensing instrument. The peaks 

are visible as horizontal bands across the time-distance image (A), which shows the dataset as 

calibrated by optimizing C and γ. The peaks are likely an artifact of the instrument because they are 

visible across the entire dataset and correspond temporally with spikes in instrument temperature 

(B). Optimization of just the C parameter was selected as the calibration method because it appears 

to reduce the magnitude of the peaks somewhat (B and fig. 7). 

False peaks

16 18 20 22 24 26

Apparent DTS temperature, in degrees Celsius C and γ explicitly computed

C and γ optimized to all four baths

Just C optimized to all four baths

DTS instrument internal reference temperature

EXPLANATION

[DTS, distributed temperature sensing]

07−28−2016 12 a.m.

07−28−2016 12 p.m.

07−29−2016 12 a.m.

07−29−2016 12 p.m.

07−30−2016 12 a.m.

07−30−2016 12 p.m.

07−31−2016 12 a.m.

07−31−2016 12 p.m.

08−01−2016 12 a.m.

0 250 500 750 1,000 1,250 1,500 1,750 22 24

Apparent DTS temperature, 

in degrees Celsius

DTS internal reference 

temperature, 

in degrees Celsius

Distance along fiber, in feet

A B 30 40

mad19-1901_fig04

Ambient temperature calibration bath

Ice-water calibration bath
8 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

−1.00

−0.75

–0.50

–0.25

0.00

0.25

0.50

0.75

1.00

−1.00

−0.75

−0.50

−0.25

0.00

0.25

0.50

0.75

1.00

Distributed temperature sensing error, in degrees Celsius Distributed temperature sensing error, in degrees Celsius

07−28−2016

07−29−2016

07−30−2016

07−31−2016

08−01−2016

07−28−2016

07−29−2016

07−30−2016

07−31−2016

08−01−2016

Date Date

Error of DTS spatial mean for calibration bath

Mean error: −0.019 degree Celsius

EXPLANATION EXPLANATION

Error of DTS spatial mean for calibration bath

Mean error: 0.020 degree Celsius

Error of DTS spatial mean for calibration bath

Mean error: −0.021 degree Celsius

EXPLANATION

Error of DTS spatial mean for calibration bath

Mean error: 0.019 degree Celsius

EXPLANATION

[DTS, distributed temperature sensing; 

RMSE, root mean squared error]

C. Near instance of ambient bath D. Far instance of ambient bath

A. Near instance of ice bath B. Far instance of ice bath

Average RMSE: 0.092 degree Celsius Average RMSE: 0.104 degree Celsius

Average RMSE: 0.079 degree Celsius Average RMSE: 0.066 degree Celsius

mad19-1901_fig05

Figure 5. Error in calibrated temperatures. A, near instance of ice bath; B, far instance of ice bath; C, near instance of 

ambient bath; and D, far instance of ambient bath. The error is defined as the difference between the spatial mean of 

distributed temperature sensing temperatures and the external reference temperature recorded by the Levelogger. 

the DGPS receiver. The position of the cable was ultimately 

interpreted by hand in a geographic information system (GIS) 

environment, through comparison of the recorded boat track 

and locations of known cable distances with satellite imagery 

and field notes (fig. 6). 

Distribution of Groundwater Discharge

A time-distance image of the complete, calibrated 

DTS dataset is shown in figure 7. Compared to figure 4A, 

which shows the dataset calibrated using C and γ, a subtle, 

but noticeable reduction in horizontal banding across the 
Distribution of Groundwater Discharge 9

distance-time plane is apparent. Only data through 10:45 a.m. 

on August 1, 2016, could be retrieved from the Oryx interrogator; the remaining data through August 3 were lost because of 

an instrument error. The spooled and calibration bath segments 

of the cable can be seen to the left of the 466-ft mark, where 

the cable enters the lake. Temperatures recorded in the lake 

(at the sediment-water interface) indicate a variation of more 

than 5 °C across the study area, with consistently cool zones 

interpreted to indicate preferential groundwater discharge. 

Horizontal banding visible across the lake temperatures (distances greater than 466 ft) in the early morning hours indicates 

apparent residual instrument noise that was not removed in the 

calibration. The source of this noise is unclear. Although no 

other independent measurements of temperature were collected along the cable away from the calibration baths, comparison of evening air temperatures recorded by the cable with 

records at nearby Lakeland Airport (fig. 1) provide additional 

confidence in the validity of the fiber temperatures (fig. 8).

Similar to Sebok and others (2013), the daily temperature range, standard deviation, and minimum temperatures 

were evaluated as possible indicators of groundwater discharge (figs. 9–11). As observed by Sebok and others (2013), 

the daily range and standard deviation have similar spatial 

patterns, but their interpretation is confounded by the effects 

of solar radiation and water depth. The daily minimum 

temperatures (fig. 11) are likely a more reliable indicator of 

groundwater discharge, because they represent early morning 

temperatures that are not affected by solar radiation. Average 

temperatures between 6 and 7 a.m. each day were ultimately 

selected to create a single map showing the thermal gradients 

across the site (fig. 12). Besides simplicity of presentation, 

averaging a 1-hour period for 5 days has the added advantage 

of further reducing instrument noise by averaging 150 temperature readings, instead of the 10 readings contained in a single 

set of daily minimums. 

The daily minimum values consistently show cooler 

temperatures near shore, where greater amounts of groundwater discharge would be expected, but also some areas of cooler 

temperatures along the outside of the floating bog, to the west 

of the dock (fig. 11), which may indicate preferential groundwater discharge in these locations. The results are consistent 

with upward gradients measured by mini-piezometers in these 

areas, as well as upward fluxes inferred from vertical temperature profiles (Leaf and Haserodt, 2020).

mad19-1901_fig06

5,088,470

5,088,480

5,088,490

5,088,500

5,088,510

5,088,520

5,088,530

5,088,540

Northing, Universal Transverse Mercator Zone 16 north, in meters

273,960 273,980 274,000 274,020 274,040 274,060 274,080

Easting, Universal Transverse Mercator Zone 16 north, in meters

600

700

900 800

980

1,000 1,050

1,100 1,200

1,300

1,400

1,500

1,600 1,700

1,820

EXPLANATION

[DTS, distributed temperature sensing]

Locations recorded by the differential global 

positioning system

Interpreted cable location

Recorded locations of marked cable distances

900

DTS instrumentation location

Base map data from Google, 2018

Figure 6. Interpreted cable location, with recorded boat stern position and recorded locations of cable distance 

markings.
10 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

mad19-1901_fig07

07−28−2016 12 a.m.

07−28−2016 12 p.m.

07−29−2016 12 a.m.

07−29−2016 12 p.m.

07−30−2016 12 a.m.

07−30−2016 12 p.m.

07−31−2016 12 a.m.

07−31−2016 12 p.m.

08−01−2016 12 a.m.

0 250 500 750 1,000 1,250 1,500 1,750

Distance along fiber, in feet

Date and time

Interpreted locations of groundwater discharge

Temperature, in degrees Celsius

16 18 20 22 24 26

EXPLANATION

Figure 7. Time-distance image of the complete distributed temperature sensing dataset. From left to 

right, the first 300 feet of fiber, which remained spooled, are followed by 66-foot (20-meter) sections 

of fiber in the ambient and ice-water calibration baths. A short section of cable following the ice bath 

shows ambient air temperatures and the heating effects of solar radiation (temperatures greater than 

25 degrees Celsius). The cable enters the lake at 466 feet. Areas that are consistently cool relative to 

most of the lake temperatures are interpreted to indicate groundwater discharge. 
Distribution of Groundwater Discharge 11

Figure 8. Air temperatures recorded by the section of fiber between the ice bath 

and lake compared to temperatures recorded at Lakeland Airport (National Oceanic 

and Atmospheric Administration, 2018), approximately 9 miles to the east. Apparent 

temperatures warmer than the airport temperatures show the heating effects of solar 

radiation on the cable. Good agreement in the evening and overnight temperatures 

provides some additional confidence in the accuracy of the calibrated fiber 

temperatures. The lag in morning temperatures recorded by the fiber is likely due to 

shading of the fiber in the eastern direction. 

Lakeland Airport (KARV)

Average DTS temperature, 

450−460 feet

EXPLANATION

[DTS, distributed temperature sensing]

10

15

20

25

30

35

40

45

07−27−2016

07−28−2016

07−29−2016

07−30−2016

07−31−2016

08−01−2016

08−02−2016

Air temperature, in degrees Celsius

Date

mad19-1901_fig08
12 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

273,960 273,980 274,000 274,020 274,040 274,060 274,080 273,960 273,980 274,000 274,020 274,040 274,060 274,080

5,088,470

5,088,480

5,088,490

5,088,500

5,088,510

5,088,520

5,088,530

5,088,540

5,088,470

5,088,480

5,088,490

5,088,500

5,088,510

5,088,520

5,088,530

5,088,540

Northing, Universal Transverse Mercator zone 16 north, in meters

Easting, Universal Transverse Mercator zone 16 north, in meters

 07−28−2016 07−29−2016

 07−30−2016 07−31−2016

0 0.5 1.0 1.5 2.0 2.5 3.0

Daily temperature range, in degrees Celsius

EXPLANATION

mad19-1901_fig09

Base-map data from Google, 2018

Figure 9. Daily temperature range (daily maximum temperature–daily minimum temperature) 

recorded by the distributed temperature sensing fiber. 
Distribution of Groundwater Discharge 13

Base-map data from Google, 2018

 07−28−2016 07−29−2016

 07−30−2016 07−31−2016

Easting, Universal Transverse Mercator zone 16 north, in meters

Northing, Universal Transverse Mercator zone 16 north, in meters

273,960 273,980 274,000 274,020 274,040 274,060 274,080 273,960 273,980 274,000 274,020 274,040 274,060 274,080

5,088,470

5,088,480

5,088,490

5,088,500

5,088,510

5,088,520

5,088,530

5,088,540

5,088,470

5,088,480

5,088,490

5,088,500

5,088,510

5,088,520

5,088,530

5,088,540

Daily standard deviation in temperature, in degrees Celsius

0 0.2 0.4 0.6 0.8 1.0

EXPLANATION

mad19-1901_fig10

Figure 10. Daily standard deviation in temperatures recorded by the the distributed temperature sensing fiber. 
14 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

Easting, Universal transverse Mercator zone 16 north, in meters

273,960 273,980 274,000 274,020 274,040 274,060 273,960 273,980 274,000 274,020 274,040 274,060

Northing, Universal Transverse Mercator zone 16 north, in meters

5,088,480

5,088,500

5,088,520

5,088,540

5,088,480

5,088,500

5,088,520

5,088,540

5,088,480

5,088,500

5,088,520

5,088,540

 07−28−2016

 07−29−2016 07−30−2016

 07−31−2016 08−01−2016

Daily minimum temperature, in degrees Celsius

16 18 20 22 24

EXPLANATION

mad19-1901_fig11

Base-map data from Google, 2018

Figure 11. Daily minimum temperatures recorded by the the distributed temperature sensing fiber. 
Distribution of Groundwater Discharge 15

1,415

1,388

1,362

1,448

1,854

1,338

1,298

526

549

1,262

583

766

796 826

1,152

856 886

1,092

915 1,059

999

603

646

676

736

706

1,488

1,521

1,801

1,761

1,591

1,625 1,684

1,664

mad19-1901_fig12

17.2 to 17.5

17.6 to 18.0

18.1 to 18.5

18.6 to 19.0

19.1 to 19.5

19.6 to 20.0

20.1 to 20.5

20.6 to 21.0

21.1 to 21.5

21.6 to 22.0

22.1 to 22.5

22.6 to 22.9

EXPLANATION

[DTS, distributed temperature sensing]

Early morning temperatures, in degrees Celsius, 

with labels of distance along the DTS cable, in feet.

Base-map data from Google, 2015 

–89°54'53" –89°54'51" –89°54'49"

45°54'49"

45°54'47"

45°54'45"

Figure 12. Average temperatures between 6 and 7 a.m. (across the full the distributed temperature sensing dataset). 
16 A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake

Summary and Conclusions

Haskell Lake is a shallow, 89-acre drainage lake in the 

headwaters of the Squirrel River, on the Lac du Flambeau 

Reservation in northern Wisconsin. Historically, this lake was 

an important producer of wild rice for the Lac du Flambeau 

Band of Lake Superior Chippewa Indians (LDF Tribe); but, 

beginning in the late 1970s, the rice began to diminish and 

by the late 1990s, the lake no longer had harvestable stands. 

Restoring wild rice to Haskell Lake is a long-term priority for 

the LDF Tribe. A first step towards that effort is the cleanup 

of a petroleum-contamination plume in the shallow aquifer 

upgradient of the northern end of the lake. Knowledge of the 

downgradient extent of the plume and the locations where 

contaminated water is discharging to the lake is needed to 

inform cleanup efforts.

A cooperative study between the U.S. Geological Survey 

and the LDF Tribe was initiated to characterize the distribution 

of groundwater discharge to Haskell Lake in the areas downgradient of the contamination plume. A fiber optic distributed 

temperature sensing (DTS) survey of lakebed temperatures 

was completed at the north end of Haskell Lake from July 27 

through August 3, 2016. Challenges during the investigation 

included data storage and power supply limitations, maintenance of calibration baths, accurate location of the cable 

in space, cable placement in weeds and soft sediment, the 

confounding effects of solar radiation, and contamination of 

the data by multiple sources of instrument noise. Instrument 

noise in the apparent fiber temperatures and the reference 

resistance temperature detector thermometers precluded automated calibration of the DTS data with the instrument control 

software, and underscores the importance of well-constructed 

calibration baths with collocated, independent measurements 

of temperature. DTS temperatures were ultimately computed 

from the raw Stokes/anti-Stokes data by solving the DTS 

calibration equation for two parameters that describe instrument noise. The cause of residual instrument noise remaining 

after the calibration is unclear, but good agreement between 

air temperatures recorded by the fiber and those recorded at a 

nearby airport provides some additional confidence in the DTS 

data. Additional independent measurements of temperature at 

other locations along the cable away from the calibration baths 

would be beneficial for future DTS surveys.

The results indicate a persistent variation in temperatures 

at the sediment-water interface of more than 5 degrees Celsius 

across the survey area, with consistently cool temperatures 

interpreted to indicate groundwater discharge. Similar to 

other studies, daily minimum temperatures provide the most 

meaningful indicator of groundwater discharge. Results of the 

study can be used to determine locations for collecting lakebed 

pore water samples to better define the extent of contamination 

discharging to the lake.

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For more information about this publication, contact:

Director, USGS Upper Midwest Water Science Center

8505 Research Way

Middleton, WI 53562

608–828–9901

For additional information, visit: https://www.usgs.gov/centers/umidwater

Publishing support provided by the

Madison and Rolla Publishing Service Centers


Leaf—A Distributed Temperature Sensing Investigation of Groundwater Discharge to Haskell Lake—Scientific Investigation Report 2020–5005

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20205005