USGS Polar Temperature Logging System,

Description and Measurement Uncertainties 

Techniques and Methods 2–E3

U.S. Department of the Interior

U.S. Geological Survey
Cover photograph: North Greenland Ice Core Project ice-coring site in central Greenland.

(Photograph by Gary D. Clow, U.S. Geological Survey)
USGS Polar Temperature Logging System, 

Description and Measurement Uncertainties 

By Gary D. Clow 

Techniques and Methods 2–E3 

U.S. Department of the Interior 

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

DIRK KEMPTHORNE, Secretary 

U.S. Geological Survey 

Mark D. Myers, Director 

U.S. Geological Survey, Reston, Virginia: 2008 

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Suggested citation:
 

Clow, Gary D., 2008, USGS Polar Temperature Logging System, Description and Measurement
 

Uncertainties: U.S. Geological Survey Techniques and Methods 2 –E3, 24 p.
 

Available online at: http://pubs.usgs.gov/tm/02e03 

iii

Contents

Abstract 1

1 Introduction 1

2 System Description 2

2.1 PTLS Design Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 Resistance (Temperature) Measurement System . . . . . . . . . . . . . . . . . . 3

2.2.1 Kelvin Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2.2 Resistance Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.4 Temperature Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Depth-Measurement System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.2 Depth Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Measurement Uncertainties 11

3.1 ITS-90 Temperature Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Resistance Readout Uncertainties . . . . . . . . . . . . . . . . . . . . . . 11

3.1.2 Kelvin Circuit Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1.3 Temperature-Sensor Calibration Uncertainties . . . . . . . . . . . . . . . 13

3.1.4 Combined ITS-90 Temperature Uncertainties . . . . . . . . . . . . . . . 16

3.2 Relative Temperature Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Depth Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Example: Proposed WAIS Divide Borehole, Antarctica . . . . . . . . . . . . . . 20

4 Summary 22

Appendix: Nomenclature 23

References 24
iv

Figures

1 Primary PTLS components . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Kelvin resistance circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Resistance corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Raw noise, example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Temperature-sensor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6 αT values for various probe series . . . . . . . . . . . . . . . . . . . . . . . . . 8

7 Temperature-sensor calibration data, example . . . . . . . . . . . . . . . . . . 8

8 Temperature resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

9 Force-dependent function F(Z ̃), example . . . . . . . . . . . . . . . . . . . . 10

10 Resistance correction uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 14

11 Temperature-sensor calibration uncertainties . . . . . . . . . . . . . . . . . . 15

12 Damping of calibration bath’s temperature fluctuations . . . . . . . . . . . . 16

13 Combined ITS-90 temperature measurement uncertainty . . . . . . . . . . . . 17

14 Combined relative temperature measurement uncertainty . . . . . . . . . . . 18

15 Example: Temperature uncertainties, WAIS Divide borehole . . . . . . . . . . 20

16 Example: Depth uncertainties, WAIS Divide borehole . . . . . . . . . . . . . 21

Tables

1 PTLS specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
USGS Polar Temperature Logging System,

Description and Measurement Uncertainties 

By Gary D. Clow

Abstract

This paper provides an updated technical description of the USGS Polar Temperature Logging System

(PTLS) and a complete assessment of the measurement

uncertainties. This measurement system is used to acquire subsurface temperature data for climate-change

detection in the polar regions and for reconstructing

past climate changes using the “borehole paleothermometry” inverse method. Specifically designed for

polar conditions, the PTLS can measure temperatures

as low as −60◦ Celsius with a sensitivity ranging from

0.02 to 0.19 millikelvin (mK). A modular design allows

the PTLS to reach depths as great as 4.5 kilometers

with a skid-mounted winch unit or 650 meters with

a small helicopter-transportable unit. The standard

uncertainty (uT ) of the ITS-90 temperature measurements obtained with the current PTLS range from

3.0 mK at −60◦ Celsius to 3.3 mK at 0◦ Celsius.

Relative temperature measurements used for borehole

paleothermometry have a standard uncertainty (ur

T )

whose upper limit ranges from 1.6 mK at −60◦ Celsius to 2.0 mK at 0◦ Celsius. The uncertainty of a

temperature sensor’s depth during a log depends on

specific borehole conditions and the temperature near

the winch and thus must be treated on a case-by-case

basis. However, recent experience indicates that when

logging conditions are favorable, the 4.5-kilometer system is capable of producing depths with a standard

uncertainty (uZ) on the order of 200–250 parts per

million.

1 Introduction

In 1993, the U.S. Geological Survey (USGS) began

developing a new borehole temperature logging system

specifically to address emerging climate issues in the

polar regions. This system, referred to as the USGS

Polar Temperature Logging System (PTLS), has two

primary functions. (1) Periodically obtain subsurface

temperature data from arrays of polar boreholes for

climate-change detection. Monitoring data acquired

by the PTLS in northern Alaska contributes to the

Global Climate Observing System (GCOS) through

the Global Terrestrial Network for Permafrost (GTN–

P). (2) Acquire data for the reconstruction of past

climate changes in the polar regions using “borehole

paleothermometry.” Climate reconstructions derived

from borehole temperature measurements are hindered

by considerable temporal smearing due to heat diffusion processes. While it cannot be eliminated, the

extent of the temporal averaging can be minimized

through optimal experimental design. Application of

Backus-Gilbert inverse methods to the paleoclimate

reconstruction problem shows that our ability to resolve past climatic events can be optimized by reducing

the uncertainty in the temperature measurements to

no more than 0.1 percent of the paleoclimate signal

we are attempting to detect (Clow, 1992). In most

places on Earth, surface-temperature changes during

the Holocene were on the order of ±1 K. Thus to

enhance our ability to resolve past climate events of

this magnitude, it is desirable to reduce the uncertainty of the borehole temperature measurements to

about 1 mK. Paleoclimate reconstruction has been

the primary driver for the design requirements of the

PTLS since its requirements are much more stringent

than those needed for detecting contemporary climate

change.

The objectives of this paper are to provide an updated technical description of the PTLS logging system

and an analysis of the measurement uncertainties. This

system and its uncertainties were originally described

by Clow and others (1996). However, the PTLS is

a continually evolving system, warranting an updated

description. In addition, calibration facilities and procedures have changed significantly since 1996. The

current paper provides a much more complete analysis
2 USGS Polar Temperature Logging System

of the measurement uncertainties than was possible

in Clow and others (1996). The need for such an

analysis is twofold: (1) The usefulness of scientific data

produced by monitoring systems critically depends on

the availability of thorough uncertainty analyses. This

is particularly true of climate-monitoring systems. (2)

To reconstruct past climate changes using borehole

paleothermometry, one needs to know the uncertainties

of the data. This requirement, shared by all geophysical inverse techniques (Parker, 1994), determines the

very structure of the derived climate histories. In

conformance with ISO standards (ISO, 1993a; ISO,

1993b), we use the CIPM1 approach for expressing and

evaluating the measurement uncertainties of the PTLS.

2 System Description

2.1 PTLS Design Overview

A variety of system designs presently (2008) are

used to measure temperatures in geophysical boreholes.

Most systems use either a temperature-dependent resistive element (thermistor or RTD) or a piezoelectric crystal whose resonant frequency is temperaturesensitive for the sensing element. In the former case,

the resistance of the sensing element is measured by

a custom-built electronic bridge or by a commercial

resistance readout. An advantage of a custom bridge

is that it can be made small enough to be included in an

instrument package located at the downhole end of the

logging cable, keeping the electronic lead lengths to the

sensor relatively short. Such a package can be designed

to measure several other parameters as well, such as

fluid pressure and borehole inclination, and the resulting data either stored within the instrument package

or digitally transmitted to the surface. A significant

disadvantage of this approach for precision thermometry is the difficulty of maintaining the calibration

of the electronic bridge while the instrument package

experiences temperature changes of 10–30 K during

the course of a logging experiment. The associated

calibration drift of the bridge can produce temperature

measurement errors of 10 mK, or more. Application of

new technologies may substantially reduce these errors,

making high-precision downhole digital thermometers

possible in the near future. The current alternative

is to locate the resistance-measuring circuitry on the

surface. The advantages of this strategy are: (1)

a high-quality commercial resistance readout can be

1International Committee for Weights and Measures.

utilized for the measuring circuitry instead of having to

develop custom miniaturized circuits, (2) the readout

can be maintained at a constant temperature, eliminating temperature-related drift in the measurement

circuit, and (3) the calibration of the readout can

be periodically rechecked while measurements are in

progress. However, the long lead lengths between the

resistance readout and the sensor, potentially up to

10 km, make the measurements vulnerable to several

sources of instrumental error. Great care must be

exercised to minimize these errors. Logging systems

with a downhole electronic bridge generally acquire

temperature measurements while lowering the sensor

downhole at a constant speed (“continuous” logging).

Another common technique is to acquire data with the

probe stopped at a fixed depth; repeating this process

at multiple depths yields an incremental or “stop-andgo” temperature log. Systems with the resistancemeasuring circuitry on the surface are sometimes limited to this mode. Although incremental logging yields

measurements at a limited number of depths, these

measurements are free of the “slip-ring” noise (see

Section 2.2) inherent to continuous temperature logs

obtained with surface measurement circuitry.

Considering the advantages and disadvantages of

various system designs along with our scientific objectives, the following requirements were established

for the Polar Temperature Logging System: the system must be modular and flexible so it can use a

variety of sensors, can make measurements using either downhole or surface measurement circuitry, can

be operated in either the continuous or incremental

logging modes, and can utilize different length logging cables depending on borehole depth and available logistics. In addition, the system must be able

to measure temperatures as low as −60◦C with an

uncertainty of about 1 mK, reach depths comparable

to the maximum thickness of the polar ice sheets (4–

5 km), work in the presence of strong environmental

noise (for example, changing electrostatic fields), and

be rugged enough to survive offloading from military

cargo aircraft. The PTLS evolved from a number

of refinements to a conventional temperature logging

system design, thereby avoiding the need to build a

radically new system. This approach took advantage of the USGS’ considerable experience in borehole thermometry. Negative-temperature-coefficient

(NTC) hermetically sealed thermistors were selected

for the primary temperature sensors because of their

ruggedness, stability, and high temperature coefficient,

which helps produce a high system sensitivity. A
System Description 3

Temperature 

sensor

Depth 

counter

Resistance 

readout

Faraday 

Logging winch cage

Slip-ring 

connector

Precision 

measuring 

wheel

Logging 

cable

Computer

Figure 1. Layout of the USGS Polar Temperature Logging System when using surface measurement circuitry.

commercial resistance readout located on the surface sources of electrical noise.

is normally used for the resistance-measuring circuitry. The three fundamental measurements made by the

This circuitry is suspended inside a Faraday cage main- PTLS are the sensor resistance, sensor depth, and time

tained at 23 ± 0.5◦C for the duration of an experi- of data acquisition. For the time measurements, we

ment; thermal stability is provided by microprocessor- simply rely on the computer’s onboard clock. The

controlled etched-foil heaters. As an alternative to resistance and depth measurements are more involved

surface measurement circuitry, a prototype downhole and are described in detail in the following sections.

digital thermometer utilizing NTC thermistors has Resistance measurements are subsequently converted

been used with the PTLS. However, this device is still to temperature using a 4-term conversion function.

in the testing phase and will not be discussed further

here. Other major system components include a 4-

conductor logging cable mounted on a motorized winch 2.2 Resistance (Temperature)

(fig. 1). Two different size winches are currently avail- Measurement System

able: a small helicopter-transportable unit with 650 m

of cable, and a much larger skid-mounted unit capable 2.2.1 Kelvin Circuit

of reaching 4.5 km. A “slip-ring” assembly provides To measure the resistance, a Kelvin (4-wire) cir- electrical continuity between the logging cable and the cuit is used in both the downhole and the surface surface electronics. Depth information is provided by measurement-circuitry configurations (fig. 2). During an optical encoder mounted on a calibrated measuring this measurement, the resistance readout produces a wheel. A laptop computer controls the system, both highly regulated current ( displaying and storing the measured resistance, depth, Is) that passes through the

sensor. The resulting voltage drop (∆ ) across the time, and logging speed. Cable tension provided by a V

probe is detected by the readout’s high-impedance strain-gage force transducer is displayed on a separate

monitor. To minimize electrical noise, all components inputs, and the probe’s resistance calculated from

R ̃s = ∆V /Is. This 4-wire measurement eliminates the are powered by DC batteries except for the winch

motors. The Faraday cage surrounding the resistance effect of the lead resistance ( ) along each conductor RL

between the resistance readout and the temperature readout, used in conjunction with cable shielding, helps sensor. There are, however, several sources of system- isolate the measurement circuitry from the remaining atic error that potentially require correction.
4 USGS Polar Temperature Logging System

Thermistor 

probe

4 - Conductor 

logging cable

Slip-ring 

assembly

Resistance 

readout

!"

Is

HI

LO

!#

!#

!#

!#

$

%

&

'

Figure 2. Kelvin (4-wire) resistance circuit used by the

PTLS when the measurement circuitry is located on the

surface. The test current Is passes through lines 1 and

2 while the voltage drop across Rs is measured using the

sense lines (3, 4). With downhole circuitry, an electronic

bridge is connected directly to the probe.

2.2.2 Resistance Corrections

Leakage paths between the conductors of the Kelvin

circuit can produce significant systematic error, particularly when the probe resistance Rs is large. Such

unintended paths arise due to leakage currents passing

directly through the conductor insulation, moisture

absorption by the insulation, or leakage due to contaminants on the surface of the insulation or connectors. Leakage currents between the circuit’s sense lines

or between the current-carrying lines will reduce the

measured resistance by

δRl = R2

s

Rs + Rl

(1)

where Rl is the leakage resistance. Teflon is used

for the Kelvin circuit insulation because of its high

volume resistivity (greater than 1016 Ω·m), low water

absorption, and a surface that tends to repel many

films. This problem is further controlled by rigorously

cleaning the connectors and by using a sensor with a

low resistance Rs. Part of our logging protocol is to

measure the resistance Rl between each pair of conductors immediately before each logging experiment.

If Rl is less than 10 GΩ for any pair of conductors,

the log is aborted until the problem is rectified. Rl is

greater than 20 GΩ for nearly all logging experiments

conducted with the PTLS.

A capacitor is occasionally introduced between the

readout’s sense lines to perform high-frequency noise

filtering. This also delays the response of the circuit so

that the measured resistance is too low by

δRc = τ ∂Rs

∂t . (2)

τ = RsC is the circuit’s natural response time where

C is the capacitance. If a filtering capacitor is used,

the resistance offset δRc is controlled by keeping τ

small relative to the measurement integration time of

the resistance readout and by using a slow logging

speed v so that the rate of resistance change ∂Rs/∂t =

v αT Rs (∂T /∂z) is also small; αT is the sensor’s temperature coefficient of resistance (αT ≡ R−1 s ∂Rs/∂T).

With typical logging speeds (2.5–5.5 cm·s−1) and temperature gradients (∂T /∂z ≤ 50 mK·m−1), the most

rapid resistance changes are on the order of 10−4Rs

per second. Without the filtering capacitor, C is determined by the capacitance of the logging cable (76 nF

for the 650-m “short” cables and 0.68 μF for the 4,600-

m “long” cable).

As the current Is passes through the temperature

sensor, power dissipates within the probe at a rate P =

I2

sRs. This warms the probe, effectively reducing its

resistance by

α = T ( 2 IsRs) δRh (3) Pd

where Pd is the probe’s power dissipation constant.

The best strategy for minimizing self-heating is to use

a resistance readout with a small source current Is and

a probe with a relatively low resistance. The source

current for the resistance readout used with the PTLS

is ≤ 10 μA.

To provide modularity, the Kelvin circuit consists

of a number of components attached to one another

using high-quality electrical connectors (fig. 2). Different portions of the circuit operate at vastly different

temperatures with the sensor-end of the circuit often

being 30–70 K colder than the resistance readout.

This situation has the potential to generate significant

thermoelectric voltages (thermal EMFs) between electrical junctions separating dissimilar metals through

the Seebeck effect (McGee, 1988). The sum of the

thermal EMFs can be found by integrating the Seebeck

coefficient Q around the entire circuit, starting and

ending at the resistance readout’s HI and LO sense

connections (junctions a1 and a2),

Vemf = −

! a2

Q(T) dT. (4) a1

Q depends primarily on metal composition and secondarily on temperature. If the metal compositions on

the HI side of the circuit exactly match those on the

LO side, the total thermal EMF can be expressed by
System Description 5

Vemf = −

! b1

a1

QA(T) dT −

! c1

b1

QB(T) dT − · · ·

−

b2

c2

QB(T) dT −

a2

b2

QA(T) dT (5) ! !

where subscripts 1 and 2 refer to the HI and LO sides of

the circuit, respectively; QA is the Seebeck coefficient

for the metal conductor between junctions a1 and b1

(and between a2 and b2), QB is the coefficient for

the metal between junctions b1 and c1, and so forth.

Equation (5) can be rewritten in terms of the adjacent

junction pairs on the HI and LO sides of the circuit

(for example, a1 and a2),

Vemf =

! a1

a2

QA(T) dT +

! b2

b1

QA(T) dT

+

"! b1

b2

QB(T) dT +

! c2

c1

QB(T) dT#+ · · · . (6)

" #

If the temperature difference between adjacent junction pairs is small enough that the temperature dependence of the Seebeck coefficient can be ignored,

equation (6) reduces to

Vemf = −QA(Ta2 − Ta1 ) + (QA − QB)(Tb2 − Tb1 )

+ (QB − QC )(Tc2 − Tc1 ) + · · · . (7)

Thus, thermal EMFs can be controlled by minimizing the temperature difference between adjacent

junction pairs. Based on this analysis, we use a

number of strategies to minimize thermal EMFs in

the PTLS’ Kelvin circuit: (1) The use of dissimilar metals is kept to a minimum. Except for the

junctions themselves, the circuit paths consist almost

entirely of copper or silver-plated copper. (2) Where

a dissimilar metal occurs on the HI side of the circuit, the metal is matched with an identical metal

at the corresponding location on the LO side. (3)

The temperature difference between adjacent junction

pairs is minimized. This is accomplished by locating

the junctions of an adjacent pair as close together as

possible, locating junction pairs within the thermally

controlled Faraday cage where thermal gradients are

very small, and (or) by locating junction pairs within

high-conductivity metal shells where temperature gradients are also small. Before every experiment, the

resistance readout is warmed up for at least an hour

to minimize thermal EMFs within the readout itself.

Considering the estimated temperature differences at

the adjacent junction pairs and the values of the Seebeck coefficients, the total thermal EMF for the Kelvin

circuit is estimated to be on the order of 0.5 μV with

the dominant sources occurring at the slip-ring assembly. Current-reversal experiments with both the 650-m

logging cables and the 4,600-m cable confirm that Vemf

is typically ≤ 0.5 μV. This voltage offset increases the

measured resistance by

δRe = Vemf

Is

. (8)

In 2008, the simple constant-current source that the

PTLS had used was changed to a reversing source.

This allowed us to switch to a current-reversal technique where a “resistance measurement” is found by

averaging two measurements made with currents of

opposite polarity. With this approach, the thermal

EMFs produced during each polarity completely cancel

out so that δRe = 0.

The first three systematic errors (δRl, δRc, δRh)

can be controlled by using a sensor with a relatively

small resistance. However, an additional constraint

imposed by the resistance readout is that Rs must

be much greater than the lead resistance RL for each

leg of the Kelvin circuit in order to make an accurate

resistance measurement. At a minimum, Rs should

be at least 20 times RL. Other factors that help

control the systematic errors are a small capacitance

C, a slow logging speed v, a small source current Is,

carefully matching the composition of the wires, and

keeping the temperature difference between adjacent

junction pairs as small as possible. Despite efforts

to control leakage paths, the capacitance effect, selfheating, and thermal EMFs, small systematic errors

will remain. We attempt to eliminate these errors by

applying equations (1) – (3) and (8) as corrections to

the resistance R ̃s recorded by the resistance readout to

obtain our estimate of the temperature sensor’s true

resistance,

Rs = R ̃s + (δRl + δRc + δRh − δRe). (9)

Figure 3 shows the magnitude of the resistance corrections for the PTLS under typical operating conditions.

Expressed in terms of temperature, the corrections

are generally limited to 0.1–0.2 mK. The uncertainty

of these systematic error corrections is discussed in

Section 3.1.2.

2.2.3 Noise

Several sources of noise also perturb the resistance

measurements when the measurement circuitry is lo-
6 USGS Polar Temperature Logging System

101 102 10!3

10!2

10!1

100

Rs (kΩ)

δR (Ω)

δRl

δRc

δRh

σRn

Figure 3. Magnitude of the resistance corrections

δRl, δRc, δRh under typical operating conditions; δRe is

essentially zero with the current PTLS design. In this

example, the capacitance correction δRc assumes a logging

speed of 5.5 centimeters per second, a temperature gradient

of 25 millikelvins per meter, and a capacitance C such that

τ = 10 milliseconds. Equivalent temperature corrections

are given by ∆Tx = δRx/(αT Rs). Also shown is the approximate standard deviation σRn of the raw noise (eq. 10)

generated in the Kelvin circuit under typical conditions.

cated on the surface. These sources include electrostatic coupling, electromagnetic EMFs, triboelectric

effects, and switching effects. Depending on the source,

the noise generated within the circuit consists either

of extraneous voltages V # or extraneous currents I#

.

The resistance readout internally converts the extraneous voltages into an apparent resistance noise, R# =

(V #

/Is), while the extraneous currents are converted

to R# = Rs(I#

/Is). In the latter case, the apparent

resistance noise increases in direct proportion to the

temperature sensor’s resistance.

Individual noise components: Electrostatic coupling occurs when an electrically charged object such

as the system operator, moves near the Kelvin circuit, generating currents in the conductors. In polar

environments, significant electrostatic interference can

also be caused by electric charges transferred to the

sheath of the logging cable by dry, blowing snow. Electromagnetic voltages (EMFs) are generated when a

changing magnetic field passes through the conductive

loop represented by the Kelvin circuit, or when some

portion of the conductive loop (for example, the logging

cable) moves relative to a magnetic field. For the

PTLS, nearby AC fields, winch motors, and the Earth’s

magnetic field are potential sources of electromagnetic

voltages. We use several strategies to mitigate the

noise generated by electrostatic coupling and electromagnetic EMFs:

(1) Once a temperature log is initiated, the system

runs in an automated mode, allowing the system

operator to remain an adequate distance from the

Kelvin circuit.

(2) The entire system is shielded from the wind and

blowing snow as much as possible by operating it

inside an insulated shelter. The Faraday cage and

associated electronics are always operated within

a protective shelter. If the wellhead cannot also

be located inside the shelter, the shelter is placed

as close as possible to the wellhead to minimize

the amount of exposed logging cable.

(3) To minimize AC power fields, all system components are powered by DC batteries except for the

winch motors.

(4) The most sensitive portions of the Kelvin circuit,

especially the resistance readout, are kept as far

as possible from the winch motors.

(5) All movement around the Kelvin circuit is kept to

a minimum during a temperature log.

(6) The loop area of the circuit is minimized by using

twisted-wire cables.

(7) The resistance readout is electrically shielded inside a Faraday cage. All the cables are also electrically shielded.

Given these noise-reduction strategies, the dominant sources of noise for the PTLS are believed to be

due to switching effects within the electromechanical

“slip-ring” assembly and to the triboelectric effect.

Triboelectric currents arise from charges generated between the insulation and conductors of the logging

cable as it flexes over the sheave wheels that guide

it into a borehole. Triboelectric currents can also

occur when the logging cable vibrates in the wind.

We manage the triboelectric currents by providing a

smooth path into the borehole, logging downhole at a

slow steady pace with negligible accelerations, and by

keeping the logging cable shielded from strong winds

as much as possible. The slip-ring noise is controlled

by using high-quality slip-rings.
System Description 7

The internal noise of the resistance readout also

contributes a small amount of noise to the recorded

resistances, as does the truncation error associated

with the instrument’s finite resistance resolution ∆Rr.

Combining the readout noise with that due to the

extraneous voltages and currents generated within the

Kelvin circuit, the standard deviation of the noise in

the resistance measurements is given by

σRn =

"

(a∆Rr)

2 +

$V #

Is

%2

+

$RsI#

Is

%2

#1/2

. (10)

Although the noise varies between temperature logs,

depending on circumstances, the constants in equation (10) are generally on the order of a ≈ 0.33,

V # ≈ 4 μV, and I# ≈ 0.14 nA for the PTLS under most

conditions. Extraneous voltages dominate the noise for

probe resistances less than 20 kΩ while extraneous currents dominate when Rs > 40 kΩ (fig. 3); the readout’s

contribution is relatively small at all resistances. The

raw noise described by equation (10) can be substantially reduced by judiciously applying the resistance

readout’s internal filters or by installing a filtering

capacitor between the circuit’s sense lines. When these

hardware noise filters are used, the noise σR ̃n actually

present in the recorded resistances is less than σRn .

The remaining noise is largely removed during data

processing by using wavelet denoising techniques.

2.2.4 Temperature Sensors

Equations (1) – (3) show that the temperature sensor is an important factor in determining the characteristics of the overall measurement system. The primary

sensors used with the PTLS consist of a parallel-series

network of 15 negative-temperature-coefficient (NTC)

thermistors divided into three packets.2 Each packet is

hermetically sealed in glass (fig. 5) to prevent changes

in the oxidation state of the metal oxide thermistors

and to relieve strain where the leads are attached to

the ceramic body of the thermistors. As a result, the

probes have good long-term stability with typical drift

rates of ≤ 0.025 percent per year. The packets are

wired in parallel so that only one third of the resistance readout’s excitation current Is passes through

any given thermistor bead, minimizing the self-heating

effect. To improve the ruggedness of the design, the

2A similar design appropriate for temperatures at midlatitudes is described by Sass and others (1971). The midlatitude

version has a much higher resistance than the polar model and

contains 20 thermistors divided into two packets.

0 2 4 6 8 10 12 !3

!2

!1

0

1

2

3

SAMPLE NUMBER (×103)

NOI SE (Ω)

GISP2!D

Figure 4. Raw noise for a typical logging experiment.

This record was acquired from the nonconvecting portion

of the GISP2-D borehole (central Greenland) without the

use of hardware noise filters. In this example, the standard deviation of the noise was σRn = 0.40 Ω with sensor

resistances Rs ranging from 11.9 to 12.7 kΩ.

thermistor packets are completely enclosed in a 4.0-

mm-diameter stainless-steel shell, allowing the probes

to withstand the pressures encountered at 7–8 km

in liquid-filled boreholes and the effects of corrosive

chemicals such as n-butyl acetate (many of the deep

boreholes drilled by the United States polar programs

are filled with n-butyl acetate). The use of many

small thermistor beads, glass encapsulation, and a

high-conductivity steel shell all help to produce a high

power-dissipation constant Pd. The Pd-value for these

custom probes is 55 mW·K−1 in circulating xylene

and is believed to be similar when logging through nbutyl acetate while the αT values range from about

−0.045 K−1 at 0◦C to −0.065 K−1 at −60◦C (fig. 6).

An inevitable disadvantage of this probe design is the

relatively slow response time. In n-butyl acetate, the

measured time constant is about 7 seconds. Five series

of custom probes, each with a different 0◦C resistance,

are currently available to optimize the characteristics

of the PTLS for any given experiment.

To convert sensor resistance to temperature, we use

the 4-term calibration function

T −1 = a0 + a1(ln Rs) + a2(ln Rs)

2 + a3(ln Rs)3 (11)

where the constants ai are determined for each sensor
8 USGS Polar Temperature Logging System

glass 

envelope

thermistor 

bead

stainless-steel shell

Figure 5. PTLS temperature sensor. The sensor consists

of a parallel-series network of 15 small bead thermistors

divided into three sealed packets. Beads extend over

a 10-centimeter length within the 4-millimeter-diameter

stainless-steel shell. The resistance readout measures the

combined resistance of the parallel-series network.

!50 !40 !30 !20 !10 0 !0.065

!0.06

!0.055

!0.05

!0.045

!0.04

T (◦C)

α

T (K−1)

T02

T01

P

Figure 6. Temperature coefficient of resistance (αT ) for

the P, T01, and T02 probe series used with the Polar

Temperature Logging System. These probe series have a

nominal resistance of 27 kΩ, 3.7 kΩ, and 2.5 kΩ at 0◦C,

respectively.

just before every field season in our thermal calibration

facility, and T is expressed in Kelvin. Equation (11) is

an extension of the often-used 3-term Steinhart-Hart

equation (Steinhart and Hart, 1968), which proves

inadequate for our purposes. An F-test (for example,

Bevington, 1969) demonstrates that a much better fit

to our calibration data can be obtained with the 4-term

function than with the standard Steinhart-Hart equation, particularly at temperatures below 0◦C. Sample

temperature-calibration data and the resulting 4-term

calibration fit (eq. 11) are shown in figure 7.

8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2 3.6

3.8

4

4.2

4.4 x 10!3

ln(Rs)

1/T

probe: T01!01

CALdate: 05APR11

coefs: 1.28652374e!03 3.01794892e!04 !4.41740779e!06 3.43578394e!07

(a)

!45 !40 !35 !30 !25 !20 !15 !10 !5 0 !1

!0.5

0

0.5

1

T (◦C)

∆

T (mK)

! = 0.153 (mK) (b)

Figure 7. Sample calibration data for one of the temperature sensors (T01-01) along with the best 4-term SteinhartHart fit to the data (a). In this case, residuals from the

fit to the calibration data have a standard deviation of

0.153 millikelvin (b).

The temperature resolution of the Kelvin circuit,

∆Tr ≈ ∆Rr

αT Rs

(12)

depends on the ratio of the smallest resistance resolvable by the resistance readout ∆Rr to the probe

resistance Rs. Thus, to achieve sub-mK sensitivity,

∆Rr/Rs must be less than 5 x 10−5. For the resistance

readout currently used with the PTLS, the ∆Rr/Rs

ratio ranges from 1.0 x 10−5 (worst case) to 1.0 x 10−6

(best case). The resulting temperature resolution is

less than 0.2 mK under all conditions (fig. 8). With the

resistance readout used prior to 2008, ∆Tr ranged from

0.1 to 1.1 mK; by judicious selection of the temperature

probe for pre-2008 logging experiments, the resolution

could almost always be reduced to less than 0.6 mK.

2.3 Depth-Measurement System

2.3.1 System Description

Depth information is obtained by measuring the

angular rotation dθ of a precision measuring wheel located within the winch assembly (fig. 1) that is pressed

tightly against the logging cable. Wheel rotation is

detected by an optical shaft encoder that transmits

quadrature waveforms to a bidirectional counter. The

counter then converts angular rotation to distance (or

depth) using dz ̃ = (Rw +r) dθ, where r and Rw are the
System Description 9

!60 !50 !40 !30 !20 !10 0 10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

T (◦C)

∆

Tr (mK)

P

T01

T02

Figure 8. Temperature resolution of the current PTLS

when using the P, T01, and T02 probe series.

radii of the logging cable and measuring wheel, respectively. The fundamental limit of the depth resolution

is determined by the effective radius of the measuring

system (Rw + r) and the number of quadrature pulses

output per revolution by the optical encoder. For the

4.5-km system, this limit is 0.254 cm. An additional

limitation is imposed by the depth counter. For the 6-

digit counter currently used with the PTLS, the depth

resolution ∆zr is 1.0 cm over the system’s full depth

range, although it can be set to ∆zr = 0.30 cm when

collecting depth-calibration data. Before 2007, ∆zr

was 0.3 cm for boreholes less than 545 m deep and

3.0 cm for deeper holes due to the limited buffer size

of the bidirectional counter used at that time.

2.3.2 Depth Corrections

To account for the force-dependent strains affecting the depth-measuring system, a depth-calibration

function Cd is established for each unique logging

environment. This is done by moving the logging

cable downhole approximately 40 m and comparing

the distance L ̃ reported by the depth counter with the

distance L measured by a fiberglass surveying tape that

has a low temperature coefficient of thermal expansion

(9.3 x 10−6 K−1); L is taken to be a measure of the

“true” distance. Cd is then defined by

Cd(Z ̃) ≡ L(Z ̃)

 ̃(Z ̃) − 1 (13) L

where Z ̃ is the depth of the sensor-end of the cable

(according to the counter) when the (L,L ̃)-data are

collected. Depth-calibration data are acquired with

the sensor-end of the cable at multiple depths Z ̃i spanning as much of a borehole’s depth range as possible.

Temperature changes in the measuring wheel and in

the test section of logging cable also affect the calibration data. Although we attempt to maintain a

consistent temperature during the calibration period,

temperature changes do sometimes occur. To remove

the temperature effects, we define thermally corrected

Cd values by

Cd(T !

w,Z ̃i) = Cd(Twi ,Z ̃i) − Rw

Rn

ewrTw

−

$ r

Rn

%

ecrTw − αfT (T !

w − Twi ) (14)

$ %

where T !

w is a reference calibration temperature and

Twi is the temperature at the measuring wheel when

the sensor-end of the cable is at Z ̃i. The second and

third terms on the right-handside of equation (14) account for changes in the effective radius of the measuring system due to thermal strains while the fourth term

accounts for the thermally induced longitudinal strain

in the cable as it enters the relatively cold, air-filled

portion of the borehole. Assuming the temperature of

the cable is approximately Twi when passing over the

measuring wheel, the radial strains in the wheel and

cable (ewrTw , ecrTw ) are both given by

exrTw = 1 + β(Twi − T !

w)

1 + α(Twi − T !

w) − 1 (15) &

where α and β are the linear and volumetric coefficients of thermal expansion. Our measuring wheels are

isotropic disks so that β = 3α. Factor Rn = m/∆θr

is the nominal radius used by the depth counter where

m is the counter’s internal multiplier and ∆θr is the

encoder’s angular resolution. Parameter fT is the

fraction of the temperature difference Twi − T(h) experienced by the cable during a calibration test where

T(h) is the temperature at the bottom of the air-filled

portion of the borehole; fT is typically about 0.3.

Once the thermally corrected Cd values have been

determined, a least-squares fit is made to

F(Z ̃i) = Cd(T !

w,Z ̃i) − Cd(T !w,Z ̃!) (16)
10 USGS Polar Temperature Logging System

where Z ̃! is a reference calibration depth selected from

one of the Z ̃i values near the middle of the depth

range; reference temperature T !

w is generally taken to

be the Twi value for the calibration data acquired at

Z ̃i = Z ̃!. The depth-calibration function is then given

by the sum of the reference Cd-value and the experimentally determined function F(Z ̃), which isolates the

force-dependent effects of the depth-measuring system

relative to C ! d(Tw, Z ̃!),

Cd(T !

w, Z ̃) = Cd(T !w, Z ̃!) + F(Z ̃). (17)

Figure 9 shows an example F(Z ̃) determined from

depth-calibration data acquired in the 1-km-deep Siple

Dome A borehole in West Antarctica.

200 400 600 800 1000 !5

!4

!3

!2

!1

0

1

2

3

4

5 x 10!3

Z ̃ (m)

F(  ̃

Z)

Figure 9. Least-squares fit to F(Z ̃i) values determined

from depth-calibration data acquired in the Siple Dome A

borehole, West Antarctica. Dashed lines indicate the uncertainty (±1σ) of the least-squares fit.

With the availability of the F(Z ̃) and Cd(T !

w, Z ̃)

functions, the total length of cable spooled into a

borehole during a logging experiment can be found

by integrating the distances dz ̃ reported by the depth

counter weighted by the depth-calibration function,

Z ≈

Z ̃

o

1 + Cd(T !

w,Z ̃ − z ̃) dz.  ̃ (18) ! ' (

Substituting from equation (17) and letting

δZF =

! Z ̃

o

F(Z ̃ − z ̃) dz ̃ (19)

be the correction for the force-dependent effects, the

length Z becomes

Z ≈

'

1 + C (T ! d Z ̃ w, !)

(

Z ̃ + δZF . (20)

This estimate accounts for most of the tension-induced

radial and longitudinal strains within the logging cable

and mechanical strains in the logging winch. However,

a number of additional corrections must be made to

obtain an estimate of the true sensor depth during

a logging experiment. These include a correction for

the buoyancy of the logging tool when immersed in

the borehole fluid, for temperature changes near the

measuring wheel affecting the radius of the depthmeasuring system, and for thermal strain in the cable

as it moves downhole.

The correction for tool buoyancy consists of a simple offset that occurs when the logging tool enters the

borehole fluid:

δZbt

clF = 0

K

) Z < h

g (mf

t − ma

t )(h + ∆x), Z > h (21)

K is the elastic stretch coefficient of the cable, g is the

gravitational acceleration, mf

t and ma

t are the weights

of the logging tool in the borehole fluid and in air, h is

the depth to the air/fluid interface in the borehole, and

∆x is the horizontal distance between the measuring

wheel and the hole. When logging with any of our

temperature sensors, δZbt

clF is less than the resolution of

the depth system and can be ignored. However, other

tools for which δZbt

clF may be larger (for example, sonic

and optical loggers) are occasionally used with our

logging winch, so we include the buoyancy correction

for completeness.

The temperature of the measuring wheel during a

logging experiment can be significantly different from

the reference calibration temperature T !

w. If the temperature of the wheel is Tw, the radial strain ewrTw

in the wheel relative to its calibration state can be

found from equation (15). Since Tw may vary considerably during a long logging run, the correction for the

thermally induced radial change of the wheel is found

through an integration:

δZwrT = Rw

Rn

Z ̃

o

ewrTw ( ̃z) dz.  ̃ (22) $ % !

The corresponding thermally induced radial strain in

the cable near the measuring wheel has a negligible

effect (< 10 parts per million [ppm]) on the estimated

depths and can be ignored.
Measurement Uncertainties 11

In polar environments, the fluid and overlying air

column in a borehole are typically much colder than

conditions on the surface near the logging winch. Thus,

the logging cable will contract as it moves beyond the

measuring wheel and enters the borehole. By the time

a section of cable reaches depth z, it will experience a

thermally induced longitudinal strain,

eclT (z) = α [T(z) − Tw] , (23)

relative to its length when it passed over the measuring

wheel. Some of this strain is built into the depthcalibration function Cd. Subtracting this portion, the

correction for the thermally induced longitudinal strain

in the cable is

δZclT =

Z

h

eclT (z) dz − αfT [ T(h) − T !

w]Z. (24) !

Applying these corrections to equation (20), our

estimate of the true sensor depth during a logging

experiment is

Z = 1 + Cd(T !

w,Z ̃!) Z ̃ + δZF + δZbtclF

+ δZwrT + δZclT . (25)

' (

For most situations, δZF is the largest correction and

δZclT is the second largest.

3 Measurement Uncertainties

A variety of factors influence the uncertainty of

the quantities being measured by the PTLS. For the

temperature-measurement process, the primary uncertainties include those related to the PTLS resistance readout, uncertainties in the corrections made for

systematic errors in the Kelvin circuit measurements

(eqs. 1, 2, 3, 8), and uncertainties in the temperature

sensor calibration used to convert measured resistance

to temperature. The primary uncertainties for the

depth-measurement process are related to the depth

corrections (eqs. 19, 21, 22, 24).

This section provides an analysis of the measurement uncertainties following CIPM guidelines (ISO,

1993b). It is assumed the resistance-measuring circuitry is located on the surface since the PTLS is normally operated in this mode; several of the uncertainties to be described are not present when using downhole measurement circuitry, although the temperaturerelated drift of the circuit potentially can be quite

large. With the CIPM approach, the components of

a measurand’s uncertainty are classified according to

the method used to evaluate them. Type A uncertainty

evaluations are based on statistical analysis of a series

of observations while Type B evaluations are performed

“by other means” using sound scientific judgment. The

information used in a Type B analysis may, for example, include a general knowledge or experience with

an instrument or the behavior of a material, manufacturer’s specifications, or calibration reports. The

degree of uncertainty for each component is given in

terms of the standard uncertainty ui that describes

the interval within which a quantity should occur with

67 percent probability. The combined standard uncertainty of a measurement is obtained by combining

the individual Type A and Type B standard uncertainties using the propagation of uncertainty law (Taylor and Kuyatt, 1994, Appendix A). We implement

the propagation law using the “root-sum-of-squares”

(RSS) method. Although some of the uncertainties to

be discussed are quite small with the current version

of the PTLS, they were in some cases substantially

larger with previous PTLS versions and therefore are

discussed for completeness.

3.1 ITS-90 Temperature Uncertainties

3.1.1 Resistance Readout Uncertainties

The PTLS generally utilizes a commercial readout

to measure the resistance of a temperature sensor

during a logging experiment. Sources of uncertainty

related to the resistance readout include the uncertainty of the resistance standards used to calibrate

the readout, nonlinearity across the resistance scales,

and internal noise. Current field procedures require

temperature logs be completed within 24 hours of the

readout’s latest calibration.

Resistance Standards. Immediately before each

logging experiment, the resistance readout is calibrated

using 10 kΩ and 100 kΩ DC resistance standards

(Fluke 742A), and a 0 Ω short. In preparation for

making measurements at the fixed calibration points,

the readout and resistance standards are warmed up

and then maintained at 23 ± 0.5◦C for at least one

hour. Once acquired, the calibration data are used to

determine the coefficients in a quadratic function fc(R)

which is used to correct the readout’s measurements

at other resistances. The uncertainties at the calibration points are found by combining the calibration

uncertainty of the standards themselves (0.5 ppm for

the 10-kΩ standard, 1.25 ppm for the 100-kΩ standard) with the uncertainty associated with their long-
12 USGS Polar Temperature Logging System

term drift (2.0 ppm·yr−1 for the 10-kΩ standard and

3.0 ppm·yr−1 for the 100-kΩ standard). With annual

recalibration, the combined standard uncertainty of

the resistance standards (in normalized form) is us,n ≡

(us/Rs) = 2.1 ppm at 10 kΩ and 3.2 ppm at 100 kΩ.

These uncertainties are propagated to other resistances

using a function of the same form as fc(R).

A different set of resistance standards was used

prior to 2008. These standards were periodically calibrated using an instrument with a standard uncertainty of 58 ppm. Long-term drift between calibrations

introduced an additional 58 ppm of uncertainty, yielding a combined standard uncertainty for these older

standards of us,n = 82 ppm at both 10 kΩ and 100 kΩ.

Resistance Readout’s Short-Term Uncertainty. The quoted short-term accuracy of the resistance readout currently used with the PTLS is ±0.25 Ω

for Rs < 5 kΩ and ±50 ppm for 5 kΩ ≤ Rs ≤ 200 kΩ.

This specification includes the nonlinearity of the readout across the measurement range and internal noise.

According to the manufacturer, the accuracy (±a)

specifies the width of a rectangular (uniform) probability distribution function; this PDF is taken to have

a corresponding standard uncertainty of a/√3 (Taylor

and Kuyatt, 1994). Thus the short-term standard

uncertainty of the readout is ur = 0.14 Ω for Rs < 5 kΩ

and ur,n ≡ (ur/Rs) = 29 ppm for 5 kΩ ≤ Rs ≤ 200 kΩ.

Before 2008, a different readout was used whose accuracy included a component for the full-scale resistance

value Rf . For this instrument the short-term standard

uncertainty was ur,n = 11.6 + 5.8 (Rf /Rs) ppm.

Combined Resistance-Readout Uncertainty

uR ̃s

. Combining the uncertainties of the resistance

standards with the short-term accuracy of the readout, we obtain the combined standard uncertainty uR ̃

of the resistance readout measurements. With thes

currently used resistance standards, uR ̃s is dominated

by the short-term uncertainty of the readout itself.

Thus uR ̃ = 0.14 Ω for Rs < 5 kΩ. For the more

common s

sensor resistances (Rs ≥ 5 kΩ), the combined

standard uncertainty is uR ̃ ,n ≡ (uR ̃ /Rs) = 29 ppm.

Prior to 2008 the uncertains

ty of the standards swas the

major contributor to uR ̃s at most resistances, leading

to combined readout uncertainties uR ̃ ,n ranging from

83 to 107 ppm. Since both of the uncertain s

ty components (us, ur) are classified as Type B, the combined

uncertainty of the resistance readout is also Type B.

3.1.2 Kelvin Circuit Uncertainties

As discussed in Section 2.2, the Kelvin circuit monitored by the resistance readout introduces multiple

sources of systematic error in the resistance measurements. These sources include leakage paths between

the circuit’s electrical conductors, capacitance effects,

self-heating effects, and thermal EMFs. Although

we correct for the systematic errors, there are uncertainties associated with the corrections. In addition,

electrostatic coupling, electromagnetic EMFs, triboelectric currents, and switching effects within the slipring assembly all generate noise in the Kelvin circuit.

This noise is largely removed during data processing

by using 1D wavelet denoising techniques (Misiti and

others, 2005). However, because the noise removal

process is imperfect, there remains an uncertainty in

the resistance measurements associated with the noise.

Leakage Paths. Applying the propagation of uncertainty law to the leakage path correction δRl (eq. 1),

the standard uncertainty ul of the leakage correction is

given by

ul = Rs

(Rs + Rl)2 (Rs + 2Rl)2 u2

Rs + R2

s u2

Rl (26) *

where uRl is the standard uncertainty of leakage resistance Rl. Since Rl ( Rs for all operational conditions,

we can re-express the leakage-path uncertainty in the

normalized form

ul,n ≡

$ ul

Rs

%

= 4

$uRs

Rl

%2

+

$Rs

Rl

%2$uRl

Rl

%2

. (27) &

The leakage resistance Rl is always ≥ 10 GΩ for the

PTLS while the standard uncertainty of its determination is uRl ≈ 11.5 GΩ based on the specifications of

the measuring instrument. With such high Rl values,

the second term within the square root of equation (27)

exceeds the first term by about 108. Thus the standard

uncertainty of the leakage correction reduces to

ul,n = Rs

Rl

uRl

Rl

. (28) $ % $ %

Capacitance Effects. The standard uncertainty

uc of the capacitance correction δRc (eq. 2) is given by

uc = τR# uRs

Rs

2

+

uC

C

2

+

uR!

R#

2

(29) &$ % + , + ,

where R# = ∂Rs/∂t is the rate of resistance change

while logging downhole. The accuracy of the instrument used to measure the capacitance of the logging
Measurement Uncertainties 13

cable, or of any filtering capacitors, establishes the

relative capacitance uncertainty (uC /C). Based on the

manufacturer’s specifications and a rectangular PDF,

(uC /C) ) 0.0074. This term completely dominates

(uRs /Rs), which is of the order 10−4 or smaller. Using

a Taylor Series expansion, the relative uncertainty of

R# is found to be

+uR!

R# ≈ 1

√3

1

m

+

∆tr

∆t (30) , $ %

where ∆t is the sampling rate, ∆tr is the resolution of

the time measurements (determined by the computer’s

clock), and m is a measure of the resistance change

between samples relative to the resolution ∆Rr of the

resistance readout,

m = Ri+1 − Ri−1

2∆Rr

. (31)

Our sampling rates are slow enough that ∆tr/∆t *

1/m under all circumstances. Dropping negligible

terms, the standard uncertainty of the capacitance

correction becomes

uc,n ≡

$ uc

Rs

%

= C∆Rr

∆t

-1

3 + m2 uCC

2

. (32) + ,

Self-Heating Effects. For the self-heating correction δRh (eq. 3), the associated standard uncertainty

uh is given by

uh = αT I2

sR2s

Pd

&

4

$uIs

Is

%2

+

$uRs

Rs

%2

+

$uPd

Pd

%2

. (33)

The relative uncertainty of the power dissipation constant (uPd /Pd) is estimated to be roughly 0.1, which is

several orders of magnitude larger than either (uIs /Is)

or (uRs /Rs). Dropping negligible terms, the uncertainty of the self-heating correction is

uh,n ≡

$ uh

Rs

%

= αT I2

sRs

Pd

$uPd

Pd

%

. (34)

Thermal EMFs. The standard uncertainty ue of

the thermal EMF correction δRe (eq. 8) is

ue = 1

Is

&

u2

Vemf + V 2

emf $uIs

Is

%2

. (35)

Since the relative uncertainty of the regulated test

current Is is several orders smaller than that of the

thermoelectric voltages, the standard uncertainty of

the thermal EMF correction is simply

ue,n ≡ ue

Rs

= uVemf

IsRs

. (36) $ %

Prior to 2008, uVemf was estimated to be about the

same magnitude as Vemf (∼ 0.5 μV). However, with the

current PTLS design, Vemf is essentially zero and thus,

so is uVemf and ue.

Noise. Extensive tests with noisy synthetic data

show that the wavelet denoising methods used during

data processing reduce the noise in the recorded resistances by a factor of 8. Thus the standard uncertainty

of the resistance measurements due to instrumental

noise is un ≈ σR ̃n /8 where σR ̃n ≤ σRn (see discussion,

Section 2.2.3).

Summary of Kelvin Circuit Uncertainties.

Equations 28, 32, 34, and 36 indicate the uncertainties

(ul, uc, uh, ue) of the Kelvin-circuit resistance corrections depend on the specific conditions during a temperature log and thus must be treated on a case-bycase basis. Despite the need to specifically consider

the conditions for each experiment when evaluating the

uncertainties, some general statements can be made.

(1) Of the resistance-correction uncertainties, the uncertainty of the leakage-path correction (ul) is the

largest with the current PTLS operating under normal

conditions (fig. 10). (2) Without the use of the resistance readout’s internal filters or a filtering capacitor,

the uncertainty un due to noise is the dominant Kelvincircuit uncertainty for sensor resistances less than 20–

30 kΩ. Even with the use of hardware filters to reduce

the noise uncertainty, un is generally still the dominant

uncertainty at low resistances (Rs < 20 kΩ). (3) At

high resistances (Rs > 70 kΩ), the uncertainty of the

leakage-path correction (ul) is the dominant uncertainty. (4) All the uncertainties associated with the

resistance corrections and noise are less than 0.1 mK

for sensor resistances in the range 10–170 kΩ. (5)

The uncertainties (ul, uc, uh, ue) associated with the

Kelvin-circuit resistance corrections are all classified as

Type B uncertainties while the noise uncertainty un is

Type A.

3.1.3 Temperature-Sensor Calibration Uncertainties

Before every set of field experiments, the PTLS

temperature sensors are calibrated on the ITS-90 temperature scale (Mangum and Furukawa, 1990) at the

USGS thermal calibration facility in Lakewood, Colorado. Temperatures on the ITS-90 scale are defined
14 USGS Polar Temperature Logging System

101 102

10!2

10!1

100

101

Rs (kΩ)

ux,n (PARTS PER MILLION)

uc,n

ul,n

uh,n

un,n

Figure 10. Standard uncertainties (ul, uc, uh) associated

with the resistance corrections, displayed in normalized

form ux,n ≡ (ux/Rs), for typical operating conditions. In

this example, the uncertainty of the capacitance correction

(uc) corresponds to the case shown in figure 3 (v = 5.5 centimeters per second, ∂T /∂z = 25 millikelvins per meter,

τ = 10 milliseconds, C = τ/Rs). The uncertainty of the

thermal EMF correction (ue) is essentially zero with the

current PTLS design. The noise uncertainty (un) shown

by the dashed line represents an upper bound for most

operating conditions; it assumes hardware noise filters are

not used. Equivalent temperature uncertainties are given

by ux,n/αT .

in terms of a set of fixed points (melting, boiling,

and triple points of pure substances), interpolating

instruments, and equations relating the property measured by each interpolating instrument to temperature.

Between 13.8 K and 1,235 K, the official interpolating

instrument is the standard platinum resistance thermometer (SPRT). Thus, equations describing how the

resistance of a standard SPRT varies with temperature are embodied in the definition of the ITS-90

temperature scale. To calibrate the PTLS temperature sensors, we use a 25.5-Ω quartz-sheath SPRT

as our local standard. The probes to be calibrated

are inserted into a copper equilibration block that is

immersed in a temperature-controlled fluid bath; the

SPRT is positioned in the equilibration block at the

same distance from the center as the probes. The

copper block effectively damps short-term temperature

fluctuations in the calibration bath and improves the

uniformity of the thermal field surrounding the probes

and the SPRT. Once the bath stabilizes at a predetermined calibration point, the data-acquisition system simultaneously acquires the SPRT reference temperature

T ! and the resistance R! of each temperature sensor

being tested. This process is repeated across the entire

calibration range in 2-K increments with upcoming

field experiments determining the calibration limits.

Total least squares is then used to find the constants

(ai) in the 4-term calibration function (eq. 11) from

the (T !, R!) calibration data. Residuals from this fit

typically have standard deviations ranging from 0.20

to 0.45 mK.

The uncertainty of the resulting PTLS

temperature-sensor calibrations is determined by

a number of factors, including: the uncertainty

of the SPRT calibration at ITS-90 fixed points,

the propagation of error between those points, the

accuracy of the SPRT readout, the accuracy of

the thermistor scanner, and the magnitude of the

temporal and spatial temperature variations within the

calibration bath. The residuals from the least-squares

fit to the calibration data do not reflect many aspects

of the total uncertainty of the temperature-sensor

calibration.

SPRT Reference Temperatures T!. The uncertainty of the SPRT reference temperature T ! is

determined by the uncertainty of the SPRT calibration and the accuracy of the instrument (readout)

used to monitor the SPRT temperatures. Our quartz

SPRT was most recently calibrated by Hart Scientific

(American Fork, Utah) who provided expanded uncertainties (coverage factor k = 2) at fixed calibration

points between −200◦C and 0◦C. The equivalent standard uncertainties are 0.5 mK at −197◦C, 0.2 mK at

−38.8344◦C (triple point of mercury), and 0.1 mK at

0.010◦C (triple point of water). Because the definition

of the ITS-90 temperature scale over this range is based

on equations describing the behavior of a standard

SPRT, the calibration uncertainties between the fixed

points are of the same order as those at the adjacent

fixed points. We use error propagation curves provided

by the National Institute of Standards and Technology to determine how the uncertainties at the triple

point of mercury (TPHg) and triple point of water

(TPW) propagate to other temperatures. Combining

the propagated TPHg and TPW uncertainties, the

standard uncertainty of the SPRT calibration ranges

from 0.27 mK at −60◦C to 0.10 mK at 0.01◦C.

The accuracy of the SPRT readout is ±0.0005 Ω for

SPRT resistances less than 25 Ω and ±20 ppm of the
Measurement Uncertainties 15

reading at higher resistances. Based on the thermal

response of SPRTs (McGee, 1988), these specifications translate to a standard uncertainty ranging from

2.77 mK at −60◦C to 2.90 mK at 0◦C. Combining the

uncertainty of the SPRT calibration with that of the

SPRT readout, we obtain the standard uncertainty uT !

of the SPRT reference temperatures. The combined

uncertainty uT ! is clearly dominated by the uncertainty of the SPRT readout with values ranging from

2.79 mK at −60◦C to 2.90 mK at 0◦C (fig. 11). Since

the uncertainty of the SPRT calibration and the SPRT

readout are both evaluated using Type B methods, the

uncertainty of the SPRT temperature measurements is

also classified as Type B.

Temperature-Sensor Resistance Measurements R!. The resistance of the PTLS temperature sensors being calibrated is monitored using

an 8-channel thermistor scanner whose accuracy is

±100 ppm of the reading. Based on a uniform PDF,

the corresponding standard uncertainty uR! of the

scanner’s resistance measurements is 58 ppm. Expressed in terms of temperature, uR! ranges from

0.88 mK at −60◦C to 1.28 mK at 0◦C for the T01

probe series; uR! is approximately 3 percent less for

the P probe series and 2 percent more for the T02

probes (fig. 11). This is a Type B uncertainty. As

with the SPRT readout, the thermistor scanner is

operated within the 18–28◦C range in order to achieve

full accuracy.

Calibration Bath and High-Conductivity

Equilibration Block. Other sources that affect the

uncertainty of the temperature-sensor calibrations include temporal and spatial variations of the thermal

field within the calibration bath. Both of these sources

can cause temperature offsets between the probes being

calibrated and the reference SPRT. The stability of the

calibration bath (Hart model 7060) is reported to be

±2.5 mK at −60◦C. This figure represents an expanded

uncertainty with coverage factor k = 2. Experiments

at −20◦C confirm this value. Thus we take the stability

of the bath to be ±2.5 mK across the full calibration

range; the corresponding standard uncertainty ubf of

the bath fluctuations is 1.25 mK. Several experiments

were done to determine the nonuniformity of the thermal field in the central portion of the bath where the

calibrations are performed. We find that the standard

uncertainty ubu of the spatial variations in this region

is 2.5 mK.

To further control the stability and uniformity of

the thermal field experienced by the probes and SPRT

during calibration, we use a 7.62-cm-diameter, high-

!60 !50 !40 !30 !20 !10 0

0

0.5

1

1.5

2

2.5

3

3.5

T (◦C)

u (mK)

uTc

uT !

uR!

uu uf

Figure 11. Combined standard uncertainty uTc of the

PTLS temperature-sensor calibration. Also shown are the

standard uncertainties of the individual components: uT ! is

the uncertainty of the SPRT reference temperature, uR! is

the uncertainty of the temperature-sensor resistance measurements, uf is the uncertainty associated with temperature fluctuations in the calibration bath, and uu is the

uncertainty due to bath nonuniformity. The three uR!

curves (dashed, solid, dash-dot) show the uncertainty of

the resistance measurements for the P, T01, and T02 probe

series, respectively.

conductivity (copper) equilibration block within the

calibration bath. The SPRT and PTLS probes are

inserted in tight-fitting holes located 2.90 cm from

the center. Heat-transfer simulations show that thermal fluctuations in the bath with periods less than

0.1 minute are completely damped at the position

of the probes, while those with periods of 3 minutes

(where the largest bath fluctuations occur) are damped

by a factor of about 0.4 (function f, fig. 12). These

fluctuations would not be an issue if the PTLS probes

and the SPRT had identical time constants so that

they would synchronously warm and cool in response

to the temperature fluctuations. However, the time

constant of the SPRT (18.5 seconds) is much longer

than that of the PTLS temperature sensors (4.0 seconds) in this situation. Convolving the response functions of the SPRT and the PTLS temperature sensors

(Saltus and Clow, 1994) with synthetic temperature

fluctuations shows that the maximum temperature discrepancy between the SPRT and the probes caused by
16 USGS Polar Temperature Logging System

dissimilar time constants occurs at a period of about

0.8 minute (function g, fig. 12). However, little power

occurs at such short periods due to the damping of

the block. Considering the joint effects of equilibration

block damping and the dissimilar time constants, the

largest discrepancies between the recorded SPRT temperatures and the probe temperatures occur at periods

of 2–3.5 minutes (function f ·g, fig. 12). This coincidentally matches the period where the bath fluctuations

have their greatest power. The resulting standard

uncertainty in temperature-sensor calibration related

to bath fluctuations is uf = (0.16) ubf = 0.20 mK.

0 2 4 6 8 10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PERIOD (minutes)

f

g

f · g

Figure 12. Damping of temperature fluctuations in

the calibration bath by the high-conductivity equilibration block. Function f = (up/ubf ) describes the relative

damping provided by the block; ubf is the magnitude of

the bath fluctuations while up is the magnitude of the

fluctuations inside the block near the probes and SPRT.

The block is essentially opaque to short-period fluctuations

(< 0.1 minute) but is transparent to periods longer than

30 minutes. Function g = (uf /up) shows the relative

temperature discrepancy between the SPRT and the probes

caused by their dissimilar time constants. Combining the

block damping with the dissimilar time-constant effect, the

standard uncertainty of the temperature-sensor calibration

due to bath fluctuations is uf = (f · g) ubf . The product

(f · g) reaches a maximum value of 0.16 at periods of 2–

3.5 minutes.

Persistent temperature gradients always exist to

some extent in calibration baths due to imperfect mixing of the bath fluid. Experiments with the Hart

7060 bath show that the standard uncertainty of the

thermal field in the vicinity of the equilibration block

is ubu = 2.5 mK. However, the field inside the block is

expected to be much more uniform. To quantify the

uniformity, the resistance change of an array of thermistors located within the block was monitored while

the block was rotated about its central axis; the bath

was held at a fixed temperature (to within ubf ) during

these tests. After removing temporal fluctuations due

to bath instability, the thermal field was found to be

uniform to within ±0.10 mK inside the block at the

location of the probes. The primary uncertainty of

this determination is associated with the noise of the

thermistor scanner (roughly ±0.04 mK) as the experiment effectively removed uncertainties associated with

the calibration of the individual thermistors; calibration, long-term drift, and nonlinearity of the thermistor

scanner; and bath stability. The standard uncertainty

of the temperature-sensor calibration related to bath

nonuniformity is then estimated to be uu = 0.10/

√3 =

0.06 mK. Both bath uncertainties (uf , uu) are classified

Type A.

Combined Temperature-Sensor Calibration

Uncertainty uTc . Combining the uncertainty of the

SPRT temperature measurements, of the thermistor

scanner, and of the bath variations, the combined

standard uncertainty uTc of the temperature-sensor

calibrations ranges from 2.93 mK at −60◦C to 3.18 mK

0◦C (fig. 11). Although the thermistor scanner and the

bath variations contribute to uTc , the uncertainty of

the SPRT temperature is the dominant factor in the

combined calibration uncertainty. A small dependence

of uR! on the αT -characteristics of each probe series

produces about a 1 percent difference in the combined

uncertainty at any given temperature; this effect is

small enough that it can be ignored. Because both

Type A and Type B methods were used to evaluate

the component uncertainties, the combined calibration

uncertainty uTc is classified as Type A,B.

3.1.4 Combined ITS-90 Temperature

Uncertainties

Combining the resistance-readout uncertainty

(uR ̃s ), the resistance-correction uncertainties (ul, uc,

uh, ue), the uncertainty due to instrumental noise (un),

and the temperature-sensor calibration uncertainty

(uTc ), we finally obtain the total standard uncertainty

uT of the PTLS temperature-measurement process. In

order to express uT in terms of temperature, most

of the component uncertainties (uR, ul, uc, uh, ue, un)

must be converted from resistances, where they are

more naturally defined, to temperatures. This conversion involves the αT -characteristics of the temper-
Measurement Uncertainties 17

ature sensors. Thus, the total uncertainty of the

temperature-measurement process depends to some extent on which probe is used during a logging experiment. This is particularly true at warm temperatures

due to the degradation of the resistance readout’s

accuracy at resistances less than 5 kΩ (fig. 13). To

avoid this degradation, we strive always to select a

probe whose resistance will remain above 5 kΩ for the

duration of an experiment; thus the T02 probes, for

example, are used only at temperatures below −15◦C

while the P-series probes can be used up to at least

0◦C. With this constraint, the standard uncertainty

of the temperature-measurement process ranges from

3.0 mK at −60◦C to 3.3 mK at 0◦C with the current

PTLS. As shown in figure 13, the total temperature uncertainty uT is strongly dominated by the temperaturesensor calibration uncertainty uTc with the current

PTLS design. The resistance readout contributes 0.5–

0.6 mK to the total while the upper limit of the

noise contribution is generally ≤ 0.25 mK. Individual

resistance-correction uncertainties (ul, uc, uh, ue) are

less than 0.1 mK under all normal conditions. The

combined uncertainty uT of the ITS-90 temperature

measurements is a Type A,B uncertainty.

Several of the temperature uncertainty components

were larger before 2008, especially the resistance readout uncertainty uR ̃ , the uncertainty of the thermal

EMF correction ( s

ue), and the uncertainty of the capacitance correction (uc). During 1993–2007, uR ̃s was

about 3 times larger (1.4–2.1 mK) than with the current system. In addition, the thermal EMF uncertainty

was comparable to the noise uncertainty un rather than

being zero. Although larger, uc was still less than

0.03 mK and thus of little consequence. Combining

all the components, the total standard uncertainty uT

of the temperature-measurement process during 1993–

2007 ranged from 3.2 mK at −60◦C to 3.8 mK at 0◦C.

3.2 Relative Temperature

Uncertainties

Section 3.1 focused on the standard uncertainty uT

of the PTLS temperature measurements relative to

the ITS-90 absolute temperature scale. For climatechange detection, this is the appropriate measure of

uncertainty. However when reconstructing past climatic changes using borehole paleothermometry, we

are not as concerned about uncertainties relative to

international absolute measurement scales as we are

about the potential distortion of a temperature profile

by measurement errors that could be misinterpreted

!60 !50 !40 !30 !20 !10 0

0

0.5

1

1.5

2

2.5

3

3.5

4

T (◦C)

u (mK)

uT

uTc

uR ̃ s

ul un

Figure 13. Combined standard uncertainty uT of the

ITS-90 temperature measurements obtained with the current PTLS when using the P, T01, and T02 probe series

(dashed, solid, dash-dot lines, respectively). Also shown

are the primary contributors to uT , specifically, uTc , the

standard uncertainty of the temperature-sensor calibrations, and uR ̃s , the standard uncertainty of the resistance

measurements. The un curves represent the upper bound

for the noise uncertainty under most operating conditions;

they assume the hardware noise filters are not used. The

standard uncertainty of the resistance corrections is less

than 0.1 millikelvin in all situations.

as being due to climate change; to date, borehole

paleothermometry generally has been used to analyze

the shape of individual temperature profiles. Thus

the offset of an entire temperature log due to miscalibration or system drift will not affect a reconstructed

climate history and is of little importance in this context. For borehole paleothermometry, the appropriate

uncertainties are those that describe the uncertainty

of a temperature profile’s shape, or expressed another

way, the standard uncertainty (ur

T ) of the temperature

measurements from a single temperature log relative

to one another.

An assessment of the temperature uncertainties discussed in Section 3.1 shows that nearly all are associated with errors that potentially can distort a profile’s

shape and thus should be included in the combined

standard uncertainty ur

T of relative temperature measurements. However, because the long-term drift of

a high-quality instrument will not in general produce

an error that distorts a profile, the drift component
18 USGS Polar Temperature Logging System

of a readout’s accuracy specification can be dropped

while the nonlinearity and internal noise components

should be retained. With this change, the standard

uncertainty ur

T of the relative temperature measurements produced by the PTLS ranges from 1.6 mK

at −60◦C to 2.0 mK at 0◦C (fig. 14). The standard

uncertainty ur

Tc of the temperature-sensor calibration

(based on instrument specifications) is still the largest

contributor, ranging from 1.6 mK at −60◦C to 1.8 mK

at 0◦C. These uncertainty values are likely to be overestimates because the dominant source of uncertainty

affecting ur

Tc and urT is the SPRT readout, and it is

used only over 1 percent of its range, whereas the

nonlinearity specification pertains to the instrument’s

entire range. Still, without tests to quantify the uncertainty over such a restricted range, we must use

the manufacturer’s stated full-range uncertainty. At

this time we simply note that the residuals from fitting

the sensor calibration data to equation (11) typically

have standard deviations ranging from 0.20 to 0.45 mK,

suggesting ur (and thus ur Tc T ) may be substantially

smaller than the values based on the SPRT readout’s

full-range nonlinearity specification. To accommodate

this possibility, we state that the “upper limit” of ur

T

ranges from 1.6 mK at −60◦C to 2.0 mK at 0◦C. As

with uT , the uncertainty ur

T of relative temperature

measurements is classified Type A,B. The ur

T upper

limit before 2008 was very similar to the current value,

ranging from 1.6 mK at −60◦C to 2.1 mK at 0◦C.

3.3 Depth Uncertainties

It is difficult to accurately determine the depth

below surface with any borehole logging system. With

the PTLS, systematic depth errors arise from forceinduced strains in the logging cable and winch, tool

buoyancy, temperature changes that alter the radius of

the measuring wheel, and thermally induced longitudinal strains in the logging cable once it enters the relatively cold borehole. We attempt to correct for these

errors (Section 2.3), although there are uncertainties

in the corrections. Errors also potentially arise from

slippage of the cable on the measuring wheel, debris in

the wheel’s cable groove, and downhole cable hangups.

Cable slippage is minimized by logging at a slow,

steady pace (5.5 cm·s−1, or less). If slippage occurs

with the PTLS, some of it presumably is incorporated

in the depth-calibration factor Cd; depth calibration

data are collected at the same downward speed and

tensions as utilized during a log. The boreholes we

log in polar environments are invariably filled with a

!60 !50 !40 !30 !20 !10 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

T (◦C)

u (mK)

ur

T

ur

Tc

uR ̃ s

u un l

Figure 14. Combined standard uncertainty ur

T of relative

temperature measurements and the individual uncertainty

components. The ur

T and urTc curves represent upper limits.

Symbols are identical to those used in figure 13.

clean, nonfreezing fluid (for example, n-butyl acetate,

arctic diesel fuel, or a nonaromatic equivalent). As

a result, debris in the groove of the measuring wheel

that would alter the effective radius of the measuring

system has generally not been an issue. Cable and (or)

logging-tool hangups within a borehole do sometimes

occur. These are detected by monitoring cable tension.

When hangups occur, the log is either stopped and

restarted once the tool is past the impediment or the

logging run is terminated, depending on the severity

of the hangup and the objective of the experiment.

In the former case, a depth offset with an unknown

uncertainty may occur at the obstruction; in the latter

case, no depth error arises. When cable hangups do

not occur, we are able to quantify the uncertainty uZ

of the logging sensor’s true depth Z using the root-sumsquare method. Individual uncertainties contributing

to uZ are as follows:

Recorded Depth Measurements. The leading

term in our estimated true sensor depth (eq. 25) involves the depth recorded by the counter weighted by a

calibration factor, [1+C ! ! ! ! d(T Z ̃ w, )]Z ̃. Since Cd(Tw, Z ̃ )

is simply a reference value that is always * 1, the

standard uncertainty of this term is equivalent to the

uncertainty uZ ̃ of the measurements reported by the

depth counter. We establish uZ ̃ through statistical
Measurement Uncertainties 19

analysis of multiple determinations of a borehole’s total

depth according to the counter. Given the PTLS’

operating environment, uZ ̃ is believed to primarily

reflect variations in cable slippage on the measuring

wheel.

Force-Induced Strains. Starting with equation (19), the standard uncertainty uF of the depth

correction for force-induced strains (δZF ) is found to

be

uF =

Z ̃

o

uF (Z ̃ − z ̃) dz ̃ (37) !

where u (Z ̃ F ) is the standard uncertainty of the experimentally determined function F(Z ̃). When F(Z ̃) is

adequately represented by a linear function, its depthdependent uncertainty is

.//

2

/

1

+

/ Z ̃ − < Z ̃i >

u (Z ̃ F ) = σ /+ . 0 n (38) n 1 +

Z ̃i − < Z ̃

,

2

i >

i=1

,

Here, σ is the standard deviation of the Fi data,

< Z ̃i > is the mean value of the calibration depths

Z ̃i, and n is the number of depth-calibration points

(Bowker and Lieberman, 1972). More complicated

expressions are required when F(Z ̃) is nonlinear.

Tool Buoyancy. Applying the propagation of

uncertainty law to the tool buoyancy correction δZbt

clF

(eq. 21), the standard uncertainty ubt of this correction

is

ubt = δZbt

clF "

+uK

K

,2

+

+u∆m

∆

,2

+

$ 2

uh

m h + ∆x

%

1

+

$ 2

u∆x

h + ∆x

% # /2

(39)

where ∆m = mf a t − mt . The fractional uncertainty

(uK/K) of the logging cable’s elastic stretch coefficient

is estimated to be about 0.1. This greatly exceeds the

fractional uncertainties associated with the mass difference ∆m and the lengths h and ∆x. Thus, uncertainty

ubt is well approximated by

ubt = Kg(mf

t − ma u t ) (h + ∆x)

+ K . (40) K

,

Radial Strain of Measuring Wheel, Thermal.

Letting φ(t) = Tw(t) − T !

w, the standard uncertainty

uwT of the correction for the thermally induced radial

strain of the measuring wheel (δZwrT , eq. 22) during

a log is

uwT =

$Rw

Rn

% 

u2

α

4! Z ̃

o

∂ewrTw

∂α dz ̃

52

+ u2

φ

4 Z ̃

o

∂ewrTw

∂φ dz ̃

52

1/2

(41) !



where

∂ewrTw

∂α = φ (1 + 3αφ)

−1/2 (1 + αφ)−3/2 (42)

∂ewrTw

∂φ = α (1 + 3αφ)

−1/2 (1 + αφ)−3/2. (43)

The uncertainty uα of the measuring wheel’s thermal

expansion coefficient is estimated to be of order 0.1α

while uncertainty uφ is typically 0.1–1.0 K. With these

values, uα and uφ are both significant contributors to

uwT .

Longitudinal Strain of Logging Cable, Thermal. Uncertainties in the logging cable’s thermal

expansion coefficient α, the temperature difference

ψ = T(z) − Tw, and parameter fT are all significant

contributors to the uncertainty ucT of the correction

for the thermally induced length change of the cable

as it descends a borehole (δZclT , eq. 24). Applying the

propagation of uncertainty law to δZclT and dropping

negligible terms, ucT is given by

ucT =





+uα ,2

4!

2 Z

2

eclT dz5+ u2

ψ [α (Z h

α − ) ]

h

1/2

+ u2

fT {α [ (h) − T ! 2 T w ]Z }

#

. (44)

For the logging cable, the fractional uncertainty (uα/α)

is estimated to be 0.1; uψ ranges 0.1–1.0 K while ufT

is about 0.1.

Combined Depth Uncertainty uZ. Combining

the individual uncertainties, the standard uncertainty

of a sensor’s true depth is

uZ =

*

u2

 ̃ + u2 + u2

F bt + u2wT + u2

Z cT . (45)

Ordinarily, uZ ̃ and uF are the dominant contributors

to uZ. Uncertainty components (uZ ̃, uF ) are classified

as Type A uncertainties, while (ubt, uwT , ucT ) are

Type B. The combined depth uncertainty uZ is thus

Type A,B. The magnitude of the individual components and of the combined uncertainty depend to a

large degree on specific borehole conditions and the

temperature near the winch.
20 USGS Polar Temperature Logging System

!40 !30 !20 !10 0

 0

 1

 2

 3

T (◦C)

Z (km)

(a)

10!3 10!2 10!1

 0

 1

 2

 3

u (mK)

uc uh ul un

(b)

0 1 2 3

 0

 1

 2

 3

u (mK)

Z (km)

un uR uTc

uT

(c)

0 0.5 1.0 1.5 2.0

 0

 1

 2

 3

u (mK)

un uR ur

Tc

ur

T

(d)

Figure 15. Temperature-measurement uncertainties for the proposed 3.5-kilometer deep WAIS Divide borehole in West

Antarctica. (a) Best-guess temperature profile at this site based on ice-flow modeling. (b) Expected resistance-correction

uncertainties (ul, uh, uc) and the noise uncertainty (un) assuming the hole is logged with the current PTLS using a

T01-series probe at 5.5 centimeters per second. (c) Combined standard uncertainty (uT ) of the ITS-90 temperature

measurements along with the largest contributing uncertainties. (d) Combined standard uncertainty (ur

T ) of the relative

temperature measurements along with the largest contributing uncertainties. The ur

T and urTc curves are upper limits.

3.4 Example: Proposed WAIS Divide modeling (Tom Neumann, written commun., 2006).

Borehole, Antarctica We anticipate the fluid in the proposed borehole will be

stably stratified (nonconvecting) within 2,000 m of the

surface once the hole is completed. Figure 15b shows To illustrate the magnitude of the uncertainties and the uncertainty of the resistance corrections assuming the degree to which they can vary with depth, we con- the hole is logged with the current PTLS using a T01- sider the conditions at the proposed WAIS Divide Ice series probe, the logging speed is 5.5 cm s−1, a 0.47- Core site in West Antarctica (79◦28# S., 112◦05# W.). ·

μF filtering capacitor is used, and the hardware noise Figure 15a shows the “best-guess” temperature profile filters are off. With a T01-series probe, the sensor resis- within the ice sheet at this location based on ice-flow
Measurement Uncertainties 21

tance should range from 20.2 kΩ at the coldest temperatures encountered (−33.9◦C) to 4.6 kΩ at the bottom

of the hole. The standard uncertainty (ul, uh, uc, ue)

of the resistance corrections are expected to be less

than 0.011 mK at all depths while the uncertainty un

associated with electrical noise is predicted to increase

from about 0.06 mK in the upper 2,000 m of the

borehole to 0.24 mK at the bottom.

Despite the 30-K temperature change along the

profile, the combined standard uncertainty uT of the

ITS-90 temperature measurements has only a small

depth dependence, varying from 3.05 mK in the upper

2,000 m to 3.19 mK at the bottom (fig. 15c). This

stems from the weak temperature dependence of the

dominant term, uTc . Similarly, the combined standard

uncertainty ur

T of the relative temperature measurements that would be used for borehole paleothermometry is only mildly depth-dependent (fig. 15d), ranging

from 1.71 mK in the upper 2,000 m to 1.86 mK at the

base of the ice sheet (about 3,465 m).

Figure 16 shows the uncertainty of the temperature

sensor’s location (depth) when logging the WAIS Divide borehole using plausible values for various parameters. However, it must be emphasized the true depth

uncertainties for WAIS Divide temperature logs will

depend on the actual borehole conditions and parameter values that occur during those logs. These factors

will not be known until the borehole is completed and

the hole has been logged several times. For the example

shown in figure 16, we assume the temperature Tw(t) of

the measuring wheel follows a diurnal cosine-function,

fluctuating ±5◦C about a mean value of −10◦C, i.e

typical summertime temperatures inside the drilling

structure where the logging winch will be located. The

reference calibration temperature of the wheel (T !

w) is

taken to be −10◦C, the fluid level in the borehole is

set at the firn/ice transition (h = 73 m), parameter

fT is 0.3, and uncertainties uφ and uψ are both 1 K.

With these values, the standard uncertainty uwT of the

depth correction for the thermally induced radial strain

in the measuring wheel during a log is limited to 11–

12 ppm. The correction for the shortening of the cable

in the cold borehole has a standard uncertainty ucT

ranging from 25 ppm near the surface to a peak value

of about 40 ppm when the sensor reaches Z ≈ 1,800 m.

For a PTLS temperature sensor, the uncertainty ubt of

the tool buoyancy correction is less than 2 ppm and

can be ignored.

To account for force-dependent effects on the depth

measuring system, we assume in this example that

nine pairs of depth-calibration data (L,L ̃) are col0 0.2 0.4 0.6 0.8

 0

 1

 2

 3

u (m)

Z (km)

uZ

uZ ̃

uF

ucT

uwT

(a)

0 50 100 150 200 250

 0

 1

 2

 3

u/Z (ppm)

Z (km)

uZ

uZ ̃

uF

ucT

uwT

(b)

Figure 16. Depth uncertainties for the proposed WAIS

Divide borehole as a function of sensor depth Z based on

plausible values for various parameters. (uF , ucT , uwT ) are

the standard uncertainties of the primary depth corrections

while uZ ̃ is the standard uncertainty of the measurements

reported by the depth counter. The combined standard

uncertainty uZ of the sensor’s true depth ranges from 200

to 250 parts per million.

lected across the range of borehole depths and that

the standard deviation of the fit to the resulting Fi

data is σ = 3.0x10−4. This value for σ is intermediate between that obtained in the recently logged 1-

km Siple Dome A borehole (2.4x10−4) and the 3-km

GISP2-D borehole (4.1x10−4); GISP2-D was logged

before the PTLS winch had a level-wind system, so
22 USGS Polar Temperature Logging System

Table 1. Specifications of the USGS Polar Temperature Logging System, mid-2008.

[

◦C, degree Celsius; mK, millikelvin; m, meter; cm, centimeter; ppm, parts per million]

Temperature range −60◦C to +23◦C

Temperature resolution 0.02–0.19 mK

Depth range 0–4,500 m

Depth resolution 1.0 cm

Standard uncertainty, ITS-90 temperature measurements 3.0–3.3 mK (Type A,B)

Standard uncertainty, relative temperature measurements 1.6–2.0 mK† (Type A,B)

Standard uncertainty, depth measurements 200–250 ppm‡ (Type A,B)

† Upper limit.

‡ 4.5-km winch with favorable logging conditions.

a much higher value for σ is expected from those

logs than would occur today. With the proposed set

of calibration data, the standard uncertainty uF of

the depth correction for force-induced strains ranges

from 200 ppm near the surface to a minimum value of

130 ppm at Z ≈ 2,500 m. The greatest unknown in

the projected depth uncertainties for the WAIS Divide

borehole involves the standard uncertainty uZ ̃ of the

measurements reported by the depth counter. For the

final set of logs obtained in the Siple Dome A borehole,

the uncertainty uZ ̃ was about 140 ppm. Thus, when

logging conditions are favorable, the repeatability of

the measurements reported by the depth counter is

fairly high. In the WAIS Divide example, we use a

nominal value for uZ ̃ of 150 ppm. Combining the

individual uncertainty terms, the standard uncertainty

of the temperature sensor’s true depth ranges from 200

to 250 ppm (fig. 16b).

4 Summary

From its origins in the early 1990s, the USGS

Polar Temperature Logging System has evolved into

a reliable high-precision data-acquisition system for

cold polar environments. This field-proven system has

been extensively used in Greenland, Antarctica, and

arctic Alaska. With a temperature resolution better

than 0.2 mK, the PTLS is capable of detecting small

subsurface temperature changes due to fluid convection

and other phenomena. Our initial goal of reducing the

uncertainty of the temperature measurements to about

1 mK has proven difficult to achieve. The standard uncertainty uT of the system’s ITS-90 temperature measurements is 3.0–3.3 mK. This is more than adequate

for climate-change detection and monitoring, especially

in the Arctic where contemporary surface-temperature

changes exceeding 1 K/decade have recently been observed. Relative temperature measurements used to

reconstruct past climate changes with borehole paleothermometry have a standard uncertainty ur

T whose

upper limit ranges from 1.6 to 2.0 mK. This is tantalizingly close to 1 mK.

The uncertainty of the temperature sensor’s location (depth) during a log depends on specific borehole

conditions and the temperature near the measuring

wheel. Thus the depth uncertainty must be treated

on a case-by-case basis. However, recent experience

with our large winch indicates that when conditions

are favorable (that is the winch is operated within a

shelter, steady power is available for the winch motor,

fluid in the borehole is free of debris, and so forth),

the 4.5-km system can produce depths with a standard

uncertainty uZ on the order of 200–250 ppm. The

small helicopter-transportable winches have undergone

a number of design changes recently. Although the

depth-measurement system for the small winches is

very similar to the 4.5-km system, we do not yet

have enough information about various parameters to

quantitatively assess uZ for logs acquired with these

portable winches. The current specifications for the

USGS Polar Temperature Logging System are summarized in Table 1.
Appendix 23

Appendix: Nomenclature

C capacitance

Cd(Tw, Z ̃) depth calibration function

eclT strain, cable, longitudinal, thermal

ecrT strain, cable, radial, thermal

ewrT strain, measuring wheel, radial, thermal

F(Z ̃) force-dependent function

g gravitational acceleration

h depth to air/fluid interface in a borehole

K elastic stretch coefficient

Is source current

I" extraneous current (noise)

Pd power-dissipation constant, thermistor

Q Seebeck coefficient

r radius, logging cable

Rl interconductor leakage resistance

RL lead resistance (Kelvin circuit)

Rs temperature-sensor resistance (true)

R ̃s temperature-sensor resistance (measured)

Rn nominal radius used by depth counter

Rw radius, depth-measuring wheel

R! sensor resistance during calibration

t time

T temperature

Tw measuring wheel temperature

T !

w reference depth-calibration temperature

T ! SPRT reference temperature

ubt standard uncertainty, tool buoyancy correction

uc standard uncertainty, capacitance correction

ucT standard uncertainty, correction for thermal

strain (longitudinal) of logging cable

ue standard uncertainty, thermal EMFs

uf standard uncertainty of temperature-sensor

calibration due to bath fluctuations

uF standard uncertainty, force-induced corrections

uF standard uncertainty of function F

uh standard uncertainty, self-heating correction

ul standard uncertainty, leakage correction

un standard uncertainty, instrumental noise

ur standard uncertainty, resistance readout

uR ̃s combined standard uncertainty, resistance

readout measurements

uR! standard uncertainty, temperature-sensor

resistance measurements during calibration

us standard uncertainty, resistance standards

uT combined standard uncertainty, ITS-90

temperature measurements

ur

T combined standard uncertainty, relative

temperature measurements

uTc combined standard uncertainty, temperature

-sensor calibration

uT ! combined standard uncertainty, SPRT reference

temperature

uu standard uncertainty of temperature-sensor

calibration due to bath nonuniformity

uwT standard uncertainty, correction for thermal

strain of depth measuring wheel

uZ combined standard uncertainty, sensor depth

uZ ̃ standard uncertainty of sensor depth

(as reported by counter)

v logging speed

V voltage

V " extraneous voltage (noise)

Vemf thermoelectric voltage (thermal EMF)

z true depth coordinate

z ̃ counter depth coordinate

Z sensor depth (true)

Z ̃ sensor depth (reported by counter)

Z ̃! reference calibration depth

α coefficient of thermal expansion, linear

αT coefficient of resistance, thermistor

β coefficient of thermal expansion, volumetric

δRc resistance correction, capacitance

δRe resistance correction, thermal EMFs

δRh resistance correction, self-heating

δRl resistance correction, leakage

∆Rr resistance resolution

∆Tr temperature resolution

∆t data sampling rate

∆x horizontal distance between measuring wheel

and borehole

∆zr depth resolution

δZbt

clF depth correction, tool buoyancy, cable,

longitudinal

δZclT depth correction, cable, longitudinal, thermal

δZF depth correction, force-induced strains

δZwrT depth correction, measuring wheel, radial,

thermal

σRn standard deviation of resistance noise

σR ̃n standard deviation of recorded noise

τ circuit response time

Acknowledgments. I gratefully thank Jack Kennelly and

Mark Ohms for their contributions to the design of the

PTLS and their exceptional skill in fabricating it. I also

thank Frank Urban for performing experiments used to

quantify some of the critical measurement uncertainties,

Tom Neumann for supplying the “best-guess” temperature

profile for the proposed WAIS Divide Ice Core site (West

Antarctica), and the reviewers for their helpful comments.

Funding for this work was provided by the U.S. Geological

Survey’s Earth Surface Dynamics Program.
24 USGS Polar Temperature Logging System

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Publishing support provided by: 

Denver Publishing Service Center 

Manuscript approved for publication, July 2008 

Edited by Mary A. Kidd 

Layout by Gary D. Clow 

For more information concerning this publication, contact: 

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(303) 202-4106 

Or visit the Earth Surface Processes Team Web site at: 

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