On the relationship between ground temperature histories ...

Ž .Global and Planetary Change 29 2001 327–348www.elsevier.comrlocatergloplacha

On the relationship between ground temperature histories andmeteorological records: a report on the Pomquet station

Hugo Beltrami)

Department of Geology, St. Francis XaÕier UniÕersity, P.O. Box 5000, Antigonish, NoÕa Scotia, Canada B2G 2W5

Accepted 28 March 2000

Abstract

ŽAn experimental air–ground climate station is operating in Pomquet, Nova Scotia, monitoring meteorological surface airtemperatures at three heights, wind velocity and direction, incoming solar radiation, precipitation, snow depth and relative

. Ž .humidity and ground thermal variables soil temperatures at depths of 0, 5, 10, 20, 50 and 100 cm . Readings are takenevery 30 s and 5 min averages are stored, in order to characterize the energy exchanges at the air ground interface. Here, Ireport on the first year of operation. For spring, summer and fall, we find that soil temperatures track surface airtemperatures with amplitude attenuation and phase lag with depth confirming that heat conduction adequately describe thesoil thermal field at the Pomquet site. For winter conditions, we find that heat transfer is dominated by latent heat releasedduring soil freezing and to a lesser extent by the insulating affect of snow cover. A numerical model of heat conduction wasused in order to estimate the magnitude of the heat released by freezing during the winter months. I also show that there is

Ž .an inverse correlation for the difference between soil 100 cm and air temperatures and the incoming solar radiation at thesite. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: ground temperature history; meteorological record; Pomquet station

1. Introduction

ŽAnalyses of meteorological records Jones et al.,.1999; Hansen and Lebedeff, 1987 and proxy cli-

Žmatic indicators e.g., Groverman and Landsberg,1979; Jacoby and D’Arrigo, 1989; Overpeck et al.,

.1997 suggest that surface air temperatures havebeen steadily rising since industrialization, particu-larly in the last century. Such evidence, and thecoincidence with the beginning of the emissions oflarge quantities of greenhouse gases into the atmo-sphere, raises questions about the effects of anthro-

) Tel.: q1-902-867-2326; fax: q1-902-867-2457.Ž .E-mail address: [email protected] H. Beltrami .

pogenic activities on the Earth’s climatic system andabout the potential consequences of associatedchanges in current world climatic patterns.

Debate on the effects of anthropogenic activitieson the climate of this century and on future climatecontinues to occupy a central part of policy develop-ers and the scientific community. The controversycenters mainly on the capacity of general circulation

Ž .models GCMs to simulate a complex system suchas the Earth’s climate. Hence, it is extremely impor-tant to ascertain the past climatic variations to allowrobust validation of GCMs. This has been accom-plished in part by the collection and analysis ofmeteorological and proxy climatic indicators in thelast decades. It remains, however, crucial to compile

0921-8181r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0921-8181 01 00098-4

( )H. BeltramirGlobal and Planetary Change 29 2001 327–348328

a consistent picture of climatic changes of the pastreconciling as many source of paleoclimatic informa-

Ž .tion as possible Overpeck et al., 1997 . Because ofŽshortcomings in the meteorological record Karl et

.al., 1989 and the fact that proxy data climaticŽreconstructions involve multiple assumptions see

.Bradley, 1985 , a complementary record has startedto be explored in the last decade. It is the determina-tion of ground temperature histories from geothermaldata. The interest in this method lies in the fact thatit examines a direct measure of temperature, free ofproblems such as variable standards and noise foundin meteorological data, and unlike proxy records, it

Žhas a very clear physical interpretation i.e., tempera-.ture . Reconstruction of past climatic changes from

geothermal data has proven, in the last few yearsŽ .e.g., Huang et al., 1997; Pollack et al., 1998 to bean additional source of information to complementmeteorological and proxy records of climatic change.

1.1. Climate from geothermal data

It has long been known that past ground surfacetemperatures can be estimated by analyzing the per-turbations to the steady state geothermal gradientŽe.g., Lane, 1923; Hotchkiss and Ingersoll, 1934;

.Birch, 1948 . Variations of the ground surface tem-perature are recorded in the subsurface as deviationsfrom steady state. Indeed, it has been customary toeliminate the effects of known climatic oscillationsŽ .mainly the last ice age from the temperature pro-

Žfiles used for HFD determination Powell et al.,.1988 . Furthermore, data obtained at many locations

around the globe often show that temperature gradi-ents are in fact disturbed for the first hundred metersŽ .e.g., Cermak et al., 1984; Pinet et al., 1991 . Al-though, non-climatic causes of the nonlinearities in

Žtemperature–depth profiles are possible e.g., ther-mal conductivity variations, subsurface heat produc-tion, ground water flow, topography, urban heat,

.changes in surface conditions, etc. , most of thesefactors can be examined and eliminated before ground

Ž .surface temperature GST analyses are performed.The abundance of borehole temperature data aroundthe world has the potential to yield ground surfacetemperature histories in vast areas of the continentsŽ .e.g., Lachenbruch and Marshall, 1986 which other-wise would remain undocumented.

In the Earth, these temperature perturbations ap-pear superimposed on the equilibrium temperatures.In a source free half space, the steady state heat flowis constant. The steady state heat flow is usuallyevaluated in the deeper part of the temperature pro-file, which is not affected by the recent temperaturechanges. The steady state temperature is then contin-ued to the surface and the perturbation is determinedas the difference between the measured temperatureand the upward continuation of the temperature pro-file. The magnitude of the anomaly is proportional tothe total amount of heat absorbed by the ground. Theshape of the perturbation is determined by the ther-mal history of the surface. This history can be in-ferred by comparing the calculated temperature per-turbation for a model of surface temperature with thedata and adjusting the model parameters until a fit isobtained or the surface temperature history can be

Žinferred directly by inversion see Lewis, 1992; seePollack and Chapman, 1993; Beltrami and Chapman,1994 for introductions to this subject; see Beltramiand Chapman on-line teaching aid at http:rrwww.

.geo.lsa.umich.edurIHFCrclimate1.html .The attractiveness of this approach to climatic

reconstruction rests on the characteristics of heatconduction into the ground. Unlike meteorologicalrecords subjected to high frequency variability andnoise, the Earth behaves as a low pass filter record-ing long-term trends of ground surface temperatureŽ . Ž .GST changes Joss, 1934 . For example, daily andannual temperature variations penetrate into theground to depths of approximately 1 and 20 m,respectively, whereas a 100-year long trend will berecorded in the subsurface and will be detectable to adepth of about 100 m. As such, climatic reconstruc-tions from geothermal data can provide a robustcomplement to the existing paleoclimatic database aswell as providing the long-term records of tempera-ture change needed for the validation of General

Ž .Circulation Models GCMs for future climate changeestimates.

Recently, several attempts have been made toŽ .reconstruct a pre observational mean POM in order

to extend the meteorological record into the past andprovide a reference on which to base the changes

Žinferred from meteorological data Harris and Chap-.man, 1997 and to calibrate proxy climatic indicators

Ž .Beltrami and Taylor, 1995; Beltrami et al., 1995 .

( )H. BeltramirGlobal and Planetary Change 29 2001 327–348 329

However, although the Earth’s response to the en-Ž .ergy balance or imbalance at the surface is related

to the surface air temperature, the temperature of theground is an integral of the effects of air temperaturevariation, vegetation cover and snow cover varia-

Ž .tions, phase changes freezing and thawing andsolar radiation changes at the ground surface. Theinteraction of all these variables determines the tem-perature of the ground in a complex and complicatedseries of processes. It is thus important to attempt toclarify the long-term effects of variations in energyexchanges at the air–ground interface on the subsur-face thermal regime.

Within this context an experimental air–groundstation operates in Pomquet, Nova Scotia, monitor-ing meteorological variables, soil thermal conditions,snow cover and vegetation cover, in order to exam-ine some of the processes involved in the energyexchanges within the first meter of the soil and at theair–ground interface.

This note provides some of the results arisingfrom these observations and carries out some simplenumerical calculations to illustrate the observations.It is shown that during spring, summer and fall,while air temperatures remain above the freezingpoint, the heat transfer within the soil is dominatedby conductive processess, and that during this timethe ground temperature tracks air temperature varia-tions closely, whereas during a period of time in

winter, freezing of the upper soil introduces non-con-Ž .ductive mechanism latent heat such that the ground

does not respond to air temperature variation untilthe upper layers of soil are completely frozen. Thatis, the ground does not appear to record air tempera-ture variations during this time period in winter. Wecompare the heat content of the first 5 cm of the soilcolumn as determined from data with the modeledsituation where soil freezing is absent in order toestimate the magnitudes of non-conductive pro-cesses.

2. Station setup

The experimental air–ground station was installedin a flat open field in Pomquet, Nova Scotia, CanadaŽ Y ? Y ?45839 27 N; 61851 25 W, elevation 5 m, see

.Fig. 1 approximately 100 m from a harbour. Thevegetation at the site consists of field grasses on aclay soil near a spruce forest some 30 m to the southof the station. The station consists of the Campbell

Ž .Scientific CS CM10 tripod supporting all instru-mentation. The instrumentation consists of a controlunit and a solar panel, two CS107 air temperatureprobes at heights of 0.17 and 1.5 m enclosed inradiation shields, a CS C5500 air temperature and

Žrelative humidity probe at a height of 2 m also.enclosed in a radiation shield , and six CS 107b soil

Fig. 1. Location of the Pomquet station in Nova Scotia, Canada.


temperature probes at depths of 0, 5, 10, 20, 50 and100 cm. A SR50 sonic ranger measuring snow coverŽ .or grass cover variations was also installed. The

Ž .sonic ranger uses ultrasound 50 kHz to measure thedistance to a target and thus it needs to be linked to atemperature probe to correct for temperature depen-dency of the sound velocity. The air temperatureprobe at 1.5 m was used for this purpose. A 05103Young Wind Monitor was installed to measure windspeed and direction at a height of 3 m. A TexasInstruments TE525M tipping bucket rain gauge mea-sures precipitation; this instrument was installed in aseparate stand at a height of 50 cm, a few metersaway from the main station to avoid a Arain-shadowBeffect from the main station tripod and instrumenta-tion. A Licor L1200S pyranometer installed at 2.8 mheight to avoid interference from other instrumentson the tripod, was used to measure incoming solarradiation. The station is operated with a CS CR-21XLdata-logger powered by rechargeable batteries and aMSX-20 solar panel. The data is stored directly in aSM716 storage module, which can be removed fordata retrieval. This Station has operated continuouslysince early August 1997. Instruments are sampledevery 30 s and 5 min averages of all sensors arerecorded. We chose a 5-min averaging interval toallow high frequency variability to be recorded forparallel studies on the signatures of conductive and

Žnon-conductive processes in the soil e.g., Hinkel et.al., 1990; Hinkel and Outcalt, 1993 .

The accuracy of the CS107 air temperature probeand CS107b soil temperature probes is -"0.2 K.Most of this error corresponds to the offset from theinterchange of the probes, but with a single pointcalibration, it is possible to eliminate the probe offsetand the working accuracy is reduced to about 0.1 K.The CS107b probes were installed using the follow-ing procedure. A hole was dug in the ground, takingcare of maintaining the statigraphy of the removedsoil as much as possible. The probes were insertedhorizontally into the vertical wall of the hole makingsure a very tight fit between the probe and the soilwas achieved. Horizontal insertion avoids the possi-bility of fluid transport through flow pathways in the

Ž .unconsolidated soil Hinkel and Nicholas, 1995 .The removed soil was then replaced as carefully aspossible to avoid further disruption of the site and toreduce water infiltration through the conduits opened

Table 1Summary of instrumentation

Parameter Precision Setupa bAir temperature -0.2 K r0.1 K 0.17, 1.5, 2.0 m

heighta bSoil temperature -0.2 K r0.1 K 0, 5, 10, 20, 50,

100 cm depthPrecipitation 0.1 mm 50 cm heightSnow–grass "1 cm or 0.04% 1.75 m heightdepthSolar radiation "3% 2.80 m heightWind speed 0.04 mrs 3.0 m heightWind direction 58 3.0 m heightRelative humidity 1–5% 2.0 m height

a Before probe calibration.bAfter calibration.

by the probes cables. A layer of grass sod wasreplaced at the surface when the setup was com-pleted in an attempt to preserve as much as possiblethe surface characteristics. The Asurface probeB was

Žinserted just below the grass sod, i.e., at the soil.surface under the organic matter layer . We did not

attempt to place the probe directly on the surface toavoid spurious heating by direct solar radiation. Al-though measurements were taken since early August1997, a few weeks for the settling of the probes inthe subsurface were allowed and we present datacovering the period from September 1, 1997 toAugust 30, 1998. A summary of the instrumentspecifications is given in Table 1.

3. Data: 1997–1998 at Pomquet

Data acquired during the period of time betweenSeptember 1, 1997 and August 30, 1998 is presentedbelow. A summary of the monthly averages is shownin Table 2. As stated above, all instrumental datawere sampled every 30 s. The data was then aver-aged over a 5-min window and recorded. There areonly two 2-h periods of missing data for the entireyear; this is due to a computer malfunction duringdata transfer. For the present analysis, these missingdata intervals were interpolated.

All reported monthly averages in Table 2 werecalculated by integrating over the period using the 5min averages, such that they are not readily compa-


Table 2Monthly data summaries calculated from integration of data at highest resolution

AIR Air Air Soil Soil Soil Soil Soil SoilŽ .2 m 1.5 m 17 cm 100 cm 50 cm 20 cm 10 cm 5 cm 0 cmŽ . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .8C 8C 8C 8C 8C 8C 8C 8C 8C

Sept. 1997 15.0 14.4 14.4 15.1 15.8 16.2 16.5 16.5 16.6Oct. 1997 8.1 7.5 7.3 12.4 11.6 11.0 10.8 10.6 10.4Nov. 1997 4.2 3.6 3.5 9.2 7.7 6.7 6.4 6.2 6.0Dec. 1997 y1.3 y2.0 y2.1 5.5 3.2 1.8 1.4 1.1 0.8Jan. 1998 y3.5 y4.1 y3.5 3.3 1.5 0.5 0.3 0.1 y0.1Feb. 1998 y2.4 y3.1 y3.1 2.5 1.0 0.2 0.1 y0.1 y0.2Mar. 1998 0.8 0.1 0.0 2.5 1.5 1.3 1.4 1.4 1.4Apr. 1998 4.1 3.5 3.7 4.0 4.3 5.1 5.6 5.6 5.9May 1998 11.3 10.7 11.2 8.4 10.4 12.3 13.4 13.6 14.1June 1998 14.5 14.0 14.7 11.9 14.1 16.1 17.2 17.5 17.9July 1998 18.7 18.1 18.3 14.8 17.1 19.0 19.9 20.2 20.5Aug. 1998 19.4 18.8 18.6 16.5 18.2 19.5 20.2 20.4 20.6Mean 7.4 6.8 6.9 8.8 8.9 9.1 9.4 9.4 9.5

Rain Wind Wind Snow– Solar RelativeŽ .mm speed direction grass radiation humidity

2Ž . Ž . Ž . Ž . Ž .mrs 8 m kWrm %

Sept. 1997 64.4 1.19 211.29 0.10 0.13 84.9Oct. 1997 29.7 1.72 248.39 0.11 0.09 81.5Nov. 1997 170.9 1.88 207.70 0.11 0.05 88.5Dec. 1997 99.0 2.05 229.77 0.09 0.04 86.1Jan. 1998 88.5 2.36 210.23 0.15 0.04 85.1Feb. 1998 71.6 2.06 218.86 0.11 0.08 88.8Mar. 1998 90.4 1.87 211.94 0.11 0.10 85.5Apr. 1998 122.6 2.06 218.21 0.08 0.13 87.2May 1998 88.1 1.43 193.72 0.08 0.21 82.4June 1998 86.1 1.39 184.99 0.10 0.20 86.1July 1998 71.3 1.19 180.89 0.13 0.21 83.9Aug. 1998 52.1 1.16 211.27 0.10 0.21 79.9

aMean 1035 1.70 210.6 0.11 0.123 85.0

aCumulative sum.

rable to the standard meteorological data means eval-Žuated from daily maxima and minima see Putnam

.and Chapman, 1996 for a discussion of this issue .Monthly air temperatures have a yearly range of 22.9K at heights of 1.5 and 2 m and a range of 22.1 K ata height of 0.17 m. All minima for the air tempera-ture records occurred in January and all maxima inAugust. Yearly ranges of soil temperatures are 20.8K at the surface, 20.5 K at 5 cm depth, 20.1 K at 10cm depth, 19.3 K at 20 cm depth, 17.2 K at 50 cmdepth and 14.1 K at 100 cm depth. All soil tempera-ture maxima occur in August; all minima occur inFebruary with the exception of the records at 100

cm, which show the minima in March. The magni-tude of the temperature ranges for the soil decreaseswith depth with the range difference between thesurface and 1 m depth being 6.7 K.

Although monthly averages are useful for thepurpose of comparison, higher resolution data arerequired to examine the processes involved in theenergy exchange at the air–soil interface. Fig. 2shows the full year daily means time series for anumber of these variables recorded in Pomquet.

Fig. 2a shows the records of air temperature atthree heights measured in Pomquet. There is littledifference between the air temperature records at


height of 2 and 1.5 m. However, air temperature at0.17 m differs significantly during the summer underthe effect of direct solar radiation on the groundsurface affecting the probe closest to the groundsurface, and sometimes during the winter when theprobe is buried by snow. Fig. 2b shows the recordsof soil temperature at the surface and at a depth of 5cm. The most remarkable feature of these records isthat the soil temperature remains nearly constantbetween days 100 and 180 in the figure, likely dueprimarily to latent heat released from the freezing ofthe soil and also, in a small part, to the insulatingeffect of snow cover. Snow cover at the station site

is sporadic and thin such that the snow cover insulat-Ž .ing effect e.g., Zhang et al., 1996 is not obvious

from the data. A control experiment at a nearby siteis in progress to address this issue. Fig. 2c shows thesoil temperature data obtained at 0.1 and 0.2 mdepths. This situation is very similar to the onedescribed above for the shallower records; but in thiscase, high frequency and amplitude attenuation are

Ževident. The onset of the zero curtain effect Hinkel.et al., 1990 occurs around day 150 rather than at

day 100 for the shallow probes. The data indicatesthat soil freezing did not reach 0.2 m, thus, thetemperature at 0.2 m is a resultant of heat transfer

Ž .Fig. 2. Daily means of all variables monitored at the station for period between September 1, 1997 and August 30, 1998. a AirŽ . Ž . Ž .temperatures at the indicated levels, b soil temperatures at the surface and 5 cm, c soil temperatures at 10 and 20 cm, d soil

Ž . Ž . Ž . Ž . Ž .temperatures at 50 and 100 cm, e incoming solar radiation, f precipitation, g snow and grass cover variations, h wind speed, i windŽ .direction, j relative humidity.


Ž .Fig. 2 continued .

from the upper and lower soil layers and the heatreleased by the moving freezing front. Fig. 2d showsthe 0.5 and 1 m soil temperature records. The lag ofthe response of these deeper temperatures with re-spect to air temperature variations is apparent as wellas the filtering of the high frequency variations.Examination of this figure reveals that in fall andwinter, heat flows out of the ground and in springand summer heat flows into the ground. This hasbeen the classical interpretation of the heat flow atthe air–soil interface and it is referred as the Aheat

Ž .valveB effect Gilpin and Wong, 1976 .Fig. 2e shows the daily average of the incoming

solar radiation measured at the site. The yearly cycleis seen as the first order variation. Superimposed onthe yearly cycle, we can clearly see shorter scale

variations due to weather system passage and associ-ated cloud cover changes. The yearly mean incomingsolar radiation at this site is 123 Wrm2 with amaximum daily value of 365 Wrm2.

Fig. 2f shows the daily cumulative rain fallrecorded at the station. Total rainfall reached 1035mm, with a daily mean of 2.83 mm. The maximum

Ž .daily precipitation recorded, 46.7 mm around day180 in Fig. 2f, is due to a blowing wet-snow eventplus the melting of the snow accumulated on and

Ž .inside the rain gauge bucket see Fig. 2f, g and h .Fig. 2g shows the variation of the vegetation coverand during the winter time, the variation of snowcover. Some of the high frequency variability ofthese records are correlated with the wind speed andit represents the motion of the long grass stands



under the influence of the wind. Recall that at thisstation, the surface cover variations are measured asa quantity proportional to the travel time of ultra-sonic pulses from the sonar ranger to the surfacewhere they reflect back to the probe. It is not possi-ble to separate the contributions of snow cover andvegetation cover in winter since it was decided not toalter the natural surface conditions at the site Forexample, the maximum daily value on the recordshows a snow depth of almost 50 cm. This anomalyis due to blowing snow that is moving almost hori-zontally such that the snow flakes reflect the ultra-sound pulses back to the detector before the beamreaches the surface of the snow accumulated on the

Žground, giving this type of spurious reading see Fig..2h . A typical example of snow compaction is appar-

ent in Fig. 2f near day 130. The sudden decrease ofthe vegetation cover around days 315 and 340 on thefigure are the results of deliberate mowing of thegrass at the station in order to examine short termeffects of vegetation cover change on the soil ther-mal regime at high frequencies. Fig. 2h and i showsthe daily mean wind speed and wind direction data,respectively. The maximum daily mean was 7.89mrs with a yearly mean reaching 1.69 mrs. Themaximum value recorded at the highest data resolu-

Ž .tion 5-min averages is 10.7 mrs recorded during aŽ .storm see Fig. 2f and g . The average wind direction

is 2108.Fig. 2j shows the recorded daily means for the

relative humidity. The yearly average is 81% makingthe climate at this site rather humid and revealing


Table 3High resolution and daily summaries of data

Variable 5-Min data Daily data

Max Min Mean Max Min Mean

Ž . Ž .Air temperature 0.17 m 8C 33.6 y18.3 7.1 23.6 y13.7 7.1Ž . Ž .Air temperature 1.5 m 8C 32.9 y17.8 6.9 25.1 y13.6 6.9Ž . Ž .Air temperature 2 m 8C 33.6 y16.9 7.6 25.7 y12.9 7.6Ž . Ž .Soil temperature 0 m 8C 28.5 y1.1 9.6 23.7 y0.6 9.6Ž . Ž .Soil temperature 5 cm 8C 26.4 y0.3 9.5 23.1 y0.2 9.5Ž . Ž .Soil temperature 10 cm 8C 25.1 y0.1 9.6 22.6 y0.0 9.6Ž . Ž .Soil temperature 20 cm 8C 22.2 0.1 9.3 21.2 0.1 9.3Ž . Ž .Soil temperature 50 cm 8C 19.1 0.8 9.0 18.9 0.8 8.9Ž . Ž .Soil temperature 100 cm 8C 16.8 2.1 8.9 16.7 2.1 8.9

Ž .Precipitation mm 7.5 0 0.01 46.7 0 2.83Ž .Snow–grass cover m 1.62 0 0.11 0.53 0.06 0.11

Ž .Wind speed mrs 10.7 0 1.69 7.89 0.37 1.692Ž .Solar radiation kWrm 1.087 0 0.123 0.326 0.002 0.123

Ž .Relative humidity % 103.6 21.3 81 103.4 56.2 81

that the role of latent heat at the air–soil interface isprobably very important.

Examination of Fig. 2a reveals that the high fre-quency variability present in the air temperaturerecords is filtered out by the ground as expected, alsowe can clearly see the occurrence of a lag betweenminima and maxima at the surface and the corre-sponding values at depth. Soil temperature at 1 mappears to have filtered out most of the high fre-quency components of the surface variation andrecords only the medium term trends of the annualcycle, although with a lag of about 2 months or so.

Daily temperature ranges for air temperature are37.2, 38.7 and 38.6 K for heights of 0.17, 1.5 and 2m, respectively. For soil temperatures, the tempera-ture ranges are 24.3, 23.32, 22.6, 21.2, 18.8 and 14.6K for depths of 0.0, 0.05, 0.1, 0.2, 0.5 and 1.0 m,respectively. A summary of the daily and high reso-lution data is presented in Table 3.

There are some features of the air and soil tem-perature records that should be examined here. The5-day period, shown in Fig. 3a between September30 and October 5 1997, illustrates the behaviour ofthe soil temperatures showing the well known damp-ing of the amplitude and the increase of the time lagas a function of depth. This is typical of summer andearly fall behaviour when the transfer of heat in thesubsurface is dominated by conduction. Fig. 3b showsthe same variables and the record of air temperatureat a height of 2 m for the 2-week period between

December 6 and 20, 1997; here the onset of groundfreezing is apparent. As air temperatures drop belowfreezing soil temperatures remain above 08C asfreezing takes place in the upper layers of the soil.This occurs around Julian day 350 in Fig. 3b wherethe surface soil temperature remains at 08C whilesoil freezes. During this time, the soil does notrecord air temperature variations. Although snowcover does have a significant effect insulating the

Žground at other locations Zhang et al., 1996; Gos-.nold et al., 1997; Beltrami and Mareschal, 1991 , our

records indicate a sporadic, thin snow cover duringthe winter at this location.

Freezing of the soil continues until February 25,Ž .1998 Julian day 56 in Fig. 3c, day 180 in Fig. 2

when a sudden air temperature increase thaws theupper layers of the soil and the subsurface startsresponding once again to air temperature variations.Notice that the surface probe responds first, then theprobe at 5 cm and then the others in order ofincreasing depth.

4. Assessing the heat transfer regime of the ground

4.1. Theoretical framework

One of the fundamental assumptions required forthe reconstruction of ground surface temperature his-tories from geothermal data and eventually past cli-


Ž .Fig. 3. a Detail view showing the record of soil temperatures at the indicated depth for a 5-day period in late summer. The decay of theŽ . Ž .amplitude and the increase in time lag with depth are apparent, b expanded view 2 weeks of the record of air and soil temperatures at theŽ .indicated height and depths showing the onset of soil freezing, c detail of the record of air and soil temperature showing the thawing of the

soil. Note the time delay between records.



matic change is that the heat transfer regime withinthe ground be conductive. In an ideal perfectly con-ductive soil periodic, variations of surface tempera-ture are propagated into the ground according to theheat conduction equation

ET E2Tsk , 1Ž .2Et Ez

where k is the thermal diffusivity, z is depth and tis time.

In order to assess the character of the heat transferŽ .in the soil, Eq. 1 can be use to solve, for example,

a forward model assuming the temperature record ofthe uppermost soil layer is periodic. In our case, aneasier approach may be taken by considering thetemperature record as a model consisting of a seriesof step changes in temperature. A series of stepchanges can approximate any real air or soil temper-

Ž .ature variation Putnam and Chapman, 1996 . Insuch case, the forward problem for a single steptemperature change occurring at time t before pre-

Ž .sent is given as Carslaw and Jaeger, 1959z

T z sDT erfc , 2Ž . Ž .0 ž /'2 k t

where k is the thermal diffusivity, t is time beforeŽ .present, DT is the surface temperature and T z is0

Žthe temperature at depth z into the soil profile z.positive downward .

For a series of steps of equal duration expressedas departures from the mean, starting at time t in thel

past, today’s temperature at depth z is given by

zT z sT erfcŽ . l '2 k t

jsly1 zq T erfcÝ j

2 k ly j q1 t( Ž .js1

zyerfc . 3Ž .(2 k ly j tŽ .

Ž .Eq. 3 can approximate a time series of tempera-ture data and be used as a forcing function at thesurface.

Ž Ž ..Alternatively, the heat equation Eq. 1 can besolved using finite differences subjected to appropri-


ate initial and boundary conditions either for a ho-mogeneous semi-infinite medium or it can be solvedfor a layered media by including the heat flowcontinuity at each interface between the layers.

For a stratified medium composed of n layers,each with constant thermal properties, the tempera-

Žture at any layer in this model must satisfy e.g.,.Clauser, 1984

ET E2Tn nsk 4Ž .n 2Et Ez

where n is the layer order, k and T are the thermaln n

diffusivity and temperature at layer n, respectively.Additionally, the continuity of temperature and heat

flow must be satisfied at the interface between layerssuch that the following conditions must be satisfied

T zs l sT zs l , 5Ž . Ž . Ž .n nq1 nq1 nq1

ET ETn nq1l zs l sl zs l , 6Ž . Ž . Ž .n nq1 nq1 nq1

Ez Ez

where l and l are the thermal conductivity forn nq1

layer n and nq1, respectively. At the surface, theŽ .temperature T zs0 sT for t)0. The conditions1 0

at the lower boundary can be set by the deepestŽtemperature record measured at the station i.e., Tlow

Ž ..sT 100 cm .data

Computations are carried out by expressing theabove equations in finite difference form and theinitial conditions are obtained from the data andstability is assured by high sampling rate.

Ž .Fig. 4. a APhase spaceB plot obtained from indicated records of air and soil temperatures treated as perpendicular superposition ofŽ . Ž .harmonic motions, b same as a , but for soil temperature records.



4.2. Analysis

A first qualitative assessment of the heat transferregime at the air–soil interface and within the soilcan be obtained under the assumption that air andsoil temperature variations over a yearly cycle areperfect sinusoidal oscillations. Perpendicular super-

Ž .position of temperature series Aphase-spaceB plots ,under this assumption, should yield regular intercep-

Ž .tion figures Beltrami, 1996 . Departures from thisbehaviour yields qualitative information about the

Ž .correlation i.e., amplitude and phase relation of thetemperature records.

Fig. 4a shows the perpendicular superposition ofthe records of air and soil temperature at the surface,10, 50 and 100 cm depth as indicated in each frame.The non-conductive character of the heat transferregime at the air–soil interface is apparent from theflattening of the interception figures around the

freezing point for all soil temperatures. Fig. 4b showssimilar plots, but in these cases, the soil temperaturerecord at 10, 20, 50 and 100 cm are plotted with soiltemperature data at the surface. The interceptionfigures are, of course, less noisy because of highfrequency filtering by the ground, and they are quali-tatively closer to the interception ellipses that wouldbe generated in a perpendicular superposition ofperfect harmonic oscillators.

As an additional approach to assess the characterof the heat transfer regime in the subsurface, we canperform Fourier analyses of the time series of soiltemperatures. Fourier modeling calculated using a

Ž .multitaper method Mann and Lees, 1996 for sam-ple soil temperature records are shown in Fig. 5. Fig.5a shows the power spectrum for the record of dailymean air temperature at 2 m height, while Fig. 5b–dshow the spectra for daily means of soil temperaturesat the surface, 20 and 100 cm depth, respectively.


Ž . Ž . Ž .Fig. 5. Power spectra for daily temperature time series a air temperature at 2 m height, b soil surface temperature, c soil temperature atŽ .20 cm depth, d soil temperature at 1 m depth. The smooth lines represent the 99% confidence level of the estimated parameters for this

Ž .oscillatory model see Table 4 .

The smooth line across the figures represents theŽ99% confidence level i.e., 0.99 probability that the

observed peaks above this level are not coincidences.due to noise of the estimated parameters for this

oscillatory model of the data. Hinkel and OutcaltŽ .1993 have shown that soils subjected to non-con-ductive processes show spectra enriched in highfrequencies. In our case, the significant dominant

periods, shown in Table 4, for all of the soil tempera-ture records are nearly identical indicating that aver-aged over the year the subsurface is dominated byconduction.

To further examine the character of the heattransfer regime in the subsurface, we can use the

Ž Ž ..forward model approach Eq. 3 using the soiltemperature at the soil surface as the driving field to


Table 4Significant periods from Fourier analyses of daily means for airand soil temperature time series. The percentages refer to theconfidence intervals of the estimated parameters for the models

Ž . Ž . Ž .T 2 m T 10 cm T 50 cmair soil soil

Conf. Period Conf. Period Conf. PeriodŽ . Ž . Ž . Ž . Ž . Ž .% d % d % d

90 31.9489 99 31.9489 99 31.948990 8.7489 99 19.3050 99 19.685090 7.9365 99 12.8041 99 15.748099 6.4809 99 10.3413 99 12.642295 5.5960 99 8.9847 99 10.661095 4.9480 99 7.2098 99 8.904799 4.3573 99 6.2814 99 7.209899 3.8066 95 5.7537 99 6.321195 3.4130 99 5.0684 99 5.506699 3.1898 99 4.6555 99 5.020190 2.3326 99 4.1964 99 4.6339

95 3.6576 99 4.248195 3.2000 99 3.6576

95 3.2000

obtain the model temperature at a given depth andcompare with the observations. Synthetic tests, usingsinusoidal temperature variations as the driving tem-perature were carried out. The forward model repro-duces the temperature predictions expected from theanalytical solutions very well.

The results from one of this trial is presented inFig. 6a shows the modeled and measured tempera-ture departures from the mean for a section of thedata set, at 10 cm depth, while Fig. 6b shows themisfit in an expanded scale. The mean of the misfitis 0.017 K.

Generally, the forward model reproduces well thethermal field observed at depth as long as the calcu-lations are performed for the shallow parts of the soilprofile. For estimates of the deeper part of the soil’sthermal regime the forward model fails to accountfor the influences that lower layers have on thetemperature of the upper layers, that is, the forward

Ž . Ž .Fig. 6. a Forward model simulation of soil temperature at 10 cm depth using the record of soil temperature at the surface, b differenceŽ .misfit between simulated and measured soil temperature for the above case in an expanded scale. The mean of the misfit is 0.017 K. Thetime axes is in 5 min. A thermal diffusivity of 0.5=10y6 m2rs was used in this simulation intervals.


model does not take into account heat flowing fromthe subsurface since it assumes that the thermalregime of the subsurface is completely driven by thesurface forcing. In other words, the forward modeldoes not incorporate the temperature changes beforethe period of data acquisition which because of thelarge thermal memory of the ground are still present

Žin the subsurface see Harris and Gosnold, 1999 for a.discussion . As such, forward modeling is more ap-

propriate to model the perturbations to the subsur-face thermal regime, rather than temperatures.

To obtain estimates of the thermal diffusivitythroughout the first meter of the soil, we use thefinite difference model driven by the surface temper-ature as the upper boundary condition and con-strained by the temperature data at a lower depth asthe lower boundary condition. For this model, syn-thetic tests were also carried out using sinusoidal

surface temperatures to ascertain the accuracy of themodeling scheme. Tests were done for a single layermodel and for a two-layer model with differentthermal parameters for each layer. Model predictionswere then compared with the analytical results. Forboth cases, the model reproduces very well the ex-pected thermal regime of the soil. Details of themodel, stability and performance will be publishedelsewhere. As an illustration of the model perfor-mance, Fig. 7a shows the modeled and observedtemperatures at 5 cm. Fig. 7b shows the differencebetween predicted and observed in an expanded scale.The misfit appears uncorrelated with a mean misfitof 0.018 K.

Sweeping over a range of values for the thermalŽdiffusivity is possible with this model Chen and

.Kling, 1996 . Additionally, since temperature recordsare available at several depths, we can determine the

Ž . Ž .Fig. 7. a Finite differences model simulation of soil temperature at 5 cm and data at the same depth, b misfit in an expanded scale; meanis 0.018 K.


variation of the apparent thermal diffusivity withdepth by modeling the thermal regime between dif-ferent levels. The method consists of using measuredtemperature series as upper and lower boundary con-ditions in addition to another temperature series at anintermediate depth. The model than is set to sweepthrough a range of thermal diffusivity values untilthe misfit is minimized.

Exploration of the variation of apparent thermaldiffusivity with depth yields the best values of thethermal diffusivity of several soil layers. The resultsfor a section of the record are shown in Fig. 8. Sincewe are assuming that the dominant heat transfermechanism is conduction, the calculation was per-formed for the late summer and fall period duringwhich there is no snow cover or ground freezing.The model is not applicable, at this early stage ofdevelopment, to the winter time data because it doesnot include the effects of freezing and thawing. Thevalues of the summer apparent thermal diffusivity

inferred from the data and finite difference model are0.42=10y6 and 0.63=10y6 m2rs for the layerbetween 0 and 10 cm and 10 and 100 cm, respec-tively. Generally, the values of the apparent thermaldiffusivity do not vary much within the soil below10 cm, such that for modeling purposes, the soil canbe adequately modeled using a two-layer model.

4.3. Discussion

In order to obtain an order of magnitude estimateof the magnitude of the non-conductive heat compo-nent during soil freezing, we attempt to answer thequestion of what the soil thermal regime would bewithout the zero curtain effect. To address this issue,a one-layer model was used to simulate a soil surfacetemperature from the air temperature records andthrough the layer of organic matter. Although infer-ring soil temperature from air temperature records isnot obvious, observations indicate that in some cases,as the one shown in Fig. 9, the temperature within

Ž .Fig. 8. Determination of the apparent thermal diffusivity k using the finite differences model. Model sweeps through a range of values ofaŽ . y6 2 Ž .k until misfit is minimized. a k for a layer from surface to 10 cm, k s0.42=10 m rs, b k for the layer from 10 to 100 cm,a a a a

k s0.63=10y6 m2rs.a


Fig. 9. Record of air temperature at 2 m height, air temperature on top of organic matter, and temperature at 1.5 cm within the organicmatter layer. Temperature within the layer of organic matter follows air temperature variations. These data were obtained a few meters fromthe Pomquet station.

the organic matter layer follows the temperatures ontop of the organic matter and above the soil. Settingthe air temperature record at a height of 2 m as theupper boundary condition while the thermal regimeof the soil was constrained by the soil temperature at100 cm to ensure a temperature bias toward thesurface. The model grid size is 0.5 cm, the integra-tion increment is 1 s and soil and air temperaturedata have a resolution of 5 min. The model yields,under these conditions, a temperature series at thesoil surface, which we use as a forcing function atthe surface. The finite difference, single-layer, purelyconductive model can be used to evaluate the ther-mal field in the soil from the derived soil surfacetemperature. The total heat content per unit mass of

Ž .the upper layers of the soil 5 cm was estimated byŽ .DeGaetano et al., 1996

zQ max

s T z d z 7Ž . Ž .HC zs0

where Q is heat per unit mass, C is the heat capacityof the soil, T is the temperature and z is the depth of

Ž . Ž .the soil positive downwards . Eq. 7 can be evalu-ated for the observed and modeled soil temperature

Ž .profiles. Fig. 10 shows the quantity QrC varia-tions over the modeled time period. Over the time

Žperiod during which soil freezing occurred 74.4.days , the total heat estimated from the data is:

Ž . 6QrC s5.8675=10 K, and for the modeledrealŽ . 6case: QrC s5.8336=10 K. Using Cmodel frozen

Ž2.1 kJrkg K and C 1.55 kJrkg K Goodrich,thaw.1982; Lettau, 1951 . We find that the difference on

heat content of the layer of soil is: Q s5.2572=real

107 Jrkg. At the 5-min data resolution, this is2445.1 Jrkg or 583.9 calrkg. This quantity is in theorder of the heat released by freezing 7.3 g of water

Žin 5 min or 2.1 kg of waterrday 2 mm of waterrday2 .m .Clearly, non-conductive heat transfer during the

winter time complicates the relation between air andground temperatures such that reconciliation of me-


Fig. 10. Heat content of the first 5 cm of the soil column. Shown are the differences between heat content calculated from the data and themodeled heat content. See text for details. Positive implies heat loss from soil, negative implies heat gained by soil.

teorological records of past climates with geothermalreconstructions of ground temperature variations issomewhat problematic in zones where soil freezingoccurs. An order of magnitude calculation of theeffects of soil freezing, neglecting the snow-coverinsulating effect, on the difference between air andsoil temperature shows that, for the full year ofrecord, 30 extra days of soil freezing can change theaverage value of the soil–air temperature differenceby 0.28C. Table 5 shows the yearly average changesas a function of the period of additional soil freezing.The length of time soil freezing occurs depends on

Žthe air temperature, snow cover Goodrich, 1982;.Beltrami, 1996 as well as on the soil moisture

content, such that systematic variations of any ofthese variables can influence the soil–air temperaturedifference and interfere with the long term couplingof air and ground temperatures.

4.3.1. Soil–air tracking and solar radiationOne of the key issues regarding the integration of

meteorological records with GSTHs inferred frominversion of geothermal data, lies on the clarificationof the long-term relationship between air and ground

Ž .temperatures. Putnam and Chapman 1996 reporteda first order positive correlation for the differencebetween air temperatures, a modeled surface soiltemperature and solar radiation for the Emigrant PassObservatory in Utah. The site in Utah receives very

Ž .little precipitation 86 mmryear such that it can beconsidered as a case for which evapotranspiration,snow-cover insulation, and latent heat effects are

Table 5Ž .Estimate of annual soil–air temperature difference soil minus air

variation as a function of additional number of soil freezing days.The number of soil-freezing days for this site is 74.4.

Ž .Number of Soil surface Soil–air DT KŽ .additional days temperature K

Ž .with Asoil freezingB yearly mean 8C

0 9.822 2.08 –5 9.812 2.07 y0.01

10 9.786 2.05 y0.0315 9.758 2.02 y0.0620 9.736 1.99 y0.0930 9.663 1.92 y0.1640 9.616 1.876 y0.2160 9.491 1.751 y0.33


minimal. At the Pomquet station site, the situation isquite different; the terrain is affected by surfaceconditions changes due to vegetation growth and

Ždecay, precipitation over 1000 mm of precipitation.recorded during 1997–1998 , a sporadically chang-

ing snow-cover, freezing of the soil during the wintermonths and thawing during spring time.

The difference between daily values of soil tem-peratures, at the surface and 100 cm, and the airtemperature at 2 m height, together with the daily

means of the incoming solar radiation record areshown in Fig. 11a and b. The thin discontinuouslines represent the soil–air temperature difference,and the thick, smooth lines represent a reconstructionof the time series using the first two principal com-ponents. The filtering was carried out using singularvalue decomposition, chosen because it has some

Žphysical meaning unlike running averages Ghil and.Vautard, 1991 . The filtered curves are entirely de-

pendent on the data themselves.

Ž . Ž . Ž .Fig. 11. Variation of the daily difference between soil and air temperature 2 m . a Soil temperature at the surface, b soil temperature at 1Ž .m depth, c daily variation of the total sky radiation incident at the site. The thick lines represent the AfilteredB series obtained by singular

spectrum analysis using two principal components.


Fig. 11c shows the daily averages of the solarŽ .radiation measured at the station thin line along

with the first two principal components for the seriesŽ .think line . It is apparent that at this site there is aninverse relationship between the soil–air temperaturedifference and the incoming solar radiation. Thelarge difference between air and soil temperature in

Ž .winter see Fig. 2 can be attributed to the latent heatreleased during soil freezing which keeps the upperlayers of the soil near the freezing point. This istypicalof the Aheat valveB effect mentioned above.Other processes are also involved in determining this

Ž .difference evaporation, wind, precipitation, etc. , butthey tend to reduce the difference rather than in-

Ž .crease it Geiger, 1965; Gosnold et al., 1997 .

5. Conclusions

Ž .1 Records of air and soil temperatures obtainedat the study site indicate that ground temperaturetracks air temperature variations during the timewhen soil freezing is absent. When soil freezing ispresent, air temperature variations are not recordedinto the ground, although high frequency variationsare filtered by the earth and would not affect thesubsurface thermal regime directly, systematic varia-tions of the soil freezing period can have an effect onthe long term soil–air temperature coupling. Similareffects can be induced by a systematic variation ofsnow cover. The annual difference between soil and

Ž .air temperatures soil minus air at the study sitevary from 2 K at the surface to 1.3 K at a depth of100 cm. The difference varies throughout the yearand at 100 cm, appears to be inversely correlatedwith the amount of incoming solar radiation.

Ž .2 Rapid, semi-qualitative determination of thecharacter of the heat transfer regime at the air groundinterface and subsurface can be made by Aphase-spaceB plots and by spectral analysis of the tempera-ture time series. Modeling of the soil thermal regimeusing a forward model produces satisfactory resultsfor the shallow layer of the soil. Finite differencemodeling can reproduce the thermal regime of thesoil very well for the period dominated by conduc-tion at all depths.

Ž .3 Soil temperature data at multiple depths per-mit the determination of apparent thermal diffusivity

for several layers within the soil. At this site, for theŽ . Ž .upper 0–10 cm and lower 10–100 cm soil layers,

the apparent thermal diffusivity was found to be0.42=10y6 and 0.63=10y6 m2rs, respectively.The value for the thermal diffusivity calculated forthe first meter of soil is 0.5=10y6 m2rs. All thesevalues were estimated from the finite differencemodel under the assumption that the thermal parame-ters of the soil are independent of time. This assump-tion is questionable during the winter.

Ž .4 A Aback of the envelopeB calculation revealsthat the average heat attributed to non-conductiveprocessess, for the soil-freezing period is on theorder of 584 calrkg every 5 min, equivalent to theheat released by freezing 2.1 kg of water per day.

Ž .5 The combination of meteorological recordswith reconstructions of ground temperature varia-tions from geothermal data should be possible inareas where freezing of the upper soil does notoccur, is short lived, or it changes randomly fromyear to year. In higher latitudes, where soil freezingis common place for extended periods and wheremeteorological data analyses reveal large magnitudetemperature changes in the last century, the couplingbetween air and ground temperatures should be ap-proached with caution.

Acknowledgements

Discussions with S. Putnam, D.S. Chapman andL. Kellman are gratefully acknowledged. Commentsfrom two anonymous reviewers and R. Harris aremuch appreciated. This research was funded by TheNatural Sciences and Engineering Research Council

Ž .of Canada NSERC through an operating grant andŽ .partially by St. Francis Xavier University UCR .

The author is grateful for this support. Bonnie Quinnassisted with the FORTRAN codes. Rob Harris han-dled the review process of this paper.

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