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

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1 Ž. Global and Planetary Change On the relationship between ground temperature histories and meteorological 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 An experimental air ground climate station is operating in Pomquet, Nova Scotia, monitoring meteorological Žsurface air temperatures at three heights, wind velocity and direction, incoming solar radiation, precipitation, snow depth and relative humidity. and ground thermal variables Ž soil temperatures at depths of 0, 5, 10, 20, 50 and 100 cm.. Readings are taken every 30 s and 5 min averages are stored, in order to characterize the energy exchanges at the air ground interface. Here, I report on the first year of operation. For spring, summer and fall, we find that soil temperatures track surface air temperatures with amplitude attenuation and phase lag with depth confirming that heat conduction adequately describe the soil thermal field at the Pomquet site. For winter conditions, we find that heat transfer is dominated by latent heat released during soil freezing and to a lesser extent by the insulating affect of snow cover. A numerical model of heat conduction was used in order to estimate the magnitude of the heat released by freezing during the winter months. I also show that there is an inverse correlation for the difference between soil Ž 100 cm. and air temperatures and the incoming solar radiation at the site. q 2001 Elsevier Science B.V. All rights reserved. Keywords: ground temperature history; meteorological record; Pomquet station 1. Introduction Analyses of meteorological records ŽJones et al., 1999; Hansen and Lebedeff, and proxy climatic indicators Že.g., Groverman and Landsberg, 1979; Jacoby and D Arrigo, 1989; Overpeck et al., suggest that surface air temperatures have been steadily rising since industrialization, particularly in the last century. Such evidence, and the coincidence with the beginning of the emissions of large quantities of greenhouse gases into the atmosphere, raises questions about the effects of anthro- ) Tel.: q ; fax: q Ž. address: hugo@stfx.ca H. Beltrami. pogenic activities on the Earth s climatic system and about the potential consequences of associated changes in current world climatic patterns. Debate on the effects of anthropogenic activities on the climate of this century and on future climate continues to occupy a central part of policy developers and the scientific community. The controversy centers mainly on the capacity of general circulation models Ž GCMs. to simulate a complex system such as the Earth s climate. Hence, it is extremely important to ascertain the past climatic variations to allow robust validation of GCMs. This has been accomplished in part by the collection and analysis of meteorological and proxy climatic indicators in the last decades. It remains, however, crucial to compile r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. Ž. PII: S

2 328 ( ) H. BeltramirGlobal and Planetary Change a consistent picture of climatic changes of the past reconciling as many source of paleoclimatic information as possible Ž Overpeck et al., Because of shortcomings in the meteorological record ŽKarl et al., and the fact that proxy data climatic reconstructions involve multiple assumptions Žsee Bradley, 1985., a complementary record has started to be explored in the last decade. It is the determination of ground temperature histories from geothermal data. The interest in this method lies in the fact that it examines a direct measure of temperature, free of problems such as variable standards and noise found in meteorological data, and unlike proxy records, it has a very clear physical interpretation Ži.e., temperature.. Reconstruction of past climatic changes from geothermal data has proven, in the last few years Ž e.g., Huang et al., 1997; Pollack et al., to be an additional source of information to complement meteorological and proxy records of climatic change Climate from geothermal data It has long been known that past ground surface temperatures can be estimated by analyzing the perturbations to the steady state geothermal gradient Že.g., Lane, 1923; Hotchkiss and Ingersoll, 1934; Birch, Variations of the ground surface temperature are recorded in the subsurface as deviations from steady state. Indeed, it has been customary to eliminate the effects of known climatic oscillations Ž mainly the last ice age. from the temperature profiles used for HFD determination ŽPowell et al., Furthermore, data obtained at many locations around the globe often show that temperature gradients are in fact disturbed for the first hundred meters Ž e.g., Cermak et al., 1984; Pinet et al., Although, non-climatic causes of the nonlinearities in temperature depth profiles are possible Že.g., thermal conductivity variations, subsurface heat production, ground water flow, topography, urban heat, changes in surface conditions, etc.., most of these factors can be examined and eliminated before ground surface temperature Ž GST. analyses are performed. The abundance of borehole temperature data around the world has the potential to yield ground surface temperature histories in vast areas of the continents Ž e.g., Lachenbruch and Marshall, which otherwise would remain undocumented. In the Earth, these temperature perturbations appear superimposed on the equilibrium temperatures. In a source free half space, the steady state heat flow is constant. The steady state heat flow is usually evaluated in the deeper part of the temperature profile, which is not affected by the recent temperature changes. The steady state temperature is then continued to the surface and the perturbation is determined as the difference between the measured temperature and the upward continuation of the temperature profile. The magnitude of the anomaly is proportional to the total amount of heat absorbed by the ground. The shape of the perturbation is determined by the thermal history of the surface. This history can be inferred by comparing the calculated temperature perturbation for a model of surface temperature with the data and adjusting the model parameters until a fit is obtained or the surface temperature history can be inferred directly by inversion Žsee Lewis, 1992; see Pollack and Chapman, 1993; Beltrami and Chapman, 1994 for introductions to this subject; see Beltrami and Chapman on-line teaching aid at geo.lsa.umich.edurihfcrclimate1.html.. The attractiveness of this approach to climatic reconstruction rests on the characteristics of heat conduction into the ground. Unlike meteorological records subjected to high frequency variability and noise, the Earth behaves as a low pass filter recording long-term trends of ground surface temperature Ž GST. changes Ž Joss, For example, daily and annual temperature variations penetrate into the ground to depths of approximately 1 and 20 m, respectively, whereas a 100-year long trend will be recorded in the subsurface and will be detectable to a depth of about 100 m. As such, climatic reconstructions from geothermal data can provide a robust complement to the existing paleoclimatic database as well as providing the long-term records of temperature change needed for the validation of General Circulation Models Ž GCMs. for future climate change estimates. Recently, several attempts have been made to reconstruct a pre observational mean Ž POM. in order to extend the meteorological record into the past and provide a reference on which to base the changes inferred from meteorological data ŽHarris and Chapman, and to calibrate proxy climatic indicators Ž Beltrami and Taylor, 1995; Beltrami et al.,

3 ( ) H. BeltramirGlobal and Planetary Change However, although the Earth s response to the energy balance Ž or imbalance. at the surface is related to the surface air temperature, the temperature of the ground is an integral of the effects of air temperature variation, vegetation cover and snow cover variations, phase changes Ž freezing and thawing. and solar radiation changes at the ground surface. The interaction of all these variables determines the temperature of the ground in a complex and complicated series of processes. It is thus important to attempt to clarify the long-term effects of variations in energy exchanges at the air ground interface on the subsurface thermal regime. Within this context an experimental air ground station operates in Pomquet, Nova Scotia, monitoring meteorological variables, soil thermal conditions, snow cover and vegetation cover, in order to examine some of the processes involved in the energy exchanges within the first meter of the soil and at the air ground interface. This note provides some of the results arising from these observations and carries out some simple numerical calculations to illustrate the observations. It is shown that during spring, summer and fall, while air temperatures remain above the freezing point, the heat transfer within the soil is dominated by conductive processess, and that during this time the ground temperature tracks air temperature variations closely, whereas during a period of time in winter, freezing of the upper soil introduces non-conductive mechanism Ž latent heat. such that the ground does not respond to air temperature variation until the upper layers of soil are completely frozen. That is, the ground does not appear to record air temperature variations during this time period in winter. We compare the heat content of the first 5 cm of the soil column as determined from data with the modeled situation where soil freezing is absent in order to estimate the magnitudes of non-conductive processes. 2. Station setup The experimental air ground station was installed in a flat open field in Pomquet, Nova Scotia, Canada Y? Y? Ž N; W, elevation 5 m, see Fig. 1. approximately 100 m from a harbour. The vegetation at the site consists of field grasses on a clay soil near a spruce forest some 30 m to the south of the station. The station consists of the Campbell Scientific Ž CS. CM10 tripod supporting all instrumentation. The instrumentation consists of a control unit and a solar panel, two CS107 air temperature probes at heights of 0.17 and 1.5 m enclosed in radiation shields, a CS C5500 air temperature and relative humidity probe at a height of 2 m Žalso enclosed in a radiation shield., and six CS 107b soil Fig. 1. Location of the Pomquet station in Nova Scotia, Canada.

4 330 ( ) H. BeltramirGlobal and Planetary Change temperature probes at depths of 0, 5, 10, 20, 50 and 100 cm. A SR50 sonic ranger measuring snow cover Ž or grass cover variations. was also installed. The sonic ranger uses ultrasound Ž 50 khz. to measure the distance to a target and thus it needs to be linked to a temperature probe to correct for temperature dependency of the sound velocity. The air temperature probe at 1.5 m was used for this purpose. A Young Wind Monitor was installed to measure wind speed and direction at a height of 3 m. A Texas Instruments TE525M tipping bucket rain gauge measures precipitation; this instrument was installed in a separate stand at a height of 50 cm, a few meters away from the main station to avoid a Arain-shadowB effect from the main station tripod and instrumentation. A Licor L1200S pyranometer installed at 2.8 m height to avoid interference from other instruments on the tripod, was used to measure incoming solar radiation. The station is operated with a CS CR-21XL data-logger powered by rechargeable batteries and a MSX-20 solar panel. The data is stored directly in a SM716 storage module, which can be removed for data retrieval. This Station has operated continuously since early August Instruments are sampled every 30 s and 5 min averages of all sensors are recorded. We chose a 5-min averaging interval to allow high frequency variability to be recorded for parallel studies on the signatures of conductive and non-conductive processes in the soil Že.g., Hinkel et al., 1990; Hinkel and Outcalt, The accuracy of the CS107 air temperature probe and CS107b soil temperature probes is -"0.2 K. Most of this error corresponds to the offset from the interchange of the probes, but with a single point calibration, it is possible to eliminate the probe offset and the working accuracy is reduced to about 0.1 K. The CS107b probes were installed using the following procedure. A hole was dug in the ground, taking care of maintaining the statigraphy of the removed soil as much as possible. The probes were inserted horizontally into the vertical wall of the hole making sure a very tight fit between the probe and the soil was achieved. Horizontal insertion avoids the possibility of fluid transport through flow pathways in the unconsolidated soil Ž Hinkel and Nicholas, The removed soil was then replaced as carefully as possible to avoid further disruption of the site and to reduce water infiltration through the conduits opened Table 1 Summary of instrumentation Parameter Precision Setup Air temperature a b -0.2 K r0.1 K 0.17, 1.5, 2.0 m height Soil temperature a b -0.2 K r0.1 K 0, 5, 10, 20, 50, 100 cm depth Precipitation 0.1 mm 50 cm height Snow grass "1 cm or 0.04% 1.75 m height depth Solar radiation "3% 2.80 m height Wind speed 0.04 mrs 3.0 m height Wind direction m height Relative humidity 1 5% 2.0 m height a Before probe calibration. b After calibration. by the probes cables. A layer of grass sod was replaced at the surface when the setup was completed in an attempt to preserve as much as possible the surface characteristics. The Asurface probeb was inserted just below the grass sod, Ži.e., at the soil surface under the organic matter layer.. We did not attempt to place the probe directly on the surface to avoid spurious heating by direct solar radiation. Although measurements were taken since early August 1997, a few weeks for the settling of the probes in the subsurface were allowed and we present data covering the period from September 1, 1997 to August 30, A summary of the instrument specifications is given in Table Data: at Pomquet Data acquired during the period of time between September 1, 1997 and August 30, 1998 is presented below. A summary of the monthly averages is shown in Table 2. As stated above, all instrumental data were sampled every 30 s. The data was then averaged over a 5-min window and recorded. There are only two 2-h periods of missing data for the entire year; this is due to a computer malfunction during data transfer. For the present analysis, these missing data intervals were interpolated. All reported monthly averages in Table 2 were calculated by integrating over the period using the 5 min averages, such that they are not readily compa-

5 ( ) H. BeltramirGlobal and Planetary Change Table 2 Monthly data summaries calculated from integration of data at highest resolution AIR Air Air Soil Soil Soil Soil Soil Soil Ž 2 m. 1.5 m 17 cm 100 cm 50 cm 20 cm 10 cm 5 cm 0 cm Ž 8C. Ž 8C. Ž 8C. Ž 8C. Ž 8C. Ž 8C. Ž 8C. Ž 8C. Ž 8C. Sept Oct Nov Dec y1.3 y2.0 y Jan y3.5 y4.1 y y0.1 Feb y2.4 y3.1 y y0.1 y0.2 Mar Apr May June July Aug Mean Rain Wind Wind Snow Solar Relative Ž mm. speed direction grass radiation humidity Ž mrs. Ž 8. Ž m. Ž 2 kwrm. Ž %. Sept Oct Nov Dec Jan Feb Mar Apr May June July Aug Mean a a Cumulative sum. rable to the standard meteorological data means evaluated from daily maxima and minima Žsee Putnam and Chapman, 1996 for a discussion of this issue.. Monthly air temperatures have a yearly range of 22.9 K at heights of 1.5 and 2 m and a range of 22.1 K at a height of 0.17 m. All minima for the air temperature records occurred in January and all maxima in August. Yearly ranges of soil temperatures are 20.8 K at the surface, 20.5 K at 5 cm depth, 20.1 K at 10 cm depth, 19.3 K at 20 cm depth, 17.2 K at 50 cm depth and 14.1 K at 100 cm depth. All soil temperature maxima occur in August; all minima occur in February with the exception of the records at 100 cm, which show the minima in March. The magnitude of the temperature ranges for the soil decreases with depth with the range difference between the surface and 1 m depth being 6.7 K. Although monthly averages are useful for the purpose of comparison, higher resolution data are required to examine the processes involved in the energy exchange at the air soil interface. Fig. 2 shows the full year daily means time series for a number of these variables recorded in Pomquet. Fig. 2a shows the records of air temperature at three heights measured in Pomquet. There is little difference between the air temperature records at

6 332 ( ) H. BeltramirGlobal and Planetary Change height of 2 and 1.5 m. However, air temperature at 0.17 m differs significantly during the summer under the effect of direct solar radiation on the ground surface affecting the probe closest to the ground surface, and sometimes during the winter when the probe is buried by snow. Fig. 2b shows the records of soil temperature at the surface and at a depth of 5 cm. The most remarkable feature of these records is that the soil temperature remains nearly constant between days 100 and 180 in the figure, likely due primarily to latent heat released from the freezing of the soil and also, in a small part, to the insulating effect of snow cover. Snow cover at the station site is sporadic and thin such that the snow cover insulating effect Ž e.g., Zhang et al., is not obvious from the data. A control experiment at a nearby site is in progress to address this issue. Fig. 2c shows the soil temperature data obtained at 0.1 and 0.2 m depths. This situation is very similar to the one described above for the shallower records; but in this case, high frequency and amplitude attenuation are evident. The onset of the zero curtain effect ŽHinkel et al., occurs around day 150 rather than at day 100 for the shallow probes. The data indicates that soil freezing did not reach 0.2 m, thus, the temperature at 0.2 m is a resultant of heat transfer Fig. 2. Daily means of all variables monitored at the station for period between September 1, 1997 and August 30, Ž. a Air temperatures at the indicated levels, Ž. b soil temperatures at the surface and 5 cm, Ž. c soil temperatures at 10 and 20 cm, Ž. d soil temperatures at 50 and 100 cm, Ž. e incoming solar radiation, Ž. f precipitation, Ž. g snow and grass cover variations, Ž. h wind speed, Ž. i wind direction, Ž. j relative humidity.

7 ( ) H. BeltramirGlobal and Planetary Change Ž. Fig. 2 continued. from the upper and lower soil layers and the heat released by the moving freezing front. Fig. 2d shows the 0.5 and 1 m soil temperature records. The lag of the response of these deeper temperatures with respect to air temperature variations is apparent as well as the filtering of the high frequency variations. Examination of this figure reveals that in fall and winter, heat flows out of the ground and in spring and summer heat flows into the ground. This has been the classical interpretation of the heat flow at the air soil interface and it is referred as the Aheat valveb effect Ž Gilpin and Wong, Fig. 2e shows the daily average of the incoming solar radiation measured at the site. The yearly cycle is seen as the first order variation. Superimposed on the yearly cycle, we can clearly see shorter scale variations due to weather system passage and associated cloud cover changes. The yearly mean incoming solar radiation at this site is 123 Wrm 2 with a maximum daily value of 365 Wrm 2. Fig. 2f shows the daily cumulative rain fall recorded at the station. Total rainfall reached 1035 mm, with a daily mean of 2.83 mm. The maximum daily precipitation recorded, Ž 46.7 mm. around day 180 in Fig. 2f, is due to a blowing wet-snow event plus the melting of the snow accumulated on and inside the rain gauge bucket Ž see Fig. 2f, g and h.. Fig. 2g shows the variation of the vegetation cover and during the winter time, the variation of snow cover. Some of the high frequency variability of these records are correlated with the wind speed and it represents the motion of the long grass stands

8 334 ( ) H. BeltramirGlobal and Planetary Change Ž. Fig. 2 continued. under the influence of the wind. Recall that at this station, the surface cover variations are measured as a quantity proportional to the travel time of ultrasonic pulses from the sonar ranger to the surface where they reflect back to the probe. It is not possible to separate the contributions of snow cover and vegetation cover in winter since it was decided not to alter the natural surface conditions at the site For example, the maximum daily value on the record shows a snow depth of almost 50 cm. This anomaly is due to blowing snow that is moving almost horizontally such that the snow flakes reflect the ultrasound pulses back to the detector before the beam reaches the surface of the snow accumulated on the ground, giving this type of spurious reading Žsee Fig. 2h.. A typical example of snow compaction is apparent in Fig. 2f near day 130. The sudden decrease of the vegetation cover around days 315 and 340 on the figure are the results of deliberate mowing of the grass at the station in order to examine short term effects of vegetation cover change on the soil thermal regime at high frequencies. Fig. 2h and i shows the daily mean wind speed and wind direction data, respectively. The maximum daily mean was 7.89 mrs with a yearly mean reaching 1.69 mrs. The maximum value recorded at the highest data resolution Ž 5-min averages. is 10.7 mrs recorded during a storm Ž see Fig. 2f and g.. The average wind direction is Fig. 2j shows the recorded daily means for the relative humidity. The yearly average is 81% making the climate at this site rather humid and revealing

9 ( ) H. BeltramirGlobal and Planetary Change Table 3 High resolution and daily summaries of data Variable 5-Min data Daily data Max Min Mean Max Min Mean Air temperature Ž 0.17 m. Ž 8C y y Air temperature Ž 1.5 m. Ž 8C y y Air temperature Ž 2 m. Ž 8C y y Soil temperature Ž 0 m. Ž 8C y y Soil temperature Ž 5 cm. Ž 8C y y Soil temperature Ž 10 cm. Ž 8C y y Soil temperature Ž 20 cm. Ž 8C Soil temperature Ž 50 cm. Ž 8C Soil temperature Ž 100 cm. Ž 8C Precipitation Ž mm Snow grass cover Ž m Wind speed Ž mrs Ž 2 Solar radiation kwrm Relative humidity Ž % that the role of latent heat at the air soil interface is probably very important. Examination of Fig. 2a reveals that the high frequency variability present in the air temperature records is filtered out by the ground as expected, also we can clearly see the occurrence of a lag between minima and maxima at the surface and the corresponding values at depth. Soil temperature at 1 m appears to have filtered out most of the high frequency components of the surface variation and records only the medium term trends of the annual cycle, although with a lag of about 2 months or so. Daily temperature ranges for air temperature are 37.2, 38.7 and 38.6 K for heights of 0.17, 1.5 and 2 m, respectively. For soil temperatures, the temperature ranges are 24.3, 23.32, 22.6, 21.2, 18.8 and 14.6 K 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 resolution data is presented in Table 3. There are some features of the air and soil temperature records that should be examined here. The 5-day period, shown in Fig. 3a between September 30 and October , illustrates the behaviour of the soil temperatures showing the well known damping of the amplitude and the increase of the time lag as a function of depth. This is typical of summer and early fall behaviour when the transfer of heat in the subsurface is dominated by conduction. Fig. 3b shows the same variables and the record of air temperature at a height of 2 m for the 2-week period between December 6 and 20, 1997; here the onset of ground freezing is apparent. As air temperatures drop below freezing soil temperatures remain above 08C as freezing takes place in the upper layers of the soil. This occurs around Julian day 350 in Fig. 3b where the surface soil temperature remains at 08C while soil freezes. During this time, the soil does not record air temperature variations. Although snow cover does have a significant effect insulating the ground at other locations ŽZhang et al., 1996; Gosnold et al., 1997; Beltrami and Mareschal, 1991., our records indicate a sporadic, thin snow cover during the winter at this location. Freezing of the soil continues until February 25, 1998 Ž Julian day 56 in Fig. 3c, day 180 in Fig. 2. when a sudden air temperature increase thaws the upper layers of the soil and the subsurface starts responding once again to air temperature variations. Notice that the surface probe responds first, then the probe at 5 cm and then the others in order of increasing depth. 4. Assessing the heat transfer regime of the ground 4.1. Theoretical framework One of the fundamental assumptions required for the reconstruction of ground surface temperature histories from geothermal data and eventually past cli-

10 336 ( ) H. BeltramirGlobal and Planetary Change Fig. 3. Ž. a Detail view showing the record of soil temperatures at the indicated depth for a 5-day period in late summer. The decay of the amplitude and the increase in time lag with depth are apparent, Ž. b expanded view Ž 2 weeks. of the record of air and soil temperatures at the indicated height and depths showing the onset of soil freezing, Ž. c detail of the record of air and soil temperature showing the thawing of the soil. Note the time delay between records.

11 ( ) H. BeltramirGlobal and Planetary Change Ž. Fig. 3 continued. matic change is that the heat transfer regime within the ground be conductive. In an ideal perfectly conductive soil periodic, variations of surface temperature are propagated into the ground according to the heat conduction equation ET E 2 T sk, Ž 1. Et Ez 2 where k is the thermal diffusivity, z is depth and t is time. In order to assess the character of the heat transfer in the soil, Eq. Ž. 1 can be use to solve, for example, a forward model assuming the temperature record of the uppermost soil layer is periodic. In our case, an easier approach may be taken by considering the temperature record as a model consisting of a series of step changes in temperature. A series of step changes can approximate any real air or soil temperature variation Ž Putnam and Chapman, In such case, the forward problem for a single step temperature change occurring at time t before present is given as Ž Carslaw and Jaeger, z TŽ z. sdt0 erfc ž, Ž 2. 2' k t / where k is the thermal diffusivity, t is time before present, DT is the surface temperature and TŽ z. 0 is the temperature at depth z into the soil profile Žz positive downward.. For a series of steps of equal duration expressed as departures from the mean, starting at time tl in the past, today s temperature at depth z is given by z TŽ z. stl erfc 2 ' k t jsly1 z q Ý T j erfc js1 2( k Ž lyj. q1 t z yerfc. Ž 3. 2 k Ž lyj. t ( Eq. Ž. 3 can approximate a time series of temperature data and be used as a forcing function at the surface. Alternatively, the heat equation ŽEq. Ž 1.. can be solved using finite differences subjected to appropri-

12 338 ( ) H. BeltramirGlobal and Planetary Change ate initial and boundary conditions either for a homogeneous semi-infinite medium or it can be solved for a layered media by including the heat flow continuity at each interface between the layers. For a stratified medium composed of n layers, each with constant thermal properties, the temperature at any layer in this model must satisfy Že.g., Clauser, ETn E 2 Tn skn Ž 4 2. Et Ez where n is the layer order, kn and Tn are the thermal diffusivity and temperature at layer n, respectively. Additionally, the continuity of temperature and heat flow must be satisfied at the interface between layers such that the following conditions must be satisfied TnŽ zslnq1. stnq1ž zsl nq1., Ž 5. ETn ETnq1 ln Ž zslnq1. slnq1 Ž zsl nq1., Ž 6. Ez Ez where ln and lnq1 are the thermal conductivity for layer n and n q 1, respectively. At the surface, the temperature T Ž zs0. 1 st0 for t)0. The conditions at the lower boundary can be set by the deepest temperature record measured at the station Ži.e., T low st Ž 100 cm.. data. Computations are carried out by expressing the above equations in finite difference form and the initial conditions are obtained from the data and stability is assured by high sampling rate. Fig. 4. Ž. a APhase spaceb plot obtained from indicated records of air and soil temperatures treated as perpendicular superposition of harmonic motions, Ž. b same as Ž. a, but for soil temperature records.

13 ( ) H. BeltramirGlobal and Planetary Change Ž. Fig. 4 continued Analysis A first qualitative assessment of the heat transfer regime at the air soil interface and within the soil can be obtained under the assumption that air and soil temperature variations over a yearly cycle are perfect sinusoidal oscillations. Perpendicular superposition of temperature series Ž Aphase-spaceB plots., under this assumption, should yield regular interception figures Ž Beltrami, Departures from this behaviour yields qualitative information about the correlation Ž i.e., amplitude and phase relation. of the temperature records. Fig. 4a shows the perpendicular superposition of the 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 transfer regime at the air soil interface is apparent from the flattening of the interception figures around the freezing point for all soil temperatures. Fig. 4b shows similar plots, but in these cases, the soil temperature record at 10, 20, 50 and 100 cm are plotted with soil temperature data at the surface. The interception figures are, of course, less noisy because of high frequency filtering by the ground, and they are qualitatively closer to the interception ellipses that would be generated in a perpendicular superposition of perfect harmonic oscillators. As an additional approach to assess the character of the heat transfer regime in the subsurface, we can perform Fourier analyses of the time series of soil temperatures. Fourier modeling calculated using a multitaper method Ž Mann and Lees, for sample soil temperature records are shown in Fig. 5. Fig. 5a shows the power spectrum for the record of daily mean air temperature at 2 m height, while Fig. 5b d show the spectra for daily means of soil temperatures at the surface, 20 and 100 cm depth, respectively.

14 340 ( ) H. BeltramirGlobal and Planetary Change Fig. 5. Power spectra for daily temperature time series Ž. a air temperature at 2 m height, Ž. b soil surface temperature, Ž. c soil temperature at 20 cm depth, Ž. d soil temperature at 1 m depth. The smooth lines represent the 99% confidence level of the estimated parameters for this oscillatory model Ž see Table 4.. The smooth line across the figures represents the 99% confidence level Ži.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 Outcalt Ž have shown that soils subjected to non-conductive processes show spectra enriched in high frequencies. In our case, the significant dominant periods, shown in Table 4, for all of the soil temperature records are nearly identical indicating that averaged over the year the subsurface is dominated by conduction. To further examine the character of the heat transfer regime in the subsurface, we can use the forward model approach ŽEq. Ž 3.. using the soil temperature at the soil surface as the driving field to

15 ( ) H. BeltramirGlobal and Planetary Change Table 4 Significant periods from Fourier analyses of daily means for air and soil temperature time series. The percentages refer to the confidence intervals of the estimated parameters for the models T Ž 2m. T Ž 10 cm. T Ž 50 cm. air soil soil Conf. Period Conf. Period Conf. Period Ž %. Ž. d Ž %. Ž. d Ž %. Ž. d obtain the model temperature at a given depth and compare with the observations. Synthetic tests, using sinusoidal temperature variations as the driving temperature were carried out. The forward model reproduces the temperature predictions expected from the analytical solutions very well. The results from one of this trial is presented in Fig. 6a shows the modeled and measured temperature departures from the mean for a section of the data set, at 10 cm depth, while Fig. 6b shows the misfit in an expanded scale. The mean of the misfit is K. Generally, the forward model reproduces well the thermal field observed at depth as long as the calculations are performed for the shallow parts of the soil profile. For estimates of the deeper part of the soil s thermal regime the forward model fails to account for the influences that lower layers have on the temperature of the upper layers, that is, the forward Fig. 6. Ž. a Forward model simulation of soil temperature at 10 cm depth using the record of soil temperature at the surface, Ž. b difference Ž misfit. between simulated and measured soil temperature for the above case in an expanded scale. The mean of the misfit is K. The time axes is in 5 min. A thermal diffusivity of 0.5=10 y6 m 2 rs was used in this simulation intervals.

16 342 ( ) H. BeltramirGlobal and Planetary Change model does not take into account heat flowing from the subsurface since it assumes that the thermal regime of the subsurface is completely driven by the surface forcing. In other words, the forward model does not incorporate the temperature changes before the period of data acquisition which because of the large thermal memory of the ground are still present in the subsurface Žsee Harris and Gosnold, 1999 for a discussion.. As such, forward modeling is more appropriate to model the perturbations to the subsurface thermal regime, rather than temperatures. To obtain estimates of the thermal diffusivity throughout the first meter of the soil, we use the finite difference model driven by the surface temperature as the upper boundary condition and constrained by the temperature data at a lower depth as the lower boundary condition. For this model, synthetic tests were also carried out using sinusoidal surface temperatures to ascertain the accuracy of the modeling scheme. Tests were done for a single layer model and for a two-layer model with different thermal parameters for each layer. Model predictions were then compared with the analytical results. For both cases, the model reproduces very well the expected thermal regime of the soil. Details of the model, stability and performance will be published elsewhere. As an illustration of the model performance, Fig. 7a shows the modeled and observed temperatures at 5 cm. Fig. 7b shows the difference between predicted and observed in an expanded scale. The misfit appears uncorrelated with a mean misfit of K. Sweeping over a range of values for the thermal diffusivity is possible with this model ŽChen and Kling, Additionally, since temperature records are 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; mean is K.

17 ( ) H. BeltramirGlobal and Planetary Change variation of the apparent thermal diffusivity with depth by modeling the thermal regime between different levels. The method consists of using measured temperature series as upper and lower boundary conditions in addition to another temperature series at an intermediate depth. The model than is set to sweep through a range of thermal diffusivity values until the misfit is minimized. Exploration of the variation of apparent thermal diffusivity with depth yields the best values of the thermal diffusivity of several soil layers. The results for a section of the record are shown in Fig. 8. Since we are assuming that the dominant heat transfer mechanism is conduction, the calculation was performed for the late summer and fall period during which there is no snow cover or ground freezing. The model is not applicable, at this early stage of development, to the winter time data because it does not include the effects of freezing and thawing. The values of the summer apparent thermal diffusivity inferred from the data and finite difference model are 0.42=10 y6 and 0.63=10 y6 m 2 rs for the layer between 0 and 10 cm and 10 and 100 cm, respectively. Generally, the values of the apparent thermal diffusivity do not vary much within the soil below 10 cm, such that for modeling purposes, the soil can be adequately modeled using a two-layer model Discussion In order to obtain an order of magnitude estimate of the magnitude of the non-conductive heat component during soil freezing, we attempt to answer the question of what the soil thermal regime would be without the zero curtain effect. To address this issue, a one-layer model was used to simulate a soil surface temperature from the air temperature records and through the layer of organic matter. Although inferring soil temperature from air temperature records is not obvious, observations indicate that in some cases, as the one shown in Fig. 9, the temperature within Fig. 8. Determination of the apparent thermal diffusivity Ž k. a using the finite differences model. Model sweeps through a range of values of Ž. y6 2 k until misfit is minimized. a k for a layer from surface to 10 cm, k s0.42=10 m rs, Ž. a a a b ka for the layer from 10 to 100 cm, k s0.63=10 y6 m 2 rs. a

18 344 ( ) H. BeltramirGlobal and Planetary Change 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 organic matter layer. Temperature within the layer of organic matter follows air temperature variations. These data were obtained a few meters from the Pomquet station. the organic matter layer follows the temperatures on top of the organic matter and above the soil. Setting the air temperature record at a height of 2 m as the upper boundary condition while the thermal regime of the soil was constrained by the soil temperature at 100 cm to ensure a temperature bias toward the surface. The model grid size is 0.5 cm, the integration increment is 1 s and soil and air temperature data have a resolution of 5 min. The model yields, under these conditions, a temperature series at the soil surface, which we use as a forcing function at the surface. The finite difference, single-layer, purely conductive model can be used to evaluate the thermal field in the soil from the derived soil surface temperature. The total heat content per unit mass of the upper layers of the soil Ž 5 cm. was estimated by Ž DeGaetano et al., Q zmax sh TŽ z. d z Ž 7. C zs0 where Q is heat per unit mass, C is the heat capacity of the soil, T is the temperature and z is the depth of the soil Ž positive downwards.. Eq. Ž 7. can be evaluated for the observed and modeled soil temperature profiles. Fig. 10 shows the quantity Ž QrC. variations over the modeled time period. Over the time period during which soil freezing occurred Ž74.4 days., the total heat estimated from the data is: Ž. 6 QrC reals = 10 K, and for the modeled Ž. 6 case: QrC models = 10 K. Using Cfrozen 2.1 kjrkg K and C 1.55 kjrkg K Ž thaw Goodrich, 1982; Lettau, We find that the difference on heat content of the layer of soil is: Qreals5.2572= 10 7 Jrkg. At the 5-min data resolution, this is Jrkg or calrkg. This quantity is in the order of the heat released by freezing 7.3 g of water in 5 min or 2.1 kg of waterrday Ž2 mm of waterrday m 2.. Clearly, non-conductive heat transfer during the winter time complicates the relation between air and ground temperatures such that reconciliation of me-

19 ( ) H. BeltramirGlobal and Planetary Change 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 the modeled heat content. See text for details. Positive implies heat loss from soil, negative implies heat gained by soil. teorological records of past climates with geothermal reconstructions of ground temperature variations is somewhat problematic in zones where soil freezing occurs. An order of magnitude calculation of the effects of soil freezing, neglecting the snow-cover insulating effect, on the difference between air and soil temperature shows that, for the full year of record, 30 extra days of soil freezing can change the average value of the soil air temperature difference by 0.28C. Table 5 shows the yearly average changes as a function of the period of additional soil freezing. The length of time soil freezing occurs depends on the air temperature, snow cover ŽGoodrich, 1982; Beltrami, as well as on the soil moisture content, such that systematic variations of any of these variables can influence the soil air temperature difference and interfere with the long term coupling of air and ground temperatures Soil air tracking and solar radiation One of the key issues regarding the integration of meteorological records with GSTHs inferred from inversion of geothermal data, lies on the clarification of the long-term relationship between air and ground temperatures. Putnam and Chapman Ž reported a first order positive correlation for the difference between air temperatures, a modeled surface soil temperature and solar radiation for the Emigrant Pass Observatory in Utah. The site in Utah receives very little precipitation Ž 86 mmryear. such that it can be considered as a case for which evapotranspiration, snow-cover insulation, and latent heat effects are Table 5 Estimate of annual soil air temperature difference Ž soil minus air. variation as a function of additional number of soil freezing days. The number of soil-freezing days for this site is Number of Soil surface Soil air DT Ž K. additional days temperature Ž K. with Asoil freezingb yearly mean Ž 8C y y y y y y y0.33

20 346 ( ) H. BeltramirGlobal and Planetary Change minimal. At the Pomquet station site, the situation is quite different; the terrain is affected by surface conditions changes due to vegetation growth and decay, precipitation Žover 1000 mm of precipitation recorded during , a sporadically changing snow-cover, freezing of the soil during the winter months and thawing during spring time. The difference between daily values of soil temperatures, at the surface and 100 cm, and the air temperature at 2 m height, together with the daily means of the incoming solar radiation record are shown in Fig. 11a and b. The thin discontinuous lines represent the soil air temperature difference, and the thick, smooth lines represent a reconstruction of the time series using the first two principal components. The filtering was carried out using singular value decomposition, chosen because it has some physical meaning unlike running averages ŽGhil and Vautard, The filtered curves are entirely dependent on the data themselves. Fig. 11. Variation of the daily difference between soil and air temperature Ž 2 m.. Ž a. Soil temperature at the surface, Ž b. soil temperature at 1 m depth, Ž. 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.

21 ( ) H. BeltramirGlobal and Planetary Change Fig. 11c shows the daily averages of the solar radiation measured at the station Ž thin line. along with the first two principal components for the series Ž think line.. It is apparent that at this site there is an inverse relationship between the soil air temperature difference and the incoming solar radiation. The large difference between air and soil temperature in winter Ž see Fig. 2. can be attributed to the latent heat released during soil freezing which keeps the upper layers of the soil near the freezing point. This is typicalof the Aheat valveb effect mentioned above. Other processes are also involved in determining this difference Ž evaporation, wind, precipitation, etc.., but they tend to reduce the difference rather than increase it Ž Geiger, 1965; Gosnold et al., Conclusions Ž. 1 Records of air and soil temperatures obtained at the study site indicate that ground temperature tracks air temperature variations during the time when soil freezing is absent. When soil freezing is present, air temperature variations are not recorded into the ground, although high frequency variations are filtered by the earth and would not affect the subsurface thermal regime directly, systematic variations of the soil freezing period can have an effect on the long term soil air temperature coupling. Similar effects can be induced by a systematic variation of snow cover. The annual difference between soil and air temperatures Ž soil minus air. at the study site vary from 2 K at the surface to 1.3 K at a depth of 100 cm. The difference varies throughout the year and at 100 cm, appears to be inversely correlated with the amount of incoming solar radiation. Ž. 2 Rapid, semi-qualitative determination of the character of the heat transfer regime at the air ground interface and subsurface can be made by AphasespaceB plots and by spectral analysis of the temperature time series. Modeling of the soil thermal regime using a forward model produces satisfactory results for the shallow layer of the soil. Finite difference modeling can reproduce the thermal regime of the soil very well for the period dominated by conduction at all depths. Ž. 3 Soil temperature data at multiple depths permit the determination of apparent thermal diffusivity for several layers within the soil. At this site, for the upper Ž 0 10 cm. and lower Ž cm. soil layers, the apparent thermal diffusivity was found to be 0.42=10 y6 and 0.63=10 y6 m 2 rs, respectively. The value for the thermal diffusivity calculated for the first meter of soil is 0.5=10 y6 m 2 rs. All these values were estimated from the finite difference model under the assumption that the thermal parameters of the soil are independent of time. This assumption is questionable during the winter. Ž. 4AAback of the envelopeb calculation reveals that the average heat attributed to non-conductive processess, for the soil-freezing period is on the order of 584 calrkg every 5 min, equivalent to the heat released by freezing 2.1 kg of water per day. Ž. 5 The combination of meteorological records with reconstructions of ground temperature variations from geothermal data should be possible in areas where freezing of the upper soil does not occur, is short lived, or it changes randomly from year to year. In higher latitudes, where soil freezing is common place for extended periods and where meteorological data analyses reveal large magnitude temperature changes in the last century, the coupling between air and ground temperatures should be approached with caution. Acknowledgements Discussions with S. Putnam, D.S. Chapman and L. Kellman are gratefully acknowledged. Comments from two anonymous reviewers and R. Harris are much appreciated. This research was funded by The Natural Sciences and Engineering Research Council of Canada Ž NSERC. through an operating grant and partially by St. Francis Xavier University Ž UCR.. The author is grateful for this support. Bonnie Quinn assisted with the FORTRAN codes. Rob Harris handled the review process of this paper. References Beltrami, H., Active layer distortion of annual airrsoil thermal orbits. Permafrost Periglacial Processes 7, Beltrami, H., Chapman, D.S., Drilling for a past climate. New Sci. 142, April 23. Beltrami, H., Mareschal, J.C., Recent warming in Eastern Canada: evidence from geothermal measurements. Geophys. Res. Lett. 18,