HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Ochsner, T. E. Articles by Baker, J. M. Search for Related Content PubMed Articles by Ochsner, T. E. Articles by Baker, J. M. GeoRef GeoRef Citation Agricola Articles by Ochsner, T. E. Articles by Baker, J. M. Related Collections Agroclimatology Soil Thermal Properties Soil Physics

SOIL PHYSICS

In Situ Monitoring of Soil Thermal Properties and Heat Flux during Freezing and Thawing

Soil and Water Management Research Unit, Agricultural Research Service, St. Paul, MN 55108

^* Corresponding author (ochsner{at}umn.edu).

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
When soil freezes or thaws, latent heat fluxes occur and conventional methods for monitoring soil heat flux are inaccurate, often wildly so. This prevents the forcing of surface energy balance closure that is used in Bowen ratio flux measurements and the assessment of closure that is used as a check on the accuracy of eddy covariance measurements. We hypothesized that heat pulse sensors could be used to obtain accurate measurements of apparent thermal conductivity (_a) and apparent volumetric heat capacity (C_a), which, together with soil temperature data, would permit accurate monitoring of soil heat flux under freezing and thawing conditions. Wintertime apparent thermal properties were monitored in situ using heat pulse sensors and independently predicted using a theoretical model. The measurements and the model both showed that for temperatures between –5 and 0°C, _a and C_a were strongly temperature dependent, varying more than two orders of magnitude. This temperature dependence is primarily the result of latent heat transfer processes. Good agreement existed between the measured and modeled thermal properties, with mean absolute differences of 20% for C_a and 37% for _a. Measured and modeled soil heat flux during spring thaw and snowmelt were similar, with cumulative totals differing by only 6% during a 7-d period. During that same period, we measured a latent heat flux into the soil of 7.9 MJ m^–2, a sizeable heat flux completely undetectable by previous methods. The results of this study support our hypothesis and indicate that this method may be useful in wintertime surface energy balance studies.

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Freezing and thawing of the soil surface are significant physical processes with implications at scales ranging from local to global. At the global scale, accurate representation of these processes is important in developing robust land surface schemes for general circulation models (Koren et al., 1999; Slater et al., 1998). At the local scale, freezing and thawing strongly influence numerous phenomena including the surface energy budget (Tanaka et al., 2003), hydrologic processes (Luo et al., 2000), and greenhouse gas emissions (Wagner-Riddle and Thurtell, 1998).

Understanding and prediction of soil freezing and thawing is hampered by the lack of methods for monitoring soil thermal properties below 0°C. Although soil temperature measurements are routine, in situ measurements of thermal properties of frozen soil are rare. Putkonen (2003) reported that the dual-probe heat-pulse method (Bristow et al., 1994) gave accurate thermal property estimates below –10°C. He also suggested that the thermal properties varied little between –10 and –2°C, permitting extrapolation within that range. Overduin et al. (2006) presented in situ estimates of the thermal conductivity of frozen soil using a continuously heated line source. These estimates require modeling the apparent heat capacity of the soil, which can vary several orders of magnitude for temperatures just below freezing. The heat capacity model, in turn, requires knowledge of the soil freezing characteristic curve. No method is yet available that can yield direct, in situ measurements of soil thermal properties for the full range of temperatures encountered in frozen soil.

Accurate measurements of soil heat flux for frozen soil are also sorely lacking. Conventional methods for measuring soil heat flux (Sauer, 2002) make no account for the latent heat transfers accompanying freezing and thawing. This omission can cause gross errors in soil heat flux estimates, as well as significant closure errors in energy balance studies (Tanaka et al., 2003).

In light of these deficiencies, the primary objectives of this work were to: (i) present the theoretical basis for the measurement of _a and C_a using heat pulse sensors; (ii) evaluate the accuracy of the resulting _a and C_a data; and (iii) demonstrate the use of _a and C_a data to monitor soil heat flux via the three-needle gradient method (Ochsner et al., 2006).

	THEORY

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
We adopted the model for latent and sensible heat transfer in partially frozen soil described by Fuchs et al. (1978). The starting point is a modified form of the conduction–convection equation:

[1]

where C is soil volumetric heat capacity (MJ m^–3 K^–1), T is temperature (K), t is time (s), L_f is the latent heat of fusion for water (J kg^–1), S_i is the mass rate of ice formation (kg m^–3 s^–1), z is depth (m), is the soil thermal conductivity (W m^–1 K^–1), J_l is the liquid water flux (m³ m^–2 s^–1), and C_l is the volumetric heat capacity of liquid water (MJ m^–3 K^–1). It is assumed that only the phase change between liquid and ice is significant, and that vapor-phase heat and mass transport are insignificant.

Conservation of mass requires that

[2]

where _l is the density of liquid water (kg m^–3) and _l is the soil liquid water content (m³ m^–3). By the chain rule, we can then write

[3]

Inserting Eq. [3] into Eq. [1] and grouping similar terms gives

[4]

The complete term in parentheses on the left-hand side of Eq. [4] is the apparent volumetric heat capacity, C_a, which may be interpreted as the quantity of heat required to raise the temperature of a unit volume of soil by 1 K while a phase change between liquid water and ice is occurring.

The water flux, J_l, is given by the Buckingham–Darcy equation:

[5]

where K is the soil hydraulic conductivity, _l is the matric potential, and _g is the gravitational potential. Omitting the gravity-driven water flux, which is of minimal significance in freezing soil (Fuchs et al., 1978), and applying the chain rule again, we obtain

[6]

Inserting Eq. [6] into Eq. [4] gives

[7]

where the apparent thermal conductivity, _a, is defined as

[8]

The apparent thermal conductivity may be interpreted as the heat flux per unit temperature gradient that occurs while temperature gradients are driving liquid water flow in soil at subfreezing temperatures.

As noted by Fuchs et al. (1978), the coefficient of the second term on the right-hand side of Eq. [7], the convection term, is at most 1/80th of that of the conduction term. This implies that convective heat transport is relatively minor and can be neglected. Therefore, heat transfer in partially frozen soil can be approximated by

[9]

and the soil heat flux, G, by

[10]

which includes both sensible heat transfer by conduction and latent heat transfer due to thermally induced liquid water flow.

Making the additional assumption that the region of interest is homogeneous and isotropic, we generalize Eq. [9] to three dimensions:

[11]

In unfrozen soil (i.e., C_a = C and _a = ), the solution to Eq. [11] for a finite-duration heat pulse from an infinite line source permits measurement of soil thermal properties by the dual-probe heat-pulse technique. The heat capacity is calculated as

[12]

where q' is the heating rate (W m^–1), t₀ is the heating duration (s), e is the base of the natural logarithm, T_m is the maximum temperature rise (K) at a distance r (m) from the heater, and is t₀/t_m with t_m being the time (s) from the beginning of heating until T_m occurs (Knight and Kluitenberg, 2004). The thermal diffusivity () is calculated by (Bristow et al., 1994)

[13]

The thermal conductivity is then simply = C.

If heat transfer in partially frozen soil is reasonably represented by Eq. [9] or more generally Eq. [11], then it may be possible to apply Eq. [12] and [13] without modification to measure _a and C_a. The restriction is that the thermal properties must be homogeneous and constant for the range of temperatures occurring in the measurement volume during the measurement. In moist unfrozen soil, temperature increases induced by the heat pulse are typically around 1 K at r and may briefly reach up to 20 K near the heater. At present, there is no evidence indicating that these temperature changes appreciably affect the thermal properties of unfrozen soil. In partially frozen soil, however, _a and C_a may vary by several orders of magnitude across a 1 K temperature range (Fuchs et al., 1978). This would at first seem to prevent the application of Eq. [12] and [13], but, precisely when the temperature sensitivity of the thermal properties becomes very large, the temperature increase induced by the heat pulse becomes very small. This occurs because an increasing fraction of the total heat input is consumed in melting ice rather than in raising the temperature of the soil. Just below the freezing point, where the temperature sensitivity of _a and C_a is greatest, almost all of the heat pulse is consumed in melting ice and the temperature in the measurement volume is nearly constant during the measurement. Therefore, we hypothesize that Eq. [12] and [13] may, in fact, produce accurate measurements of _a and C_a. If _a is accurately determined, then soil heat flux can be calculated from Eq. [10]. This would be the reference soil heat flux (G_r) at the depth of the sensor (z_r). The heat flux at the soil surface, G₀, would be given by

[14]

	MATERIALS AND METHODS

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Field Site
Data were recorded during the winter of 2006–2007 in Field G19 at the University of Minnesota Outreach, Research, and Extension Park in Rosemount, MN. Soybean [Glycine max (L.) Merr.] had been harvested the previous growing season. The soil in G19 is predominantly Waukegan silt loam (fine-silty over sandy or sandy-skeletal, mixed, superactive, mesic Typic Hapludoll).

Data Acquisition System and Sensors
The data acquisition system consisted of a datalogger (CR10X, Campbell Scientific, Logan, UT), a multiplexer (AM16/32), and a 12-V relay switch in a fiberglass enclosure. Power was supplied by a 12-V battery and solar panel. Eight three-needle heat pulse sensors were installed, four at the 2.5-cm depth with the needles aligned horizontally and four at 5-cm depth with the needles aligned vertically. The sensor needles were parallel stainless steel tubes 4 cm long and 0.13 cm in diameter with 0.6-cm spacing. The exact needle spacings were determined by calibration in agar-stabilized water (Ochsner et al., 2003). The heating element in the central needle of each sensor was constructed of two loops of 38 American wire gauge, Nichrome 80 enameled resistance wire (Pelican Wire Co., Naples, FL).

An 8-s heat pulse was generated by activating the relay and simultaneously applying 12 V to the heating elements in the center needle of each sensor. The heating rate, q', was calculated based on the measured current through each heater and the resistance of the heating element (533 m^–1). The current was measured using a precision power shunt (0.1 ± 0.1%, PLV2, Precision Resistor Co., Largo, FL). Typical heating rates were 85 W m^–1 giving a typical heat input of 680 J m^–1. The resulting temperature increases were measured using thermistors (10K3MCD1, BetaTherm, Shrewsbury, MA) encapsulated in the outer needles. The multiplexer sequentially connected the thermistors in series with a reference resistor (10 k ± 0.1%). The datalogger measured the thermistor resistance and converted it to a temperature by the Steinhart–Hart equation (Steinhart and Hart, 1968). The scan rate was 2 Hz.

Ambient temperature drift rates were measured and subtracted from the temperature increase data. The maximum temperature increase and the time of the maximum temperature increase were recorded for the outer needles. These two parameters were used in Eq. [12] and [13] to obtain estimates of _a and C_a. Apparent thermal conductivity was calculated as the product of _a and C_a. Thermal property estimates from the two outer needles were averaged to give one estimate of each property from each sensor.

The temperature gradient at 5-cm depth was determined using the sensors with vertically aligned needles. The gradient was calculated by dividing the difference in ambient temperatures between the two outer needles by the sum of the calibrated needle spacings. Heat flux at the soil surface was calculated by applying Eq. [10] and [14], with G_r determined using the sensors at 5 cm and the change in heat storage determined using the sensors at 2.5 cm. Thermal properties and ambient temperature changes were measured at 30-min intervals, and temperature gradients were measured every 5 min and averaged over 30 min.

Modeling
Predicting the apparent thermal properties of the partially frozen soil required knowledge of the soil freezing characteristic and the soil hydraulic conductivity function. The soil freezing characteristic is similar to the soil water retention curve (Koopmans and Miller, 1966; Spaans and Baker, 1996). For adsorbed water, there is a 1:1 correspondence between the two, while capillary water requires a scaling factor of 2.2 to account for the difference in surface tension between air–water interfaces and ice–water interfaces. The Waukegan silt loam at this field site is relatively fine textured, so as a first approximation we assumed that the freezing characteristic could be directly represented by the water retention curve. This assumption permitted the use of soil property data collected by Arya et al. (1975). They measured soil hydraulic conductivity and water retention for Waukegan silt loam in the field and undisturbed samples in the laboratory. We fit the van Genuchten (1980) equation to the water retention data, leading to the following parameter estimates: saturated water content, 0.445 m³ m^–3; residual water content, 0.181 m³ m^–3; and shape factors n = 1.48 and = 0.13 kPa^–1. A simple power function of the form K = K_s(_l/_s)^m was used for hydraulic conductivity (Fuchs et al., 1978). The saturated hydraulic conductivity, K_s, was determined to be 1.51 cm h^–1 in previous experiments with this soil. The fitting parameters _s and m were then optimized using the unsaturated hydraulic conductivity data, resulting in _s = 0.487 m³ m^–3 and m = 18.

Spaans and Baker (1996) presented an integrated form of the Clapeyron equation:

[15]

where _l is the osmotic potential of the liquid phase. The soil temperature, T, is expressed on the Kelvin scale, and T₀ is 273.15 K. The osmotic potential (kJ kg^–1) is a function of the liquid water content defined by

[16]

where _sp (1.53 mS cm^–1) is the electrical conductivity (measured at temperature T_r = 292 K) of the saturated paste extract from soil samples obtained on 1 Dec. 2006, W_sp is the wetness of the saturated paste (0.48 kg kg^–1), and _b is the soil bulk density (1.30 Mg m^–3). Likewise, the soil matric potential is represented as a function of liquid water content by inverting the water retention curve.

The freezing point, T_f, was found by first using the total water content of the soil to estimate values of _l and _l at a temperature above T_f. For the freezing event, the total water content (0.30 m³ m^–3) was estimated using the average measured heat capacity value (2.42 MJ m^–3 K^–1) from the sensors just before the onset of subzero temperatures. For the thawing curve, total water content (0.38 m³ m^–3) was determined from soil samples collected before the thaw. In both cases, inverting the water retention curve gave _l based on the total water content. Next, _l for T > T_f was calculated by solving Eq. [16] with _l equal to the total water content, T set to 273.15 K, and the measured value for _sp. Then, these values of _l and _l were inserted into Eq. [15] and the FMINBND routine in MATLAB (Version 7.0, MathWorks, Nantick, MA) was used to identify the value of T that satisfied the equality. The T value thus calculated is T_f. Next, liquid water content was calculated for the desired temperature range. For T > T_f, the liquid water content was considered to be constant and equal to the total water content. For T T_f, the liquid water content was calculated by simultaneously solving Eq. [15–16] and the van Genuchten equation. Again, the FMINBND routine in MATLAB was used. The result was a simulated freezing characteristic for the soil that included the effect of osmotic potential.

The apparent heat capacity, C_a, was calculated using this simulated freezing characteristic curve. The partial derivative of liquid water content with respect to temperature was approximated by finite differences. The temperature dependence of L_f was included using the polynomial relationship from Spaans and Baker (1996). The volume fractions of water, solids, and ice were used to determine C in Eq. [4] (Kluitenberg, 2002). Specific heat values of 4.22, 0.87, and 2.07 kJ kg^–1 K^–1 were used for the liquid water (Lide, 2003), soil solids (Ochsner et al., 2001), and ice (Lide, 2003), respectively. Densities of 1000 and 918 kg m^–3 were used for liquid water and ice, respectively (Lide, 2003). Specific heat and density were treated as independent of temperature. Ice content was estimated as the total water content minus the liquid water content at each temperature.

The apparent thermal conductivity, _a, was calculated by Eq. [8]. The de Vries (1963) model was used to calculate in Eq. [8]. The approach of Campbell et al. (1994) for representing vapor-phase thermal conductivity in the de Vries model was used. We assumed a geometric mean grain diameter of 7.9 µm, 98 kPa atmospheric pressure, a 0.071 shape factor for the soil solids, a thermal conductivity of 2.31 W m^–1 K^–1 for the soil solids, and a liquid water recirculation parameter of 4.14. These parameter values are those specified for Palouse silt loam soil by Campbell et al. (1994). The hydraulic conductivity as a function of temperature was calculated based on the predicted _l. The partial derivative of the matric potential with respect to temperature was approximated by finite differences, using the matric potential and temperature pairs from the simulation of the freezing characteristic.

	RESULTS AND DISCUSSION

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Freezing
Our analysis will focus on a soil freezing event that occurred in November and December 2006 and a soil thawing event that occurred in February and March 2007. Soil temperatures at the 2.5- and 5-cm depths were above freezing in late November 2006 until a significant 10-d cold period beginning 28 November dropped the soil temperatures to lows in the range of –7°C (Fig. 1 ). Note how the freezing-point temperature (approximated by the 0°C line) acts as a fairly effective barrier to soil temperature change.

View larger version (11K): [in this window] [in a new window]   Fig. 1. November and December 2006 soil temperatures at 2.5- and 5-cm depths in Waukegan silt loam under soybean residue in Field G19.

View larger version (9K): [in this window] [in a new window]   Fig. 2. Soil apparent heat capacity (Ca), apparent thermal conductivity (a), and apparent thermal diffusivity (a) during a November and December 2006 freezing event. Data (symbols) are from 2.5- and 5-cm depths. The model (line) is that of Fuchs et al. (1978).

The reason for this discrepancy is evident in the apparent thermal diffusivity data. Recall that measured _a is actually the product of measured C_a and measured _a. The measured _a is computed from Eq. [13] and is inversely related to the time of the maximum temperature rise, t_m. The flat-bottomed region in the measured _a data from –2 to 0°C is a measurement artifact. In this region, the actual t_m occurred after the readings on the heat-pulse sensors had stopped (60 s in this case). Therefore, the recorded t_m values were too small, inflating the _a measurements and subsequently the _a measurements. The delay in t_m is an effect of the solid–liquid phase change caused by the heat pulse in this ambient temperature range. These results showed that to accurately measure _a and _a just below freezing, the sensors must be monitored for a greater length of time following the application of the heat pulse. As a result, the monitoring period was extended from 60 s to 5 min.

Thawing
Soil temperatures during spring thaw are shown in Fig. 3 . Subfreezing temperatures prevailed until mid-February, when a warming trend began. Soil temperatures rose from –6°C to just below the freezing point during the week beginning 15 February. Subsequent colder air temperatures and snowfall delayed thawing and kept soil temperatures in the range of –2 to –1°C for 2 wk more. Warmer air temperatures beginning 9 March led to snowmelt and soil temperatures above freezing by 13 March. Apparent heat capacity and thermal conductivity varied with time in response to the temperature fluctuations (Fig. 3). Note the strong diurnal fluctuation in C_a at the 2.5-cm depth from 19 through 23 February. The apparent thermal conductivity at 5 cm was more stable in time, but exhibited two significant increases associated with temperatures just below the freezing point.

View larger version (14K): [in this window] [in a new window]   Fig. 3. February and March 2007 soil temperatures (top panel), and measured soil apparent heat capacity (Ca) at 2.5-cm depth and apparent thermal conductivity (a) at 5-cm depth (bottom panel).

During this thawing event, we selected thermal property estimates for all sensors whenever the mean soil temperature across all sensors was higher than any previously recorded mean soil temperature. The measured and modeled thermal properties as functions of temperature for the thawing event are shown in Fig. 4 . The agreement between measured and modeled thermal properties is good. Measured and modeled C_a reached peaks of 800 MJ m^–3 K^–1 followed by identical steep declines (Fig. 4). The 5-min monitoring period permitted the first direct measurements of the theoretically predicted narrow spike in _a just below the freezing point. The spike was approximately 0.2°C wide in this case and reached a maximum of around 100 W m^–1 K^–1. Extending the monitoring period also permitted accurate measurement of _a down to 0.03 mm² s^–1, approximately 10 times lower than the diffusivity of the unfrozen soil. The few _a values below 0.03 mm² s^–1 (Fig. 4) resulted from data collected when the monitoring period was temporarily set to 7.5 min.

View larger version (8K): [in this window] [in a new window]   Fig. 4. Measured (symbols) and modeled (line) soil apparent heat capacity (Ca), apparent thermal conductivity (a), and apparent thermal diffusivity (a) during a February and March 2007 thawing event.

View larger version (16K): [in this window] [in a new window]   Fig. 5. Selected heat pulse curves recorded by a single sensor at 2.5-cm depth on 21 Feb. 2007 for three different ambient temperatures (symbols). Corresponding modeled heat pulse curves (lines) were based on the assumptions discussed in relation to Eq. [11–13].

We will focus on the thawing event data because these data were collected with a sufficient heat-pulse monitoring period, i.e., 5 min as opposed to only 60 s for the freezing event. We will include in the comparison only those measurements for which we are 95% confident that the ambient temperature was below the modeled freezing temperature. For ambient temperature measurement, a 95% confidence interval of ±0.093°C was established in prior laboratory tests with these thermistors.

Figures 6 and 7 present comparisons of measured and modeled C_a and _a for the thawing event based on the above screening criteria. Since the data span several orders of magnitude, they were plotted in log–log space. For both thermal properties, the measured and modeled data are positively correlated, and the data tend to follow the 1:1 line. The data scatter at values of _a <0.1 mm² s^–1 results from imprecision in the identification of t_m when t_m becomes very large. Linear regressions performed on the log-transformed thermal properties yielded r² values of 0.936 for C_a and 0.769 for _a. These statistics indicate strong linear relationships between the measured and modeled thermal properties.

View larger version (12K): [in this window] [in a new window]   Fig. 6. Measured vs. modeled soil apparent heat capacity (Ca) during a February and March 2007 thawing event.

View larger version (17K): [in this window] [in a new window]   Fig. 7. Measured vs. modeled apparent thermal diffusivity (a) during a February and March 2007 thawing event.

Soil Heat Flux during Thawing
Here we focus on soil heat flux during the 7-d period from 9 through 15 March, a period marked by snowmelt and soil thawing. Using the measured _a and C_a data, along with measured soil temperatures, the heat flux at the soil surface was calculated. The mean thermal gradient at the 5-cm depth was used in Eq. [10] along with the measured _a time series. The mean rate of temperature change at the 2.5-cm depth was used in Eq. [14] along with the C_a time series and a 5-cm reference depth. Heat flux at the soil surface was positive (into the soil) for most of this period and reached a maximum of 150 W m^–2 on 13 March (Fig. 8 ). The maximum flux occurred just after the soil temperature rose above freezing at the 2.5-cm depth and while the soil temperature at the 5-cm depth was still below the freezing point.

View larger version (15K): [in this window] [in a new window]   Fig. 8. March 2007 instantaneous (upper panel) and cumulative (lower panel) heat fluxes at the soil surface.

The modeled soil heat flux is shown as the solid line in Fig. 8 (upper panel). The modeled flux closely follows the data, with a small peak on 9 March, a steadily increasing flux from 11 through 13 March, and a sharp peak on 13 March coinciding with the thawing of the surface soil. The model and the measured data are also in close agreement for cumulative soil heat flux (Fig. 8, lower panel). The cumulative measured soil heat flux was 16.0 MJ m^–2 and the model prediction was 15.0 MJ m^–2, a 6% difference.

To quantify the magnitude of the latent heat fluxes in the soil, we estimated the heat flux due to conduction alone. These estimates were derived from the modeled thermal properties excluding the latent heat effects ( and C). Values for these "conduction-only" properties were determined for each data point in the observed temperature series. These values were then used in Eq. [10] and [14] along with the observed temperature gradients and rates of temperature change. The result was a modeled soil surface heat flux time series with the latent heat flux term removed. This time series is labeled "conduction only" in Fig. 8. Latent heat effects dominated in this thawing period, as demonstrated by the marked differences between the modeled heat flux and the conduction-only flux (Fig. 8). Particularly notable is the latent soil heat flux from 11 through 13 March, a period characterized by high _a values and a sustained downward temperature gradient.

Latent heat flux accounted for 7.9 MJ m^–2 or 52% of the cumulative soil heat flux from 9 through 15 March. This latent heat flux would be undetected by conventional methods for measuring soil heat flux. The latent flux arose from two phenomena: thawing of the soil surface layer (0–5 cm) and downward liquid water flow past the 5-cm depth. From 24 February through 8 March, the cumulative liquid water equivalent of snowfall was 42 mm. This produced a snow pack that melted 9 through 15 March, providing a water supply at the soil surface more than sufficient to explain the observed latent heat flux into the soil. In fact, our method probably slightly underestimated the latent heat flux into the soil during the snowmelt infiltration. Some of the infiltrated water was probably stored in the top 5 cm of soil above the reference depth. The latent heat flux associated with that water would not have been detected.

Practical Considerations
The results of this study support our hypothesis that heat pulse sensors can be used to obtain accurate measurements of soil thermal properties and heat flux during freezing and thawing. We know of no other method for obtaining such data. The approach presented here, however, is not without challenges. Measuring thermal properties just below the freezing point strains the limits of the available instrumentation. For example, with a heating power of 700 J m^–1, the temperature increase would be only 0.005°C when the apparent heat capacity reached 500 MJ m^–3 K^–1. This is approaching the temperature measurement resolution for the system used in this study, which was 0.002°C. Also, uncertainty in peak time increases due to the flattening of the temperature increase curve. As a result, the stability of the thermal property estimates decreases as the temperature approaches the freezing point. The simple harmonic averaging used here proved sufficient to overcome these challenges in this case. Further testing is warranted to optimize the method in terms of number of sensors needed, optimum monitoring period, and enhancing resolution of the temperature increase curve. A separate but related issue that merits attention is thermistor drift. Small but differing drifts in the resistance characteristics of the two thermistors in a given sensor could degrade the accuracy of the temperature gradient estimates.

A final issue should be mentioned at this point, namely the complications that could arise in some instances due to frost heave. Heave occurs where there is a ready source of water near the surface, minimal overburden pressure, and a rate of latent heat loss during freezing that is matched by convective transport of water to the freezing front (Miller, 1980). Under such circumstances, lenses of pure ice can form, lifting the soil above. Heaving could result in a dynamic z_r, indeterminate _a and C_a, and deformation of sensor needles. Fortunately, there are many situations where soils freeze with little likelihood of appreciable frost heave, including the field site where this research was conducted.

	CONCLUSIONS

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
We have presented in situ measurements of apparent soil thermal properties across the full range of temperatures encountered in freezing and thawing soil. The measured properties show excellent agreement with the preexisting theoretical model. The thermal properties permitted soil heat flux measurements that included the effects of phase change and latent heat transfer. The magnitude of these heat flux values was significantly greater than heat flux estimates based on conduction alone. The largest measured latent heat flux was associated with spring snowmelt infiltration, representing 7.9 MJ m^–2 during the course of 7 d. This heat flux would be undetectable to prior methods of measurement. Earlier studies have demonstrated that a three-needle gradient method like the one used here provides accurate soil heat flux data for unfrozen conditions (Cobos and Baker, 2003; Ochsner et al., 2006). This study has shown that the method can work in frozen soil as well, creating the possibility of obtaining accurate year-round soil heat flux data for long-term energy balance studies. Future research should evaluate the three-needle gradient method for monitoring frozen soil thermal properties and heat flux within the context of complete surface energy balance measurements during freeze–thaw and snowmelt events.

	ACKNOWLEDGMENTS

 
We thank Todd Schumacher, USDA-ARS, St. Paul, MN, for his valuable assistance in all aspects of the data collection for this research.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

Received for publication July 27, 2007.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION THEORY MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

• Arya, L.M., D.A. Farrell, and G.R. Blake. 1975. A field study of soil water depletion patterns in presence of growing soybean roots: I. Determination of hydraulic properties of the soil. Soil Sci. Soc. Am. Proc. 39:424–430.
• Bristow, K.L., G.J. Kluitenberg, and R. Horton. 1994. Measurement of soil thermal properties with a dual-probe heat-pulse technique. Soil Sci. Soc. Am. J. 58:1288–1294.[Abstract/Free Full Text]
• Campbell, G.S., J.D. Jungbauer, Jr., W.R. Bidlake, and R.D. Hungerford. 1994. Predicting the effect of temperature on soil thermal conductivity. Soil Sci. 158:307–313.
• Cobos, D.R., and J.M. Baker. 2003. In situ measurement of soil heat flux with the gradient method. Vadose Zone J. 2:589–594.[Abstract/Free Full Text]
• de Vries, D.A. 1963. Thermal properties of soils. p. 210–235. In W.R. van Wijk (ed.) Physics of plant environment. North-Holland Publ. Co., Amsterdam.
• Fuchs, M., G.S. Campbell, and R.I. Papendick. 1978. An analysis of sensible and latent heat flow in partially frozen unsaturated soil. Soil Sci. Soc. Am. J. 42:379–385.[Abstract/Free Full Text]
• Kluitenberg, G.J. 2002. Heat capacity and specific heat. p. 1201–1208. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis. Part 4. Physical methods. SSSA Book Ser. 5. SSSA, Madison, WI.
• Knight, J.H., and G.J. Kluitenberg. 2004. Simplified computational approach for dual-probe heat-pulse method. Soil Sci. Soc. Am. J. 68:447–449.[Abstract/Free Full Text]
• Koopmans, R.W.R., and R.D. Miller. 1966. Soil freezing and soil water characteristic curves. Soil Sci. Soc. Am. J. 30:680–685.[Abstract/Free Full Text]
• Koren, V., J. Schaake, K. Mitchell, Q.Y. Duan, F. Chen, and J.M. Baker. 1999. A parameterization of snowpack and frozen ground intended for NCEP weather and climate models. J. Geophys. Res. 104D:19569–19585.[CrossRef][Web of Science]
• Lide, D.R. (ed.). 2003. CRC handbook of chemistry and physics. CRC Press, Boca Raton, FL.
• Luo, W., R.W. Skaggs, and G.M. Chescheir. 2000. DRAINMOD modifications for cold conditions. Trans. ASAE 43:1569–1582.[Web of Science]
• Miller, R.D. 1980. Freezing phenomena in soils. p. 254–299. In D. Hillel (ed.) Applications of soil physics. Academic Press, New York.
• Ochsner, T.E., R. Horton, and T. Ren. 2001. A new perspective on soil thermal properties. Soil Sci. Soc. Am. J. 65:1641–1647.[Abstract/Free Full Text]
• Ochsner, T.E., R. Horton, and T. Ren. 2003. Use of the dual-probe heat-pulse technique to monitor soil water content in the vadose zone. Vadose Zone J. 2:572–579.[Abstract/Free Full Text]
• Ochsner, T.E., T.J. Sauer, and R. Horton. 2006. Field tests of the soil heat flux plate method and some alternatives. Agron. J. 98:1005–1014.[Abstract/Free Full Text]
• Overduin, P.P., D.L. Kane, and W.K.P. van Loon. 2006. Measuring thermal conductivity in freezing and thawing soil using the soil temperature response to heating. Cold Reg. Sci. Technol. 45:8–22.[CrossRef]
• Putkonen, J. 2003. Determination of frozen soil thermal properties by heated needle probe. Permafrost Periglacial Processes 14:343–347.[CrossRef]
• Sauer, T.J. 2002. Heat flux density. p. 1233–1248. In J.H. Dane and G.C. Topp (ed.) Methods of soil analysis. Part 4. Physical methods. SSSA Book Ser. 5. SSSA, Madison, WI.
• Slater, A.G., A.J. Pitman, and C.E. Desborough. 1998. Simulation of freeze–thaw cycles in a general circulation model land surface scheme. J. Geophys. Res. 103:11303–11312.[CrossRef]
• Spaans, E.J.A., and J.M. Baker. 1996. The soil freezing characteristic: Its measurement and similarity to the soil moisture characteristic. Soil Sci. Soc. Am. J. 60:13–19.[Abstract/Free Full Text]
• Steinhart, J.S., and S.R. Hart. 1968. Calibration curves for thermistors. Deep Sea Res. 15:497–503.
• Tanaka, K., I. Tamagawa, H. Ishikawa, Y. Ma, and Z. Hu. 2003. Surface energy budget and closure of the eastern Tibetan Plateau during the GAME-Tibet IOP 1998. J. Hydrol. 283:169–183.[CrossRef]
• van Genuchten, M.Th. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892–898.[Abstract/Free Full Text]
• Wagner-Riddle, C., and G.W. Thurtell. 1998. Nitrous oxide emissions from agricultural fields during winter and spring thaw as affected by management practices. Nutr. Cycling Agroecosyst. 52:151–163.[CrossRef]

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Ochsner, T. E. Articles by Baker, J. M. Search for Related Content PubMed Articles by Ochsner, T. E. Articles by Baker, J. M. GeoRef GeoRef Citation Agricola Articles by Ochsner, T. E. Articles by Baker, J. M. Related Collections Agroclimatology Soil Thermal Properties Soil Physics