AU2018200711B2 - Method for measurement of subterranean soil characteristics for water management purposes - Google Patents

Abstract

The invention defined herein is a method intended for use in water management, for example agriculture, where mapping of soil water concentration and aeration may assist in improving yields and reducing water waste. It uses temperature data measured in the air above the soil and the temperature at two or more depths in the soil to generate information concerning water concentration and soil aeration at any geographical point in a field. 7. DIAGRAMS Land Sur-face- SoilI Water o -0 Intermediate vadose water + -------------------------------------------- Capillary Fringe WaterTable 0 -. Figure 1. Hydro-geologic zones and types of water in the subsurface. (Modified from Meinzer, O.E., U.S. Geological Survey Water Supply Paper 494, Washington D.C., 1923b, 71p) Soil Temperature Probe TI Air Figure 2. Illustration of one embodiment of the Soil Temperature Probe concept using 3 equal-distant subterranean sensors and one air sensor.

Description

7. DIAGRAMS

Land Sur-face-

SoilI Water

o -0

Intermediate vadose water

+ --------------------------------------------

Capillary Fringe WaterTable 0 -.

Figure 1. Hydro-geologic zones and types of water in the subsurface. (Modified from Meinzer, O.E., U.S. Geological Survey Water Supply Paper 494, Washington D.C., 1923b, 71p)

Soil Temperature Probe

TI Air

Figure 2. Illustration of one embodiment of the Soil Temperature Probe concept using 3 equal-distant subterranean sensors and one air sensor.

TECHNICAL FIELD

The present disclosure broadly relates to soil water management and, more particularly, to a soil temperature probe for determining water concentration in soil and a soil water analysis system.

BACKGROUND

In order to understand and map the water content of soils as well as water flow within the Vadose zone (the zone between the water table and the surface, see Figure 1), different techniques were investigated for their suitability in long term monitoring of fields used for agricultural purposes. Standard techniques used in the measurement of ground water flow such as the measurement of a hydraulic head in wells or through Magnetic Resonance Imaging are not always able to clearly illustrate the Vadose zone in detail over longer periods of time. This is particularly true for the Soil Water sub zone used by plants, see Figure 1, since it is often some distance above the water table.

Other more direct techniques, such as measurement of soil resistance and dielectric strength using either direct connection to the soil or through the use of capacitive coupling, may show some promise. However, they lack the reliability needed and are subject to large inaccuracies or complete failure caused by momentary changes in electrical charge within the soil caused by such phenomena as lightning. Additionally, these methods are heavily influenced by small changes in soil density and void space, that may be introduced by the introduction of the probes themselves.

Any discussion of documents, acts, materials, devices, articles or the like which has been included in the present specification is not to be taken as an admission that any or all of these matters form part of the prior art base or were common general ?5 knowledge in the field relevant to the present disclosure as it existed before the priority date of each claim of this application.

SUMMARY

Throughout this specification the word "comprise", or variations such as "comprises" or "comprising", will be understood to imply the inclusion of a stated element, integer or step, or group of elements, integers or steps, but not the exclusion of any other element, integer or step, or group of elements, integers or steps.

In one aspect there is provided a soil temperature probe for determining water concentration in soil, the probe comprising: an elongate body having a first end and a second end, the second end adapted for inserting into soil; a data collection unit comprising a thermal sensor and a processor, the data collection unit positioned proximate the first end of the elongate body; and provided along the elongate body, spaced from the data collection unit and toward the second end, and in spaced relationship to one another, a plurality of thermal sensors in data communication with the data collection unit, the plurality of thermal sensors adapted for subterranean operation, wherein the plurality of thermal sensors comprises a first sensor and a second sensor spaced a first distance from the first sensor toward the second end of the elongate body, wherein, in use, the second sensor is subterraneously positionable and the first sensor is subterraneously positionable to be a second distance from an air-soil interface, and wherein the data collection unit is configured to determine the soil temperature profile along a submersed length of the elongate body, based on the first distance and the second distance; and

determine, using iterative linear regression, water concentration changes with soil depth by deriving, based on a measured difference in temperatures measured at the first sensor and at the second sensor, a heat capacity relative to moisture concentration.

?5 The second distance may sustantially equal to the first distance; the plurality of thermal sensors may comprises a third sensor spaced a third distance from the second sensor toward the second end of the elongate body, wherein the third distance is substantially equal to both the first distance and the second distance, and the data collection unit may be configured to determine the soil temperature profile along the submersed length of the elongate body, based on the first distance, the second distance, and the third distance.

At least one of the data collection unit and one of the thermal sensors may comprise a demodulator comprising at least one of: a bandpass filter; and a mixer, wherein the demodulator is configured to operate with a carrier with a frequency substantially equal to one daily cycle (1/86400 Hz).

The data collection unit may be configured to determine, using iterative linear regression, soil aeration changes with soil depth.

The data collection unit may be configured to calculate a thermal time constant

The data collection unit may be configured to determine: a thermal resistivity of the thermal time constant, wherein the thermal resistivity is indicative of soil aeration and/or soil tension; and a thermal capacitance of the thermal time constant, wherein the thermal capacitance is indicative of soil moisture content.

In another aspect there is provided a soil water analysis system comprising an array of soil temperature probes as described herein, wherein the soil temperature probes are placed at different geographical positions so that the system collates and displays calculated variations in soil aeration and water content over a geographical area.

As a consequence of investigating existing techniques while incorporating temperature-based calibration, the inventor discovered that variations in temperature throughout the day could also be directly influenced by the water content in the soil, as well as other aspects such as soil type, aeration and the water distribution profile. The methods and systems described herein are the result of this discovery and relate to the original problem of mapping the water content of soil in the Vadose zone in a unique way that proves to be both reliable and accurate.

Described herein is an algorithmic technique using measurements of ground temperature at varying depths in the soil over a period of time to determine its thermal ?5 profile. This profile may then be used to determine soil parameters such as relative water density, soil aeration and concentration with respect to depth, all of which may be later used to build a 3D-model of subterranean water concentration and flow.

To extract the soil's thermal profile at any one geographical point, a calculation is performed that uses the demodulation of cyclic data as observed through changes within normal daily temperature cycles. An iterative linear regression method is applied using the demodulated data extracted from the different depths, which is first converted to magnitude and relative phase for each measurement, to construct a Soil Thermal Profile Model.

This model can then be used to calculate a relative thermal time constant of the soil with respect to time that is comprised of thermal resistivity multiplied by the thermal capacity, which may thus be separated and extracted. These values can be used in conjunction with the extracted water concentration gradient, based on an adjustment of error, and virtual air-soil interface temperature magnitude - both extracted from the model - to illustrate the approximate water content and soil aeration.

When data is extracted from many devices in a field using this technique, it is then possible to apply techniques such as Finite Differential Method, Finite Element Method and multi-dimensional cross correlation to map the water concentration and movement throughout the field in the upper Vadose Zone, hence providing useful information for agricultural purposes.

DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic representation of hydro-geologic zones and types of water in the subsurface. (Modified from Meinzer, O.E., U.S. Geological Survey Water Supply Paper 494, Washington D.C., 1923b, 71p)

_0 Figure 2 illustrates an embodiment of a Soil Temperature Probe concept using 3 equal distant subterranean sensors and one air sensor.

Figure 3 is a circuit diagram of an electrical equivalent thermal model of the configuration illustrated in Figure 2.

Figure 4 is a schematic representation of I&Q demodulation of data around a fixed ?5 carrier using a "Mixer".

Figure 5 is a graphical representation of typical variations in thermal profile with respect to depth due to changes in soil characteristics. Here an offset parameter Xoff (see equation (5)) is used to model the changes and it is assumed that the rate of change with respect to depth is consistent.

Figure 6 is a graphical representation of typical variations in thermal profile with respect to depth due to changes in soil characteristics, using a logarithmic scale to illustrate linearity. Here, the ideal response curve where Xoff = 0 is a straight line.

Figure 7 is an example plot of the Linear Regression Error vs Changes to Time Constant Gradient Parameter for a perfectly homogenous soil profile.

Figure 8 is a diagram of a process of iterative linear regression to reduce the Linear Regression Error illustrated in Figure 7.

Figure 9 is a circuit diagram of a simplified field probe device equivalence circuit.

Figure 10 is an example statistical analysis of capacitance readings to evaluate the saturation point and absolute dryness point.

BENEFITS

The benefits of the methodology described herein are that it:

1. Constructs a model for Thermal Response of the soils that can be used to derive values for thermal time constant, comprised of both capacity and resistance, of the soils in a unique way using a minimum number of sensors. From this it is possible to determine the relative proportion of water content and aeration of the soil. 2. Provides information concerning the homogeneity of the soil. (using the error of regression) 3. Extrapolates a gradient parameter illustrating an approximated water density profile with depth. 4. Monitors the above measurable characteristics of the soil in real time (minimum resolution of less than half a day). 5. Only requires measurements of the relative change in soil temperature at various depths to achieve its objective without direct electrical contacts with the soil; hence cost for implementation are minimal and problems due to corrosion, aging and a need for calibration are reduced or eliminated entirely making it suitable for use in large-scale systems requiring long-term usage without need of maintenance. 6. Enables better understanding of the water content and flow within the soil used for agriculture, therefore allowing for an optimization of water usage and distribution. Hence, helping to limit agricultural pollution while improving yields.

DETAILED DESCRIPTION

Since water has a thermal mass that is roughly 10 times that of dry soil, thermal modeling of the soil can provide useful information in the form of water retention, as well as approximate depth to impermeable layers and/or to the water table when measured at different depths over time. Additionally, the soil's thermal conductivity can provide information about the soil type and density, as different soils conduct heat better than others. Using data collected over time at many positions in a field, we may later estimate the flow of water through the field.

COLLECTIONAND PREPARATION OF DATA

Described herein is a probe design concept which is comprised of a series of temperature sensors placed at equally spaced depths in the soil, as presented in Figure 2.

Figure 2 shows one possible embodiment of a probe where measurements of temperatures can be taken at various depths. For ease of computation, all measurements should be taken at the same time at regular intervals and the distance between sub-soil temperatures should be the same as it should be between the soil surface and the first sensor. It should be noted that the above ground air temperature sensor (measuring Tair) will be subject to large variations in solar radiation due to cloud obstruction and local weather, therefore appropriate housing and shielding should be ?5 in place to minimize such variations.

Any data acquired from the field will be subject to problems that result in sample misalignment, inconsistent sampling intervals caused by device reset or otherwise, and possibly containing missing segments caused by momentary failures in probe sensors.

For practical use, particularly when intending to perform cross-correlation between data collected at different geographical points, all data collected needs to be aligned by time. To do this, it is first necessary to ensure that appropriate synchronization is employed such that data is collected and stored using a common time reference in the form of a time stamp derived from a centralized clock source.

Once the data collection time reference is synchronized, each of the samples will need to be adjusted and possibly re-sampled using interpolation between recorded data samples to create synchronized data sample sets.

Further interpolation may still be required in the event that data is missing or lost. It is important to mark these sections in the data record accordingly as any interpolation technique used can only predict what the missing data should be, based on the preceding and following data of the missing section.

ELECTRONIC CIRCUIT MODEL ANALOG

As with all materials, soil has thermal conductivity and capacity that may be modeled using an analogous electrical circuit chain model with a series of Resistor-Capacitor chains linked together as shown in Figure 3.

In Figure 3, the primary heat sources, as indicated by an alternating voltage symbol, are from solar radiation received from the sun or through convection currents in air (wind) and will vary with the daily cycle, along with impacts from other random weather events, which contains a primary frequency component of 1/86400 Hz. Earth is represented with the electrical Ground symbol and is assumed to be a constant as the depth approaches infinity, applicable when using Alternating Current (AC) analysis techniques.

The values of components R1, R2 and R3 will be relative to the distance, soil density, ?5 air content, soil type and water content each between sensors at various depths at any given time. The values of C1, C2 and C3 are related to the specific heat, or thermal capacity, of the soil, as seen between sensors, that are mostly related to the water content of the soil, at any given time. The value of RAIR represents the thermal resistivity between the soil and the air, which is dependent on the transmissivity of infra-red radiation (received and emitted) and the process of convection and conduction with the surround atmosphere. The component Re represents the residual heat flux contribution as a result of a theoretical propagation of the RC chain and has a complex value that changes with time.

UNITS OF MEASURE

The value of the units used to represent the thermal characteristics of the soil and their electrical analog are defined in the table below:

Table 1: Units used to represent the thermal characteristics of soil and their electrical analog

Characteristic Unit Equivalence Equivalent Unit Circuit Component

Thermal Resistance A0C/Watt Resistors Ohms

Thermal Capacity Joules/°C Capacitors Farads

Heat Flux Joules/s Current Amps

(or Watts) Source

Temperature 0C Voltage Volts Source

ASSUMPTIONS AND SIMPLIFICATIONS FOR PRACTICAL USE

The model presented in Figure 3 above contains too many unknown variables to be of any practical use. Therefore, several basic assumptions are needed in order to simplify the model into a usable form. The first such assumption is that the soil shall be considered homogeneous or if not, it shall be considered to have a gradual but uniform change with respect to depth. That is, we assume that the soil type, aeration and water content are consistent at all depths, or it is consistently changing with respect to depth in a linear fashion.

By making this assumption we may then begin to construct a model by first considering that with an equivalent distance between sensors ds, i.e. d1=d2=d3. Soil conductivity between the probe sensors should be considered equal, hence R=R2=R3 =R. In turn, soil heat capacity may also be considered the same, which is C=C2=C3 =C.

From this we may then assume that the ratio of heat flux into the T1 node through R1 to that flowing to T2 through R2 is approximately the same as that of the heat flux into

T2through R2with respect to that flowing to T3 through R3. Hence -"')"1R 2 (t) , where 1R2(tW IR1(t)

IR1(t) is the instantaneous heat flux into R1 at time t, IR2(t) is the flux into R2 and IR3(t) is the flux into R3.

O By making these basic assumptions we may then apply an approach based on uniform modeling of exponential decay, similar to the voltage response with respect to distance in electrical transmission lines.

TRANSIENT THERMAL ANALYSIS

To begin to derive meaningful values for the time-variant equivalent components R(t) and C(t) that are modeled in the RC chains presented in Figure 3, we must first convert the recorded temperature data into a more useful and reliable form. This form must convert or remove transitional effects of the alternating signal and offsets that occur due to poorly calibrated sensors, as well as the effects from other fixed or semi-fixed environmental heat sources or sinks such as nearby rivers and aquifers that regularly occur in nature.

Here, using the circuit model we may treat the temperature changes that are a result of the daily temperature cycle as an alternating single that is fed as the input to the circuit. From this we may use the principles of demodulation around a daily frequency to extract the effective amplitudes and phase shifts in the time domain of the signals ?5 received at each sensor propagated down through the RC chains starting from the air soil interface.

The alternating temperature signals Taw(n, t) , where n is the sensor number and t is sample time, taken from the field that vary with the daily cycle can be represented as a combination of two orthogonal components plus a semi-fixed offset as follows:

TRaw(n, t) = in-(t) - cos(t) + Qn_(t) - sin(wt) + pn (°C) Equation (1)

Where I~n(t) is the instantaneous magnitude of a real contribution at time t, Q(t) is the instantaneous magnitude of the imaginary contribution (having a 900 offset to the real) at time t, a = 2rcf where f = 10Hz, and pn is the contribution from very low

frequency components including any fixed offset such as those mentioned earlier.

The process of extracting the components in(t) and Q~(t) for each temperature signal with respect to the daily cycle may be illustrated by the mixer circuit shown in Figure 4.

In Figure 4, the temperature sensordata is firstfed through a band-pass filter to remove the very low frequency (f-- 0 Hz ) components including the fixed offset pn, as well as any higher-frequency signals (f> 86400 Hz ) that are a result of noise or otherwise.

After filtering, assuming an ideal filter, the signal then loses its offset component and becomes:

TFilter(ft) in(t) - cos(t + (p) + Qn(t) - sin(t + p) Where the parameter 'p is the phase shift introduced by the filter, and a is the angular frequency of the daily cycle (a = 2) 86400

Provided the phase distortion introduced by the filters is insignificant, for purposes of simplification we may set the parameter 'p = 0 as we are only interested in relative phase shifts between sensors and any shift introduced by the process can be assumed ?0 to apply to all temperature signals equally. This reasoning may be applied to the absolute phase offset introduced by the oscillator signal o also; hence it shall be assumed that parameter o = 0.

Once filtered, the signal is then fed through the mixer where it is multiplied by an oscillator signal with a frequency f = 86400 Hz. This is described as follows for each of

?5 the two derived paths leading to In(t) and Q(t):

I-Path

Here we can derive the real component In(t) as:

In (t) = TFilter(n, t) - CoS(ot)

in-(t) cos 2 (t) + Q~(t) cos(ot) sin(wt)

Since:

2 1+ cos2x coszx 2

And:

sin2x cos(x) sin(x) = 2

We may re-write In(t) as:

II(t) i~n(t) cos (2wt) Q~(t) sin (2wt) 0It)= + 2 2 2 +

After applying a Low Pass filter with a stop-band starting from f 86400 Hz to remove

the residual upper image, we then have:

I~n(t) In(t) = 2

Q-Path

Deriving the imaginary component Qn(t) gives:

Qnt) = TFilter(ft) sinl(at)

= in(t) - cos(ot) -sin(wt) + Q~(t) -sin 2 (at) T,(t Tt)-cos zU~t) + 1nt)-sin z2at) 2 2 2

After applying a Low Pass filter with a stop-band starting from f 86400 Hz to remove

?0 the residual upper image, we get:

Q (t) Q,(t) =2

Combining the Paths

Both the I,(t) and Q,(t) should be multiplied by 2 before further usage to correct for the true magnitude of the original signal components, which may then be calculated as follows taking this fact into account:

Tn(t) ITFilter(nt)In 22(t) +Qn(t) 2

The instantaneous phase may be then derived from:

cpn(t) = atan2 In(t)

The values for Tn(t) and cpn(t) now provide a more stable and usable form of the raw measurements and may therefore be used in later calculations.

DERIVING THE SOIL TEMPERATURE PROFILE MODEL

Using the concept that the soil temperature with respect to depth can be treated as a continuous transmission line we may model the temperature at any particular depth d using the Soil Temperature Profile Model as follows:

i(d, t) = fo(t) - e-(t)d (°C) Equation (2)

'5

Where T(d, t) is the complex Thermal Response, comprised of the demodulated I and Q data extracted from temperature measurements with both phase and amplitude, at time t measured at depth d, io(t) is the initial propagated complex temperature at the air-soil interface at time t, f(t) is the complex propagation ?0 constant made up of a(t), the real-valued attenuation constant, and p(t) is the Phase Constant where ?(t) = a(t) + jp(t). The value of the propagated temperature at the air-soil interface will be adjusted later on with Equation (5).

In order to profile the soil at any given geographical point and at any given time we need to derive values for fo(t), a(t) and (t) given that we know the complex values for T(d, t). By first applying the natural logarithm to the equation, we attain:

In (T(d, t)) = In (TO (t)) - y(t). d (In( 0C)) Equation (3)

Which conforms to a linear form y, = mx, + c. From this, we may use linear regression of the temperature data from each sensor position to derive values for the gradient y and the offset In (iO(t)). Here, the linear regression may follow the standard formula:

1

Ex'-1 (zX)2

And: C= Y -iu

Note that the above equations are applied to complex variables, where:

ln(i) = log(|z|) +jtan-1m() Re(z)

The values for the instantaneous Thermal Response at the air-soil interface io(t) may then be therefore found using:

fo(t) = exp (Re(a)) - cos (awt + Im()) (°C) Equation (4)

The instantaneous wave parameter value ?(t) is equal tofn in the complex form.

CONSIDERATION FOR A NON-HOMOGENEOUS SOIL PROFILE

Using the Ideal model that assumes a homogeneous soil with constant moisture concentration, the Thermal Response with respect to depth should follow the ?0 transmission line equation stated above. And, when represented graphically using a logarithmic scale, the relationship should be perfectly linear. In reality, however, deeper soils are often more compact and/or have a higher water content than soils closer to the surface, hence their capacitive and resistive properties will change accordingly.

These phenomena mean that the thermal response will deviate from the ideal model stated in equation (2) above as illustrated in Figure 5 and Figure 6. These illustrations show how the Thermal Response can vary depending on changes to the soil characteristics. For the purposes of illustration, it is assumed the Thermal Responses for each case are the same at the soil surface.

The term Xoff(t) is introduced as a correction parameter and added to equation (2) in order to compensate for any relative change in the Thermal Response with respect to depth that may cause the profile to deviate from the ideal logarithmic curve as follows:

T (d, t) = fo(t) - e-I) - Xeff(t) (°C) Equation (5)

Where T(d, t) is the complex form of the Thermal Response being the demodulated temperature measurements at depth d and at time t, fo(t) is the complex zero intercept of the function, and f(t) is the complex wave parameters for the model, which is equal to a(t) +jp(t).

When three or more measurement points are available, we may use an iterative technique of curve fitting to derive a suitable value for the offset parameter Xff (t) by adjusting this parameter in such a way as to minimize the resultant Mean-Squared Error when applying linear regression to the logarithm of the measured Thermal ?0 Responses.

Figure 7 shows a plot of changes in Xeff(t) with respect to the calculated Mean Squared Error when applied to a homogenous soil profile. Here it is shown how the point at which the Mean Squared Error reaches a minimum is when Xeff(t) has the value of 0, indicating no changes in the thermal behavior of the soil with respect to ?5 depth. In reality this point will shift left or right depending on whether the thermal time constant reduces or increases with depth respectively and the final error value will rarely be so close to zero.

The Mean-Squared Error may be calculated using the following:

N

Error = [In (f(t)) - f(t). d, x n - In (i(d, x n, t)) n=O

Where N is the number of sensors, d, represents the distance between sensors (assuming this distance is constant), and n = sensor number.

The iterative approach can be described in Figure 8.

DETERMINING THE POINT OF SATURATION

Once a suitable value for Xoff (t) has been established, we may then determine a value for the point of intersect with the x-axis in the logarithmic scale, noted as dsat, where the Thermal Response approaches zero, i.e. lT(d, t)I -- 0, using the magnitude and attenuation constants as follows:

iot)| - e-a(t)dsat Xoff(t)

Applying a logarithm to this we attain:

ln(Ifo (t)|) - a(t) - dsat In (Xoff (t))

Rearranging for d:

dsat = n(|fo (t)|) - In (Xoff (t)) (meters) Equation (6) a(t)

The resultant value for dsat as derived in equation 6 is only a relative indicator used to extrapolate the theoretical point at which there is no longer an apparent temperature change caused by the daily cycle. This point can be used as an indication of a high water table, where the thermal time constant approaches infinity due to the higher ?0 thermal mass and increased conduction with lower layers. It is important to note, however, if d becomes multiple orders of magnitude larger than the distance between the air-soil interface and the lowest sensor the calculation will saturate. Hence, suitable limits must be applied.

CALCULATION OF THE THERMAL TIME CONSTANT

Once the model parameters are derived for any time t, it is now possible to calculate the thermal time constant of the soil using the standard equation to calculate the wave parameters, as follows:

y= (R +jwL)(G + jwC)

Which, due to that we have no inductive or trans-conductive components to our model, can be expressed as:

y(t) = AjwR(t)C(t)

Therefore:

y(t)2 T(t)= R(t)C(t)= jw

However, for practical purposes, only the real values need to be considered since the complex component of y(t) is a phase shift, hence we may simplify to:

T(t) (s) Equation (7)

SEPARATING THERMAL RESISTIVITYAND CAPACITY FROM THE TIME CONSTANT

In order to model moisture concentration without the influences from soil tension and aeration, it is important to separate the thermal resistivity from the thermal capacitance after extracting the thermal time constant.

It is possible to derive a value for the resistivity using the assumption that the value of the air-soil thermal resistance RAIR isalways constant for all nodes and at all times in ?0 a field where measurements are taken and are subject to the same environmental conditions. Using this assumption, along with the projected value for i(O, t) using equation (5), we may derive an approximate value forIR(t)Iusing the potential-divider concept as follows:

IT(, ) -IT~s)t)I TAir -|Tds, t)|| R(t) R(t)+RAIR()

Where ds is the distance from the soil surface to the first underground sensor.

Assuming a constant for the air-soil interface, that is RAIR(t) = 1, rearranging we get:

R ~-I(t) IT(dst)I A°C/Watt Equation (8) TAIR(0 - IT(O1t0I

As mentioned in the previous section, the thermal time constant may be expressed as:

T(t) = R(t)C(t)

Therefore, the heat capacity (that is relative to moisture concentration) may be derived as:

C(t) = (t) Joules/°C Equation (9)

SIMPLIFIED CONCEPT MODEL

It is optimal to use a minimum of three subterranean sensors, since this allows us to establish a water concentration profile. However, in one embodiment to reduce complexity of implementation, it is also possible to use a reduced set of RC chain links to extract critical information concerning the thermal time constant given certain conditions.

Using the temperature information gathered at each of at least two positions, Ti and T2, it is possible to calculate values fitting the model describe in Equation 2 using the ?0 reduced electrical equivalence model shown in Figure 9 for thermal behavior.

Figure 9 shows a model very similar to the model presented in Figure 3 only without the additional RC link represented by R3 and C3 in the earlier model.

TAIR isthe measured temperature at the Data Collection Unit, T1 is the measured temperature at the upper or most shallow sensor and T2 is the measured temperature at the lower or deepest sensor. RAIR represents the thermal junction between the soil and air, the value of R1 represents the thermal resistance in the soil between the soil air junction and the upper sensor, C1 represents the thermal capacity at the point of the upper sensor, R2 represents the thermal resistance in the soil between the upper sensor and the lower sensor and C2 the thermal capacity of the earth at and below the Lower Sensor.

This model assumes that the soil is homogeneous and has consistent properties between the lower sensor and the air-soil interface. It is therefore not possible to derive an indication of the homogeneity of the soil; hence it is not possible to attain the water concentration gradient with respect to depth.

In all other aspects, the derivation of the parameters in Equations (2), (8) and (9) may be done in exactly the same way as for the device using three subterranean sensors only with a reduced number of array elements fed into the linear regression formula and by setting the parameter XOff(t) to zero.

CALIBRATION OF RESULTS OF THE THERMAL MODEL

When combined with soil characteristic data as analyzed in a laboratory, observations over time using statistical data collected during dry periods and extremely wet periods can provide baseline limit information for the thermal resistivity and capacity of the soil. These limits will become evident by finding the points at which the values no longer change and appear to hit a limiting point as illustrated in Figure 10.

?5 Once the limit points have been established, it is then possible to adjust the data accordingly.

EXAMINING THE STATIC/ULTRA-LOW FREQUENCY DATA

The raw temperature data measured at each point can provide useful information concerning the presence of nearby streams or aquifers since they introduce additional heat sources or sinks that may contribute a steady state heat flux to the system. The degree of influence of this heat flux on temperature can be observed by extracting the value of p, from the modulated data, see Equation 1 above, by applying a very low frequency low-pass filter to the original temperature data with a cut-off frequency of less than 1Hz. 172800

It is important, however, to consider that adequate calibration of sensors is required, as well as the application of compensation to measurements when performing any such analysis as any small error may lead to inaccurate results.

Described herein is a technique that provides data that may be used to enable improved efficiency in water usage, improved yield and enable better crop selection in agricultural environments.

The technique uses the principals of demodulation around a carrier with a frequency equal to one daily cycle (1/86400 Hz) to extract relative magnitude and phase information as a result of changes in temperature as measured at various depths that occur as a result of the natural daily temperature cycle.

The technique uses the magnitude and relative phase information extracted from measurements in soil temperature taken at two or more depths within the top of the Vadose Zone of the soil to derive a Soil Temperature Profile Model (See equations (2) and (5)).

The technique uses the Soil Temperature Profile Model derived using soil temperature data from two or more depths to calculate a momentary thermal time constant of the soil at any given time with a resolution of less than or equal to half a day.

The technique uses the Soil Temperature Profile Model derived using soil temperature ?5 data from two or more depths to calculate a virtual value for the temperature at the air soil interface.

One embodiment uses the Soil Temperature Profile Model with soil temperature data taken at three or more depths to estimate a time-constant/depth gradient using an iterative Linear Regression technique to adjust the model in order to reduce error, using an additional offset parameter. This then provides information about how the water concentration and soil aeration changes with depth.

Using the time constant, the virtual value derived for temperature at the air-soil interface and the principal of the potential divider, the invention can then derive separate values for thermal resistivity, indicating aeration and soil tension, and thermal capacity, indicating moisture content.

The technique can be used to find the presence of sub-aerial heat sinks and sources indicating the presence of nearby streams.

O The technique processes data taken from an array of devices placed at different geographical positions, which may then be collated and graphed to show the variations in soil aeration and water content over a geographical area.

The data generated may be used as part of a multi-dimensional correlation to provide information concerning sub-aerial water flow of the Vadose Zone, including quantity and direction.

Claims (7)

1. A soil temperature probe for determining water concentration in soil, the probe comprising:

an elongate body having a first end and a second end, the second end adapted for inserting into soil;

a data collection unit comprising a thermal sensor and a processor, the data collection unit positioned proximate the first end of the elongate body; and

provided along the elongate body, spaced from the data collection unit and toward the second end, and in spaced relationship to one another, a plurality of thermal sensors in data communication with the data collection unit, the plurality of thermal sensors adapted for subterranean operation,

wherein the plurality of thermal sensors comprises a first sensor and a second sensor spaced a first distance from the first sensor toward the second end of the elongate body,

wherein, in use, the second sensor is subterraneously positionable and the first sensor is subterraneously positionable to be a second distance from an air-soil interface, and

wherein the data collection unit is configured to:

determine the soil temperature profile along a submersed length of the elongate body, based on the first distance and the second distance; and

determine, using iterative linear regression, water concentration changes with soil depth by deriving, based on a measured difference in temperatures measured at the first sensor and at the second sensor, a heat capacity relative to moisture concentration.

2. The soil temperature probe of claim 1,

wherein the second distance is substantially equal to the first distance;

wherein the plurality of thermal sensors comprises a third sensor spaced a third distance from the second sensor toward the second end of the elongate body, wherein the third distance is substantially equal to both the first distance and the second distance, and

wherein the data collection unit is configured to determine the soil temperature profile along the submersed length of the elongate body, based on the first distance, the second distance, and the third distance.

3. The soil temperature probe of claim 1 and claim 2, wherein at least one of the data collection unit and one of the thermal sensors comprises a demodulator comprising at least one of:

a bandpass filter; and

a mixer,

wherein the demodulator is configured to operate with a carrier with a frequency substantially equal to one daily cycle (1/86400 Hz).

4. The soil temperature probe of any one of the preceding claims, wherein the data collection unit is further configured to determine, using iterative linear regression, soil aeration changes with soil depth.

5. The soil temperature probe of any one of the preceding claims, wherein the data collection unit is further configured to calculate a thermal time constant

6. The soil temperature probe of claim 5, wherein the data collection unit is configured to determine: a thermal resistivity of the thermal time constant, wherein the thermal resistivity is indicative of soil aeration and/or soil tension; and a thermal capacitance of the thermal time constant, wherein the thermal capacitance is indicative of soil moisture content.

7. A soil water analysis system comprising an array of soil temperature probes according to any one of claims 1 to 6, wherein the soil temperature probes are placed at different geographical positions so that the system collates and displays calculated variations in soil aeration and water content over a geographical area.

7. DIAGRAMS 2018200711

Figure 1. Hydro-geologic zones and types of water in the subsurface. (Modified from Meinzer, O.E., U.S. Geological Survey Water Supply Paper 494, Washington D.C., 1923b, 71p)

Figure 2. Illustration of one embodiment of the Soil Temperature Probe concept using 3 equal-distant subterranean sensors and one air sensor.