ESTIMATING EVAPORATION

BACKGROUND OF THE INVENTION

THIS invention relates to a method of and a system for estimating sensible heat flux and hence evaporation representative of an area substantially in real-time for example sub-hourly. The invention also relates to a datalogger device and a data-logging kit for estimating evaporation.

Evaporation is a key component of the water balance at the Earth's surface. While its determination is important for water resource management, evaporation is seldom measured directly and usually inferred from other measurements. For example, data from an automatic weather station allow grass reference evaporation and tall-crop reference evaporation to be estimated in near real-time. The disadvantage of this method is that a crop factor (K) is required to calculate offline the actual evaporation: actual evaporation = x grass reference evaporation. The crop factor varies with crop type, stage of crop growth and management practice(s). Other methods and/or systems to determine evaporation are computationally intensive and do not allow or provide for near real-time estimation of evaporation. Also, other methods and/or systems to determine evaporation are prohibitively expensive, are high maintenance, or require specialised skills to operate.

A need exists for an inexpensive, low-power and reasonably accurate system that allows sub-hourly estimates of evaporation and does not require calibration.

It is an object of the present invention at least to address the abovementioned problems and need.

SUMMARY OF THE INVENTION

According to a first aspect of the invention there is provided a method of estimating sensible heat flux representing an area at a particular location substantially sub-hourly, the method comprising: receiving air temperature information from temperature sensors at the particular location; using the received air temperature information to determine average air temperature, standard deviation of the air temperature, and skewness of the air temperature associated with the particular location substantially sub-hourly; and determining, substantially sub-hourly, sensible heat flux associated with the particular location by using at least the determined average air temperature, standard deviation of the air temperature, and skewness of the air temperature associated with the particular location. The method may include determining an atmospheric stability condition from an air temperature difference between two levels above a canopy surface. Instead, or in addition, the method may include determining said atmospheric stability condition from a third-order air temperature structure function for a defined time lag.

The method may preferably comprise estimating sensible heat flux substantially in real-time.

According to a second aspect of the invention there is provided a method of estimating evaporation representing an area at a particular location, the method comprising: receiving air temperature information from temperature sensors at the particular location; using the received air temperature information to determine at least average air temperature, standard deviation of the air temperature, and skewness of the air temperature at the particular location substantially sub-hourly; receiving soil heat flux information, the soil heat flux information being indicative of soil heat flux at the particular location; receiving net irradiance information, the net irradiance information being indicative of net irradiance at the particular location; determining, substantially sub-hourly, sensible heat flux at the particular location by using at least the determined average air temperature, standard deviation of the air temperature, and skewness of the air temperature associated with the particular location, and determining, substantially sub-hourly, an estimate of the evaporation at the particular location by using the determined sensible heat flux, received soil heat flux information, and received net irradiance information.

The method may comprise estimating evaporation substantially in real-time, near real-time, or sub-hourly.

The method may comprise receiving the air temperature information indicative of the skewness of air temperature from a mobile or portable datalogger device, the datalogger device comprising a statistical moment function to determine the skewness of the air temperature substantially in real-time. Instead, or in addition, the method may comprise determining the skewness of the air temperature substantially in real-time from statistical moment information associated with the air temperature data received from the datalogger.

The method may comprise: determining a structure function of air temperature, C _j substantially in real-time and using the determined structure function of air temperature C _T ² to determine a structure parameter of refractive index, ,

substantially in real-time.

In particular, the method may comprise: receiving air temperature difference information between air temperatures measured by first and second air temperature sensors respectively; and using the received air temperature difference information and a sensor distance between the first and second temperature sensors to determine the structure function of air temperature C _j . The method may comprise receiving the sensor distance from a user. Instead, or in addition, the sensor distance is a pre-specified distance.

The method may comprise receiving the air temperature difference information from an air temperature difference sensor. The temperature difference sensor may comprise the first and second temperature sensors spaced at a known sensor distance. The sensor distance may be a specified or user-defined sensor distance.

The method may comprise determining the sensible heat flux by a temperature-variance method, including adjustment for air temperature skewness, in the inertial sub-layer. The temperature variance method may rely on Monin-Obukhov Similarity Theory (MOST).

The method may comprise using the determined structure parameter of refractive index to determine the sensible heat flux offline by way of an iterative procedure using MOST.

The method may comprise determining the sensible heat flux, for the roughness sub-layer, by way of an air temperature structure function for a user-specified time lag. In particular, the method may comprise determining sensible heat flux from an air temperature structure function of order three.

Determining the estimate of evaporation may comprise subtracting the determined sensible heat flux and received soil heat flux from the net irradiance.

The method may comprise determining air temperature structure functions of order two, three and five respectively from which the method may comprise using the determined air temperature structure functions to determine sensible heat flux offline by way of a surface renewal method typically by using the determined air temperature structure functions of order two, three and five. The method may further comprise: receiving relative humidity information associated with the particular location; receiving wind speed information associated with the particular location; determining grass reference evaporation; and determining tall-crop reference evaporation.

According to a third aspect of the present invention, there is provided a system for estimating evaporation representative of an area at a particular location, the system comprising: an air temperature receiver module arranged to receive air temperature information from temperature sensors at the particular location; a processor operable to use the received air temperature information to determine at least average air temperature, standard deviation of the air temperature, and skewness of the air temperature at the particular location substantially sub-hourly; a soil heat flux receiver module arranged to receive soil heat flux information, the soil heat flux information being indicative of soil heat flux of the particular location; a net irradiance receiver module arranged to receive net irradiance information, the net irradiance information being indicative of net irradiance associated with the particular location; a sensible heat flux determining module arranged to determine, substantially in real-time, sensible heat flux associated with the particular location by using at least the determined at least average air temperature, standard deviation of the air temperature, and skewness of the air temperature at the particular location substantially sub-hourly, and an evaporation determining module arranged to determine, substantially in real-time, an estimate of the evaporation level of the particular location by using at least the determined sensible heat flux, received soil heat flux information, and received net irradiance information.

At least the air temperature receiver module may be communicatively coupled with a mobile or portable datalogger device, the datalogger device comprising a statistical moment function to determine the skewness of the air temperature substantially in real-time.

The sensible heat flux determining module may be arranged to determine the sensible heat flux by a temperature variance method, including adjustment for air temperature skewness, in the inertial sub-layer. The temperature variance method may rely on Monin-Obukhov Similarity Theory (MOST).

The evaporation determining module may be arranged to determine the estimate of evaporation by subtracting the determined sensible heat flux and received soil heat flux from the net irradiance.

The system may be arranged to: determine a structure function of air temperature, substantially in real-time and use the determined structure function of air temperature to determine a structure parameter of refractive index, C _n ² , substantially in real-time. The system may further be arranged to: receive air temperature difference information between air temperatures measured by first and second air temperature sensors respectively; determine or receiving a sensor distance between the first and second temperature sensors; and use the received air temperature difference information and the determined or received sensor distance to determine the structure function of air temperature C .

According to a fourth aspect of the invention there is provided a machine- readable medium embodying instructions which, when executed by a machine, cause the machine to: receive air temperature information from temperature sensors at a particular location; use the received air temperature information to determine average air temperature, standard deviation of the air temperature, and skewness of the air temperature associated with the particular location substantially sub-hourly; receive soil heat flux information, the soil heat flux information being indicative of soil heat flux associated with the particular location; receive net irradiance information, the net irradiance information being indicative of net irradiance associated with the particular location; determine, substantially sub-hourly, sensible heat flux associated with the particular location by using at least the determined average air temperature, standard deviation of the air temperature, and skewness of the air temperature associated with the particular location substantially sub-hourly, and determine, substantially sub-hourly, an estimate of the evaporation level of the particular location by using at least the determined sensible heat flux, received soil heat flux information, and received net irradiance information.

The machine-readable medium may cause the machine to: determine a structure function of air temperature, substantially in real-time; and use the determined structure function of air temperature 0 to determine a structure parameter of refractive index, C _n ² , substantially in real-time.

The machine-readable medium may further cause the machine to: receive air temperature difference information between air temperatures measured by first and second air temperature sensors respectively; determine or receive a sensor distance between the first and second temperature sensors; and use the received air temperature difference information and the determined or received sensor distance to determine the structure function of air temperature C .

In an example embodiment, the machine may be a datalogger device. The machine-readable medium may therefore comprise embedded code executable by the datalogger device. According to a fifth aspect of the invention there is provided a datalogger device, the datalogger device comprising: means for receiving air temperature information from temperature sensors at a particular location; means for using the received air temperature information to determine average air temperature, standard deviation of the air temperature, and skewness of the air temperature associated with the particular location substantially sub-hourly; means for receiving soil heat flux information, the soil heat flux information being indicative of soil heat flux associated with the particular location; means for receiving net irradiance information, the net irradiance information being indicative of net irradiance associated with the particular location; means for determining, substantially sub-hourly, sensible heat flux associated with the particular location by using at least the determined average air temperature, standard deviation of the air temperature, and skewness of the air temperature associated with the particular location, and means for determining, substantially sub-hourly, an estimate of the evaporation level of the particular location by using at least the determined sensible heat flux, received soil heat flux information, and received net irradiance information.

The device may comprise: means for determining a structure function of air temperature, C _j substantially in real-time and means for using the determined structure function of air temperature C _j to determine a structure parameter of refractive index, C _n ² , substantially in real-time.

The device may further comprise: means for receiving air temperature difference information between air temperatures measured by first and second air temperature sensors respectively; means for determining or receiving a sensor distance between the first and second temperature sensors; and means for using the received air temperature difference information and the determined or received sensor distance to determine the structure function of air temperature .

The datalogger device may preferably be a datalogger with a statistical moment instruction so as at least to determine the skewness of the air temperature. The datalogger device may be arranged to determine skewness from the moment of order three, average air temperature and the standard deviation of air temperature.

According to a sixth aspect of the invention there is provided a data-logging kit, comprising: a datalogger device as hereinbefore described; and an air temperature difference sensor comprising: a first air temperature sensor; and a second air temperature sensor spaced at a predetermined horizontal sensor distance from the first air temperature sensor. BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 shows a schematic drawing of a system in accordance with an example embodiment illustrating at least an evaporation system as herein described;

Figure 2 shows a schematic drawing of the evaporation system of

Figure 1 in greater detail;

Figure 3 shows a high level flow diagram of a method in accordance with an example embodiment;

Figure 4 shows a high level flow diagram of another method in accordance with an example embodiment; and

Figure 5 shows a schematic drawing of an air temperature difference sensor in accordance with an example embodiment.

DESCRIPTION OF PREFERRED EMBODIMENTS

In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of an embodiment of the present disclosure. It will be evident, however, to one skilled in the art that the present disclosure may be practiced without these specific details.

Referring to Figures 1 , 2, and 5 of the drawings, a system for determining an estimate of evaporation at a particular location or canopy area is generally indicated by reference numeral 10. The system 10 may conveniently comprise a near real-time evaporation estimation station for the inertial layer for which Monin-Obukhov Similarity Theory (MOST) applies. The system 10 is communicatively coupled to a fine-wire thermocouple/s 12 (in parallel or in triplets), for example unshielded and naturally-ventilated fine-wire (75 pm) thermocouples for high frequency air temperature measurements, a soil heat flux plate/s 14, a net radiometer 16, and soil and temperature sensors 18 to receive soil heat flux information respectively therefrom. In other example embodiments (not shown), the fine-wire thermocouple/s 12, the soil heat flux plate/s 14, the net radiometer 16, and soil and temperature sensors 18 may form part of the system 10.

The system 10 may comprise a plurality of components or modules which correspond to the functional tasks to be performed by the system 10. In this regard, "module" in the context of the specification will be understood to include an identifiable portion of code, computational or executable instructions, data, or computational object to achieve a particular function, operation, processing, or procedure. It follows that a module need not be implemented in software; a module may be implemented in software, hardware, or a combination of software and hardware. Further, the modules need not necessarily be consolidated into one device but may be spread across a plurality of devices.

In particular, the system 10 comprises an air temperature receiver module 20 arranged to receive air temperature information associated with the particular area or location. The system 10 may comprise a processor 21 arranged to use the received air temperature information to determine the average air temperature, T , standard deviation of the air temperature, σ _τ , and/or skewness of the air temperature or air temperature skewness, S _r , associated with the area. In other example embodiments, the air temperature receiver module 20 is arranged to receive the average air temperature, T , standard deviation of the air temperature, σ _τ , and/or skewness of the air temperature or air temperature skewness, S _T .

The processor 21 may advantageously be arranged to control the operation of the system 10. It is to be understood that the processor 21 may be one or more microprocessors, controllers, or any other suitable computing device, resource, hardware, software, or embedded logic.

The system 10, particularly the module 20, may be communicatively coupled to a datalogger or datalogger device (not shown) to receive the air temperature information therefrom. The datalogger device may be coupled to, or may optionally comprise, the thermocouples 12 to obtain air temperature information therefrom. Similarly, the datalogger device may also be coupled to, or comprise, the soil heat flux plates 14, the net radiometer 16, the sensors 18, and/or any other sensor/s (not illustrated) used by the system 10 to receive data therefrom respectively for use by the system 10 as will be described below.

The datalogger device advantageously comprises a statistical moment instruction to facilitate the system 10, or the datalogger device, to determine the skewness of the air temperature substantially in real-time.

The statistical moment instruction has already been installed by Campbell Scientific, Inc. into many of their commercially available dataloggers, e.g. those marketed with the model designations CR1000, CR3000 and CR5000. However, dataloggers near the lower end of the range (e.g. the model designation CR1000) may be too slow efficiently to run the code which is necessary to implement the method and system as herein described.

The skewness of air temperature may be determined sub-hourly. Determined online, air temperature skewness involves the sum over a time interval of the cube of the air temperature deviation from the mean. In particular, the skewness of air temperature S _T may be determined by way of the following equation:

S _r = -^-∑(7. - T) ³ / n where σ _τ is the standard deviation in air temperature over an averaging period, T, is the / ^' th air temperature sample within the averaging period , T is the average air temperature and n is the number of air temperature measurements during the averaging period - n would be equal to 18000 for 0-Hz air temperature measurements and an averaging period of 30 min.

corresponds to the moment value provided by the datalogger for each averaging period. The averaging period is typically sub-hourly (30 minutes).

In an example embodiment, the system 10, or parts thereof, may advantageously be provided in the datalogger device such that the datalogger device is arranged to provide the functionality of the system 10 as herein described. Instead, or in addition, the system 10, or parts thereof, may be provided in or on a computing device such as a remotely located computer, or the like. In the latter example embodiment, the datalogger device may advantageously comprise a suitable modem, for example a wireless modem, to allow the datalogger device to communicate information remotely to the system 10.

The system 10 further comprises a soil heat flux receiver module 22 arranged to receive soil heat flux information S, from the soil heat flux plates 14 or the datalogger device. The soil heat flux information is indicative of soil heat flux, S, associated with the location particularly the soil temperature, soil water content and soil heat flux at a predetermined depth. In this regard, where applicable within the specification, "information" is meant to indicate the quantity or value measured by the respective sensors.

The system 10 also comprises a net irradiance receiver module 24 arranged to receive net irradiance information from the net radiometer 16 or datalogger device, the net irradiance information being indicative of net irradiance, R _net , associated with the area.

The system 0 comprises a sensible heat flux determining module 26. The module 26 is conveniently arranged to determine, online or substantially in near real-time, sensible heat flux, H, associated with the area by using at least the received air temperature information. The module 26 may be arranged to determine sensible heat flux H by way of various methods to be discussed below.

In particular, the sensible heat flux determining module 26 is preferably arranged to determine the sensible heat flux, H, by a temperature variance or flux variance method in the inertial sub-layer i.e. which is corrected for skewness using the received or determined skewness of air. The temperature variance method typically relies on onin-Obukhov Similarity Theory (MOST).

In particular, the module 26 determines the sensible heat flux H _n online according to the following equation:

H = -0.993 ,oc _p (o¾ k g z/ ff ⁵ xf(S _T ) (found to be valid for the range 0.03 « -z l L < 60 ) where p is the density of air (kg m ^"3 ), c _p the specific heat capacity of air at constant pressure (J kg ^"1 K ^"1 ), g is the acceleration of gravity (m s ^"2 ) and z is the measurement height (m) with k = 0.41 , where σ _τ (°C) is the standard deviation of air temperature determined online within a given time period, and T is the average air temperature (°C).

It will be noted that: A stability condition is determined online from the air temperature difference between two levels above the canopy surface and/or from third-order air temperature structure function S ³ (r) where r is the air temperature time lag.

Of note then is that the temperature variance online method with adjustment for skewness relies on the average air temperature T , the standard deviation of the air temperature σ _τ and the air temperature skewness S _r . This triplet of air temperature information, obtained for each 2-min and 30-min period, allows H = H _TV to be calculated with the atmospheric stability state determined from S ³ (r) and the state confirmed using the sign of the air temperature difference between two atmospheric levels.

The system 10 also advantageously comprises an evaporation determining module 28. The evaporation determining module 28 is configured to determine, substantially in real-time for example half-hourly, an estimate of the evaporation level of the area, LE, by using at least the determined sensible heat flux H, received soil heat flux information S, and received net irradiance information R _net . It will be appreciated that the module 28 may be arranged to determine the estimate of evaporation LE by subtracting the determined sensible heat flux, for example (corrected for air temperature skewness) and the received soil heat flux information S from the received net irradiance information R _nel according to the equation below:

LE = LE _n = R _net - S - H _TV

The system 10 also comprises a database or memory means 30 operable to store information received by the system 10 as well as information determined or calculated by the system 10. Information stored in the database 30 may be advantageously accessible by a user. The database or memory means 30 may include a machine-readable medium, e.g. memory, main memory, and/or hard disk drive, which carries a set of instructions to direct the operation of the system 10 in accordance with an example embodiment.

The sensible heat flux determining module 26 may also be arranged to determine sensible heat flux by way of structure functions such that H = H _SF . In this regard, for the roughness sub-layer, the module 26 is arranged to determine sensible heat flux from structure functions [SV)/r] _max where

1 ^m

SV) =—∑(τ;. - _ _; . ) ³

I ll - J where m is the number of data points in a sub-hourly interval measured at frequency f, j is a sample lag between data points corresponding to a time lag (r = j/f ), T, is the air temperature at time / ^" and T that at an earlier time / ^' - j . While the temperatures and S ³ (r)/ r values are available to the system 10 in near real-time, the maximum value of S ³ (r)/r is determined by the module 26 offline unless it is known a priori. In any event, the sensible heat flux determining module 26 is arranged to determine H _SF for the inertial sub-layer from the following equations:

H ₌ H _SF = ^¾^ c _p (z - d (σ _τ I (S ³ (r)/r)" ³

K

or

H = H _SF = 0.575 c _p (z - df (σ _τ /f) (S ³ (r)/ r)" ³ where p is the density of air, c _p the specific heat capacity of air, z the measurement height and d approximately 2/3 of the vegetation canopy height. For the roughness sub-layer, z is replaced by z - d . As alluded to above, if the maximum of S ³ (r)/r and time delay are known a priori, the module 26 may be arranged to determine H _SF substantially in real-time.

It follows that the evaporation determining module 28 is accordingly arranged to determine the evaporation estimate LE _SF , in near real-time if the maximum of S ³ (r)/r is known, using the determined sensible heat flux HSF as described above.

The sensible heat flux determining module 26 is also arranged to determine sensible heat flux by way of a surface renewal method. In this regard, it will be noted that the temperature variance measurement protocol may be extended to include the storage of the second-, third- and fifth-order air temperature structure functions (S ² (r), S ³ (r) and S ⁵ (r) respectively).

In particular, the three functions S ² (r), S ³ (r) and S ⁵ (r) are obtained online for each averaging period for two values of r - usually for r = 0.4 s and r = 0.8 s unless the user specifies otherwise. The module 26 then uses these data to determine sensible heat flux H _S R offline using the surface renewal method according to the following equation: H u = a zp c _n — ^dT ,

p dt where a is a correction factor (regression coefficient fit to the above equation when H is measured independently using other methods such as eddy covariance) and ar _ a

dt ^~ τ where a is the amplitude of the air temperature ramps (°C) and r the ramping period (s). An estimate of the mean value for amplitude a during an averaging time interval is determined by solving the following equation for real roots:

a ³ + pa + q = 0

where p = 10S ² (r) _S 3 and

q = 10S ³ (r) .

The ramping period τ is calculated using

aV

S ³ (r) ^'

It will be appreciated that the time lag r must be much less than τ , typically τ > 5 r , or otherwise the structure function theory is invalid. The roots of a ³ + pa + g = 0 are obtained offline by iteration in a spreadsheet from which r is calculated using the equation τ -— -— above, and

S (r)

dT a

dT l dt is calculated using — =— and hence H _SR calculated using dt τ

3T ^~

H = ct zpc _p -^ as hereinbefore described from knowledge of the measurement height z and prior knowledge of a . Of particular note is that the surface renewal method does not depend on MOST and may therefore be applied in the roughness and inertial sub-layers.

In one example embodiment, the third-order structure function may be used for determining whether atmospheric conditions are stable or unstable.

It follows that the module 28 is also arranged to determine LE _S R using the determined H _SR which advantageously does not require MOST.

The module 26 is further arranged to determine the sensible heat flux by way of an air temperature structure function, . In a preferred example embodiment, the system 10, and module 26 in particular, is advantageously arranged to determine the structure function of air temperature, ; and to use the determined structure function of air temperature to determine a structure parameter of refractive index, C _n ² , substantially in real-time.

The module 26 is arranged to determine by way of the following equation:

where the overbar indicates a time average (typically sub-hourly), T and T _n are 0-Hz air temperatures measured a horizontal distance x apart at height z, .

In a preferred example embodiment, the system 10 is in communication with an air temperature difference sensor 80 (Figure 5). The sensor 80 comprises a first temperature sensor 82 operable to measure the first temperature T and a second temperature sensor 84 operable to measure a second temperature T ₂ , the first and second temperature sensors 82 and 84 are spaced from each other at the predetermined sensor horizontal distance x. It will be noted that:

G - refers to the datalogger ground;

H - refers to the datalogger high analogue channel; and

L - refers to the datalogger low analogue channel.

Tu therefore corresponds to the voltage between L and G; T ₁₂ that between H and G, and Tu - T ₂ that between H and L.

The sensor 80 may be similar to the thermocouple 12 and allows air temperature differences Tu - T ₂ to be measured as well (H and L) as the individual air temperatures. The air temperature difference 7 ^" _n - Γ ₁₂ and the air temperature Tu may be measured at high frequencies (10 Hz), and sub-hourly averages obtained. It will be understood the sensors 82 and 84 are aligned in the horizontal plane. It follows that the module 26 is conveniently arranged to receive the first air temperature u from the first air temperature sensor 82; and to receive the second air temperature T ₁₂ from the second air temperature sensor 84. The module 26 may be arranged to determine the sensor distance x and the air temperature difference u - T ₂ between the sensors 82 and 84. Instead, or in addition, the system 10 may be arranged to receive the sensor distance x depending on the sensor 80. The sensor distance x may optionally be made known a priori to the system 10. The module 26 is arranged to use the first and second air temperatures u and T ₂ (particularly the temperature difference Tu - T ₂ ) and the sensor distance x to determine the structure function of air temperature, C using the equation as previously presented. The optimum distance x may preferably be less than 0.5 m. Since the air temperature may vary in the vertical due to the temperature difference between the canopy surface and the overlying air, measurements of T _n and T _l2 should be in the horizontal plane separated by a known distance.

In an example embodiment, the module 26 is preferably arranged to receive the temperature difference Tu - T ₁₂ between the first and second temperature sensors 82 and 84 respectively from the sensor 80.

In this embodiment, high frequency measurements allow the air temperature structure parameter to be calculated if a pair of thermocouples are used at a single measurement height and configured to measure the air temperature difference between two fine-wire thermocouples a known distance apart. Using , the structure parameter for refractive index C _n ² may be determined. Together with wind speed measurements, the application of MOST and an iterative procedure applied offline, sensible heat flux H - H _M0ST may be calculated. This then allows another estimate of evaporation. The method forms the basis for scintillometry except that in scintillometry is obtained through the scattering of a horizontal laser or near-infrared beam above canopies. The inventor believes that inexpensive measurements of C from high frequency air temperature measurements, as provided by the embodiment under discussion, can be used to validate scintillometer measurements in situ.

Referring again to Figure 5, the module 26 is then further arranged to determine C _n ² using the following equation: assuming a perfect correlation between water vapour pressure and air temperature fluctuations, where l is the air temperature (K), a = 0.789 ^χ 10 ^"3

K kPa ^" , P is the atmospheric pressure (kPa) and β the Bowen ratio.

If a wind speed sensor is provided, the friction velocity may be estimated offline using an iterative procedure. H = H _M0ST may be determined offline by module 26 using MOST.

In summary, the module 26 is arranged to determine the structure parameter of temperature (K ² m ^"2/3 ) online from the air temperature difference between a known horizontal distance as hereinbefore described.

The sensible heat flux is:

H = p Cp U. T. (1 ) where p is the density of air (kg m ^"3 ), c _p the specific heat capacity of air at constant pressure (J kg ^"1 K ^" ), u. the friction velocity (m s ^"1 ) and T. (K) the temperature scaling parameter. Invoking MOST, T. is given by -1/2

T. = ^: C _T - (Z - d) - [f( )] (2) where z (m) is the measurement height (m), d the zero-plane displacement (m) (approximately 0.67 times the canopy height) and ζ = ^Z ^ the argument of the MOST semi-empirical and dimensionless function ί(ζ) = 4.9 {\ - Ί ζ)- ²¹³ where L is the Obukhov length (m) is defined by where k is the von Karman constant (0.41 ), g the acceleration of gravity (m s ^"2 ) and u. the friction velocity estimated from horizontal wind speed U using: u. = 0.14 1/

It will be appreciated that it is not possible to solve the above equations (1 ) to (5) analytically for H. Hence the module 26 uses an offline iterative procedure. Combining equations ( 1 ) to (5) allows L and H to be estimated using equation (1 ) by iteratively varying L. The module 26 may be arranged to perform these calculations by way of a spreadsheet.

Since the structure parameter of refractive index C _n ² (K ² m ^{" 3} ) is measured using scintillometers and possibly other measurement systems, it is calculated for possible reference purposes using:

assuming a perfect correlation between air temperature and water vapour pressure fluctuations where T is the air temperature (K), a = 0.789 χ 10 ^'3 K kPa ^"1 , P the atmospheric pressure (kPa) and β the Bowen ratio calculated using:

-R _N - S - H where R _NET is measured or received using a net radiometer as hereinbefore described, S is calculated or received using soil temperature as hereinbefore described, and soil heat flux and soil water content measurements and H is obtained using the temperature variance method as hereinbefore described, including the adjustment for skewness also as hereinbefore described.

It follows that the module 28 is then arranged to determine LE _M OST using the determined H _M OST offline.

The system 10 may further be arranged to receive relative humidity information associated with the area; and wind speed information associated with the area. In this example embodiment, the system 10 is communicatively coupled to a solarimeter, relative humidity sensor, wind speed and direction sensors, and a rain gauge (not shown). The system 10 may then be arranged to determine a grass reference; and also to determine an estimate for tall-crop reference evaporation (ET ₀ ) , for example by using the Penman-Monteith method. It will be noted that the system 10 may therefore be arranged to determine crop factors online using the following equation:

K = LE _RV / ET ₀

It will be noted that the system 10 may allow a user to select the method of determining the evaporation estimate as desired. Instead, or in addition, the system 10 may be arranged to provide all determined information to the user for example via a graphical user interface (GUI), or the like. Example embodiments will now be further described in use with reference to Figures 3 and 4. The example methods shown in Figures 3 and 4 are described with reference to Figures 1 , 2 and 5, although it is to be appreciated that the example methods may be applicable to other systems (not illustrated) as well.

Referring now to Figure 3, where a flow diagram of a method in accordance with an example embodiment is generally indicated by reference numeral 40.

The method 40 comprises receiving, at block 42, air temperature information associated with the area for example by way of the air temperature receiver module 20 as hereinbefore described.

The method 40 then comprises receiving, at block 44, soil heat flux information for example by way of the soil heat flux receiver module 22 as described above.

The method 40 also comprises receiving, at block 46, net irradiance information from the net irradiance receiver module 24.

The method 40 then comprises determining, at block 48, substantially sub- hourly, sensible heat flux via the sensible heat flux determining module 26 by using at least the received air temperature information as hereinbefore described. The user may be permitted to select one or more ways in which sensible heat flux is calculated. However, in a preferred example embodiment, the method comprises determining the sensible heat flux by way of the temperature variance method as hereinbefore described.

The sign of the sensible heat flux may be determined by the sign of the third-order air temperature structure function (discussed below).

The method 40 further comprises determining, at block 50, substantially in real-time, an estimate of the evaporation level LE of the area by using at least the determined sensible heat flux, received soil heat flux information, 0 053946

- 27 -

and received irradiance information for example by way of the evaporation determining module 28 also as hereinbefore described.

This determined evaporation LE may be presented to the user via a GUI, or the like together with any other information determined by the system 10.

The system 10 may also be arranged to store the determined LE or other information in the database 30.

Referring now to Figure 4 of the drawings where another method in accordance with an example embodiment is generally indicated by reference numeral 60. It will be noted that the method 60 may follow from or may optionally form part of the method 40.

In any event, the method 60 comprises receiving, at block 62, a first temperature T from the first temperature sensor 82 of the sensor 80.

The method 60 further comprises receiving, at block 64, a second temperature 7 ^" ₂ from the second temperature sensor 84 of the sensor 80.

The method 60 may comprise determining an air temperature difference 7 ^" n - Γ-Ι 2 between the first and second temperatures Tn and 7i ₂ . The method 60 may comprise receiving the temperature difference T - T ₁₂ from the sensor 80.

The method 60 typically comprises determining or receiving, at block 66, the sensor distance x between the first and second temperature sensors 82 and 84. This sensor distance x may be specified by the user. In this regard the sensor distance x is typically pre-specified or user-specified data.

The method 60 then typically comprises using, at block 68, at least the received first and second temperatures, 7 _{Ί 1} and 7 ^" i ₂ , or preferably the determined temperature difference Tn - 7 ₁₂ , and the sensor distance x to determine the structure function of air temperature, as hereinbefore described. Typica!ly the method 60 comprises determining air temperature structure functions of orders of two, three and five. As hereinbefore described the sign of the sensible heat flux is determined from the third-order air temperature structure function.

These determined air temperature structure functions may conveniently be used to determine sensible heat flux offline using the surface renewal method hereinbefore mentioned.

In any event, the method 60 further comprises using, at block 70, the determined structure function of air temperature C _j to determine a structure parameter of refractive index C _n ² , substantially in real-time as hereinbefore described.

It will be noted that the determined structure parameter of refractive index C _n ² may be used to determine H _MQS r offline using an iterative procedure as hereinbefore described.

The structure function method may be used to determine sensible heat flux sub-hourly for the roughness sub-layer.

It will be noted that if the system is arranged to receive wind speed information, the system 10 is optionally arranged to determine friction velocity u. , based on MOST, involving the air temperature mean, standard deviation and skewness and semi-empirical constants, for the forced and free convection stability range.

In an example embodiment, two estimates of (and hence LE _W if R _net and S are also measured) may be obtained: T _2l and 7 ^" ,, at height z, and T _u and T _n at height z, . Two estimates of C may be obtained: one using ^c i = (T _2I - T ₂₂ f l x; for height z ₂ and = (7 _M - T f / x, ^2/3 for height z, , for the offline calculation of H = H _M0ST using MOST using additional the measurement of wind speed measurements. Four estimates of air temperature structure function (of order two, three and five), two for each of the two heights z, and z, , for four different offline calculations of sensible heat flux by surface renewal.

The methods 40 and 60 may preferably be computer implemented methods.

It will be appreciated that the methods 40 and 60 may be implemented on a suitable computing device, for example on the computer or the datalogger device by way of associated software. For example, the methods 40 and 60 (or portions thereof) may be implemented by the datalogger device by way of a set of embedded computer executable instructions arranged to instruct the datalogger device to perform at least some of the steps of the method 40 and 60. The instructions may comprise embedded code or software provided on machine readable medium/s associated with the datalogger device, for example, a memory means of the datalogger device.

Example of Detailed Implementation

In the following, the main elements of one detailed implementation of a system according the invention are described:

1 . a datalogger with a PC card storage device, cell-phone capability, enclosure, battery, and instrument mast. Typically, a CR3000 datalogger, available from Campbell Scientific Inc. (Logan, Utah, USA), is sufficient and has been used in all testing by the Inventor.

2. a datalogger program containing instructions for simple measurements and output instructions for , corrected for skewness; 3. sensors: net radiometer, soil heat flux plate(s), soil and temperature sensors, and for the high frequency air temperature measurements, the fine-wire thermocouples (in parallel or triplets); and

4. final online calculation of LE from R _net - S - Η _η as part of the datalogger program.

The evaporation estimation system and method herein described allow substantially real-time estimation (at roughly sub-hourly intervals) of evaporation for the inertial layer, using MOST, without the need for calibration, and the mean, standard deviation and skewness of air temperature.

The temperature-variance method is not the only one that can be used to estimate evaporation in near real-time, and the following additional methods may be used:

Additional methods of estimating evaporation

Sensible heat flux from the air temperature structure function of order three

High frequency air temperature measurements and storage of the mean, standard deviation and skewness of air temperature by the system allow sensible heat flux to be determined. However, since it is not possible to determine the direction of the sensible heat flux using MOST, it is determined using the third-order air temperature structure function as is commonly used in surface renewal analysis. The sensible heat flux determined together with soil heat flux and net irradiance measurements, and knowledge of the canopy and temperature sensor heights, allow evaporation to be estimated in near real-time for the so-called inertial layer using MOST, without the need for calibration against other methods. The system therefore approaches a real-time evaporation estimation station for the inertial layer for which MOST applies.

For the roughness sub-layer, it has been shown that the sensible heat flux could be estimated from structure functions [S ³ (r)/r] _max where

1 m

ill - J /=y ₊ i where m is the number of data points in the 30-min interval measured at frequency f, j is a sample lag between data points corresponding to a time lag (r = jlf ), T, is the air temperature at time / ^' and T _H that at an earlier time / ^' - _/ ^' . While the temperatures and S (r)/r values are available in near real-time, the maximum value of S ³ (r)/ r may not always be known at the time of data collection and would therefore be determined offline unless it is known a priori. It has been shown that, without proof, that H = H _SF is given by:

H = H _SF - ^^p c _p (z - dr (o> I TT (S _r ³ lr )" ³

π ^' or

H = H _SF = 0.575/9 c _p (z -d) ^m (σ _τ I T) (S ³ 1 r)

where p is the density of air, c _p the specific heat capacity of air, z the measurement height and d approximately 2/3 of the canopy height.

Surface renewal If the second-, third- and fifth-order air temperature structure functions are stored sub-hourly, it has been shown that offline estimates of sensible heat flux using surface renewal ( H _SR ) are possible without the use of MOST. Thus, the temperature-variance measurement protocol may be extended to include the storage of the second-, third- and fifth-order air temperature structure functions. These functions allow the offline calculation of sensible heat flux using the so-called surface renewal method. The surface renewal method requires a demanding iterative procedure for the calculation of /-/ = H _SR .

Air temperature structure function

Another important attribute of the atmosphere is the air temperature structure function C _j from which C _n ² , the structure parameter of refractive index, can be calculated. The parameter C ² may be estimated using

From air temperature difference measurements where the overbar indicates a time average (typically 20, 30 or 60 min), T and T _l2 are air temperatures measured a horizontal distance x apart and C _n ² is determined using: r n _{a p} i \ \ β assuming no correlation between water vapour pressure and air temperature fluctuations, where T is the air temperature (K), a = 0.789 ^χ 10 ^'3 K kPa ^"1 at 670 nm, P is the atmospheric pressure (kPa) and β the Bowen ratio. The optimum distance x has not been stated in the literature but typically it probably less than 0.5 m. Since the air temperature may vary in the vertical due to the temperature difference between the canopy surface and the overlying air, measurements of 7 _U and 7,, should be in the horizontal plane separated by a known distance. If a wind speed sensor is part of the measurement system, the friction velocity may be estimated. Offline, using an iterative procedure, H = H _M0ST may be estimated using MOST.

This method of determining in approximate real-time provides another use of the measurements from the fine-wire thermocouples. It also provides for an inexpensive method of determining C _T ² in near real-time.

Reference evaporation

If relative humidity and wind speed are also measured, grass reference and tall-crop reference evaporation (ET ₀ ) may. also be calculated online and sub-hourly using the Penman-Monteith method. Hence crop factors may be determined online from K = LE^ / E7 ₀ .

The above methods of estimating evaporation in near real-time are summarised in Table 1 and in the flowchart below.

The invention as hereinbefore described provides a relatively inexpensive way of obtaining evaporation estimates over a large area and is therefore potentially useful for validating remote sensing and other estimates of evaporation. For example, the invention may provide a method of "ground- truthing" evaporation data obtained by satellites.

The system is also conveniently an evaporation estimation and an atmospheric stability station. The surface renewal analysis method for determining the direction of sensible heat flux avoids the need for additional measurements such as wind speed and air temperature profile measurements to be taken to determine the direction of the flux. Sensible heat flux, together with a stability correction using skewness, and the direction of the flux, can be determined from high frequency measurements using a single fine-wire thermocouple in near real-time. If net irradiance and soil heat flux sensors are available, evaporation may then be calculated. These results are outputs of the invention.

The invention reduces the tediousness and computational complexity required to determine evaporation estimates. The system conveniently allows for evaporation estimates to be determined directly and substantially in real-time.

Table 1 : Summary of procedures for near real-time estimation of evaporation.

(Offline evaporation estimation procedures are included).

Sensors Measurements Estimation/calculation Method Comment Additional measurements for estimating LE

Fine-wire T _n at high frequency H = H _JV , corrected for Temperature variance MOST is assumed. The sign of

thermocouple at skewness, online corrected for skewness H is determined from the sign of

height z. for the inertial subthe ramp amplitude, using online

layer surface renewal analysis, for

each sub-hourly interval

Fine-wire temperature T„, T _l2 , C _j (related to C , online Direct calculation for Additional measurement of

difference pair at 7 , - 7;, ) at high the inertial sub-layer horizontal wind speed allows

height z, frequency H = H _M0ST to be calculated

offline using an iterative

procedure

Fine-wire 7 _n at high frequency H - H _SF , online if the Structure function Requires the third-order ^R net > S

thermocouple at value of rfor which S _r ³ / r method for the temperature structure function

height z, is a maximum is known a roughness sub-layer from online measurements and

priori the maximum of a ratio needs to

be determined offline. MOST is

not assumed and method may

be used in the roughness sublayer

Fine-wire T _u at high frequency H - H _SR , offline Surface renewal Requires knowledge of

thermocouple at weighting factor by comparing

height z. H _SR estimates with H _EC ; MOST

not assumed

Solarimeter, relative Solarimeter irradiance, ET ₀ (grass and tall-crop), Penman- onteith for The net irradiance and soil heat

humidity, air water vapour pressure, online. Hence the crop estimating grass flux measurements would be

temperature, wind air temperature, wind factor K = H _jy I ET ₀ may reference evaporation useful but are not essential

speed, wind speed, wind direction at be calculated

direction, rain gauge low frequency

Flowchart illustrating free convection, temperature variance with skewness, air temperature difference, structure function and surface renewal methods for determination of evaporation (LE).

Key to selected variables in Flowchart

1

m - j =/+!

1 m

m - j

1

m - j

where m is the number of high frequency measurements in the averaging period, typically 20 or 30-min (e.g. at 10 Hz measurement frequency, m = 12000 sample temperature measurements for a 20-min averaging period); and j is the number of lags for which r = i /j is the time lag (e.g. if j = \ lag then r = 1/(10 Hz) = 0.1 s).

The sum is performed over / from / + j to m where 7 ^" , is the / th air temperature sample.