2.3 Bowen ratio

The lysimeter is designed to be the representative of the surrounding field so that measured lysimeter ET closely mimics field ET. Experienced support scientists and technicians are responsible for maintaining lysimeter representativeness as compared to surrounding fields. Careful attention is given to agronomic operations including planting, harvesting, tillage, fertilization, irrigation, and pesticide application such that there should be no distinguishable differences, particularly in height, between the crop grown on the lysimeter and that grown in the surrounding field. To confirm this, multiple neutron probe access sites were located both throughout the field and in the lysimeter to monitor the soil profile water content. Weekly soil water content (SWC) readings from the neutron probes throughout the field are compared to SWC readings from the lysimeter to determine similitude representativeness. In addition to SWC readings, plant mapping and stand counts were periodically taken to ensure the crop growth on the lysimeter approximates the surrounding field. The lysimeter box contains a 50 mm freeboard lip that extends above the soil surface to limit runoff or run-on to the lysimeter. Similarly,

Advanced Evapotranspiration Methods and Applications

furrow dikes are used to limit runoff and run-on for the surrounding field.

However, there are many types and sizes of lysimeters. Some are constantly weighing, such as those at the CPRL, while others are weighed periodically. In addition, lysimeters can vary in size. The large weighing lysimeters at the CPRL are considered highly accurate due to their large size, where the effects of the enclosed space on the plants are minimal. Smaller lysimeters will contain more error, especially if the soil volume is small enough where root growth is impeded. With lysimeters, the accuracy is dependent on the lysimeter design, representativeness, maintenance, and operation. Smaller lysimeters can have value, even if they are not highly accurate. An example of the usefulness of smaller lysimeters is the Soil-Plant-Environment Research (SPER) facility, also at the CPRL (see Figure 3). This facility is equipped with 48 lysimeters, each measuring 1 m by 0.75 m by 2.3 m deep [19]. The 48 lysimeters are comprised of 12 replications each of Ulysses silt loam soil from the Garden City, KS area; Pullman clay loam soil from Bushland, TX; Amarillo sandy loam soil from the Big Spring, TX area; and Vingo fine sand soil from the Dalhart, TX area. These represent the four main soil types of the Southern Great Plains of the United States. The SPER contains an automatically controlled rainout shelter that covers the lysimeters during precipitation events, which allows water additions to be precisely controlled through surface drip irrigation. The size of the

The Soil-Plant-Environment Research (SPER) facility at the Conservation and Production Research Laboratory (CPRL) in Bushland,TX. This facility contains 48 smaller lysimeters consisting of 12 replications of the 4 main soil types throughout the Southern Great Plains region of the United States. An automatic rainout shelter (seen in the background) covers the lysimeters during precipitation events so that water can be precisely

Figure 3.

10

controlled through surface drip irrigation.

The lysimeters at the CPRL are a great example of large weighing lysimeters.

Bowen ratio is a method of partitioning fluxes between latent and sensible heat based on flux-profile relationships for energy and mass exchange [21]. This method assumes flux directions are vertical and no horizontal flux movement occurs. Measurements of air temperature and relative humidity are taken at two different heights in the same location. The relative humidity is used to calculate the vapor pressure. The Bowen ratio is the ratio of sensible heat flux to latent heat flux and can be calculated as

$$
\beta = \chi \frac{\Delta T}{\Delta \varepsilon} \tag{6}
$$

#### Figure 4.

An example of a "micro lysimeter" used to determine soil evaporation. The inner soil container can be removed from the outer housing and manually weighed.

where β is the Bowen ratio, γ is the psychometric constant, ΔT is the temperature difference between the two measurements, and Δe is the vapor pressure difference between the two measurements. Using the Bowen ratio, the sensible and latent heat flux are calculated by

$$LE = \frac{R\_n - G}{1 + \beta} \tag{7}$$

The flux for any gas can be calculated from the EC data by

Field-Scale Estimation of Evapotranspiration DOI: http://dx.doi.org/10.5772/intechopen.80945

LE ¼ λ

the footprint will increase with higher sensor heights [24].

calculated by

and

fluxes.

13

using EC is around 20–30% [29].

from mean vapor pressure.

where ρ is the mean air density and w` and s` are deviations from the mean for wind speed and dry mole fraction, respectively [24]. The dry mole fraction can be determined for any gas or variable of interest. From this principle, H and LE can be

Mw=Ma

where Cp is the specific heat of air, T` is deviation from mean temperature, λ is latent heat of vaporization, Mw is the molecular weight of water vapor, Ma is the molecular weight of dry air, P is mean atmospheric pressure, and e` is the deviation

To detect the fast movements of certain eddies, EC measurements are typically taken at very short intervals, often 10–20 measurements per second (10– 20 Hz sampling rate). A very fine measurement resolution is needed to capture the rapid changes in gas concentration and eddy movements. The quantity of data acquired also provides adequate sample size for the covariance analysis. Although measurement acquisition is very frequent, the data will typically be averaged to 30 minutes for flux computations. The 30 minute time step is comparable to the period of significant, unsteady atmospheric motions [25]. The spatial scale of EC measurements is directly affected by sensor height. A sensor height of 2 m will have a measurement footprint of approximately 150 m, and

Several corrections are typically applied to raw EC data to compensate for instrumentation arrangement and ensure that the assumptions of the EC technique are generally valid [26]. These include corrections for coordinate rotation, air density, frequency-dependent signal loss, and Webb, Pearman, and Leuning (WPL) corrections [27]. The coordinate rotation correction converts the flux data so that the orientation is where fluxes are perpendicular to the surface. The air density correction accounts for density fluctuations due to temperature and humidity fluctuations [26]. Frequency-dependent signal loss corrections account for signal losses in the high and the low frequency ranges [27]. The WPL corrections account for fluctuations in gas concentration due to temperature and humidity fluctuations, which do not contribute to the gas

ETa can be determined from EC systems where the water vapor flux is calculated. EC systems can be used to determine the energy balance when the Rn and G are also measured. The basic energy balance equation is given in Eq. 4. Based on this equation, the sum of H and LE should equal the difference between Rn and G. It has been acknowledged that EC systems have an issue with energy balance closure where Rn–G 6¼ LE + H [28]. Previous studies have typically shown that there will be residual energy which is unaccounted. Even with the energy balance closure error, the error of ET calculated from the LE

F ¼ ρw`s` (9)

H ¼ ρCpw`T` (10)

<sup>P</sup> <sup>ρ</sup>w`e` (11)

and

$$H = \frac{\beta}{1+\beta}(R\_n - G) \tag{8}$$

where LE is the latent heat flux, Rn is net radiation, G is soil heat flux, and H is sensible heat flux [21]. All units are W m�<sup>2</sup> . The Bowen ratio method has been shown to contain errors of 25–30% [22, 23].

## 2.4 Eddy covariance

Eddy covariance (EC) systems are based on the theory that as wind moves, it does not move unidirectionally but in three-dimensional circular patterns, or eddies [24]. In addition, as the air moves, it carries with it molecules of water vapor and other gases such as carbon dioxide, methane, and others. If the speed of these eddies can be determined in all three directions, then the movement of the molecules can be determined. In conjunction, a gas analyzer can be used to measure the amounts of water vapor (or other gases) the air contains at that moment in time. The covariance between the movement of the air mass and the composition of that same air mass can be used to determine the water flux (or fluxes of carbon dioxide and methane), in addition to H, LE, and ET. This is the basis for EC systems (see Figure 5), where a three-dimensional sonic anemometer and an infrared gas analyzer (or krypton hygrometer) are used to collect the aforementioned data.

#### Figure 5.

A typical eddy covariance system consisting of a three-dimensional sonic anemometer (CSAT-3, Campbell Scientific Inc., Logan, UT) and an infrared gas analyzer (LI-7500, LI-COR Biosciences, Lincoln, NE).

The flux for any gas can be calculated from the EC data by

$$F = \overline{\overline{\rho}\overline{w'}\overline{s'}}\tag{9}$$

where ρ is the mean air density and w` and s` are deviations from the mean for wind speed and dry mole fraction, respectively [24]. The dry mole fraction can be determined for any gas or variable of interest. From this principle, H and LE can be calculated by

$$H = \overline{\rho} \mathbf{C}\_p \overline{w'} \overline{T'} \tag{10}$$

and

where β is the Bowen ratio, γ is the psychometric constant, ΔT is the temperature difference between the two measurements, and Δe is the vapor pressure difference between the two measurements. Using the Bowen ratio, the sensible and latent heat

LE <sup>¼</sup> Rn � <sup>G</sup>

where LE is the latent heat flux, Rn is net radiation, G is soil heat flux, and H is

Eddy covariance (EC) systems are based on the theory that as wind moves, it does not move unidirectionally but in three-dimensional circular patterns, or eddies [24]. In addition, as the air moves, it carries with it molecules of water vapor and other gases such as carbon dioxide, methane, and others. If the speed of these eddies can be determined in all three directions, then the movement of the molecules can be determined. In conjunction, a gas analyzer can be used to measure the amounts of water vapor (or other gases) the air contains at that moment in time. The covariance between the movement of the air mass and the composition of that same air mass can be used to determine the water flux (or fluxes of carbon dioxide and

<sup>H</sup> <sup>¼</sup> <sup>β</sup>

methane), in addition to H, LE, and ET. This is the basis for EC systems

(see Figure 5), where a three-dimensional sonic anemometer and an infrared gas analyzer (or krypton hygrometer) are used to collect the aforementioned data.

A typical eddy covariance system consisting of a three-dimensional sonic anemometer (CSAT-3, Campbell Scientific Inc., Logan, UT) and an infrared gas analyzer (LI-7500, LI-COR Biosciences, Lincoln, NE).

sensible heat flux [21]. All units are W m�<sup>2</sup>

Advanced Evapotranspiration Methods and Applications

shown to contain errors of 25–30% [22, 23].

<sup>1</sup> <sup>þ</sup> <sup>β</sup> (7)

<sup>1</sup> <sup>þ</sup> <sup>β</sup> ð Þ Rn � <sup>G</sup> (8)

. The Bowen ratio method has been

flux are calculated by

2.4 Eddy covariance

and

Figure 5.

12

$$LE = \lambda \frac{\mathcal{M}\_w/\mathcal{M}\_d}{\overline{P}} \overline{\rho} \overline{w'e'} \tag{11}$$

where Cp is the specific heat of air, T` is deviation from mean temperature, λ is latent heat of vaporization, Mw is the molecular weight of water vapor, Ma is the molecular weight of dry air, P is mean atmospheric pressure, and e` is the deviation from mean vapor pressure.

To detect the fast movements of certain eddies, EC measurements are typically taken at very short intervals, often 10–20 measurements per second (10– 20 Hz sampling rate). A very fine measurement resolution is needed to capture the rapid changes in gas concentration and eddy movements. The quantity of data acquired also provides adequate sample size for the covariance analysis. Although measurement acquisition is very frequent, the data will typically be averaged to 30 minutes for flux computations. The 30 minute time step is comparable to the period of significant, unsteady atmospheric motions [25]. The spatial scale of EC measurements is directly affected by sensor height. A sensor height of 2 m will have a measurement footprint of approximately 150 m, and the footprint will increase with higher sensor heights [24].

Several corrections are typically applied to raw EC data to compensate for instrumentation arrangement and ensure that the assumptions of the EC technique are generally valid [26]. These include corrections for coordinate rotation, air density, frequency-dependent signal loss, and Webb, Pearman, and Leuning (WPL) corrections [27]. The coordinate rotation correction converts the flux data so that the orientation is where fluxes are perpendicular to the surface. The air density correction accounts for density fluctuations due to temperature and humidity fluctuations [26]. Frequency-dependent signal loss corrections account for signal losses in the high and the low frequency ranges [27]. The WPL corrections account for fluctuations in gas concentration due to temperature and humidity fluctuations, which do not contribute to the gas fluxes.

ETa can be determined from EC systems where the water vapor flux is calculated. EC systems can be used to determine the energy balance when the Rn and G are also measured. The basic energy balance equation is given in Eq. 4. Based on this equation, the sum of H and LE should equal the difference between Rn and G. It has been acknowledged that EC systems have an issue with energy balance closure where Rn–G 6¼ LE + H [28]. Previous studies have typically shown that there will be residual energy which is unaccounted. Even with the energy balance closure error, the error of ET calculated from the LE using EC is around 20–30% [29].
