2.1. Site description

serious situation of water supply for various users. Agricultural production will be one of the sectors most vulnerable to climate change and variability. The water budget must now be shared with agriculture, urban use, industry, recreation and livestock watering; the future will be seeing an increasing competition for water. Spatial and temporal changes in precipitation and temperature patterns will have an impact on the viability of dry land farming and therefore necessitate irrigation where rainfall was previously adequate. Efficiency improvement in irrigation lies among the key strategies for saving more water and promote a sustainable intensification of agriculture when water scarcity becomes a major constraint to production [2]. Nevertheless, irrigation water for crops is globally the major consumptive use of water resources. Due to the above-mentioned challenges, it is important to improve the management of agricultural water, which would involve the accurate estimation of consumptive uses. One of the techniques is the measurement of evapotranspiration which is a major component of the hydrologic cycle. Evapotranspiration (ET) is an essential component of the water balance, and it is a significant consumptive witness of precipitation and water applied for irrigation of cropland [3]. ET can help for highly efficient management of water uses in

Basically, ET includes two processes: One is evaporation and the second is transpiration. The latter is the process of removing water from vegetation or any other moisture containing living surface. Evapotranspiration includes two processes. During the plant growth, the water stored in the soil is taped and transferred in the atmosphere. Transpiration is the evaporation of water in the vascular system of plants through the leaf stomata when they open and close controlled by their guard cells. Based on this bio-physical process, transpiration involves a living organism and its tissues. ET is then the process, whereby water originating from a wide range of sources is transferred from the soil compartment and/or vegetation layer to the atmosphere. ET is the largest outgoing water flux from the Earth's surface and accurately quantifying ET is critical for the development of crop cultures in an increasing drier environment, and it can contribute to a greater understanding of a range of agricultural ecosystem processes. ET is particularly fundamental when dealing with water resource management issues such as irrigation water or water reserve management [4]. ET cannot be directly measured but it has to be estimated by monitoring the exchange of energy/water above the vegetated surface (remote

Several methods are currently used to measure and estimate ET: One of them is the lysimeter method or soil water budget. That method may be accurate but lysimeters are expensive, and the extent of their measurement is localized (i.e., they provide data for a very small area compared to the field surface, so it can only be used in field locations). Another one uses micrometeorological data to compute ET. A widely used approach by these data is the FAO-24 and by extension the FAO-56 procedure, based on ET0 and Kc [5]. ET acquisition can be obtained with different instruments at the scale of: the leaf (porometer), an individual plant (i.e., sapflow, lysimeter), the field scale (i.e., field water balance, Bowen ratio, scintillometer) and the landscape scale (i.e., eddy correlation and catchment water balance) [6]. The flux measurement of micro-meteorological station can only represent the value in a point or a limited area (several meters to several hundred meters). However, a scintillometer can measure averaged sensible heat fluxes in a distance of 500m to 10 km, which is an average of time

agriculture and set up real water-saving systems.

26 Current Perspective to Predict Actual Evapotranspiration

sensing) or as a residual term of the hydrological balance.

The study was carried out in the west part of France near to Niort (France). The site of the intercomparison of evapotranspiration measurements is located in the village of Sainte Soline (contained near 46�15<sup>0</sup> 27.7″N—0�02<sup>0</sup> 32.0″E) (Figure 1), and the area's elevation is 117—145 m above the sea level. According to data from the Meteorologisk Institute, the daily mean temperatures vary significantly from 5�C in January to 26�C in July. The average days with precipitation per month are 12 days in January and 6 days in August. Mean annual rainfall is 6.4 mm and is distributed relatively evenly across all months. The dominant wind directions are from the south-west and west-south-west and north. The site consists of a field with homogeneous corn crop. Corn corresponds to plants DKc 4590. Corn was planted in April, and the measurements were made at the stage of 4 months (almost 5 months) after planting corresponding to about 65% of maximum plant growth and to 3 months (just before) of the final harvest.

The soil type is clay, and the typical porosity of this soil type is about 0.30 m3 m�<sup>3</sup> with grain size <0.002 mm.

Figure 1. Location map of the measurements during the summer time and contained between 46�15<sup>0</sup> 27.7″N and 0�02<sup>0</sup> 32.0″E.

#### 2.2. Measurement description

The scintillometer provides the opportunity to obtain surface fluxes of sensible heat across a distance of several kilometers and over a heterogeneous landscape [10]. As shown by different authors, it is feasible to use the scintillometer for estimating area-averaged sensible heat flux <λE> (λE ¼ Rn—G—H) as the residual term of the energy balance equation, providing estimations of area-average available energy (λE ¼ Rn—G) with E the sensible heat flux, λ the latent heat, Rn the net radiation and G the soil heat flux [11]. The transmitter and receiver of the scintillometer system were installed at opposite edges of the field, and the electromagnetic radiation was transmitted across the field. Scintillometry measurements are based on the propagation of electromagnetic waves in atmosphere and the measurement of its disturbance by atmospheric turbulence. The turbulence effect induces laser beam fluctuations leading to beam scintillations, wanderings as a result of random fluctuations of atmospheric temperature and refractive index changes, humidity, pressure and their interactions. A scintillometer measures the normalized variance of radiation intensity.

The scintillometer set up consists of an emitter and a receiver, placed in front of each other at the distance L, where the measurement is made.

The scintillometer consists in an emitter and a receiver. The emitter includes a continuous laser and a pair of lenses to collimate the beam over the optical path. The laser wavelength used is 532 nm with an average power of 70 mW. The output beam of the laser beam is expanding with a Galilean telescope with chosen lenses. The beam is then collimated over a long distance typically for distances less than 200 m. The optical system has a plano-convex lens with a focal length of 15 mm after the laser output. In order to have a magnification of 5 a second planoconvex lens with a 300 mm, focal length is placed 30 cm from the first one. Finally, at the output of the emitter, the diameter of the beam is then 2 cm. A Rayleigh range of around 142 m for the output collimated beam is obtained with the pair of lenses. The receiver uses a Galilean telescope to recollect the light. A position sensing detector sensor with lateral effect (Duo lateral PSD) defined by the size of the light spot is used as the detector and provide position informations only up to the point where the edge of the spot reaches the gap. The lateral effect position sensing detector is 100 mm2 (10 mm x 10 mm). Additionally, it is important to enlarge the beam with a combination of two lenses enabling a magnification of 5 in order to have a sufficiently large measurement field. The first lens is plano-convex with a focal length of 60 mm, and the second is plano-concave with a focal length of �24 mm. The two lenses are separated with a distance of 86 mm. For stability during the measurements, all the optical components are mounted on a metal board. The electronic system includes an electronic system for data acquisition and a remote interface with the operators. The scintillometer is a stand-alone system with batteries, solar cells and a communicating system to send data. That device has been built for simultaneously recording both random intensity fluctuations and displacement of the beam centroid (wandering).

The scintillometer provides a measurement of the structure parameter for the refractive index (C<sup>2</sup> <sup>n</sup>) along the optical path. The structure parameter of the refractive index of air C<sup>2</sup> <sup>n</sup> was calculated from the natural logarithm of the intensity of light (I)

2.2. Measurement description

28 Current Perspective to Predict Actual Evapotranspiration

0�02<sup>0</sup> 32.0″E.

sures the normalized variance of radiation intensity.

the distance L, where the measurement is made.

The scintillometer provides the opportunity to obtain surface fluxes of sensible heat across a distance of several kilometers and over a heterogeneous landscape [10]. As shown by different authors, it is feasible to use the scintillometer for estimating area-averaged sensible heat flux <λE> (λE ¼ Rn—G—H) as the residual term of the energy balance equation, providing estimations of area-average available energy (λE ¼ Rn—G) with E the sensible heat flux, λ the latent heat, Rn the net radiation and G the soil heat flux [11]. The transmitter and receiver of the scintillometer system were installed at opposite edges of the field, and the electromagnetic radiation was transmitted across the field. Scintillometry measurements are based on the propagation of electromagnetic waves in atmosphere and the measurement of its disturbance by atmospheric turbulence. The turbulence effect induces laser beam fluctuations leading to beam scintillations, wanderings as a result of random fluctuations of atmospheric temperature and refractive index changes, humidity, pressure and their interactions. A scintillometer mea-

27.7″N and

Figure 1. Location map of the measurements during the summer time and contained between 46�15<sup>0</sup>

The scintillometer set up consists of an emitter and a receiver, placed in front of each other at

The scintillometer consists in an emitter and a receiver. The emitter includes a continuous laser and a pair of lenses to collimate the beam over the optical path. The laser wavelength used is 532 nm with an average power of 70 mW. The output beam of the laser beam is expanding

$$
\sigma\_{lnA}^2 = 0.031k^{7/6}L^{11/6}\mathcal{C}\_n^2 \tag{1}
$$

where L is the beam path length (m), k is the optical wave number (m�<sup>1</sup> ) defined for the wavelength <sup>λ</sup> as: <sup>k</sup> <sup>¼</sup> <sup>2</sup>π=<sup>λ</sup> and <sup>σ</sup><sup>2</sup> lnA <sup>¼</sup> <sup>1</sup> <sup>4</sup> ln <sup>1</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup> I with σ<sup>2</sup> <sup>I</sup> defined as: σ<sup>2</sup> <sup>I</sup> ¼ 〈I 2 〉 � 〈I〉 2 =〈I〉 2 : So the representative value of C<sup>2</sup> <sup>n</sup> is 10�<sup>15</sup> to 10�18m�2/3.

The parameters such as temperature (T), humidity (q) and pressure (P) generate fluctuations in the refractive index of air C<sup>2</sup> <sup>n</sup>; however, as the proportion of pressure is very small, this value is always neglected. In the range of visible and near-infrared region, the temperature is the main parameter, assuming that temperature and humidity are perfectly correlated, the structure parameter C<sup>2</sup> <sup>n</sup> can be related to the structure parameter CT <sup>2</sup> for temperatures by [12]

$$\mathbf{C}\_{\rm T}^{2} = \mathbf{C}\_{\rm n}^{2} \left(\frac{0.78 \times 10^{-6} \rm \rm P}{\rm T}\right)^{-2} \left(1 + \frac{0.03}{\beta}\right)^{-2} \tag{2}$$

where β is the Bowen ratio, which connect temperature and humidity by the ratio of sensible flux and latent heat flux (β ¼ H=λE). The second term in brackets is a correction for the effects of humidity. C<sup>2</sup> <sup>T</sup> is given in (K<sup>2</sup> .m�2/3).

The sensible heat flux can be derived from the Monin-Obukhov Similarity Theory (MOST) [13] when C<sup>2</sup> <sup>T</sup> is known. This value depends on the stability parameter ζ ¼ (zscin - d)/L, where zscin and d are the effective height of the scintillometer above the surface and the displacement height, respectively. L<sup>O</sup> is the Monin-Obukhov length (m) given by

$$L\_O = \frac{\mu^2 T}{k \lg T^\*} \tag{3}$$

with <sup>k</sup> <sup>¼</sup> <sup>0</sup>:41 is the von Karman constant, <sup>g</sup> <sup>¼</sup> <sup>9</sup>:<sup>81</sup> ms�<sup>2</sup> the gravity and <sup>u</sup>� <sup>m</sup>:<sup>s</sup> �<sup>1</sup> the friction velocity, given by

$$
\mu^\* = \frac{ku}{\ln\left(\frac{z-d}{z\_0}\right) - \psi} \tag{4}
$$

where u is the wind speed, z<sup>0</sup> ¼ 0:1hveg is the surface roughness length and ψ is the stability correction function depending on z=LO. The universal function ψ is only related to the atmosphere stability and has different expression under stable and unstable conditions [14]. The sensible heat flux Hscin can be then computed iteratively as follows

$$H\_{\rm scin} = -\rho c\_p \mu^\* T^\* \tag{5}$$

where ρ and cp are the density and specific heat capacity of the air, respectively. During the iteration, β is calculated using Hscin, net radiation (Rn) and soil heat flux (G)

$$\beta = \frac{H\_{\rm scin}}{R\_n - G - H\_{\rm scin}} \tag{6}$$

The value of the latent heat flux (evapotranspiration) can then be calculated as the residual of the energy balance

$$
\lambda\_v E\_{\rm scin} = R\_n - G - H\_{\rm scin} \tag{7}
$$

where Rn W:m�<sup>2</sup> is the net radiation and G W:m�<sup>2</sup> is the soil heat flux. Additional data of temperature, pressure and humidity are necessary to compute the characteristic parameters of the latent heat flux. More specific information on the described approach is found in Ref. [15].

Simultaneously, the air and ground temperature were measured with a thermistor device and linked to the transmission system. The humidity was measured with a capacitive sensor and the wind speed with an anemometer. All the data were collected by a data acquisition electronic system, based on an Arduino board [16], and sent as text files by a modem through the GPRS network and a SIM card.

#### 2.3. Estimation of evapotranspiration based on micro-meteorological datasets

In addition to the data provided by the scintillometer, estimation of the reference crop evapotranspiration ET0 can be based on energy balance schemes and the Penman-Monteith (FAO-PM56) method [17, 18]; they are used to assess ET0 from meteorological variables. The reference crop evapotranspiration or reference evapotranspiration, denoted as ET0 or ETref, is the estimation of the evapotranspiration from a "reference surface." The reference surface is a hypothetical grass reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 S/m and an albedo of 0.23. In the reference evapotranspiration definition, the reference surface is specifically defined as the reference crop, and this crop is assumed to be free of water stress and diseases with a fixed surface resistance of 70 S/m. This reference surface has grass with a uniform height, normally growing and totally covering the ground. The soil surface is moderately dry resulting from about a weekly irrigation frequency.

The sensible heat flux can be derived from the Monin-Obukhov Similarity Theory (MOST) [13]

LO <sup>¼</sup> <sup>u</sup><sup>2</sup><sup>T</sup>

with <sup>k</sup> <sup>¼</sup> <sup>0</sup>:41 is the von Karman constant, <sup>g</sup> <sup>¼</sup> <sup>9</sup>:<sup>81</sup> ms�<sup>2</sup> the gravity and <sup>u</sup>� <sup>m</sup>:<sup>s</sup>

<sup>u</sup>� <sup>¼</sup> ku ln <sup>z</sup> � <sup>d</sup> z0 

where u is the wind speed, z<sup>0</sup> ¼ 0:1hveg is the surface roughness length and ψ is the stability correction function depending on z=LO. The universal function ψ is only related to the atmosphere stability and has different expression under stable and unstable conditions [14]. The

Hscin ¼ �ρcpu�

<sup>β</sup> <sup>¼</sup> Hscin

where ρ and cp are the density and specific heat capacity of the air, respectively. During the

Rn � G � Hscin

The value of the latent heat flux (evapotranspiration) can then be calculated as the residual of

where Rn W:m�<sup>2</sup> is the net radiation and G W:m�<sup>2</sup> is the soil heat flux. Additional data of temperature, pressure and humidity are necessary to compute the characteristic parameters of the latent heat flux. More specific information on the described approach is found in Ref. [15]. Simultaneously, the air and ground temperature were measured with a thermistor device and linked to the transmission system. The humidity was measured with a capacitive sensor and the wind speed with an anemometer. All the data were collected by a data acquisition electronic system, based on an Arduino board [16], and sent as text files by a modem through the

In addition to the data provided by the scintillometer, estimation of the reference crop evapotranspiration ET0 can be based on energy balance schemes and the Penman-Monteith

2.3. Estimation of evapotranspiration based on micro-meteorological datasets

height, respectively. L<sup>O</sup> is the Monin-Obukhov length (m) given by

30 Current Perspective to Predict Actual Evapotranspiration

sensible heat flux Hscin can be then computed iteratively as follows

iteration, β is calculated using Hscin, net radiation (Rn) and soil heat flux (G)

<sup>T</sup> is known. This value depends on the stability parameter ζ ¼ (zscin - d)/L, where zscin and d are the effective height of the scintillometer above the surface and the displacement

� ψ

kgT� <sup>ð</sup>3<sup>Þ</sup>

T� ð5Þ

λvEscin ¼ Rn � G � Hscin ð7Þ

�<sup>1</sup> the friction

ð4Þ

ð6Þ

when C<sup>2</sup>

velocity, given by

the energy balance

GPRS network and a SIM card.

The FAO Penman-Monteith method has been reported as providing consistent ET0 values in many regions and climates [19]; it has long been accepted worldwide as an excellent ET0 estimator when it is compared with other methods. The application of ET0 models with fewer meteorological variable requirements is recommended under situations where weather data sets are incomplete. Those values are multiplied by an empirical crop coefficient to obtain the ET from the crop (ETc). The crop coefficient accounts for the difference between the standard surface and the crop. Reference ET is expressed in units of depth time�<sup>1</sup> , for example, mm day�<sup>1</sup> . It is a climatic parameter expressing the evaporative power of the atmosphere at the given space and time coordinates [20].

Empirical formulas have been developed to estimate solar radiation using some normal observations from meteorological stations, such as maximum and minimum temperatures, sunshine hours, cloud, precipitation, latitude and elevation. FAO Penman-Monteith procedures allow applying the method when only air temperature and wind speed are available. In these methods, saturation vapor pressure and actual vapor pressure were estimated from Tmax and Tmin, as recommended by Allen et al. [22] for situations where air humidity data are lacking or are of questionable quality.

The standard FAO Penman-Monteith method is based on the following equation [21]

$$\text{ET}\_0 = \frac{0.408\Delta (R\_n - G) + \gamma \left(\frac{0.37}{(T\_a + 273)}\right) u\_2 (e\_s - e\_d)}{\Delta + \gamma (1 + 0.34u\_2)} \tag{8}$$

where ET0 represents the hourly reference evapotranspiration (mm h�<sup>1</sup> ), Δ represents the slope vapor pressure curve (kPa.�C�<sup>1</sup> ), Rn is the net radiation at the crop surface (MJ m�<sup>2</sup> h�<sup>1</sup> ), G indicates the soil heat flux density (MJ.m�<sup>2</sup> .h�<sup>1</sup> ), γ is the psychrometric constant (kPa.�C�<sup>1</sup> ), T<sup>a</sup> is the mean air temperature at 2 m height (�C), u<sup>2</sup> is the mean hourly wind speed at 2 m height (m s�<sup>1</sup> ), e<sup>s</sup> defines the saturation vapor pressure at air temperature T<sup>a</sup> (kPa) and e<sup>a</sup> indicates the actual vapor pressure (kPa). All meteorological data required by the equation were collected by the aid of a weather station that was placed on the reference crop.

The Penman-Monteith equation requires the following parameters:

a. Minimum and maximum daily temperature.

