3. Results and discussion

## 3.1. Comparison between micrometeorological measurements and scintillometry

The comparison period for the ET measured by scintillometry and micro-meteorology measurements covered 2 months between July and August 2015, which included a range of climatic conditions to test the performance of the proposed scintillometry calculation method. The average air temperature was 23C and ranged between a minimum of 9C and a maximum of 32C. The average ground temperature was 22C and ranged between a minimum of 16C and a maximum of 25C. The C<sup>2</sup> <sup>n</sup> measurements were made on a continuous time scale at 60 min intervals and averaged every 1 min and were synchronized with a weather station. Rn and G are calculated based on other meteorological data. Sensible heat fluxes with 60 min intervals were calculated using a step by step methodology provided by the method previously developed. The 60 min ET rates were computed as a residual from the energy balance equation, with calculated Rn and G fluxes and using an estimated H. Figures 2 and 3 show the data acquired by the micro-meteorological station. Figure 2 displays air and ground temperature measurements and, besides, the wind speed.

Figure 3 presents the measurements of humidity and pressure. All the data were acquired, at the same time, and stored by the electronic system. The measurements are detailed on a period of 7 days for simplicity of analysis. The air temperature was measured at a height of 0.3 m above the crop canopy and shows large variations between the maxima and minima. We calculate a ΔT around 15C. The ground temperature was measured beneath the canopy foliage

Assessment and Prediction of Evapotranspiration Based on Scintillometry and Meteorological Datasets http://dx.doi.org/10.5772/intechopen.68538 33

b. Relative humidity. Depending on the availability of data, different equations are used. The data requirements are the following: (i) minimum and maximum daily relative humidity, (ii) maximum daily relative humidity or (iii) average daily relative humidity. In case where no humidity data are available, an estimation is required considering that the dew

c. Solar radiation. Different equations are used to consider the solar radiation. In order to calculate the solar radiation, if we do not access to the solar radiation directly we need (i) hours of sunshine per day or (ii) cloudiness fraction or the Hargreaves formula, based on minimum and maximum daily temperature and an adjustment coefficient (Krs) to esti-

d. Wind speed. (An adjustment can be made if the wind speed measurement height has been

f. The meteorological data measured and used in this study are mean daily air temperature (Tmean); maximum and minimum air temperature (Tmax and Tmin); mean daily relative

The comparison period for the ET measured by scintillometry and micro-meteorology measurements covered 2 months between July and August 2015, which included a range of climatic conditions to test the performance of the proposed scintillometry calculation method. The average air temperature was 23C and ranged between a minimum of 9C and a maximum of 32C. The average ground temperature was 22C and ranged between a minimum of

60 min intervals and averaged every 1 min and were synchronized with a weather station. Rn and G are calculated based on other meteorological data. Sensible heat fluxes with 60 min intervals were calculated using a step by step methodology provided by the method previously developed. The 60 min ET rates were computed as a residual from the energy balance equation, with calculated Rn and G fluxes and using an estimated H. Figures 2 and 3 show the data acquired by the micro-meteorological station. Figure 2 displays air and ground tempera-

Figure 3 presents the measurements of humidity and pressure. All the data were acquired, at the same time, and stored by the electronic system. The measurements are detailed on a period of 7 days for simplicity of analysis. The air temperature was measured at a height of 0.3 m above the crop canopy and shows large variations between the maxima and minima. We calculate a ΔT around 15C. The ground temperature was measured beneath the canopy foliage

<sup>n</sup> measurements were made on a continuous time scale at

humidity (RH); mean daily wind speed (u) and daily net radiation (Rn).

3.1. Comparison between micrometeorological measurements and scintillometry

point temperatures are the same as the daily minimum temperatures.

e. Latitude and altitude of the climate measurement station.

mate the solar radiation.

32 Current Perspective to Predict Actual Evapotranspiration

previously measured).

3. Results and discussion

16C and a maximum of 25C. The C<sup>2</sup>

ture measurements and, besides, the wind speed.

Figure 2. Measurements of air, ground temperature and wind during considered period. The lines give the average minimal and maximal air temperature.

with a sensor at 0.05 m underground. The ground temperature data show small amplitudes of variation with an average ΔT between the maximum and minimum of temperature around 5C. The comparison between the two measured temperatures at two different heights shows a constant average value for the ground temperature and a limited variation of the average temperature with a maximum value of 25C. It is interesting to note that the maximum of average air temperature value corresponds to the days where the wind is the maximum. The ground temperature is not sensible to the wind and account for the temperature changes with the canopy as shelter. The maximum in the average value for the air temperature corresponds also to the maximum of humidity. However, the atmospheric pressure is not related to the air temperature during the presented period of analysis. Based on the acquired micro-meteorological parameters and atmospheric turbulence measurements, evapotranspiration was calculated.

Figure 4 presents the comparison between the evapotranspiration data acquired with the scintillometer and the FAO-56 method during the same period of atmospheric parameter measurements. Differences are observed, in particular, during the night where the temperature falls. Those differences can be attributed to the few numbers of parameters used in the calculation with the FAO-56 method. The discrepancies between the two measurements of ET correspond to the maximum of humidity and minimum of wind. The variation between the two measurements can be checked in Figure 5, where the ETP computed using the FAO method regarding the ETP calculated with scintillometer data are plotted. A coefficient of

Figure 3. Measurement of the atmospheric humidity and pressure.

0.78 is found between the two methods meaning that ETPFAO ¼ 0.78 ETPscin. Therefore, the values are lower with FAO than with scintillometry and, consequently, evapotranspiration is underestimated. Note that the evapotranspiration measurement with scintillometry has proven being close to the data measured with Eddy-covariance [22, 23].

Assessment and Prediction of Evapotranspiration Based on Scintillometry and Meteorological Datasets http://dx.doi.org/10.5772/intechopen.68538 35

Figure 4. Comparison of the ET measured with the FAO-PM56 model based on the measurements of a limited number of parameters (Tmin, Tmax, Tavg, Rs) and scintillometric data.

Figure 5. Comparison of the two measured ET data. The curves show the fitting points calculated with linear regression and the ideal curve representing a perfect similar relation of the two ET.

#### 3.2. Influence of environmental parameters

0.78 is found between the two methods meaning that ETPFAO ¼ 0.78 ETPscin. Therefore, the values are lower with FAO than with scintillometry and, consequently, evapotranspiration is underestimated. Note that the evapotranspiration measurement with scintillometry has

proven being close to the data measured with Eddy-covariance [22, 23].

Figure 3. Measurement of the atmospheric humidity and pressure.

34 Current Perspective to Predict Actual Evapotranspiration

In order to account the influence of the main meteorological parameters on the measurement sensibility of ETP, the effect of temperature variations is observed as the main influence on the measurements obtained by the FAO-56 and the scintillometer. Thus, the calculation is limited to temperature differences since scintillometer is more sensitive to small fluctuations of the refractive index of the air caused by those variations of temperatures.

Firstly, considering the ETP solution from a set of variable values (Eq. (8)) given by the FAO-56 where the dominant variable is the air temperature (TA). Indeed, each term in Eq. (8) can be rewritten as a function of the temperature, thus

$$\rm ET\_0 = \frac{[0.408.\Delta R\_n + \gamma.\frac{900}{\left(T\_A + 273\right)}\ .\ u\_2.(\mathbf{e}\_s - \mathbf{e}\_s.H\_D)]}{\left(\Delta + \gamma.\left(1 + 0.34.\nu\_2\right)\right)}\tag{9}$$

where u<sup>2</sup> is the wind speed and HD is the relative humidity. Rn, es, γ and Δ are depending on T<sup>A</sup> (see Appendix A).

The dominant variable value is fluctuated by a small amount while keeping all other values constant, and we note the change of the solution. The goal is to determine how sensitive the output calculation of evapotranspiration could be with respect to the calculation elements which are subject to uncertainty of variability.

Figure 6 shows that a variation of �0.5�C of T<sup>A</sup> leads to a small variation of ET0 (�1.3 mm/day) with the FAO method. However, a variation of �0.5�C leads to a variation of �2.2 mm/day with the scintillometric method. Therefore, the scintillometer method is more sensitive to fluctuations of air temperature. This is not a novelty because small fluctuations of air temperature induce random variations in the refractive index of the turbulent atmosphere by changing the intensity of turbulence C<sup>2</sup> n. The propagation distance enhances any fluctuations of the laser beam. Moreover, it was shown that the C<sup>2</sup> <sup>n</sup> can be measured with a good precision [24]. According to this result, a sensitivity analysis based on the analytical calculations was conducted.

The approach consists in mathematically differentiate the equation under study to derive equations for the change rate of the independent variable with respect to each dependent variable. The sensitivity for the air temperature is calculated applying the PM FAO-56 method. The ET0 is considered as a function with multi-variables v1, v2, v3, …, as ET0 ¼ f(v1, v2, v3, …) with v1 ¼ Ta, v2 ¼ Rn, v3 ¼ u2 and so on. The sensitivity equation can be developed by

$$\text{ET}\_0 + \Delta \text{ET}\_0 = f(\mathbf{v}\_1 + \Delta \mathbf{v}\_1, \mathbf{v}\_2 + \Delta \mathbf{v}\_2 \mid \mathbf{v}\_3 + \Delta \mathbf{v}\_3 \mid \dots) \tag{10}$$

After applying the Taylor's theorem and considering only the first order, the expression yields

$$
\Delta \text{ET}\_0 = \frac{\partial \text{ET}\_0}{\partial \mathbf{v}\_1} \Delta \mathbf{v}\_1 + \frac{\partial \text{ET}\_0}{\partial \mathbf{v}\_2} \Delta \mathbf{v}\_2 + \frac{\partial \text{ET}\_0}{\partial \mathbf{v}\_3} \Delta \mathbf{v}\_3 + \dots \tag{11}
$$

The P–M method is a multi-variable model. Several variables have different dimensions and various ranges of values, which makes it difficult to compare the sensitivity by partial derivatives. The partial derivative is transformed into a non-dimensional form.

The substitution of the relative forms, (ET0)rel ¼ (ΔET0/ET0) and vrel ¼Δv/v for each variable, yields

$$(\text{ET}\_0)\_\text{rel} = (\Delta \text{ET}\_0 / \text{ET}\_0) = \left(\frac{\partial \text{ET}\_0}{\partial \mathbf{v}\_1} \frac{\mathbf{v}\_1}{\text{ET}\_0}\right) \frac{\Delta \mathbf{v}\_1}{\mathbf{v}\_1} + \left(\frac{\partial \text{ET}\_0}{\partial \mathbf{v}\_2} \frac{\mathbf{v}\_2}{\text{ET}\_0}\right) \frac{\Delta \mathbf{v}\_2}{\mathbf{v}\_2} + \left(\frac{\partial \text{ET}\_0}{\partial \mathbf{v}\_3} \frac{\mathbf{v}\_3}{\text{ET}\_0}\right) \frac{\Delta \mathbf{v}\_3}{\mathbf{v}\_3} + \dots \quad(12)$$

Assessment and Prediction of Evapotranspiration Based on Scintillometry and Meteorological Datasets http://dx.doi.org/10.5772/intechopen.68538 37

Firstly, considering the ETP solution from a set of variable values (Eq. (8)) given by the FAO-56 where the dominant variable is the air temperature (TA). Indeed, each term in Eq. (8) can be

where u<sup>2</sup> is the wind speed and HD is the relative humidity. Rn, es, γ and Δ are depending on T<sup>A</sup>

The dominant variable value is fluctuated by a small amount while keeping all other values constant, and we note the change of the solution. The goal is to determine how sensitive the output calculation of evapotranspiration could be with respect to the calculation elements

Figure 6 shows that a variation of �0.5�C of T<sup>A</sup> leads to a small variation of ET0 (�1.3 mm/day) with the FAO method. However, a variation of �0.5�C leads to a variation of �2.2 mm/day with the scintillometric method. Therefore, the scintillometer method is more sensitive to fluctuations of air temperature. This is not a novelty because small fluctuations of air temperature induce random variations in the refractive index of the turbulent atmosphere by changing the intensity

The approach consists in mathematically differentiate the equation under study to derive equations for the change rate of the independent variable with respect to each dependent variable. The sensitivity for the air temperature is calculated applying the PM FAO-56 method. The ET0 is considered as a function with multi-variables v1, v2, v3, …, as ET0 ¼ f(v1, v2, v3, …)

After applying the Taylor's theorem and considering only the first order, the expression yields

∂ET0 ∂v2

The P–M method is a multi-variable model. Several variables have different dimensions and various ranges of values, which makes it difficult to compare the sensitivity by partial deriva-

The substitution of the relative forms, (ET0)rel ¼ (ΔET0/ET0) and vrel ¼Δv/v for each variable,

∂ET0 ∂v2

v2 ET0 Δv2

v2 þ ∂ET0 ∂v3

v3 ET0 Δv3

v3

þ … ð12Þ

Δv2 þ

with v1 ¼ Ta, v2 ¼ Rn, v3 ¼ u2 and so on. The sensitivity equation can be developed by

Δv1 þ

tives. The partial derivative is transformed into a non-dimensional form.

v1 ET0 Δv1

v1 þ

n. The propagation distance enhances any fluctuations of the laser beam. More-

ET0 þ ΔET0 ¼ fðv1 þ Δv1, v2 þ Δv2, v3 þ Δv3, …Þ : ð10Þ

∂ET0 ∂v3

Δv3 þ … ð11Þ

<sup>n</sup> can be measured with a good precision [24]. According to this

<sup>ð</sup>TA<sup>þ</sup> <sup>273</sup><sup>Þ</sup> :u2:ðes � es:HDÞ�

ð Þ <sup>Δ</sup> <sup>þ</sup> <sup>γ</sup>: <sup>ð</sup><sup>1</sup> <sup>þ</sup> <sup>0</sup>:34:u2<sup>Þ</sup> <sup>ð</sup>9<sup>Þ</sup>

ET0 <sup>¼</sup> <sup>½</sup>0:408:ΔRn <sup>þ</sup> <sup>γ</sup>: <sup>900</sup>

result, a sensitivity analysis based on the analytical calculations was conducted.

<sup>Δ</sup>ET0 <sup>¼</sup> <sup>∂</sup>ET0 ∂v1

∂v1

rewritten as a function of the temperature, thus

36 Current Perspective to Predict Actual Evapotranspiration

which are subject to uncertainty of variability.

(see Appendix A).

of turbulence C<sup>2</sup>

yields

<sup>ð</sup>ET0Þrel ¼ ðΔET0=ET0Þ ¼ <sup>∂</sup>ET0

over, it was shown that the C<sup>2</sup>

Figure 6. Comparison of the influence of a small variation of temperature (� 0.5�C) on the two methods of measurements of ET.

where Svi is called the sensitivity coefficient and it is equal to <sup>∂</sup>ET0 ∂vi vi ET0 for the variable vi. This term becomes a dimensionless coefficient which expresses the percentage of the relative variable change transmitted to the relative dependent variable. Basically, a positive/negative sensitivity coefficient of a variable indicates that ET0 will increase/decrease as the variable increases. The bigger the sensitivity coefficient, the larger the effect a given variable has on ET0. A sensitivity coefficient Svi of 0.2 would show that a 10% change in v1 (Δv1/v1 ¼ 0.10) would cause a 2% change in ET0 (ΔET0/ET0 ¼ 0.02) if (ET0)rel is dependent of the relative change ΔV1/V1 in Eq. (12) [25].

The partial derivatives needed for the determination of the sensitivity coefficient STA corresponding to the influence of air temperature:

$$\mathbf{S}\_{\rm TA} = \lim\_{\Delta \mathbf{T}\_{\rm A} \to 0} \begin{pmatrix} \frac{\Delta \mathbf{E} \mathbf{T}\_0}{\mathbf{E} \mathbf{T}\_0} \\ \frac{\Delta \mathbf{T}\_{\rm A}}{\mathbf{T}\_{\rm A}} \end{pmatrix} = \frac{\partial \mathbf{E} \mathbf{T}\_0}{\partial \mathbf{T}\_{\rm A}} \cdot \frac{\mathbf{T}\_{\rm A}}{\mathbf{E} \mathbf{T}\_0} \tag{13}$$

The calculation is done analytically by means of symbolic calculation of Mathematica (Wolfram) in Appendix A. It found a sensitivity coefficient value of 0.12 for the maximum measured temperature of 32.8�C, a humidity of 24.7%, a wind measurement of 3.9 m/s, an evapotranspiration of 10.4 mm/day and an atmospheric pressure of 1002 mbar.

This sensitivity obtained for the FAO-56 measurement and the one given by the scintillometer is compared. For the latter instrument, based on optical metrology, the intensity fluctuations of visible beams are more sensitive to temperature fluctuations than humidity fluctuations.

In the displaced-beam scintillometer measurements, the path-averaged measurements of C<sup>2</sup> n are obtained. Additional measurements have separately carried out including temporally averaged pressure, air temperature, humidity, as well as the height of the beam above the field and the Bowen ratio. All those sources of measurements contain uncertainties. Uncertainty is propagated from the measured parameters to the derived variables through the set of equations employed and written previously (Eq. (1)–(7)). Different scintillometer sensitivity studies have been done. One of them uses the Monte-Carlo error analysis [26] and shows that the experimental coupling of inertial-dissipation methods is promising, since the propagation of statistical errors in the acquired parameters to the final value is limited. Those methods are based on measurements of the structure parameters of momentum, temperature and humidity with optical methods leading to the calculation of the momentum flux and the heat flux. Another study [27] calculates the relative uncertainty of the friction velocity u\* or turbulence velocity scale. The goal was to know how precisely the measurement of the friction velocity u\* can be done by using a path-averaged optical propagation. The conclusion is that the measurement of the inner scale of turbulence (λo) contributes to the largest uncertainty and must be done precisely. A recent study analyses the impact of the Bowen ratio on the flux value and uncertainty [28]. It is shown that the Bowen ratio has a large impact on the accuracy of CT <sup>2</sup> and on the sensible heat flux estimation in the case of strong humidity conditions (β < 1). A β > 1 was registered during the summer experiment. A relative uncertainty is estimated on the measurements, considering only the temperature with the scintillometer and following the procedure described for remote sensing [29]

$$\frac{\Delta \mathbf{ET}\_0}{\mathbf{ET}\_0} = \left(\frac{\Delta \mathbf{T}\_\mathbf{A}}{\mathbf{T}\_\mathbf{A}}\right) \mathbf{S}\_{\mathbf{T}\_\mathbf{A}}.\tag{14}$$


The following tolerances used to estimate uncertainties have been taken:

A value of 0.05 is found for the scintillometer sensitivity corresponding to sensitivity 2.4 lower than the FAO-56 sensitivity.

The main factor of uncertainty comes from the measurement of C<sup>2</sup> n. The scintillometer uncertainty is lower than the FAO-56 uncertainty.

#### 3.3. Neural network for estimating evapotranspiration

Several researchers have used artificial neural network (ANN) models to estimate or forecast evapotranspiration as a function of micro-meteorological data [30, 31]. Neural networks are an information processing technique based on a biologically-inspired programming paradigm, such as the brain enabling computer softwares to learn from observational data. The similarity with the human brain consists in the following characteristics: (i) a neural network acquires knowledge or informations through a process of learning; (ii) a neural network's knowledge is stored within inter-neuron connection strengths known as synaptic weights. In a feed-forward ANN model, a neuron performs two functions; it sums the weighted inputs from several connections and then applies a nonlinear function to the sum. The resulting value is propagated through outgoing connections to other neurons. The neurons or interconnection points are arranged in layers. The input layer receives data as inputs from real data acquisition; succeeding layers receive weighted outputs from the preceding layer as inputs, and the last layer gives the final results. ANNs are trained using a training algorithm and a training data set to adjust the connection weights, which result in an ANN model that can generate the most similar output vector to the target vector [32]. It is important to note that in most of the papers, different ANN models are considered including the generalized feedforward (GFF), linear regression (LR), multi-layer perceptron (MLP) and probabilistic neural network (PNN) [33].

with optical methods leading to the calculation of the momentum flux and the heat flux. Another study [27] calculates the relative uncertainty of the friction velocity u\* or turbulence velocity scale. The goal was to know how precisely the measurement of the friction velocity u\* can be done by using a path-averaged optical propagation. The conclusion is that the measurement of the inner scale of turbulence (λo) contributes to the largest uncertainty and must be done precisely. A recent study analyses the impact of the Bowen ratio on the flux value and uncertainty [28]. It is shown that the Bowen ratio has a large impact on the accuracy of CT

on the sensible heat flux estimation in the case of strong humidity conditions (β < 1). A β > 1 was registered during the summer experiment. A relative uncertainty is estimated on the measurements, considering only the temperature with the scintillometer and following the

> <sup>¼</sup> <sup>Δ</sup>TA TA

Quantities Unit Assumed standard deviation

Temperature �C �1�C (�20–0�C)

Wind speed m.s�<sup>1</sup> � 0.5 m/s (0–20 m/s)

Atmosphere pressure Pa � 50 Pa (300–1100 hPa)

Humidity % � 2% (0–90%)

A value of 0.05 is found for the scintillometer sensitivity corresponding to sensitivity 2.4 lower

.m�2/3 � 0.5%

Several researchers have used artificial neural network (ANN) models to estimate or forecast evapotranspiration as a function of micro-meteorological data [30, 31]. Neural networks are

The main factor of uncertainty comes from the measurement of C<sup>2</sup>

Path length m � 3 Path height m 0.2

ΔET0 ET0

The following tolerances used to estimate uncertainties have been taken:

procedure described for remote sensing [29]

38 Current Perspective to Predict Actual Evapotranspiration

than the FAO-56 sensitivity.

C2

tainty is lower than the FAO-56 uncertainty.

<sup>n</sup> <sup>K</sup><sup>2</sup>

3.3. Neural network for estimating evapotranspiration

<sup>2</sup> and

STA : ð14Þ

� 0.5�C (0–40�C) � 1�C (40–60�C)

� 3% (20–60 m/s)

� 3% (90–99%)

� 0.05% RH�C�<sup>1</sup>

Temperature dependence

n. The scintillometer uncer-

The most common neural network model is the multi-layer perceptron (MLP). The MLP and many other neural networks learn using an algorithm called backpropagation artificial neural networks (BPANN). With backpropagation, the input data are repeatedly presented to the neural network. As soon as the calculation is done, the obtained result at the final layer of the neural network is compared to the desired output, and an error is calculated. This error is then fed back (backpropagated) to the neural network input layer and used to adjust the synaptic weights such that the error decreases with each iteration. Finally, the neural model of synaptic connections converges closer and closer to the desired output. These calculations with feedbacks are known as "training."

The objective of this study was to test BPANN models for forecasting daily ETO with input data based on minimum meteorological data, considering the mean for maximum and minimum air temperatures and extraterrestrial radiation for the FAO-PM56 and scintillometry model for finally to compare them. The comparisons were based on statistical differences during a period of measurements with forecasted data by a set of measured data as input parameters and compared to data measured using FAO-PM56 or scintillometry daily ETO values as references.

Firstly, the FAO-PM56 method was used to calculate daily ET values from climatic data. The ET data were then used to train and test the ANN model. 120 h are considered corresponding to 5 days as training data. Secondly, evapotranspiration data based on the scintillometer data were used to train and test the ANNs model. The same number of days is kept as input data.

Figure 7(a) shows the plot of the predicted data as a function of the measured data for scintillometry. A shift in the plot of the predicted values for the input data acquired with the scintillometry method is seen. However, the predicted data follow the measured data variations. The slope of the fitting curve is 0.76 close to the perfect value of 1 in the case of similar values between the predicted and measured data (Figure 7c). With FAO-PM-56

Figure 7. Predicted values of ET based on two different input training data of ET one with FAO-PM56 and the other one with scintillometric data. The calculation is done with an artificial neural network (ANN).

data, the BPANN calculations show that the predicted values have no time shift but large differences in intensity (Figure 7b). (Figure 7d) presents the corresponding plot of the predicted values as a function of the measured values. The slope is 0.62 meaning that the predicted values are almost close to twice the measured values. The comparison between the two predicted values is presented in Figure 8 where the plot of the two calculations with the ANN model shows a slope of 1.5 demonstrating the big difference in the obtained values of ET. As a conclusion, the scintillometry data are better input values for the forecasting of ET.

In order to know if the difference in the final results of the predicted values done with the ANN model comes from the capacity to sufficiently have training data, the difference between the predicted and measured values as a function of the number of days of input data is calculated. Figure 9 displays the optimum values. It is observed that up to 2.5 days of forecasting, there is no difference between the two methods of evapotranspiration calculations. Nevertheless, after 2.5 days, the evapotranspiration calculation with the scintillometer shows constant values in the difference between measured and predicted scintillometric input data. This is not the case with FAO-PM56 where the difference between predicted and measured data increases. The scintillometry is more able to predict for more days than the FAO-PM56

Assessment and Prediction of Evapotranspiration Based on Scintillometry and Meteorological Datasets http://dx.doi.org/10.5772/intechopen.68538 41

Figure 8. Comparison of the two sets of forecasted values with an artificial neural network. The curves show the fitting points and the ideal case of similar values.

data, the BPANN calculations show that the predicted values have no time shift but large differences in intensity (Figure 7b). (Figure 7d) presents the corresponding plot of the predicted values as a function of the measured values. The slope is 0.62 meaning that the predicted values are almost close to twice the measured values. The comparison between the two predicted values is presented in Figure 8 where the plot of the two calculations with the ANN model shows a slope of 1.5 demonstrating the big difference in the obtained values of ET. As a conclusion, the scintillometry data are better input values for

Figure 7. Predicted values of ET based on two different input training data of ET one with FAO-PM56 and the other one

with scintillometric data. The calculation is done with an artificial neural network (ANN).

40 Current Perspective to Predict Actual Evapotranspiration

In order to know if the difference in the final results of the predicted values done with the ANN model comes from the capacity to sufficiently have training data, the difference between the predicted and measured values as a function of the number of days of input data is calculated. Figure 9 displays the optimum values. It is observed that up to 2.5 days of forecasting, there is no difference between the two methods of evapotranspiration calculations. Nevertheless, after 2.5 days, the evapotranspiration calculation with the scintillometer shows constant values in the difference between measured and predicted scintillometric input data. This is not the case with FAO-PM56 where the difference between predicted and measured data increases. The scintillometry is more able to predict for more days than the FAO-PM56

the forecasting of ET.

Figure 9. Calculation of optimal forecasted days as a function of the number of input training days in the ANN calculation for two different methods of ET measurements.

method. This result can be explained by the low propagation of small variations or errors in the calculation of ET using the scintillometer method. However, in the FAO-PM56 method with few input variables, small variations in the parameters for the calculation of ET lead to larger uncertainties.
