6.3 FAO-56 PM-based ANN models

AER Location ANN

Advanced Evapotranspiration Methods and Applications

; R<sup>2</sup> and Rratio = dimensionless.

; R<sup>2</sup> and Rratio = dimensionless.

Performance of ANN and MLR based ETo models during testing.

AER Location MLR ANN

Performance of ANN based ETo models during training.

RMSE = mm day<sup>1</sup>

RMSE = mm day<sup>1</sup>

Table 4.

38

Table 3.

Semi-arid Parbhani 0.141 0.991 0.997

Arid Anantapur 0.363 0.972 0.986

Sub-humid Raipur 0.255 0.981 0.982

Humid Palampur 0.177 0.988 0.999

Semi-arid Parbhani 0.308 0.963 1.002 0.115 0.995 0.994

Arid Anantapur 0.275 0.977 1.000 0.222 0.984 0.998

Sub-humid Raipur 0.420 0.943 1.002 0.296 0.972 1.005

Humid Palampur 0.313 0.952 1.003 0.228 0.979 1.031

Solapur 0.313 0.959 1.003 0.228 0.979 0.988 Bangalore 0.159 0.980 1.000 0.201 0.968 0.994 Kovilpatti 0.233 0.977 0.999 0.200 0.984 1.004 Udaipur 0.295 0.975 1.001 0.119 0.996 0.992

Hissar 0.434 0.951 0.999 0.280 0.980 1.000

Faizabad 0.357 0.957 1.002 0.286 0.973 1.011 Ludhiana 0.348 0.971 0.999 0.279 0.981 1.000 Ranichauri 0.265 0.961 0.999 0.137 0.989 1.005

Jorhat 0.151 0.978 1.000 0.137 0.985 1.019 Mohanpur 0.170 0.983 1.001 0.123 0.991 1.007 Dapoli 0.177 0.973 1.001 0.152 0.981 1.009

Solapur 0.271 0.969 1.000 Bangalore 0.296 0.972 1.005 Kovilpatti 0.254 0.991 1.000 Udaipur 0.391 0.952 1.003

Hissar 0.052 0.999 1.000

Faizabad 0.060 0.999 1.001 Ludhiana 0.289 0.977 0.999 Ranichauri 0.909 0.411 1.004

Jorhat 0.615 0.943 1.001 Mohanpur 0.377 0.904 1.002 Dapoli 0.150 0.990 1.000

RMSE R<sup>2</sup> Rratio RMSE R2 Rratio

RMSE R<sup>2</sup> Rratio

ETo process is a function of various climatic factors (Tmax, Tmin, RHmax, RHmin, WS, and Sra). Therefore, it is pertinent to take into account the combined influence of all the climatic parameters on ETo estimation. The ANN models corresponding to

Figure 7.

Scatter plots of ANN models estimated ETo with respect to FAO-56 PM ETo for 15 climatic locations in India.

the FAO-56 PM were developed considering Tmax, Tmin, RHmax, RHmin, Ws, and Sra as input and the FAO-56 PM ETo as target. Table 4 shows the performance statistics of ANN and MLR models for 15 locations during testing. Comparison of results obtained using MLR and ANN models indicated that the ANN models performed better than the MLR models for all locations except for Bangalore. This is confirmed from the low values of RMSE (mm day<sup>1</sup> ) and high values of R<sup>2</sup> for ANN models as compared to the MLR models.

The Rratio values of MLR models for 15 locations are nearly approaching one, which simply indicates that on an average these models neither over- nor underestimated ETo. However, high values of RMSE and R<sup>2</sup> indicate that on a daily basis, these models over- and under-estimated ETo values. Though the performance of ANN models was good as compared to MLR models, in some locations these models over- or under-estimated the ETo values. The ANN models overestimated (Rratio > 1) ETo values at Palampur. The over- and under-estimations by all ANN models for the above locations were less than 3% which is negligible. The overall performance of all the models was represented as ANN > MLR for most of the locations except for Bangalore where, the performance of models was represented as MLR > ANN. The results suggest that the non-linearity of ETo process can be adequately modeled

Nonlinear Evapotranspiration Modeling Using Artificial Neural Networks

DOI: http://dx.doi.org/10.5772/intechopen.81369

The scatter plots of the FAO-56 PM ETo and ETo estimated with the ANN models for 15 climatic locations in India are shown in Figure 7. The scatter plots confirm the statistics given in Table 4. Regression analysis was performed between the FAO-56 PM ETo and ETo estimated with the ANN and the best-fit lines are shown in Figure 7. The values of R<sup>2</sup> for ANN models were found to be >0.968. The fit line equations (y = a0x + a1) in Figure 7 gave the values of a0 and a1 coefficients closer to one and zero, respectively. Due to the superior performance of ANN models over the MLR models, the time series plots of these models with 1 year data (during testing) for four selected locations Parbhani, Hissar, Faizabad, and Dapoli are shown in Figure 8. The location figures indicated that, ETo estimated using ANN models matched well with the FAO-56 PM ETo except for a few peak values in

Evapotranspiration is an important and one of the most difficult components of the hydrologic cycle to quantify accurately. Prior to designing any irrigation system, the information on crop water requirements or crop evapotranspiration is needed, which can be calculated using reference evapotranspiration. There exist direct measurement methods (lysimeters) and indirect estimation procedures (physical and empirical based) for modeling ETo. Direct methods have the limitations of arduous, cost-effective, and lack of skilled manpower to collect accurate measurements. The difficulty in estimating ETo with the indirect physically based methods is due to the limitations of unavailability of all necessary climate data, whereas the application of empirical methods are limited due to unsuitability of these methods for all climatic conditions and need of local calibration. ANNs are efficient in modeling complex processes without formulating any mathematical relationships related to the physical process. This study was undertaken to develop ANN models corresponding to FAO-56 PM conventional ETo method for 15 individual stations

The potential of ANN models corresponding to the FAO-56 PM method was evaluated for 15 locations. The ANN models were developed considering six inputs (Tmax, Tmin, RHmax, RHmin, Ws, and Sra) and the FAO-56 PM ETo as target. The optimum number of hidden neurons was finalized with a trial of 1–15 hidden nodes. The ANN models gave lower RMSE values at i +1(i = number of inputs) hidden nodes for estimating ETo. Comparison results of MLR and ANN models indicated that the ANN models performed better for all locations. However, on an average the over- and under-estimations of ETo (<3% which is negligible) estimated by using MLR models was less as compared to ANN models. In brief, based on the above discussion on ETo modeling, the following specific conclusions are drawn:

using ANN models.

case of Faizabad.

in India.

41

7. Summary and conclusions

Figure 8. Time series plots of ANN and FAO-56 PM ETo for (a) Parbhani, (b) Hissar, (c) Faizabad, and (d) Dapoli locations.

Nonlinear Evapotranspiration Modeling Using Artificial Neural Networks DOI: http://dx.doi.org/10.5772/intechopen.81369

The Rratio values of MLR models for 15 locations are nearly approaching one, which simply indicates that on an average these models neither over- nor underestimated ETo. However, high values of RMSE and R<sup>2</sup> indicate that on a daily basis, these models over- and under-estimated ETo values. Though the performance of ANN models was good as compared to MLR models, in some locations these models over- or under-estimated the ETo values. The ANN models overestimated (Rratio > 1) ETo values at Palampur. The over- and under-estimations by all ANN models for the above locations were less than 3% which is negligible. The overall performance of all the models was represented as ANN > MLR for most of the locations except for Bangalore where, the performance of models was represented as MLR > ANN. The results suggest that the non-linearity of ETo process can be adequately modeled using ANN models.

The scatter plots of the FAO-56 PM ETo and ETo estimated with the ANN models for 15 climatic locations in India are shown in Figure 7. The scatter plots confirm the statistics given in Table 4. Regression analysis was performed between the FAO-56 PM ETo and ETo estimated with the ANN and the best-fit lines are shown in Figure 7. The values of R<sup>2</sup> for ANN models were found to be >0.968. The fit line equations (y = a0x + a1) in Figure 7 gave the values of a0 and a1 coefficients closer to one and zero, respectively. Due to the superior performance of ANN models over the MLR models, the time series plots of these models with 1 year data (during testing) for four selected locations Parbhani, Hissar, Faizabad, and Dapoli are shown in Figure 8. The location figures indicated that, ETo estimated using ANN models matched well with the FAO-56 PM ETo except for a few peak values in case of Faizabad.
