# Artificial Neural Networks for the Prediction of the Reference Evapotranspiration of the Peloponnese Peninsula, Greece

^{*}

## Abstract

**:**

_{2}) and altitude (Z). Nineteen Multi-layer Perceptron (MLP) and Radial Basis Function (RBF) models were tested and compared against the corresponding FAO-56 Penman Monteith (FAO PM) estimates of a previous study, via statistical indices. The MLP1 7-2 model with all the variables as inputs outperformed the rest of the models (RMSE = 0.290 mm d

^{−1}, R

^{2}= 98%). The results indicate that even ANNs with simple architecture can be very good predictive models of ETo for the Peloponnese, based on the literature standards. The MLP1 model determined Tmean, followed by u

_{2,}as the two most influential factors for ETo. Moreover, when one input was used (Tmean, Rn), RBFs slightly outperformed MLPs (RMSE < 0.385 mm d

^{−1}, R

^{2}≥ 96%), which means that even a sole-input ANN resulted in satisfactory predictions of ETo.

## 1. Introduction

^{2}= 0.978. Shamshirband et al. (2016) [73] used data from twelve meteorological stations in Serbia for optimizing an ANN with very low error levels, but an R

^{2}below 0.97. Gavili et al. (2017) [74] tested soft computing methods versus empirical ones and deduced that the former exhibited better performance in modeling ETo. Amongst these methods, the ANN had the best performance. As far as Greece is concerned, Diamantopoulou et al. (2011) [75] tested two ANNs to estimate daily ETo with limited meteorological data, separately for four meteorological stations in the Northern Greece. The best results obtained an RMSE = 0.545 mm d

^{−1}and an R

^{2}= 95.7%. Antonopoulos et al. (2016) [76] applied ANNs also in the Northern Greece (Lake Vegoritis) to predict ETo. For years 2003 and 2004, they obtained: RMSE = 0.69 mm d

^{−1}, R

^{2}= 79.2% and RMSE = 1.09 mm d

^{−1}, R

^{2}= 82.8%, respectively. Antonopoulos and Antonopoulos (2017) [77], in consecutive research in the same study area, trained ANNs with datasets from one meteorological station (Amyntaio) over the period 2009–2013 to estimate ETo. Their best results yielded an RMSE = 0.574 mm d

^{−1}and an R

^{2}around 97.2%, while the indices’ values were slightly deteriorated for lesser (i.e., three and two) inputs.

## 2. Materials and Methods

#### 2.1. The Study Area

^{2}), with a population of 1086.935 (census 2011; https://www.statistics.gr/el/statistics/-/publication/SAM03/2011 (accessed on 10 March 2022). A large part is covered by high hills and mountains, running NW to SE, with an elevation up to 2407 m. Lithology, tectonic activity and climate conditions have resulted in the relief formation of the study area. A well-developed hydrographic network, though with few large rivers, has formed [78]. Based on the latest Copernicus LU/LC classification, the widest urban area is located at the northmost edge [79]. In addition to urban areas, the main LU/LC types are forest and transitional vegetation, as well as crop plots covering the plains (Figure 1). The broadest plain lies over the western coastal part. According to Köppen-Geiger’s classification, the climate of the Peloponnese is Mediterranean warm temperate with dry summers and mild winters (Csa) [80]. The annual normal measurements (1971–2000) of air temperature, precipitation and sunshine range between 8–20 °C, 400 to over 2000 mm and 1900–3100 h, respectively (http://climatlas.hnms.gr/sdi/?lang=EN (accessed on 27 April 2022).

#### 2.2. Methods

_{2}) and altitude (Z). The first three were previously calculated as functions of the station latitude and the Julian day, as in Zanetti et al. (2008) [36]. Based on Rahimikhoob (2020) [84], the input combinations were subsequently limited, aiming to explore the possibility of producing acceptably accurate predictions of ETo with fewer variables than the available seven or even with a sole input variable (such as Tmean or Rn). About three fifths of the sample data were used for training and the other two fifths were used for testing and validation (about one fifth each) [40]. The tested architecture was based on the trial-and-error method and the ANNs were trained using the Levenberg-Marquardt algorithm [40,41]. Hyperbolic tangent (Equation (1); [85]) was the utilized activation function, based on the literature [71,86]. The hyperbolic tangent, along with the sigmoid function, is a non-linear function widely used as an activation function in ANNs [85]. The hyperbolic tangent exhibits the advantage of giving higher enhancement to the negative values. The output of the former spans in [−1, 1] while the sigmoid outputs are only half of the previous ([0, 1]) [87].

^{−}

^{1}), Normalized Root Mean Square Error (NRMSE, %), Mean Absolute Error (MAE, mm d

^{−}

^{1}), Mean Bias (MB, mm d

^{−}

^{1}) and Sum of Squares Error (SSE, mm

^{2}d

^{−}

^{1}) (Table 1). The error values depict the magnitude of the computed ETo values, except from NRMSE, which is expressed in *100%. Mean Bias is a signed measure so that, in addition to producing the Mean Bias Error (MBE = |MB|), it provides some extra information; the minus sign depicts that the reference ETo value (by FAO PM) is greater than the model predicted value and vice versa. Moreover, three measures that express correlation, strength of fit or agreement were used, namely, Pearson correlation coefficient (Pearson’s r), coefficient of determination (R

^{2}) and Index of Agreement (IoA) (Table 1).

_{i}stands for the ith predicted value by an ANN, o

_{i}stands for the ith observed value, which in this study is the ith reference value estimated by FAO PM, $\stackrel{\u203e}{o}$ is the mean of the observed (reference) values and n = 290 is the sample size.

## 3. Results

^{2}, Pearson’s r and IoA) between prediction and reference values. The architecture is simple, consisting of one hidden layer with two neurons (Figure 2).

_{2}and Tmean. The data of the aforementioned parameters are usually available either from meteorological stations or via remote sensing. Moreover, in the event of any missing data, the parameters can be easily computed [59]. It is obvious that the RBF network displays inferior performance to MLP for our data. RBF3 6-9 is the best among the RBF networks and fourth in the total rank of model performance. The relative errors of MLPs in the validation phase were between 2.2–4.2% for all trials, whereas for RBFs the relative errors lay between 2.8–10%. For the majority of the models, the holdout RE values were greater than the testing RE values, despite the satisfactory error levels (2.8–4.5%). This indicates that those models were overtrained towards the testing data.

^{−}

^{1}and R

^{2}= 96.5% with RE = 3.3%. In the case of Tmean as the sole input, the RMSE was around 0.360 mm d

^{−}

^{1}and the R

^{2}was above 96.7%. However, as previously commented, there was evidence of overtraining of some models (Table 2). Therefore, those models are not recommended. The influence of each climatic variable on ETo presented is considered important in respect of the ANN that best fits the data and bears interesting determination [14]. As shown in Figure 3, the most influential factor is Tmean followed by u

_{2}. The third factor in the rank is vapour pressure deficit (es-ea). Those results are aligned with the ETo estimates by FAO PM of the same period for the Peloponnese [63].

## 4. Discussion

^{−1}and the relative error of the testing phase was below 4%. MLPs performed generally better than RBFs for multiple inputs, whereas RBFs performed slightly better when only one input (Rn or Tmean) was set. The model that best fits the reference values was that with the most input parameters and only one hidden layer (MLP1 7-2), bearing RMSE = 0.290 mm d

^{−1}, R

^{2}= 98% and RE of testing and validation phases equal to 2.7% and 2.2%, respectively. The different runs with the same input combination, but different model architecture, showed that any increase in the number of hidden layers and the number of neurons in the hidden layer exhibited negligible improvement in prediction accuracy. Those conclusions are in line with the findings by Tabari et al. (2012) [71]. The data of the seven used inputs can be easily derived, either by meteorological stations or via remote sensing, or can be easily computed as missing data by FAO guidelines [59]. However, during the trials, the number of the inputs was gradually limited in order to examine whether ANNs can provide satisfactory estimates of ETo, when incorporating only the most commonly available climate data. It is interesting that the MLP10 with four climate parameters as inputs exhibited results very close to the best model (MLP1). Moreover, models with two basic parameters as inputs, exhibited RMSE up to 0.352 mm d

^{−1}, testing RE below 3% and R

^{2}at least equal to 97% (MLP6, MLP13). When only one input was used (i.e., Tmean or Rn) in RBF models, the RMSE was below 0.385 mm d

^{−1}, testing RE was below 3.6% and R

^{2}was at least equal to 96%. According to the literature, those values are considered very good to excellent. For example, Rahimikhoob (2010) recommended an ANN for the coastal area of the Caspian Sea in Northern Iran, which used only air temperature as an input, with an RMSE = 0.41 mm d

^{−1}and R

^{2}= 95% [84], whereas in this study MLP14 with Tmean as an input has better accuracy (RMSE = 0.360 mm d

^{−1}and R

^{2}= 96.9%). In the same vein, Zanetti et al. (2008) used MLP ANN with only temperature and radiation inputs to predict ETo for Campos dos Goytacazes, Brazil [66], while Ravindran et al. (2021) deduced that Rs was the most influential parameter to ETo and used it as a sole input in ANNs for California (R

^{2}up to 95.4%) [14]. This proves that ANNs with simple architecture can be good predictive models of ETo over the Peloponnese for the examined period. In addition, based on the best ANN model (MLP1), we found that Tmean and u

_{2}were the two most influential factors on ETo, out of the seven examined. This is in line with the findings of a previous study of the same period for the Peloponnese, where ETo had been computed by FAO PM [63]. Tmean, as a proxy of the energy state of the system, is one of the most influential factors on ETo. This depicts the altitude and land cover difference over short distances across the Peloponnese. Probably, due to the fact that the Peloponnese has a very low variance in latitude, the radiation factors were not that influential for the determination of the ETo. Regarding the second most influential factor (u

_{2}), in contrast with December (winter), increased values of u

_{2}are not frequent in Greece during August (summer). Therefore, where increased u

_{2}values occurred in August, they affected the determination of the local ETo values. In conclusion, ANNs resulted in predictions very close to FAO PM, which is the most established reference method, for the examined period for the Peloponnese. Therefore, ANNs present the potential of general usage in modeling ETo across Greece, after further investigation.

## 5. Conclusions

^{−1}, R

^{2}= 98% and RE values of testing and validation phases equal to 2.7% and 2.2%, respectively. The former proves that even simple ANN architectures can constitute very satisfactory predicting models. Models with only two parameters as inputs exhibited RMSE values up to 0.352 mm d

^{−1}and R

^{2}values at least equal to 97% (MLP6, MLP13). When one sole input was used (Tmean or Rn) in RBF models, RMSE was below 0.385 mm d

^{−1}and R

^{2}was at least equal to 96%. The results in both cases are very satisfactory. The MLP1, which outperformed the rest of the ANNs, determined the order of importance of parameters that affect ETo. The first two most influential parameters were Tmean and u

_{2}. Tmean is commonly a parameter to which ETo variances are attributed, as it depicts the overall energy state of the system. For the Peloponnese, where the variance of the latitude (and consequently of solar radiation) values is minor, Tmean variances occur mostly due to distinguished differences in relief, LU/LC types and proximity to the coast over short distances. Wind speed (u

_{2}) plays a substantial role, especially in August, when any increased u

_{2}values directly affect the ETo values, since those are not frequent in summertime. Future research could test the MLP1 performance for a larger period and across different areas of Greece that differentiate in micro-climatic conditions and regimes. Moreover, direct measurements such as pan evaporation measurements employing ANNs could be investigated on a local scale. Another interesting idea, based on the satisfactory results of this study regarding a sole input variable, would be to explore the potential of multilinear regression analysis, which is a simpler method and comprehensible by a wider interdisciplinary audience.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Meteorological stations (62) used (source: https://meteosearch.meteo.gr (accessed on 15 April 2022)).

ID | Station | X | Y | Elevation (m) | Municipality | ID | Station | X | Y | Elevation (m) | Municipality |
---|---|---|---|---|---|---|---|---|---|---|---|

Meteorological Stations for the 3 Empirical Methods (ETo) | Meteorological Stations for the 3 Empirical Methods (ETo) | ||||||||||

1 | Kalavrita | 334349.9 | 4210128 | 781 | Achaia | 32 | Oleni | 282783.4 | 4177872 | 61 | Ilia |

2 | Kato Vlassia | 317683.4 | 4208558 | 773 | Achaia | 33 | Pineia | 285425.3 | 4191240 | 184 | Ilia |

3 | Lappa | 273550 | 4218928 | 15 | Achaia | 34 | Pirgos | 273886.9 | 4171891 | 22 | Ilia |

4 | Olenia | 288845.1 | 4221654 | 34 | Achaia | 35 | Vartholomio | 253773.8 | 4193127 | 15 | Ilia |

5 | Panachaiko | 313491.4 | 4235800 | 1588 | Achaia | 36 | Zacharo | 290302.6 | 4150806 | 5 | Ilia |

6 | Panagopoula | 318709.5 | 4243842 | 15 | Achaia | 37 | Amoni Sofikou | 424227.5 | 4186898 | 55 | Korinthia |

7 | Panepistimio | 305972.3 | 4239289 | 66 | Achaia | 38 | Derveni | 362057.1 | 4221737 | 5 | Korinthia |

8 | Patra | 301697.8 | 4236694 | 6 | Achaia | 39 | Isthmos | 408645.4 | 4200499 | 6 | Korinthia |

9 | Rio | 305898.1 | 4242177 | 2 | Achaia | 40 | Kiato | 389163.5 | 4207722 | 15 | Korinthia |

10 | Romanos | 313476.1 | 4235744 | 228 | Achaia | 41 | Krioneri | 378491.9 | 4203310 | 887 | Korinthia |

11 | Sageika | 280638.4 | 4219575 | 26 | Achaia | 42 | Loutraki | 410248.7 | 4202636 | 30 | Korinthia |

12 | Argos | 386329.1 | 4165059 | 38 | Argolida | 43 | Nemea | 381197.9 | 4188976 | 290 | Korinthia |

13 | Didima | 426936.9 | 4146702 | 175 | Argolida | 44 | Perigiali | 397303.1 | 4199344 | 38 | Korinthia |

14 | Kranidi | 424615.7 | 4137411 | 110 | Argolida | 45 | Trikala Korinthias | 365493.7 | 4206835 | 1077 | Korinthia |

15 | Lagadia | 326139.9 | 4172057 | 970 | Arkadia | 46 | Agioi Theodoroi | 423533.6 | 4198395 | 37 | Korinthia |

16 | Levidi | 349386.5 | 4171330 | 853 | Arkadia | 47 | Apidia | 392819.7 | 4082655 | 230 | Lakonia |

17 | Lykochia | 337772.6 | 4151113 | 870 | Arkadia | 48 | Asteri | 386527.1 | 4076757 | 8 | Lakonia |

18 | Magouliana | 334497.7 | 4171275 | 1256 | Arkadia | 49 | Geraki | 384706.6 | 4094508 | 330 | Lakonia |

19 | Megalopoli | 335363 | 4140782 | 432 | Arkadia | 50 | Krokees | 371576.2 | 4082640 | 241 | Lakonia |

20 | Stemnitsa | 330377.8 | 4157967 | 1094 | Arkadia | 51 | Molaoi | 397984.6 | 4072957 | 128 | Lakonia |

21 | Tripoli | 359989.3 | 4152250 | 650 | Arkadia | 52 | Monemvasia | 413811.4 | 4059051 | 17 | Lakonia |

22 | Vytina | 339989.8 | 4170409 | 1013 | Arkadia | 53 | Sparti | 360929.9 | 4101670 | 204 | Lakonia |

23 | Spetses | 424919.5 | 4124662 | 3 | Attiki | 54 | Alagonia | 343840.9 | 4107863 | 765 | Messinia |

24 | Taktikoupoli Troizinias | 443373.2 | 4152374 | 15 | Attiki | 55 | Arfara | 326299.4 | 4113666 | 96 | Messinia |

25 | Ydra | 452645.8 | 4133727 | 2 | Attiki | 56 | Filiatra | 285439.9 | 4115175 | 65 | Messinia |

26 | Amaliada | 264604.9 | 4186923 | 26 | Ilia | 57 | Kalamata | 331127 | 4098974 | 5 | Messinia |

27 | Andritsaina | 314220.3 | 4152125 | 731 | Ilia | 58 | Kalamata Dytika | 329347.3 | 4100001 | 10 | Messinia |

28 | Archaia Olympia | 287981.3 | 4163856 | 45 | Ilia | 59 | Kardamili | 347857.7 | 4074651 | 13 | Messinia |

29 | Foloi | 297082.7 | 4174732 | 600 | Ilia | 60 | Kopanaki | 306288.6 | 4128741 | 184 | Messinia |

30 | Katakolo | 263537.2 | 4169327 | 2 | Ilia | 61 | Kyparissia | 291691 | 4123584 | 36 | Messinia |

31 | Lampeia | 306840.3 | 4192041 | 840 | Ilia | 62 | Pylos | 294556.8 | 4087590 | 5 | Messinia |

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**Figure 1.**Land use/land cover map of the Peloponnese (Adapted with permission from Ref. [79] 2018, © European Union).

**Figure 2.**MLP1 model with the best performance on ETo predictions for the Peloponnese (August and December of 2016–2020).

**Figure 3.**Normalized importance of the input variables of the model with the best performance (MLP1) in ETo prediction of the Peloponnese.

Performance Evaluating Indices | ||
---|---|---|

$\mathrm{RMSE}\sqrt{\raisebox{1ex}{${{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{p}}_{\mathrm{i}}-{\mathrm{o}}_{\mathrm{i}}\right)}^{2}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{n}$}\right.}$ | $\mathrm{NRMSE}=\frac{\sqrt{\raisebox{1ex}{${{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{p}}_{\mathrm{i}}-{\mathrm{o}}_{\mathrm{i}}\right)}^{2}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{n}$}\right.}}{\stackrel{\u203e}{\mathrm{o}}}$ | $\mathrm{{\rm I}}\mathrm{o}\mathrm{{\rm A}}=1-\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{p}}_{\mathrm{i}}-{\mathrm{o}}_{\mathrm{i}}\right)}^{2}}{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}(\left|{\mathrm{p}}_{\mathrm{i}}-\stackrel{\u203e}{\mathrm{o}}\right|-{\left|{\mathrm{o}}_{\mathrm{i}}-\stackrel{\u203e}{\mathrm{o}}\right|}^{2}}$ |

$\mathrm{MAE}=\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{p}}_{\mathrm{i}}-{\mathrm{o}}_{\mathrm{i}}\right|}{\mathrm{n}}$ | $\mathrm{MB}=\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{p}}_{\mathrm{i}}-{\mathrm{o}}_{\mathrm{i}}\right)}{\mathrm{n}}$ | $\mathrm{r}=\frac{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{p}}_{\mathrm{i}}-\stackrel{\u203e}{\mathrm{p}}\right)\left({\mathrm{o}}_{\mathrm{i}}-\stackrel{\u203e}{\mathrm{o}}\right)}{\sqrt{{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{p}}_{\mathrm{i}}-\stackrel{\u203e}{\mathrm{p}}\right)}^{2}{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{o}}_{\mathrm{i}}-\stackrel{\u203e}{\mathrm{o}}\right)}^{2}}}$ |

$\mathrm{SSE}={\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{p}}_{\mathrm{i}}-{\mathrm{o}}_{\mathrm{i}}\right)}^{2}$ | $\mathrm{RE}=\left|\frac{{\mathrm{p}}_{\mathrm{i}}-{\mathrm{o}}_{\mathrm{i}}}{{\mathrm{o}}_{\mathrm{i}}}\right|$ | ${\mathrm{R}}^{2}={\left(\frac{\mathrm{n}{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}}{\mathrm{o}}_{\mathrm{i}}-{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}}{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{o}}_{\mathrm{i}}}{\sqrt{\mathrm{n}{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}}{}^{2}-{\left({{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}}\right)}^{2}}\ast \sqrt{\mathrm{n}{{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{o}}_{\mathrm{i}}{}^{2}-{\left({{\displaystyle \sum}}_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{p}}_{\mathrm{i}}\right)}^{2}}}\right)}^{2}$ |

ANN | Architecture | RMSE | NRMSE | MAE | MBE | R^{2} | Pearson’s r | IoA | SSE Testing | RE Testing | RE Holdout |
---|---|---|---|---|---|---|---|---|---|---|---|

7 inputs: N, Rs, Rn, u_{2}, es-ea, Tmean, Z | |||||||||||

MLP1 | 7-2 | 0.290 | 0.086 | 0.217 | 0.017 | 0.980 | 0.990 | 0.995 | 0.695 | 0.027 | 0.022 |

MLP2 | 7-4-3 | 0.305 | 0.090 | 0.230 | 0.024 | 0.978 | 0.989 | 0.994 | 0.573 | 0.021 | 0.029 |

RBF1 | 7-5 | 0.423 | 0.125 | 0.267 | 0.004 | 0.957 | 0.978 | 0.989 | 0.948 | 0.027 | 0.100 |

RBF2 | 7-9 | 0.333 | 0.098 | 0.246 | −0.032 | 0.974 | 0.987 | 0.993 | 1.547 | 0.045 | 0.028 |

6 inputs: Rs, Rn, u2, es-ea, Tmean, Z | |||||||||||

MLP8 | 6-4 | 0.311 | 0.092 | 0.240 | 0.005 | 0.977 | 0.988 | 0.994 | 0.827 | 0.024 | 0.025 |

MLP9 | 6-4-3 | 0.296 | 0.088 | 0.218 | −0.008 | 0.979 | 0.989 | 0.995 | 1.188 | 0.035 | 0.024 |

RBF3 | 6-9 | 0.318 | 0.094 | 0.232 | 0.016 | 0.976 | 0.988 | 0.994 | 0.623 | 0.026 | 0.022 |

4 inputs: Rs, u_{2}, es-ea, Tmean and 4’ inputs: Rn, u2, es-ea, Tmean | |||||||||||

MLP7 | 4-3 | 0.309 | 0.091 | 0.233 | −0.002 | 0.977 | 0.989 | 0.994 | 0.543 | 0.020 | 0.027 |

MLP10 | 4-3-2 | 0.300 | 0.089 | 0.221 | 0.001 | 0.978 | 0.989 | 0.995 | 0.541 | 0.020 | 0.028 |

RBF4 | 4-10 | 0.406 | 0.120 | 0.263 | −0.042 | 0.961 | 0.980 | 0.990 | 1.044 | 0.031 | 0.092 |

MLP3 | 4’-1 | 0.319 | 0.094 | 0.245 | −0.025 | 0.976 | 0.988 | 0.994 | 0.459 | 0.160 | 0.300 |

3 inputs: Rn, u_{2}, Tmean | |||||||||||

MLP5 | 3-1 | 0.314 | 0.093 | 0.244 | −0.019 | 0.976 | 0.988 | 0.994 | 1.101 | 0.032 | 0.030 |

2 inputs: Rn, Tmean; 2’ inputs: Rn, u2; 2’’ inputs: u2, Tmean | |||||||||||

MLP4 | 2-1 | 0.377 | 0.111 | 0.268 | −0.023 | 0.966 | 0.983 | 0.991 | 1.443 | 0.042 | 0.034 |

MLP6 | 2’-1 | 0.343 | 0.101 | 0.268 | 0.026 | 0.972 | 0.986 | 0.093 | 0.961 | 0.037 | 0.028 |

MLP13 | 2’’-1 | 0.352 | 0.104 | 0.267 | −0.008 | 0.970 | 0.985 | 0.992 | 0.819 | 0.029 | 0.029 |

1 input: Tmean; 1’ input: Rn | |||||||||||

MLP14 | 1-1 | 0.360 | 0.106 | 0.258 | 0.014 | 0.969 | 0.984 | 0.992 | 0.747 | 0.027 | 0.041 |

MLP16 | 1’-1 | 0.404 | 0.119 | 0.313 | −0.014 | 0.961 | 0.980 | 0.990 | 0.594 | 0.030 | 0.042 |

RBF6 | 1-1 | 0.363 | 0.107 | 0.259 | 0.006 | 0.968 | 0.984 | 0.992 | 0.710 | 0.028 | 0.033 |

RBF9 | 1’-1 | 0.383 | 0.113 | 0.298 | −0.005 | 0.965 | 0.982 | 0.991 | 1.109 | 0.036 | 0.033 |

^{−}

^{1}and SSE in mm

^{2}d

^{−}

^{1}.

Predictor | Predicted | |||
---|---|---|---|---|

Hidden Layer 1 | Output Layer | |||

H (1:1) | H (1:2) | ETο | ||

Input Layer | (Bias) | −0.616 | −0.638 | |

Rs | −0.010 | −0.355 | ||

Rn | 0.397 | 0.173 | ||

es-ea | 0.224 | −0.181 | ||

u_{2} | 0.214 | −0.049 | ||

N | −0.100 | −0.520 | ||

Tmean | 0.461 | −0.394 | ||

Z | 0.059 | −0.040 | ||

Hidden Layer 1 | (Bias) | −0.009 | ||

H (1:1) | 0.578 | |||

H (1:2) | −0.867 |

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**MDPI and ACS Style**

Dimitriadou, S.; Nikolakopoulos, K.G.
Artificial Neural Networks for the Prediction of the Reference Evapotranspiration of the Peloponnese Peninsula, Greece. *Water* **2022**, *14*, 2027.
https://doi.org/10.3390/w14132027

**AMA Style**

Dimitriadou S, Nikolakopoulos KG.
Artificial Neural Networks for the Prediction of the Reference Evapotranspiration of the Peloponnese Peninsula, Greece. *Water*. 2022; 14(13):2027.
https://doi.org/10.3390/w14132027

**Chicago/Turabian Style**

Dimitriadou, Stavroula, and Konstantinos G. Nikolakopoulos.
2022. "Artificial Neural Networks for the Prediction of the Reference Evapotranspiration of the Peloponnese Peninsula, Greece" *Water* 14, no. 13: 2027.
https://doi.org/10.3390/w14132027