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Keywords:

  • neural networks;
  • neuro-fuzzy;
  • geographical inputs;
  • periodicity component

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results and discussions
  6. 4. Conclusions
  7. References

Air temperature as a major climatic component is important in land evaluation, water resources planning and management, irrigation scheduling and agro-hydrologic planning. In this paper, the capabilities of Adaptive Neuro-Fuzzy Inference System (ANFIS) and Artificial Neural Networks (ANNs) were evaluated in predicting long-term monthly air temperature values at 30 weather stations of Iran. Monthly data of 20 weather stations were used for training and 10 stations' data were used for testing. Consequently, the periodicity component, station latitude, longitude and altitude values were introduced as input variable to predict the long-term monthly temperature values. The estimates of the ANFIS and ANN models were compared with each other with respect to root mean-squared error, mean absolute error and determination coefficient statistics. The ANN models generally performed better than the ANFIS model in the test period. For the ANN model, the maximum and minimum determination coefficient values were found to be 0.995 and 0.921 in Semnan and Bandar-e-Abbas meteorological stations, respectively. The maximum and minimum determination coefficient values were found as 0.999 and 0.876 for the ANFIS model in Shiraz and Bandar-e-Abbas stations. Copyright © 2013 Royal Meteorological Society

1. Introduction

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results and discussions
  6. 4. Conclusions
  7. References

Prediction of air temperature is of primary importance for land evaluating and characterizing systems as well as hydrological and ecological models (Benavides et al., 2007). In such models, air temperature is applied as input parameter to derive other processes such as evapotranspiration, soil decomposition and plant productivity (Dodson and Marks, 1997). Accurate forecasting of this parameter is also needed for determining the site suitability for agricultural and forest crops, predicting of the soil surface temperature and avoiding the hazardous influences of temperature variations (Hudson and Wackernagel, 1994; George, 2001; Ustaoglu et al., 2008).

In recent years, global warming has considerably attracted attentions of scientists. Global warming is related with an average increase in the Earth surface temperature and lower atmosphere, which in turn causes climate changes. Increasing Earth surface temperature may lead to changes in rainfall patterns, a rise in sea level, and a wide range of impacts on plants, wildlife and humans. For this reason, the importance of temperature predictions has been increased all over the World (Bilgili and Sahin, 2010).

So far, a number of attempts have been carried out to model air temperature variations (Kiraly and Janosi, 2002; Bartos and Janosi, 2006; Gyure et al., 2007; Guan et al., 2009), which have emphasized the need to accurate estimation of air temperature in various aspects of meteorology, hydrology and agro-hydrology. Therefore, there are essential needs to better models with high accuracies to address the nonlinearity in air temperature variation process.

In the recent past, Artificial Intelligence (AI) approaches [e.g. Artificial Neural Networks (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), etc] have been successfully used in a wide range of scientific applications including water resources engineering, agro-hydrology and agro-meteorology. The complete review of such applications is beyond the scope of this paper and only some relevant literature will be discussed here.

Tatli and Sen (1999) introduced a fuzzy modelling approach for predicting air temperature. Abdel-Aal (2004) applied abductive neural network approach to forecast hourly air temperature. Smith et al. (2005) developed an enhanced ANN for air temperature prediction by including information on seasonality and modifying parameters of an existing ANN model. Shank et al., (2008) applied neural networks for predicting dew-point temperature. Partal and Kisi (2007) introduced a new wavelet-neuro-fuzzy conjunction model for precipitation forecasting. Bilgili and Sahin (2010) used ANN for predicting long-term monthly temperature and rainfall in Turkey. Kisi and Shiri (2011) introduced new hybrid wavelet-AI models for precipitation forecasting. Shiri et al. (2011) applied ANFIS for estimating daily pan evaporation values from weather data in at station as well as cross station scales. Kisi et al. (2012) introduced a generalized ANFIS model of daily pan evaporation estimation using weather data.

In this study, the applicability of ANFIS and ANN models were investigated for predicting long-term monthly air temperature using the geographical input data. The data from 30 weather stations in Iran were used for training and testing of the ANFIS and ANN models.

2. Materials and methods

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results and discussions
  6. 4. Conclusions
  7. References

2.1. Study area and data analysis

In this study data from 30 weather stations in Iran were used. Figure 1 represents an illustrative map of the studied weather stations. Also the corresponding geographical positions of the stations are given in Table 1. Figure 2 displays the long-term average air temperature values. These values have been obtained through the averaging of air temperature in the whole studied weather stations. A linear variation of temperature between the minimum and maximum temperature values was assumed for calculating average air temperature. Data cover the long-term averaged temperatures between the periods of 1986–2000. It is clear from Figure 2 that a dramatic variation in the long-term monthly temperature in Iran occurs during a year. The long-term monthly temperature ranges from as low as −2.91 °C in January (Zanjan station) to as high as 38.21 °C in July (Ahwaz station).

image

Figure 1. The location of study area.

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Table 1. Summary of the geographical information of the studied weather stations
Station codeStation nameLatitude (°N)Longitude (°W)Altitude (m)T(°C)a
  1. a

    T(°C), average air temperature during the study period.

1Tabriz38.0546.17136112.40
2Urmia37.3245.05131611.00
3Ardabil38.1548.1713328.71
4Zanjan36.4148.29166310.62
5Sanandaj35.247137313.84
6Rasht37.1249.3936.715.80
7Sari36.33532317.35
8Gorgan36.5154.1613.317.21
9Tehran35.4151.19119117.77
10Qazvin36.1550.03127913.47
11Hamadan34.5248.32174211.66
12Qom34.4250.5187718.07
13Arak34.0649.46170813.54
14Kermanshah34.2147.09131914.93
15Ilam33.3846.26133717.11
16Khorramabad33.2648.17114816.27
17Ahwaz31.248.422.525.74
18Shahrekord32.1750.51204911.80
19Yasuj30.551.41183215.01
20Isfahan32.3751.4155016.59
21Semnan35.3553.33113117.95
22Bojnurd37.2857.19109113.00
23Mashhad36.1659.3899914.55
24Birjand32.5259.12149116.34
25Zahedan29.2860.53137018.94
26Kerman30.1556.58175416.5
27Yazd31.5454.17123719.48
28Shiraz29.3252.36148418.44
29Bandar-e-Abbas27.1356.229.826.63
30Bushehr28.5950.519.624.84
image

Figure 2. Averaged long-term air temperature values in the studied weather stations.

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2.2. Artificial neural networks

An ANN has one or more hidden layers, whose computation nodes are correspondingly called hidden neurons of hidden units. The hidden neurons intervene between the external input and the output in some useful manner. The network is enabled to extract higher order statistics by adding one or more hidden layers. In a rather loose sense, despite its local connectivity due to the extra set of synaptic connections and the extra dimension of network interconnections, the ANN acquires a global perspective.

The ANN was trained using Levenberg–Marquardt (LM) technique here due to that this technique is more powerful and faster than the conventional gradient descent technique (Hagan and Menhaj, 1994; Kisi, 2007). The back propagation with gradient descent technique is a steepest descent algorithm, while the LM algorithm is an approximation to Newton's method (Marquardt, 1963). If we want to minimize a function V(x) with respect to the parameter vector x, then Newton's method would be

  • display math(1)

where inline image, is the Hessian matrix and inline image, the gradient. Let us assume that V(x) is a sum of square functions

  • display math(2)

then it can be shown that

  • display math(3)
  • display math(4)

where J(x) is the Jacobean matrix and

  • display math(5)

For the Gauss–Newton method, it is assumed that S(x) ≈ 0, and the update of Equation (1) becomes

  • display math(6)

The LM modification to the Gauss–Newton method is

  • display math(7)

The parameter μ is multiplied by some factor (β) when a step increases V(x). When a step would result in a reduced V(x), μ is divided by β. When μ is large the algorithm becomes steepest descent (with step 1/μ), while the algorithm becomes Gauss–Newton for small μ. The LM algorithm can be considered a trust-region modification to Gauss–Newton. The computation of the Jacobean matrix is the key step in this algorithm. The terms in the Jacobean matrix can be computed by a simple modification to the back propagation algorithm for the neural network-mapping problem (Hagan and Menhaj, 1994).

2.3. Adaptive neuro-fuzzy inference system

An ANFIS is a combination of an adaptive ANN and a fuzzy inference system (FIS). The parameters of the FIS are determined by the neural network learning algorithms. Since this system is based on the FIS, reflecting amazing knowledge, an important aspect is that the system should be always interpretable in terms of fuzzy IF-THEN rules. ANFIS is capable of approximating any real continuous function on a compact set of parameters to any degree of accuracy (Jang et al., 1997). ANFIS identifies a set of parameters through a hybrid learning rule combining back propagation gradient descent error digestion and a least-squared error method. There are mainly two approaches for fuzzy inference systems, namely the approaches of Mamdani (Mamdani and Assilian, 1975) and Sugeno (Takagi and Sugeno, 1985). The differences between the two approaches arise from the consequent part where Mamdani's approach uses fuzzy membership functions, while linear or constant functions are used in Sugeno's approach. The neuro-fuzzy model used in this study implements the Sugeno's fuzzy approach with geographical information of each station as input variables and air temperature values as output variable.

As a simple example an FIS with two inputs x and y and one output z is assumed. Here, x and y may be considered as latitude (ϕ) and longitude (λ) where as the output z represents the air temperature (TA). Suppose that the rule base contains two fuzzy IF-THEN rules:

  • display math(8)
  • display math(9)

The IF (antecedent) part is fuzzy in nature, while the THEN (consequent) part is a crisp function of an antecedent variable (as a rule, a linear equation). The study presented here for ground water table, for the above example Equations (8) and (9) can be written as:

  • display math(10)
  • display math(11)

where pi, qi and ri are parameters with i = 1, 2, 3, …, n corresponding to Rule 1, Rule 2, Rule 3, …, Rule n. In a Type 3 Sugeno fuzzy model, the output of each rule is a linear combination of input variables plus a constant term and the final output z is the weighted average of each rule output. More information about ANFIS theory can be found in the study of Jang (1993) and Jang et al., (1997). As mentioned in previous section, for a given input–output dataset (similar to predicting air temperature or precipitation using chronological or geographical data), various Sugeno models may be developed by using different identification methods (i.e. grid partitioning and subtractive clustering), but the commonly used grid partitioning identification method was used in this study. The grid partitioning identification method proposes independent partitions of each antecedent variable through defining the membership functions of all antecedent variables.

2.4. Performance evaluation parameters

Three statistical evaluation criteria were used to assess the models' performances: the Correlation Coefficient (R2):

  • display math(12)

Since the Pearson correlation coefficient (R) term and the coefficient of determination (R2) provide information for linear dependence between observations and corresponding simulations, they should not be alone applied as performance indicators (Legates and McCabe, 1999). Therefore, other statistical measures such as MAE (which is a linear scouring rule and describes only the average magnitude of the errors, ignoring their direction) and RMSE (which describes the average magnitude of the errors by giving more weight on large errors) should be applied to evaluate the models' performance. The mentioned scours can be defined as:

Root mean-squared error (RMSE):

  • display math(13)

Mean absolute error (MAE):

  • display math(14)

where, xi and yi denote the observed and corresponding simulated values at the ith time step, respectively and n is the number of time steps. Also inline image and inline image represent the mean values of observed and simulated values, respectively.

3. Results and discussions

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results and discussions
  6. 4. Conclusions
  7. References

This paper aims at estimating monthly averaged temperature and precipitation values at 30 weather stations in Iran by using ANFIS and ANN techniques. In this way, the number of the months, station latitude, longitude and altitude values were used as input parameters to the ANN and ANFIS for estimating long-term temperatures. Monthly data of 20 weather stations (20 stations × 12 months = 240 data) were used for training and 10 stations' data (10 stations × 12 months = 120 data) were used for testing. The stations were randomly selected for training and testing periods. The stations used for the testing procedure are Bandar-e-Abbas, Birjand, Bojnurd, Bushehr, Kerman, Mashhad, Semnan, Shiraz, Yazd and Zahedan. Before applying the ANN models to the data, training input and output values were normalized using the following equation

  • display math(15)

where xmin and xmax are the minimum and maximum of the training dataset. In this study, a and b were taken as 0.6 and 0.2. The training data were normalized into range [0.2, 0.8] following the suggestion of Cigizoglu (2003). Cigizoglu (2003) showed that scaling input data between 0.2 and 0.8 gives the ANNs the flexibility to predict beyond the training range. LM algorithm was used for calculating the ANN weights in this study because this technique is more powerful and faster than the conventional gradient descent technique (Hagan and Menhaj, 1994; Kisi, 2007). A difficult task with ANN involves choosing the hidden nodes' number. Here, the ANN with one hidden layer was used and the hidden nodes' number was determined using trial and error method. The tangent sigmoid activation function was used for the hidden and output nodes. The ANN network training was stopped after 100 epochs since the variation of error was too small after this epoch. For the ANFIS model, Gaussian membership functions and 200 iterations were used. In implementation of fuzzy logic, several types of membership functions (MFs) can be used. However, recent studies have shown that, the type of MF does not affect the results fundamentally (Vernieuwe et al., 2005). Different numbers of membership functions were tested and the best one that gave the minimum mean square errors (MSE) was selected, which was 3 MFs for each variable.

ANN and ANFIS model is compared for the training stations in Table 2. The ANN model has the lowest RMSE (0.68 °C) and MAE (0.54 °C) for the Rasht station. The worst ANN estimates belong to the Ardabil station with the RMSE of 2.72 °C and MAE of 2.35 °C. In the case of ANFIS, the best and worst models were obtained for the Yasuj (RMSE = 0.29 °C, MAE = 0.25 °C) and Tabriz (RMSE = 2.19 °C, MAE = 1.91 °C) stations. It can be obviously seen from Table 2 that the ANFIS model (RMSE ranges 0.29–2.19) are better than the ANN (RMSE ranges 0.68–2.72) in training period.

Table 2. Summary of the training process of ANN and ANFIS models
StationANN modelsANFIS models
RMSE (°C)MAE (°C)R2RMSE (°C)MAE (°C)R2
Ahwaz1.931.660.9690.410.340.999
Arak1.090.910.9940.660.530.996
Ardabil2.722.350.9681.611.330.984
Qazvin0.930.720.9920.390.290.998
Qom1.020.810.9900.770.640.999
Gorgan0.800.690.9930.620.460.996
Hamadan1.331.150.9911.020.710.994
Ilam1.701.420.9900.790.520.998
Isfahan1.211.040.9890.560.460.999
Kermanshah1.180.950.9870.480.340.997
Khorramabad2.221.860.9780.530.420.997
Rasht0.680.540.9910.470.360.998
Sanandaj1.020.910.9890.740.570.996
Sari0.690.590.9920.710.580.996
Shahrekord0.900.760.9920.720.560.995
Tabriz2.602.360.9892.191.910.995
Tehran2.402.300.9950.700.460.997
Urmia1.250.920.9871.591.480.996
Yasuj1.331.100.9860.290.250.999
Zanjan1.270.950.9891.080.750.990

Testing results of the ANN and ANFIS model for each station are given in Table 3. It is clear from the table that the RMSE values range from 0.1.53 to 4.20 °C differ from the observed value for the ANN model, while the RMSE values range from 0.1.18 to 9.25 °C differ from the observed. For the ANN model, the maximum RMSE (4.20 °C) and MAE (3.79 °C) values were found for the Zahedan station. For the ANFIS model, however, the maximum RMSE and MAE values were found to be 9.25 and 7.91 °C in the Bandar-e-Abbas station. However, the best ANN (RMSE = 1.53 °C, MAE = 1.27 °C) and ANFIS (RMSE = 1.18 C° MAE = 0.82 °C) results were found for the Yazd station. It is clearly seen from Table 3 that the performance values of the ANN model are generally better than the performance values of the ANFIS model in long-term monthly temperature prediction. In seven of ten stations, the ANN model performs better than the ANFIS model. The maximum R2 values between the observed and predicted values for the ANN and ANFIS models were found to be 0.995 and 0.999 in Semnan and Shiraz meteorological stations, respectively. However, the minimum R2 values were respectively found as 0.921 and 0.876 for the ANN and ANFIS models in Bandar-e-Abbas station. Both ANN and ANFIS models give poor estimates for the coastal stations (Bandar-e-Abbas and Bushehr). The reason behind this may be the fact that most of the training data composed of inland stations. The training data samples may be not enough for learning the coastal stations.

Table 3. Summary of the testing process of ANN and ANFIS models
StationANN modelsANFIS models
RMSE (°C)MAE (°C)R2RMSE (°C)MAE (°C)R2
Bandar-e-Abbas3.663.360.9219.257.910.876
Birjand2.622.330.9921.941.520.969
Bojnurd1.581.290.9844.273.550.920
Bushehr3.633.300.9387.176.140.949
Kerman2.192.020.9852.702.010.994
Mashhad2.051.830.9854.673.680.868
Semnan1.951.790.9951.991.700.980
Shiraz2.261.990.9691.961.760.999
Yazd1.531.270.9821.180.820.993
Zahedan4.203.790.9657.386.390.948

The test results of the ANN and ANFIS models are compared in Figures 3-12. It can be obviously seen from the figures that the ANN predictions are generally closer to the corresponding temperatures than those of the ANFIS model. ANFIS seems to perform better than the ANN for the Semnan, Birjand, Kerman and Yazd stations. Both ANN and ANFIS models overestimate the observed monthly temperatures of the Bandar-e-Abbas, Birjand, Bushehr, Kerman, Shiraz and Zahedan. For the Bojnurd, Mashhad and Yazd stations, the ANN model generally overestimates while the ANFIS model underestimates. For the Semnan, however, the ANN model underestimates while the ANFIS overestimates the observed temperatures.

image

Figure 3. Observed versus predicted air temperature values in Semnan weather station.

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Figure 4. Observed versus predicted air temperature values in Bojnurd weather station.

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image

Figure 5. Observed versus predicted air temperature values in Mashhad weather station.

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Figure 6. Observed versus predicted air temperature values in Birjand weather station.

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image

Figure 7. Observed versus predicted air temperature values in Zahedan weather station.

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image

Figure 8. Observed versus predicted air temperature values in Kerman weather station.

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image

Figure 9. Observed versus predicted air temperature values in Yazd weather station.

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image

Figure 10. Observed versus predicted air temperature values in Shiraz weather station.

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Figure 11. Observed versus predicted air temperature values in Bandar-e-Abbas weather station.

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Figure 12. Observed versus predicted air temperature values in Bushehr weather station.

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4. Conclusions

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results and discussions
  6. 4. Conclusions
  7. References

The knowledge of air temperature values is of great importance for irrigation scheduling and hydrological management as well as for soil- and plant-related studies and agro-hydrologic fields. In this article, the abilities of ANFIS and ANN models were investigated to predict air temperature and precipitation values using the geographical input data. The data from 30 weather stations in Iran were used for training and testing of the introduced models. The ANFIS and ANN models were compared with each other with respect to root mean-squared error, mean absolute error and determination coefficient statistics. ANFIS model was found to be better than the ANN in the training period. In the test period, however, the ANN model performed better than the ANFIS model in seven of ten stations. For the ANN and ANFIS models, the maximum determination coefficient values were found to be 0.995 and 0.999 in Semnan and Shiraz meteorological stations, respectively. The minimum determination coefficient values were respectively found as 0.921 and 0.876 for the ANN and ANFIS models in Bandar Abbas station. As a conclusion, it can be said that the ANN technique can be successfully used to predict the long-term monthly temperatures of any site at a location with no measurement based on the temperature data and geographical variables of the neighbour stations.

This study applied ANN and ANFIS techniques for modelling long-term air temperature values by using geographical information. Further investigations may be carried out with other techniques and data management scenarios for generalization of the obtained results. Nevertheless, the techniques applicability may be examined for other important climatologic variables (e.g. rainfall, snow, avalanches, etc).

References

  1. Top of page
  2. ABSTRACT
  3. 1. Introduction
  4. 2. Materials and methods
  5. 3. Results and discussions
  6. 4. Conclusions
  7. References
  • Abdel-Aal RE. 2004. Hourly temperature forecasting using abductive networks. Engineering Applications of Artificial Intelligences 17: 543556.
  • Bartos I, Janosi IM. 2006. Nonlinear correlations of daily temperature records over land. Nonlinear Processes in Geophysics 13: 571576.
  • Benavides R, Montes F, Rubio A, Osoro K. 2007. Geo-statistical modeling of air temperature in a mountainous region of Northern Spain. Agricultural and Forest Meteorology 146: 173188.
  • Bilgili M, Sahin B. 2010. Prediction of long-term monthly temperature and rainfall in Turkey. Energy Sources, Part A. 32: 6071.
  • Cigizoglu HK. 2003. Estimation, forecasting and extrapolation of flow data by artificial neural networks. Hydrological Sciences Journal 48(3): 349361.
  • Dodson R, Marks D. 1997. Daily air temperature interpolated at high spatial resolution over a large mountainous region. Climatic Research 8: 120.
  • George RK. 2001. Prediction of soil temperature by using artificial neural networks algorithms. Nonlinear Analysis 47(3): 17371748.
  • Guan BT, Hsu HW, Wey TH, Tsao LS. 2009. Modeling monthly mean temperatures for the mountain regions of Taiwan by generalized additive models. Agricultural and Forest Meteorology 149: 281290. DOI: 10.1016/2008.08.10
  • Gyure B, Bartos I, Janosi IM. 2007. Nonlinear statistics of daily temperature fluctuations reproduced in a laboratory experiment. Physical Review E 76: 037301.
  • Hagan MT, Menhaj MB. 1994. Training feed forward networks with the Marquaradt algorithm. IEEE Transactions on Neural Networks 6: 861867.
  • Haykin S. 1998. Neural Networks - A Comprehensive Foundation, 2 edn. Prentice-Hall: Upper Saddle River; 2632.
  • Hudson G, Wackernagel H. 1994. Mapping temperature using kriging with external drift: theory and example from Scotland. International Journal of Climatology 14: 7791.
  • Jang JSR. 1993. ANFIS: adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics 23(3): 665685.
  • Jang JSR, Sun CT, Mizutani E. 1997. Neurofuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence. Prentice-Hall: New Jersey.
  • Kiraly A, Janosi IM. 2002. Stochastic modeling of daily temperature fluctuations. Physical Review E 65: 051102.
  • Kisi O. 2007. Streamflow forecasting using different artificial neural network algorithms. ASCE Journal of Hydrologic Engineering 12(5): 532539.
  • Kisi O, Shiri J. 2011. Precipitation forecasting using wavelet-genetic programming and wavelet-neuro-fuzzy conjunction models. Water Resource Management. 25(13): 31353152.
  • Kisi O, Pour Ali Baba A, Shiri J. 2012. Generalized neuro-fuzzy models for estimating daily pan evaporation values from weather data. ASCE Journal of Irrigation and Drainage Engineering 138(4): 349362.
  • Legates DR, McCabe GJ. 1999. Evaluating the use of goodness-of-fit measures in hydrologic and hydroclimatic validation. Water Resources Research 35(1): 233241.
  • Mamdani EH, Assilian S. 1975. An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man Machine Studies 7(1): 113.
  • Marquardt D. 1963. An algorithm for least squares estimation of non-linear parameters. Journal of the Society for Industrial and Applied Mathematics 11(2): 431441.
  • Partal T, Kisi O. 2007. Wavelet and neuro fuzzy conjunction model for precipitation forecasting. Journal of Hydrology 342: 199212.
  • Shank DB, Hoogenboom G, McClendon RW. 2008. Dewpoint temperature prediction using artificial neural networks. Journal of Applied Meteorology and Climatology 47: 17571769.
  • Shiri J, Dierickx W, Pour-Ali Baba A, Neamati S, Ghorbani MA. 2011. Estimating daily pan evaporation from climatic data of the State of Illinois, USA using adaptive neuro-fuzzy inference system (ANFIS) and artificial neural networks (ANN). Hydrology Research 42(6): 491502.
  • Smith BA, McClendon RW, Hoogenboom G. 2005. An enhanced artificial neural network for air temperature prediction. Proceedings of World Academy of Science, Engineering and Technology (PWASET) 7: 712.
  • Takagi T, Sugeno M. 1985. Fuzzy identification of systems and its application to modeling and control. IEEE Transactions on System, Man and Cybernetics 15(1): 116132.
  • Tatli H, Sen Z. 1999. A new fuzzy modeling approach for predicting the maximum daily temperature from a time series. Turkish Journal of Engineering and Environmental Science 23: 173180.
  • Ustaoglu B, Cigizoglu HK, Karaca M. 2008. Forecast of daily mean, maximum and minimum air temperature time series by three artificial neural network methods. Meteorological Applications 15: 431445.
  • Vernieuwe H, Georgieva O, De Baets B, Pauwels VRN, Verhoest NEC, De Troch FP. 2005. Comparison of data-driven Takagi-Sugeno models of rainfall-discharge dynamics. Journal of Hydrology 302(1-4): 173186.