Forecasting soil temperature at multiple-depth with a hybrid artificial neural network model coupled-hybrid firefly optimizer algorithm

Accepted Manuscript Forecasting soil temperature at multiple-depth with a hybrid artificial neural network model coupled-hybrid firefly optimizer algorithm Saeed Samadianfard, Mohammad Ali Ghorbani, Babak Mohammadi PII: DOI: Reference:

S2214-3173(18)30038-6 https://doi.org/10.1016/j.inpa.2018.06.005 INPA 141

To appear in:

Information Processing in Agriculture

Received Date: Revised Date: Accepted Date:

5 February 2018 12 June 2018 15 June 2018

Please cite this article as: S. Samadianfard, M. Ali Ghorbani, B. Mohammadi, Forecasting soil temperature at multiple-depth with a hybrid artificial neural network model coupled-hybrid firefly optimizer algorithm, Information Processing in Agriculture (2018), doi: https://doi.org/10.1016/j.inpa.2018.06.005

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Forecasting soil temperature at multiple-depth with a hybrid artificial neural network model coupled-hybrid firefly optimizer algorithm Saeed Samadianfard1*, Mohammad Ali Ghorbani1,2, Babak Mohammadi3 1

2

Department of Water Engineering, University of Tabriz, Tabriz, IRAN

Engineering Faculty, Near East University, 99138 Nicosia, North Cyprus, Mersin 10, TURKEY 3

Department of Irrigation and Reclamation Engineering, University of Tehran, Karaj, IRAN * Corresponding author: [email protected], [email protected]

Abstract Forecasting soil temperature at multiple depths is considered to be a core decision-making task for examining future changes in surface and sub-surface meteorological processes, land-atmosphere energy exchange, resilient agricultural systems for improved crop health and eco-environmental risk assessment. The aim of this paper is to estimate monthly soil temperature (ST) at multiple depth: 5, 10, 20, 50 and 100 cm with a hybrid multi-layer perceptron algorithm integrated with the firefly optimizer algorithm (MLPFFA). To develop the hybrid MLP-FFA model, the monthly ST and relevant meteorological variables for the city of Adana (Turkey) are collated for the period of 2000-2007. Construction of hybrid MLP-FFA model is drawn upon a limited set of predictors, denoted as soil depth, periodicity (or the respective month), air temperature, pressure and solar radiation, while the objective variable for MLP-FFA model is the forecasted ST at multiple depths. To the evaluate MLP-FFA, statistical metrics applied to test the model’s performance are: the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and mean bias error (MBE) where the sign of the difference is also considered. In conjunction with statistical metrics, a Taylor diagram is utilized to visualize the degree of similarity between the observed and forecasted soil moisture. In terms of the forecasted results, the hybrid MLPFFA model is seen to outperform the standalone MLP model. The optimal MLP-FFA is attained for soil temperature forecasting at a depth of 20 cm (RMSE, MAPE of 0.546 ˚C, 2.40%) whereas the optimal MLP is attained for soil temperature forecasting at a depth of 50 cm (RMSE of 0.544˚C, 2.21%). Conclusively, the study advocates through statistical metrics attained the better utility of the hybrid MLPFFA hybrid model. Given its superior performance, it is ascertained that the hybrid MLP model integrated with Firefly optimizer is a qualified ancillary tool that can be applied to generate precise soil temperature forecasts at multiple soil depths.

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Key word:

artificial neural network, hybrid firefly algorithm, soil temperature, Turkish State Meteorological Service.

1.0

Introduction

Soil temperature (ST) is a critical variable that controls the underground physical processes, global and continental carbon and energy budgets, and has a primary role playing as an indicator for the overall health of the underlying soil necessary for socio-economic related activities (e.g. agriculture). In practical terms, this property of soil can expressively affect the germination of seeds [1], plant growth [2], nutrient’s uptake [3] and respiration within the soils [4]. Other activities such as soil evaporation [5] and the intensity of physical [6], chemical [7, 8], and microbiological processes [9, 10] in the soil media are also greatly governed by the thermal state of the soil, therefore, a knowledge of ST is particularly important in several decision-making tasks. As it is well-known, the overall ST is significantly influenced by a number of pertinent factors including those related to, or having a meteorological origin (such as it dependence on solar energy fluxes and air temperature variations within the soil and the lower atmosphere), variations in local topography and the soil water content, soil texture and the area of the land surface covered by litter and the canopies of various plants. Consequently, some currently available physical models that are applied for an estimation of ST are intrinsically dependent upon the state of soil heat flow and the energy balance in the underlying soils. Physical models applied for ST prediction are thus highly complex, as they are bound to rely on mathematical equations, inherently requiring a set of initial and boundary conditions as the model’s initializers which are difficult, if not impossible to acquire in a range of spatial locations. Such forms of data may be unavailable in a number of remote or regional locations especially in developing countries where instrumental set-ups have not been erected for logistic and budgetary reasons [11]. Hence datadriven models that solely rely on historical observations to generate the prediction of ST can help the modelers to overcome the challenges faced, and so, it can provide a viable alternative for the forecasting of soil temperature. Other than using physical or data-driven models, soil temperature is also monitored by measured soil properties but these are difficult to acquire especially in developing nations, such as the Middle East region. For a developed nation like the United States of America, long-term records of daily air temperature and precipitation are available, yet only a few of those climate stations actually monitor ST data in a regular and a systematic way. Notwithstanding this challenge, earlier work of Toy et al. [12] aimed to implement monthly mean air temperature data for predicting ST values over continental scales. However, the effect of ST on soil respiration and its decomposition is often not linear [13, 14], such that 2

the simulation of ecosystem processes beneath the surface of the earth over continental scales based on monthly time steps can be subjected to errors or biases. Moreover, several studies dealing with ST estimation have established forecasts based on theories and equations of energy balance and heat flow from the soil into the lower atmosphere [15, 16, 17, 18, 19]. Importantly, the key driving force determining the changes in ST are air temperature and solar radiation, influenced by several elements such as soil texture, precipitation, moisture content and the type of surface cover [9]. It is noteworthy that the acquired solar radiation on the surface of the earth depends upon the climatological conditions and other environmental features of a site specific location [20]. Although heat flux plates can be used to make direct measurements of ST [21, 22] several alternatives approaches have been developed in literature for the modeling and the predicting of ST data, as accurate measurement of ST is a certainly a difficult task [23]. In published literature, there are three category of forecasting models applied for forecasting the ST data [24]. These are: (1) empirical models, established on relationships among ST at pre-specified depth and climatological conditions [12]; (2) mechanistic models that focus on physical processes for predicting ST values at soil surface and various depths using Fourier’s equation [25]; (3) combined models, which calculate the ST values on the basis of physical principles of heat flow. It should be noted that ST at the soil surface have to be provided empirically (e.g., [26]). The key purpose of the ST forecasting model is to explain the processes of the complicated atmosphere-soil-plant system by means of mathematical tools. In the recent decades, there have been quite a lot of researches regarding the estimation of ST values using analytical, experimental and numerical methods [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38]. Additionally, predicting algorithms based on the Fourier methods and ANN tools have been developed. Studies that developed data-driven models for soil temperature forecasting can be summarized from various previous works. For example, Bilgili [39] attempted to model the ST values by applying linear and nonlinear regressions (LR and Non-LR) and artificial neural network (ANN) methods for the City of Adana, Turkey with meteorological parameters taken from Adana meteorological station from 2000 to 2007. Their result indicated that the ANN methodology was a dependable model for predicting monthly mean ST data. Kim and Singh [40] assessed the abilities of adaptive neuro–fuzzy inference system (ANFIS) and multilayer perceptron (MLP) for an estimation of ST. They noted that the MLP provided enhanced outcomes in contrast with ANFIS at different depths for both studied stations. In another study, the precision of three different neural networks techniques was evaluated by Kisi et al. [41] for modeling ST values at Mersin Station, Turkey. They inspected the effect of meteorological parameters and declared that air temperature had the most impressive effect on predicting ST values. Tabari et al. [42] scrutinized the capabilities of artificial neural networks (ANN) to predict ST at two weather stations of Iran. The 3

outcomes for these studies ascertained that ANN models could be used satisfactorily to forecast shortterm ST values. Behmanes and Mehdizadeh [43] implemented gene expression programming (GEP) and ANN for estimating ST values at six various depths (5, 10, 20, 30, 50 and 100 cm) for the Sanandaj synoptic station, Iran. The results revealed that the ANN provided more accurate predictions of ST values than GEP model. In another study, Kisi et al. [44] examined the applicability of ANN, ANFIS and genetic programming (GP) for estimating ST values at different depths in two weather stations, Mersin and Adana, Turkey. GP was found to be more sufficient than other considered models in estimating monthly ST. Firefly Algorithm (FFA) is a new generation of nature-inspired optimization algorithm presented by Yang [45, 46], which is a heuristic algorithm inspired by the flashing behavior of fireflies and experience shows its successful performances over its previous generation of optimization techniques as FFA solutions tend to home in to the global minimum. The applications of support vector machine (SVM) to diverse fields include: soil moisture prediction [47], forecasting of river water quality modeling [48], pan evaporation estimation [49], stream flow prediction [50], stock price index [51], global solar radiation [52], daily dew point temperature estimation [53], predicting the inside environment variables in greenhouses [54], and detecting sugarcane borer diseases [55]. FFA has been integrated with various data-driven modelling strategies, including SVM and these typically show a noticeable improvement in model performances over training using past generations of approaches. This paper seeks to apply the hybrid of SVM-FFA to river flow problems. The objective of the present research is to explore the capabilities of artificial neural network models coupled with hybrid firefly optimizer algorithm for modeling monthly soil temperature at a depth of 5, 10, 20, 50 and 100 cm depths or Adana station, Turkey. Hence, the soil temperature estimations of MLP-FFA models are compared with the estimates of typical MLP models. The performance of the MLP-FFA models experimented in the training and testing phases are compared with the measured ST values and the precise model is recognized based on performance metrics.

2.0

Materials and method

2.1

Site description

Adana is a major city in southern Turkey. The city is positioned on the Seyhan River, 35 km inland from the Mediterranean Sea, in south-central Anatolia. Adana city, has a population of 1.7 million, and is ranked as the fifth most crowded city in Turkey. It is situated at the northeastern edge of the

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Mediterranean, where it serves as the gateway to the Çukurova plain. The north of the Adana city is bounded by the Seyhan reservoir, which was finalized in 1956. The dam was built for hydroelectric power and to irrigate the lower Çukurova plain where agriculture is a primary socio-economic activity. The monthly climatological data utilized in the present study were recorded between 2000 and 2007, which acquired from Adana meteorological station (see Fig.1), located at 36°59′N, 35°18′E. The station is positioned at an altitude of 28 m above sea level in the eastern Mediterranean district of Turkey. Figure 1. Location of Adana meteorological station in the region

2.2

Multi-layer Perceptron Neural Networks (MLP)

In this paper, we adopt a particular form of the ANN model, known as the Multi-Layer perceptron (MLP) as a primary modeling tool to forecast soil temperature at multiple depths with limited predictor dataset. Basically, the MLP model is a feed forward neural network with one or more layers among input and output layers [56]. The term, feed forward denotes that the data feature extraction process moves in one direction from the input to output layer. The MLP is trained with the back propagation learning algorithm, a most common algorithm used in several prediction problems [57, 58]. In general, MLPs are extensively utilized for approximation, prediction, recognition and pattern classification. An MLP model can solve complicated problems which are not linearly detachable. Multilayer feed-forward Perceptron back propagation learning algorithm (MLP-BP), as one of the popular MLP architectures, involves input, hidden and output layers. Moreover, specific weights are linked among neurons of input and hidden layers and also from neurons of hidden and output layers by suitable activation functions. Additionally, the activation functions between input and hidden layers and between hidden and output layers are sigmoid and linear functions, respectively. These activation functions limit the input data to fluctuate between 0 to 1. So, by assuming that input data = d = (Tmean, Patm, SR and M), the mathematical description is as follows: (1) (2) Where d is the array of input parameters including meteorological parameters; functions,

and

are bias values of

and

and

and

are actuation

is weight parameter. In the current research,

backpropagation algorithm, which employs the extensively implements Levenberg-Marquardt, and the proposed FFA optimization algorithm were utilized for minimizing the error functions of MLP.

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2.3

Firefly Algorithm

To improve the performance of the basic MLP model, the Firefly Algorithm (FFA) as a metaheuristic search tool applied in this research. FFA is based on the social dashing behavior of fireflies in nature [45, 46, 59]. The two main issues in FFA are the variation of light intensity and formulation of attractiveness. Considering maximizing objective function for optimal design, the objective function is proportional to the light intensity released by a firefly. The Gaussian procedure of the light concentration with varying distance can be written as: (3) In Eq. (3), I = light intensity for a distance r located from a firefly, I0 = initial light intensity at a location of r = 0 and

= light absorption coefficient bounded by [0.1, 10] representing the attractiveness of a

firefly related to the light intensity observed by adjacent fireflies. The attractiveness (ώ) at a distance r from the firefly can be formulated as: (4) In Eq. (4), x0 = attractiveness at r = 0. The Cartesian distance between any two fireflies i and j (i.e., xi and xj) is written as: (5) In Eq. (5), n = the dimensionality, xi,k = kth component of xi of the ith firefly and xj,k = kth component of xj of the jth firefly. The motion of a firefly (i) attracted to the other brighter fireflies (j) is formulated as: (6) In Eq. (6), first term = attraction, the second term = the α-denoted randomization coefficient bounded by [0, 1] and

= random number vector following a Gaussian distribution.

The flowchart of MLP-FFA algorithm and schematic structure designed for ST prediction is shown in Figs. 2 and 3. Figure 2.

Flowchart of the MLP-FFA structure. Redrawn after Yang [45, 46].

Figure 3.

Schematic structure of the MLP-FFA method for ST prediction. Redrawn after Yang [45, 46].

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2.4

Forecasting Model Development

In order to develop an MLP-FFA model, monthly meteorological variables measured between the years of 2000 and 2007 were acquired from Turkish State Meteorological Service (TSMS). These comprised of time-series of soil temperature (ST), atmospheric temperature (Tmean), atmospheric pressure (P) and the solar radiation (SR). The statistical properties of the data are displayed in Table 1. In the present models, the predictor (input) variables are made up of the soil depths (at 5, 10, 20, 50, 100 cm), respective month number considering the periodicity (i.e., 1, 2…12), air temperature (˚C), atmospheric pressure (bar) and solar radiation (Kcal/cm2), while the output (objective) variable is the forecasted ST data at multiple depths (i.e., 5, 10, 20, 100 cm). Table 2 shows the correlation coefficient computed between the predictor variables with the respective objective variable (ST values) at different depths considered in this paper. Before training the MLP and MLP-FFA models, the normalization was carried out for the utilized data. The key aim of normalization is scaling the data in a specific range for minimizing bias in the considered models. In the current research, Eq. (7) has been applied for the min-max normalization. It changes the scale of target values to be in the range of 0.1 to 1. (7) where

is the normalized value of ,

and

are the minimum and maximum values of each

parameter, respectively. Moreover, for developing the MLP and MLP-FFA models, the data were first divided into the training (70 % of the total data) and the testing (30 %) subsets. In the classical MLP-based modeling, the trial-anderror procedure is often used to select the optimal number of neurons in the selected single hidden layer. The number of neurons for each MLP model structure was investigated by training the network in 200 epochs, in which the learning rate was 0.0015 and momentum coefficient was 0.74. For each model structure, the better performing model was then selected from a total of 30 different topologies which were best regarded as the representative of the particular model structure. For the hybrid MLP-FFA model, the initial weight values used by Firefly Algorithm were recorded as

,

and Table1. Statistical characteristics of used data Table2. Correlation coefficients of all mentioned variables with ST values at different depths 2.5

Performance Evaluation

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To evaluate the performance of the MLP-FFA approaches relative to the MLP model applied for forecasting soil temperature at multiple depths, a number of statistical score metrics were used to compare the observed and forecasted dataset. I: Mean absolute percentage error [60], expressed as: MAPE 

1 n Pi  Oi 100  n i 1 Oi

(8)

II: Root mean square error (RMSE; oC ) expressed as: (9)

1 N ( Pi  Oi )2  N i 1

RMSE 

III: Mean absolute error (MAE; oC ) expressed as: MAE 

1 N

(10)

N

 P O  i

i 1

i

IV: Mean bias error (MBE; oC ) expressed as: (11)

n

MBE 

 (O  P ) i 1

i

i

N

Note that the values Oi and Pi are the observed and predicted ST values and

is the average of observed

values within the model’s testing period. Other than the statistical metrics defined in Eq. (5–8), we also utilized the Taylor diagram [61] to incorporate its importance in model evaluation. Basically, a Taylor diagram is a graphical illustration of the observed and predicted data [62]. Use of Taylor diagram allows modelers to utilize a single diagram to summarize several predictive features of the forecasting model relative to the observed data. Remarkably, Taylor diagrams highlight the goodness of different models in comparison to observations wherever the diagram can be pictured as a series of points on a polar plot. The azimuth angle denotes to the correlation (R) value between the predicted and observed data while the radial distance from the origin signifies the ratio of the normalized standard deviation (SD) of the simulation to that of the

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observation. In order to provide a broader picture of model evaluation, the ratio of the variance is calculated to specify the relative amplitude of the predicted and observed variations, whereas the correlation in the plot can display whether the fields have similar patterns of variation, regardless of amplitude. Additionally, the normalized RMSE can be resolved into a part due to differences in the overall means, and a part due to errors in the pattern of variations [61, 62, 63]. 3.0

Results and Discussion

In this section, the performance of the hybrid MLP-FFA forecasting model relative to the classical MLP model has been evaluated in light of the statistical and visual assessment of forecasted and observed soil temperature data at multiple depths. Table 3 presents the performance of the MLP-FFA versus MLP within the model development (training) and model evaluation (testing) datasets. For each mode, the performance at 5, 10, 20, 50 and 100 cm depth has been listed in terms of RMSE, MAE, MAPE and MBE. Table 3. Performance criteria of the MLP-FFA and MLP models for training and testing stages at the Adana station

A close examination of the forecasting model performances shows that the RMSE of the MLP model range between 0.614 to 0.770 C in the testing period, while the RMSE values for the MLP-FFA model are found to be between 0.546 to 0.652C. For the forecasted model tested at the 5 cm depth, the MLPFFA model produced superior results in comparison with the MLP model. In other words, the MLP-FFA model yielded an RMSE of 0.652 oC, MAE of 0.532 oC, MAPE of 2.489% and MBE of -0.485 oC, which shows a greater precision than the MLP model without its integration with the Firefly Algorithm. Also, the integration of the FFA algorithm with the MLP model led to a reduction in the RMSE and MAE by about 10.2% and 9.4%, respectively. In the case of the model applied to forecast temperature at about 10 cm below the surface, the MLP-FFA model resulted in RMSE of 0.597 oC, MAE of 0.467 oC, MAPE of 2.096% and MBE of -0.408 oC, indicating that the utilization of the Firefly Algorithm improved the 9

predicted ST accuracy compared with the MLP model. Additionally, the MLP-FFA generated lower values of the RMSE and MAE compared to the classical MLP model, by about 22.5% and 24.8%, respectively. In congruence with the present results, similar trend can be seen for the case of the forecasting models applied at 20 cm depth. At this depth, MLP-FFA produced more precise results than the classical MLP model without the Firefly Algorithm. The MLP-FFA attained an RMSE value of 0.546 oC, MAE of 0.456 o

C, MAPE of 2.21% and MBE of -0.411 oC . In fact, the RMSE and MAE values of MLP-FFA model were

lower by about 19.0% and 15.1%, respectively. Unlike the trend found for previous depths, the MLP-FFA model showed somewhat different trends in forecasting the ST data at a depth of 50 cm below the soil surface. For the case of 50 cm depth, the MLP-FFA model resulted in a lower RMSE value compared to the classical MLP model by about 5.9%, but the former model also led to an increase in MAE of the MLP model by about 9.0%. Furthermore, in the case of forecasting ST at 100 cm depth, the MLP-FFA model resulted in an RMSE of about 0.618 oC, which in fact, was lower than the RMSE value generated by the classical MLP model by about 9.3%. Conversely, the MLP-FFA model did not have significant effect in reducing the MAE values compared to the MLP model. To concur with this result, it can be concluded that the use of the FFA-based model had a significant effect in reducing the forecasting errors for temperature data forecasted at a depths of 5, 10 and 20 cm below the soil surface. In contrast, the MLPFFA model was unable to increase the precision of ST forecast for a depth of 50 and 100 cm. Moreover, the prediction error reduced by increasing the soil depth. This conclusive remark is in agreement with obtained results of Tabari et al. [42]. The time-series of the observed and forecasted ST values at different depths by the classical MLP and the hybrid MLP-FFA models are illustrated in Fig. 4(a-e). Additionally, the scatterplots of observed and predicted ST values are also presented in Fig. 5. Consistent with previous results, the superiority of MLPFFA over the MLP models is evident from these figures. Comparison of the model forecasts for different 10

depths, as exhibited in Fig. 4(a-e), clearly shows that the MLP-FFA model able to approximate the soil temperature values more precisely than the classical MLP models. Figure 4. Observed and predicted ST values by MLP and MLP-FFA models in the test period. Figure 5. Scatterplots of the predicted-observed ST for test section

To further evaluate the MLP-FFA model, a supplementary analysis has been performed based on the observed and predicted soil temperature values using probability distribution of the data in the testing period (Fig. 6). It is noteworthy that these figures aim to illustrate the probability occurrence of forecasted ST values within a set of exact predefined intervals. It can be comprehended from Fig. 6 that the probability distribution of data generated from the MLP-FFA are much closer to the observed ST values compared to the classical MLP models for majority of the data intervals. Figure 6. Histograms of ST values at testing period

Besides, a Taylor diagram was also used for inspecting the standard deviation and correlation coefficient (R) values between the observed and predicted soil temperature values at various depths. Fig. 7 also exhibits the Taylor diagram for both models utilized at different depths, whereby the distance from the reference point (i.e., a point with green color) is a quantity of the centered RMSE difference [61]. Accordingly, a superior model is normally depicted by the reference point with a correlation coefficient of 1 with nearly the same amplitude of variations compared with the observations. It is obvious from Fig. 6 that the MLP-FFA (i.e., circle) was able to yield more accurate forecasts of soil temperature values compared to classical MLP model (i.e., square points) applied at all soil depths. Figure 7. Taylor diagram of the predicted ST values in test period 4.0

Conclusion

Core decisions in farming and agricultural precision require versatile predictive models with good ability to simulate several soil properties as primary variables that control crop yield amounts and their quality. 11

In this paper the utility of a newly constructed, high-performance hybrid model (MLP-FFA) designed by integrating Firefly Algorithm with a Multi-layer Perceptron-based predictive system is validated to estimate monthly soil temperature (ST) at multiple depths for the city of Adana in Turkey. To develop the hybrid model, ST and meteorological input variables including air temperature, atmospheric pressure and solar radiation for the period 2000–2007 were acquired for Adana meteorological station. The capability of the hybrid MLP-FFA and the standalone MLP model for prediction of ST in an independent test dataset was comprehensively examined using statistical metrics. A Taylor diagram was implemented for model evaluation where a joint assessment of the model’s precision was carried out. In accordance with statistical metrics and visual assessment of observed and forecasted ST in the testing phase, the results indicated that the MLP-FFA model was able to forecast the ST data more precisely than the standalone MLP model. Conclusively, we aver that the hybrid MLP-FFA model can be recommended as a suitable tool for ST estimation at multiple soil depths to yield an acceptable degree of statistical accuracy. The present study has amicable implications for agriculture and a number of environmental applications that require expert decision-systems to be developed that allows the forecasting of soil properties.

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Figure 1. Location of Adana meteorological station in the region

17

Figure 2.

Flowchart of the MLP-FFA structure. Redrawn after Yang (2010a, b).

18

Figure 3.

Schematic structure of the MLP-FFA method for ST prediction. Redrawn after Yang (2010a, b).

19

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Figure 4. Observed and predicted ST values by MLP and MLP-FFA models in the test period.

21

Figure 5. Scatterplots of the predicted-observed ST for test section

22

23

Figure 6. Histograms of ST values at testing period

24

Figure 7. Taylor diagram of the predicted ST values in test period

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Table1. Statistical characteristics of used data Statistics

Tmean

Patm

SR

M

STD5cm

STD10cm

STD20cm

STD50cm

STD100cm

Mean

19.24

1.0099

0.37

6.5

22.17

21.68

21.4

21.39

21.44

Minimum

6.8

1.0012

0.12

1

7.1

7.8

8.5

10.4

12.3

Maximum

29.7

1.021

0.65

12

37.6

36.2

34

32.8

30.9

Standard deviation

7.26

0.004

0.13

3.47

9.61

8.89

8.36

7.44

6.09

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Table2. Correlation coefficients of all mentioned variables with ST values at different depths Statistics

Tmean

Patm

SR

M

STD5cm

STD10cm

STD20cm

STD50cm

STD100cm

STD5cm

0.994

-0.897

0.882

0.255

1

0.998

0.992

0.966

0.893

STD10cm

0.996

-0.887

0.862

0.288

0.998

1

0.997

0.977

0.913

STD20cm

0.995

-0.864

0.831

0.339

0.992

0.997

1

0.99

0.939

STD50cm

0.975

-0.809

0.753

0.437

0.966

0.977

0.99

1

0.978

STD100cm

0.911

-0.697

0.612

0.569

0.893

0.913

0.939

0.978

1

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Table 3. Performance criteria of the MLP-FFA and MLP models for training and testing stages at the Adana station Models

Depth

Structures

MLP

5 10 20 50 100

5_8_1 5_3_1 5_6_1 5_8_1 5_16_1

RMSE(˚C) 0.702 0.67 0.587 0.544 0.611

MLP-FFA

5 10 20 50 100

5_8_1 5_3_1 5_6_1 5_8_1 5_16_1

0.553 0.469 0.491 0.462 0.485

Train MAE(˚C) MAPE 0.526 2.518 0.493 2.485 0.442 2.345 0.422 2.276 0.465 2.348 0.418 0.377 0.401 0.392 0.407

1.861 1.831 1.859 1.844 1.887

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MBE (˚C) 0.0376 -0.055 0.029 0.003 0.023

RMSE(˚C) 0.726 0.770 0.674 0.614 0.681

MAE(˚c) 0.587 0.621 0.537 0.457 0.533

Test MAPE 2.853 3.055 2.831 2.4 2.66

MBE (˚C) 0.147 0.288 0.271 0.173 0.158

0.374 -0.306 0.356 0.343 0.354

0.652 0.597 0.546 0.578 0.618

0.532 0.467 0.456 0.498 0.533

2.489 2.096 2.21 2.391 2.441

-0.485 -0.408 -0.411 -0.461 -0.47