Environmental Science and Pollution Research https://doi.org/10.1007/s11356-018-3650-2
RESEARCH ARTICLE
Modeling daily water temperature for rivers: comparison between adaptive neuro-fuzzy inference systems and artificial neural networks models Senlin Zhu 1 & Salim Heddam 2 & Emmanuel Karlo Nyarko 3 & Marijana Hadzima-Nyarko 4 & Sebastiano Piccolroaz 5,6 & Shiqiang Wu 1 Received: 5 July 2018 / Accepted: 31 October 2018 # Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract River water temperature is a key control of many physical and bio-chemical processes in river systems, which theoretically depends on multiple factors. Here, four different machine learning models, including multilayer perceptron neural network models (MLPNN), adaptive neuro-fuzzy inference systems (ANFIS) with fuzzy c-mean clustering algorithm (ANFIS_FC), ANFIS with grid partition method (ANFIS_GP), and ANFIS with subtractive clustering method (ANFIS_SC), were implemented to simulate daily river water temperature, using air temperature (Ta), river flow discharge (Q), and the components of the Gregorian calendar (CGC) as predictors. The proposed models were tested in various river systems characterized by different hydrological conditions. Results showed that including the three inputs as predictors (Ta, Q, and the CGC) yielded the best accuracy among all the developed models. In particular, model performance improved considerably compared to the case where only Ta is used as predictor, which is the typical approach of most of previous machine learning applications. Additionally, it was found that Q played a relevant role mainly in snow-fed and regulated rivers with higher-altitude hydropower reservoirs, while it improved to a lower extent model performance in lowland rivers. In the validation phase, the MLPNN model was generally the one providing the highest performances, although in some river stations ANFIS_FC and ANFIS_GP were slightly more accurate. Overall, the results indicated that the machine learning models developed in this study can be effectively used for river water temperature simulation. Keywords River water temperature . Air temperature . River flow discharge . Gregorian calendar . MLPNN . ANFIS . Hydrological regime Responsible editor: Marcus Schulz * Senlin Zhu
[email protected] 1
State Key Laboratory of Hydrology-Water resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, China
2
Faculty of Science, Agronomy Department, Hydraulics Division, University 20 Août 1955, Route El Hadaik, BP 26 Skikda, Algeria
3
Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, University J.J. Strossmayer in Osijek, Kneza Trpimira 2b, 31000 Osijek, Croatia
4
Faculty of Civil Engineering Osijek, University J.J. Strossmayer in Osijek, Osijek, Croatia
5
Institute for Marine and Atmospheric Research, Department of Physics, Utrecht University, Princetonplein 5, 3584, CC Utrecht, The Netherlands
6
Service for Torrent Control, Autonomous Province of Trento, via Trener 3, I-38121 Trento, Italy
Introduction Water temperature is a key factor for the health of aquatic ecosystems. It controls several physical and bio-chemical processes in rivers, such as reoxygenation processes and the temperature-dependent metabolism of aquatic plants and animals (Rajwakuligiewicz et al. 2015; Sandersfeld et al. 2017). All aquatic organisms have a typical water temperature range for tolerance and abrupt variations of river thermal conditions may seriously impact their metabolism, behavior, and survival (Caissie et al. 2007; Carolli et al. 2011; Verbrugge et al. 2012; Casas-Mulet et al. 2016; Westhoff and Rosenberger 2016). For example, previous studies have shown that the migration of river fishes is more probable when the maximum water temperature exceeds its optimal temperature range (Eaton et al. 1995; Howell et al. 2010), and in general, fish mortality increases with the number of days on which river
Environ Sci Pollut Res
water temperature exceeded its temperature tolerance (Phelps et al. 2010). Hence, the reliable prediction of river water temperature is particularly relevant due to its significant ecological role in affecting aquatic systems (Grbić et al. 2013). Besides meteorological forcing and climate, several other factors control thermal dynamics in rivers, such as the hydrological regime, riverbed conditions, fluvial topography, and anthropic activities (Caissie 2006; Hester and Doyle 2011; Kelleher et al. 2012; Lisi et al. 2015; Piccolroaz et al. 2016; Cai et al. 2018). When the aim is to accurately predict river water temperature, it is necessary to understand in detail how all these factors combine in affecting river thermal processes (Hadzima-Nyarko et al. 2014), considering also the impact of extreme climatic events such as heat waves (Piccolroaz et al. 2018). A large number of models for river water temperature prediction have been proposed and successfully applied in the past decades, which can be divided into two main categories: physically based deterministic models and statistical models (Benyahya et al. 2007; Cole et al. 2014). Deterministic models simulate the spatio-temporal variations of water temperature in rivers based on the mathematical description of the heat fluxes exchanged between the river and the surrounding system (Hebert et al. 2011). Some famous examples of this type of models are the widely used HEC-RAS model (Jensen and Lowney 2004) and the MIKE 11 model (Wang 2013). Deterministic models are generally complex, and rely on a large number of requirements for inputs, such as fluvial topography, the whole set of meteorological variables, and the hydrological conditions, and therefore are frequently impractical when observed data are scarce. This fostered the development of statistical models, which have been widely used in river water temperature predictions because of their simplicity and minimal data requirements. Linear (Morrill et al. 2005; Krider et al. 2013) and non-linear regression models (Mohseni et al. 1998; Vliet et al. 2012), stochastic regression models (Ahmadi-Nedushan et al. 2007; Rabi et al. 2015), and hybrid statistical-physical based models (Gallice et al. 2015; Toffolon and Piccolroaz 2015; Piccolroaz et al. 2016) have been implemented successfully to model river water temperature. In addition, machine learning models have been increasingly used in river water temperature predictions in recent years, with artificial neural network (ANN) models being the most widely used approaches (Karaçor et al. 2007; Sahoo et al. 2009; Hadzima-Nyarko et al. 2014; DeWeber and Wagner 2014; Piotrowski et al. 2014, 2015; Rabi et al. 2015; Temizyurek and Dadasercelik 2018; Zhu et al. 2018). For example, Piotrowski et al. (2015) compared different types of ANN models for short time river water temperature predictions. Results showed that simple and popular multi-layer
perceptron neural networks are in most cases not outperformed by more complex and advanced models, and ANN models are useful tools for river water temperature modeling. Adaptive neuro-fuzzy inference systems (ANFIS) are widely used in various fields, such as daily evaporation estimation (Shiri et al. 2011; Sanikhani et al. 2012; Kisi and Zounemat-Kermani 2014), municipal water consumption modeling (Yurdusev and Firat 2009), river flow forecasting (He et al. 2014), water quality simulation (Heddam 2014), and estimation of oxidation parameters for food (Karaman et al. 2012). For example, Karaman et al. (2012) compared ANFIS and ANN models for estimating oxidation parameters of sunflower oil, and results showed that ANFIS model outperformed ANN model for the prediction of oxidation parameters. Currently, few studies have been directed toward the use of ANFIS model for river water temperature modeling, and the intercomparison between ANFIS and ANN for water temperature simulation is limited. Statistical models typically use air temperature as the only independent variable, considering it as a proxy for the net heat exchanges with the atmosphere (Stefan and Preud’homme 1993; Mohseni and Stefan 1999; Webb et al. 2003; Caissie 2006; Hadzima-Nyarko et al. 2014; Rabi et al. 2015; Zhu et al. 2018). However, some researchers also considered other impact factors, such as river flow discharge (Webb et al. 2003; Ahmadi-Nedushan et al. 2007; Arismendi et al. 2014; Toffolon and Piccolroaz 2015; Piccolroaz et al. 2016; Laanaya et al. 2017), solar radiation (Sahoo et al. 2009), riparian shade (Johnson et al. 2014), landform attributes, and forested land cover (Deweber and Wagner 2014). Air temperature and river flow discharge are generally the most available variables for modeling temperatures in rivers, and they have been shown to have the greatest impact on water temperature (Webb et al. 2003; Vliet et al. 2011). However, the role of flow discharge in machine learning models has seldom been investigated, and most of the previous studies employed only atmospheric factors as predictors (Sahoo et al. 2009; HadzimaNyarko et al. 2014; Rabi et al. 2015; Zhu et al. 2018; Temizyurek and Dadasercelik 2018). The stimulus for this research is therefore to implement ANN and ANFIS models to simulate water temperature for various river systems characterized by different hydrological conditions with air temperature (Ta ) and river flow discharge (Q) as predictors. According to Heddam (2016b) and Heddam and Kisi (2017), the inclusion of the components of the Gregorian calendar (CGC) improved significantly the performance of the machine learning models in the case of water quality modeling. Thus, the components of the CGC (year, month, and day) were also considered in the ANN and ANFIS models. The aim is to contribute to river water temperature modeling, deepening our understanding of river thermal behavior and providing references for water resource management.
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Materials and methods Study area In this study, we tested the performances of the proposed ANN and ANFIS models considering one river in Croatia and three rivers in Switzerland, which are characterized by different hydrological conditions. The cases are briefly introduced below and summarized in Table 1, where the periods of data availability are also listed. (i) The Drava River is located in the southern Central Europe, and it is one of the largest tributaries of the Danube River. The hydrological parameters of the Drava River are regularly monitored at Botovo, Terezino Polje, Donji Miholjac, and Osijek stations by the Meteorological and Hydrological Service of Croatia in Croatia. Two stations (Botovo and Donji Miholjac) were considered here. The Botovo station is located at about 20 km downstream of the Dubrava Reservoir (Bonacci and Oskoruš 2008). The Dubrava Reservoir was mainly constructed for water supply, irrigation, and hydropower generation. It has a total volume of 93.5 × 106 m3, and a maximum water level of about 149.60 m. This case (case 1) is representative of a large lowland river downstream of a reservoir. The Donji Miholjac station is located in a city and is close to a large fish pond. It is far downstream from the Dubrava Reservoir (120 km), and this case (case 2) is representative of a large lowland river far for regulations. (ii) The Mentue River flows through the Swiss plateau at low altitude. It drains through a sparsely inhabited area predominantly devoted to agriculture, and unaffected by strong anthropogenic thermal alterations. This case (case 3) was selected as representative of the typical condition of a small natural lowland river. (iii) The Rhône River is approximately 813 km in length, and it is one of the major rivers in Europe. The Rhône Table 1
River at the Sion hydrological station lies at the bottom of a populated Alpine valley. Since the beginning of the twentieth century, with the construction of a large highhead hydropower storage system, its hydrological regime has been dramatically altered and now it is affected by strong hydropeaking and thermo-peaking (Meile et al. 2011). This case (case 4) is taken as representative of a strongly regulated river due to the presence of highelevation hydropower reservoirs. (iv) The Dischmabach River is approximately 15 km in length. It is locate at high altitude in a steep glacial valley (Dischma), which is uninhabited and mainly used for mountain pastures. Due to the significant influence of snow melting in the warm season, this case (case 5) is considered as representative of a river with a clear nivoglacial regime.
Figure 1 presents the time series of the annual averaged air temperature (Ta), water temperature (Tw), and river flow discharge (Q) for the five stations. The seasonal dynamics of Ta, Tw, and Q are presented in Fig. 2 through the climatological year, which is defined by averaging for each day of the year all measurements available over the observation period for that same specific day. This figure effectively exemplifies the different hydrological and thermal regimes of the considered river stations, and indicates the different effect of Q in altering Tw dynamics. The response of Tw to changes in Ta is almost linear for the Mentue River (Fig. 2c), suggesting an overall negligible effect of Q due to low water fluxes throughout the year and absence of a strong seasonal pattern. Similar conditions can be observed for the Drava River (Fig. 2a, b), although the higher values and more marked seasonal pattern of Q result in a damped response of Tw to changes in Ta in spring and summer, when river flow discharge is higher. This effect is clearer for the Botovo station (Fig. 2a), likely due to the effect of the upstream Dubrava Reservoir, whose larger thermal
Characteristics of the studied river and meteorological stations
Case
1, 2
3
4
5
River name
Drava
Mentue
Rhône
Dischmabach
River station name River station elevation (m a.s.l.) Catchment area (km2) Calibration period Validation period Meteorological station name Meteorological station elevation (m a.s.l.) Distance from river station (km)
Botovo 121.55 31,038 1991–2008 2009–2016 Koprivnica 141 11.8
Yvonand 449 105 2002–2009 2010–2012 Mathod 437 12.7
Sion 484 3,373 1984–2003 2004–2013 Sion 482 2.14
Davos 1,668 43.3 2004–2009 2010–2012 Davos 1,594 4.9
Donji Miholjac 88.57 37,142 1993–2008 2009–2016 Donji Miholjac 97 1.0
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(a) Botovo
12 600
10 8
400
6 4
Ta
2
Tw
200
Q
Discharge (m3/s)
14 Temperature (eC)
Fig. 1 Time series plot of annual averaged air temperature (Ta), water temperature (Tw), and river flow discharge (Q) for the five case studies. a Drava at Botovo. b Drava at Donji Miholjac. c Mentue. d Rhône. e Dischmabach
0 0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 Year 1000
(b) Donji Miholjac
12
800
10 8
600
6
400
4
Ta
2
Tw
Q
Discharge (m3/s)
Temperature (eC)
14
200
0 0 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 Year 2.5
(c) Mentue
2
10
1.5 9.5 1 9
Ta
8.5 2000
Tw
2002
Q
2004
Discharge (m3/s)
Temperature (eC)
10.5
0.5
2006
2008
2010
2012
0 2014
Year 140
(d) Rhône
120
10
100
8
80
6
60
4
Discharge (m3/s)
Temperature (eC)
12
40 Ta
2 0 1980
Tw
1985
Q 1990
20 1995
2000
2005
2010
0 2015
Year 2.5
(e) Dischmabach
5
2
4
1.5
3 1
2 1
Ta
Tw
0.5
Q
0 2003
2004
inertia in comparison to that of the Drava River determines a time-lagged response of Tw to Ta, similarly to what observed downstream of large dams (see, e.g., Cai et al. 2018) and to thermal dynamics in deep lakes (Toffolon
2005
2006
Discharge (m3/s)
Temperature (eC)
6
2007
2008 2009 Year
2010
2011
2012
0 2013
et al. 2014; Piccolroaz et al. 2015). A similar effect, although much stronger, is evident in the Rhône River at the Sion station (Fig. 2d), where releases of cold water from high-altitude hydropower reservoirs cause a clear
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25 Ta
Tw
a) Botovo
Q
700
Temperature (eC)
20
500
10
400 300
5
Discharge (m3/s)
600 15
200 0 0
30
60
90
120
150
-5
180
210
240
270
300
330
360 100 0
Day of year
800
25 Tw
b) Donji Miholjac
Q
700
Temperature (°C)
20
600 15
500 400
10
300
5
Discharge (m3/s)
Ta
200 0 0
30
60
90
120
150
180
210
240
270
300
330
360
100 0
-5 Day of year
7
25 Tw
c) Mentue
Q
6
Temperature (eC)
20
5
15
4 10 3 5
2
0 0
30
60
90
120
150
180
210
240
270
300
330
Discharge (m3/s)
Ta
1
360
-5
0 Day of year
25
300 Tw
Q
d) Rhône
20
250
15
200
10
150
5
100
0
50 0
30
60
90
120
150
180
210
240
270
300
330
Discharge (m3/s)
Temperature (eC)
Ta
360
-5
0 Day of year 5
15 Ta
Tw
Q
e) Dischmabach
4.5 3.5 3
5
2.5 0 0
30
60
90
120
150
180
210
240
270
300
330
2 360 1.5 1
-5
0.5 0
-10 Day of year
Discharge (m3/s)
4
10 Temperature (eC)
Fig. 2 Climatological (reference) years for the five case studies. a Drava at Botovo. b Drava at Donji Miholjac. c Mentue. d Rhône. e Dischmabach. Ta air temperature, Tw water temperature, Q river flow discharge
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of the ANN and contains several neurons generally determined using trial and error. The neurons in the hidden layer need to perform linear and nonlinear operations. In a first stage, the neurons in the hidden layer receive the input variables multiplied by the corresponding links (the weights), perform a summation, and in the second stage, the result is passed to the second layer through a nonlinear activation function, generally the sigmoid. In the output layer we have only one neuron that corresponds to the dependent variables (water temperature). In the present investigation, we have used the widely used multilayer perceptron neural network (MLPNN) (Rumelhart et al., 1986), which has a standard structure: input, one hidden, and one output layer, and was reported in the literature as universal approximators (Hornik et al. 1989; Hornik 1991). MLPNN with one hidden layer contains n neurons and one output layer with only one neuron, and is expressed as follows (Fig. 3): " " !# #
flattening of the seasonal pattern of Tw, especially in summer when hydropower production is significant (Meier and Wüest 2004; Piccolroaz et al. 2016). Finally, in the Dischmabach River (Fig. 2e), Tw is generally low throughout the year due to the high altitude and the contribution of snow melting that, similarly to the cold hydropower releases discussed above, determine a cooling of Tw during the warm season. The nivo-glacial regime of this river is well described by the annual cycle of flow discharge, with no flow in winter and rapid variations of the flow discharge starting in spring due to snow melting waters (Toffolon and Piccolroaz 2015). The basic statistical characteristics of Tw, Ta, and Q for the five cases are summarized in Table 2, through the average, minimum, maximum, standard deviation, and coefficient of variation values of the daily data sets.
Multilayer perceptron neural network
n
Y ¼ f 2 ∑ wjk f 1
Artificial neural network is the most and well-known approach for building robust nonlinear models (Haykin 1999). ANN models were inspired from the function of the human brain in which an undetermined number of biological neurons were fully interconnected and play a key role in delivering a reliable transmission of information. The ANN models are organized in several parallel layers, and each layer contains several neurons. There are three kinds of layers: the input, hidden, and output layers. The input layer performs no calculation and only contains the input variables. The hidden layer is the most important part
Table 2 Daily statistical parameters of the used data sets for all stations
River station Botovo
Donji Miholjac
Mentue
Rhône
Dischmabach
j¼1
n
∑ xi wij þ δ j
þ δ0
ð1Þ
j¼1
where xi is the input variable, wij is the weight between the input i and the hidden neuron j, δj is the bias of the hidden neuron j, f1 is the activation sigmoid function, wjk is the weight of connection of neuron j in the hidden layer to unique neuron k in the output layer, δ0 is the bias of the output neuron k, and finally f2 is a linear activation function for the neuron in the output layer. The weights (wij) and bias levels (δ0) are the only free parameters that can be adjusted when the structure of the
Item
Unit
Xmean
Ta
°C
11.39
Tw Q Ta Tw Q Ta Tw Q Ta Tw Q Ta Tw Q
°C m3/s °C °C m3/s °C °C m3/s °C °C m3/s °C °C m3/s
11.43 478.09 11.76 11.96 515.23 9.97 9.72 1.40 10.33 7.00 103.71 3.78 4.29 1.68
Xmax
Xmin
Sx
Cv
30.10
− 15.00
8.46
0.74
25.20 2345.00 30.40 27.20 2166.00 25.55 21.70 36.29 27.60 12.16 757.30 20.12 11.02 13.14
0.00 103.00 − 14.80 0.00 175.00 − 10.14 0.00 0.08 − 15.00 0.31 17.09 − 22.18 0.17 0.24
6.22 231.64 8.68 7.17 225.44 7.38 5.80 2.07 7.88 2.17 78.42 7.72 2.88 1.57
0.54 0.48 0.74 0.60 0.44 0.74 0.60 1.48 0.76 0.31 0.76 2.04 0.67 0.93
Xmean mean, Xmax maximum, Xmin minimum, Sx standard deviation, Cv coefficient of variation, Tw water temperature (°C), Ta air temperature (°C), and Q river flow discharge (m3 /s)
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δj δ0
Ta Q Tw
CGC Input Layer
Output Layer
Wij
Wjk
river flow discharge (Q), also the components of the Gregorian calendar (year number YY, number of months from 1 to 12 MM, and number of days from 1 to 31 DD) were used as input variables. Data normalization is an important step in modeling with ANN models. It removes the dimensional differences in the data and improves the prediction ability of the ANN models. In this study, all the variables were normalized to have zero mean and unit variance using the Z-score method (Olden et al. 2004; Heddam 2016a):
Hidden Layer Fig. 3 Multilayer perceptron neural network (MLPNN) architecture. Ta air temperature, Q river flow discharge, CGC the components of the Gregorian calendar, Tw water temperature
neural network has been defined (number of layers, number of neurons in each layer, activation function for each layer). Modification of these parameters will change the output values of the designed network. The weights (wij) and bias levels (δ0) need to be adjusted to minimize the model error (difference between the modeled value and observed value), which is referred to as the training or calibration process of the network. The root-mean-square error (RMSE) and the mean-squared error (MSE) is often used to define the network error. In the present application of the MLPNN model, besides air temperature (Ta) and
xni;k ¼
xi;k −mk SdK
ð2Þ
where xni,k is the normalized value of the variable k (input or output) for each sample i, xi,k is the original value of the variable k (input or output), and mk and Sdk are the mean value and standard deviation of the variable k (input or output). The script of the MLPNN model was implemented in MATLAB. In this study, the MLPNN model has one hidden layer with sigmoidal activation function, and one output layer with linear activation function. The number of neurons in the hidden layer varies from one station to another and from one version to the other; however, in the major part of the present investigation, the number was generally between 10 and 13.
Fig. 4 Structure of the ANFIS model developed for predicting river water temperature (Tw)
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ANFIS The ANFIS is a machine learning model composed of two different paradigms: the ANN and the fuzzy logic (FL) (Jang 1993). ANFIS architecture includes the structure through several layers similar to the ANN, and fuzzification using the concept of the fuzzy inference system (FIS) from the FL paradigms (Jang et al. 1996). Contrary to the ANN model for which the parameters (weights and biases) are stored between the layers from the input to the output, ANFIS model possesses two kinds of parameters: linear and nonlinear (Jang 1993), which are adjusted during the training process. The FIS is an ensemble of logical rule-based in the form of (if A and B, then C). Similar to any regression model, the FIS transforms the input variables using the membership functions. Hence, the rule bases are composed from the results of the membership functions (MFs) (Jang et al. 1996). The complete structure of ANFIS consists of five layers, in addition to the input layer (Fig. 4): (i) the fuzzification layer, (ii) the base rules layer, (iii) the normalized layer, (iv) the defuzzification layer, and (v) the output layer (Jang 1993). The parameters of the ANFIS model are stored in (i) the fuzzification layer which contains the nonlinear parameters for the MFs, also called the premise parameters, updated during the training process using the back-propagation (BP) algorithm (forward step), and (ii) the linear parameters, also called consequent parameters, which are stored in the defuzzification layer, also updated during the training process using the least squares (LS) method (backward step) (Jang 1993). Consequently, each IF-THEN fuzzy rule contains at the same time, the linear and nonlinear parameters. The MFs plays an important role in the ANFIS models, and a good choice of the MFs among several available kinds with a best optimization of the parameters, leads to a model with high accuracy. For example, a Gaussian MFs possesses two adjustable parameters: Y¼e
−ðx−cÞ2 2σ2
ð3Þ
where Ai (or Bi − 2) is the linguistic label, μΑi ðxÞ and μΒi−2 ðyÞ are the fuzzy membership functions, and x and y are the input variables. Layer 2: the base rule layer Ο2i ¼ wi ¼ μAi μBi ; i ¼ 1; 2
ð5Þ
where wi is the firing strength of a rule. Layer 3: the normalized firing strengths Ο3i ¼ wi ¼ ðwi =ðw1 þ w2 ÞÞ; i ¼ 1; 2
ð6Þ
Layer 4: the defuzzification layer Ο4i ¼ wi f i ¼ wi ðpi x þ qi y þ ri Þ; i ¼ 1; 2
ð7Þ
where wi is the output of layer 3 and pi, qi, and ri are the consequent parameters. Layer 5: the output of the ANFIS model Ο5i ¼ ∑ wi f i ¼ ∑ wi f i =ðw1 þ w2 Þ : ð8Þ i¼1
i¼1
The most important step in developing ANFIS model is the creation of the fuzzy rule base. The number of fuzzy rule for any ANFIS model is directly related to the identification method used for partitioning the input space. There are three identification methods mainly used for ANFIS model: (i) grid partition method (GP), (ii) subtractive clustering (SC), and (iii) fuzzy c-means clustering (FC). Consequently, three models were developed using three different MATLAB functions: (i) ANFIS_GP using the genfis1 function for the partition method, (ii) ANFIS_SC using the genfis2 for the SC method, and (iii) ANFIS_FC using the genfis3 for the FC method (Jang 1993; Jang et al. 1996). The difference between the three models is directly related to the number of fuzzy rules generated by the partitioning method. Using the grid partition method, the number of fuzzy rule is calculated as follow: if β is the number of input variables, and α is the number of fuzzy subset for each input, the number of fuzzy rule is α β (Wei et al. 2007). The grid partition method is not suitable if the number of inputs is superior to 6 (Jang 1993). Using the SC method, the number of fuzzy rules is related to the cluster center radii: the number of fuzzy rules is equal to the number of clusters (Cakmakci 2007). Unlike the first two methods, when using FC method, the number of fuzzy rules is equal to the clusters and fixed by the user.
where c and σ are the parameters of the MFs (the premise parameters) that must be updated during the training process, x is an input variable, and Y is the response of the MFs. For more details about this method, the reader can refer to Jang (1993) and Jang et al. (1996). From the input to the output the model can be expressed as follow: Layer 1: the fuzzification layer
Model evaluation
Ο1i ¼ μΑi ðxÞ; i ¼ 1; 2; and Ο1i ¼ μΒi−2 ðyÞ; i ¼ 3; 4
In this study, model performance was evaluated using the following statistical indices metrics: the coefficient of
ð4Þ
Environ Sci Pollut Res
correlation (R), the Willmott index of agreement (d), the RMSE, and the mean absolute error (MAE). 2 3 1 ∑ðΟi −Οm ÞðΡi −Ρm Þ 6 7 Ν ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 7 ð9Þ R¼6 4 1 n 5 n 1 ∑ ðΟi −Οm Þ2 ∑ ðΡi −Ρm Þ2 Ν i¼1 Ν i¼1 N
∑ ðΡi −Οi Þ2 d ¼ 1−
i¼1 N
ð10Þ
∑ ðjΡi −Οm j þ jΟi −Οm jÞ
2
i¼1
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Ν ∑ ðΟi −Ρi Þ2 RMSE ¼ Ν i¼1 MAE ¼
ð11Þ
1 N ∑ jΟi −Ρi j N i¼1
ð12Þ
where N is the number of data points, Oi is the observed, and Pi is the corresponding predicted value of water temperature at time i. Om and Pm are the average values of Oi and Pi. The Willmott index of agreement is a standardized measure of the degree of model prediction error and varies between 0 and 1: a value of 1 indicates perfect agreement, while 0 indicates no match at all.
Results and discussion Daily water temperature (Tw) at the five reference stations described in the BStudy area^ section was predicted by using the MLPNN, ANFIS_GP, ANFIS_SC, and ANFIS_FC models. The four models were developed according to the following three different versions: (i) version 1 with only one input variable (Ta), (ii) version 2 with two inputs variable Table 3 Performances of different models in modeling water temperature (Tw; °C) for Botovo station
Model version
(Ta and Q), and (iii) version 3 with three inputs (Ta, Q, and the CGC). While for each machine learning model the three versions were based on the same architecture (the MLPNN model or the ANFIS models), we stress that they represent three substantially different river water temperature models due to the different combinations of variables used as predictors. The different machine learning models were compared based on the four statistical indices: RMSE, MAE, R, and d. According to the results obtained (Tables 3, 4, 5, 6, and 7), the following conclusions can be drawn. The comparative results between the three versions of the MLPNN, ANFIS_FC, ANFIS_GP, and ANFIS_SC, models revealed that the version 3 (i.e., the one with three inputs as predictors: Ta, Q, and the CGC) yielded the best accuracy among all the developed models, and outperform all the other versions in term of higher R and d and lower RMSE and MAE values, at the five stations. This result indicates that the use of CGC is complementary (not redundant) to the use of Ta and Q, as it provides additional information on the seasonality of the river thermal dynamics compared to that encapsulated in the Ta and Q time series. The comparison between the improvement in river water temperature prediction obtained using model version 3 and version 2 relative to model version 1 indicated that the inclusion of river flow discharge alone (model version 2) provided a lower gain than including CGC for case studies 1, 2, and 3, although its relative importance increases for cases 4 and 5, both in calibration and in validation. This confirms previous findings, which suggested that the role of flow discharge on river water temperature modeling is more relevant for high-altitude snowmelt-fed rivers and highly regulated river stations with hydropower plants at higher altitudes (Piccolroaz et al. 2016; Sohrabi et al. 2017). Figure 5 shows the monthly distribution of RMSE for each version of the MLPNN model and each river station considered in the analysis. In this case, the RMSE values for each
Training (calibration)
Validation
R
d
RMSE (°C)
MAE (°C)
R
d
RMSE (°C)
MAE (°C)
MLPNN3 MLPNN2 MLPNN1 ANFIS_GP3
0.981 0.933 0.926 0.982
0.990 0.964 0.961 0.991
1.227 2.267 2.366 1.193
0.956 1.725 1.838 0.923
0.977 0.926 0.922 0.972
0.988 0.961 0.958 0.986
1.307 2.287 2.350 1.435
1.040 1.763 1.836 1.127
ANFIS_GP2 ANFIS_GP1 ANFIS_SC3 ANFIS_SC2 ANFIS_SC1 ANFIS_FC3 ANFIS_FC2 ANFIS_FC1
0.932 0.926 0.972 0.932 0.926 0.979 0.933 0.926
0.964 0.961 0.985 0.964 0.960 0.989 0.964 0.961
2.276 2.365 1.483 2.283 2.368 1.281 2.263 2.366
1.735 1.837 1.171 1.744 1.840 1.006 1.726 1.837
0.926 0.922 0.972 0.927 0.922 0.974 0.926 0.922
0.961 0.958 0.986 0.961 0.958 0.987 0.961 0.958
2.287 2.348 1.429 2.283 2.350 1.368 2.291 2.349
1.761 1.833 1.128 1.755 1.835 1.076 1.763 1.835
Environ Sci Pollut Res Table 4 Performances of different models in modeling water temperature (Tw; °C) for Donji Miholjac station
Model version
Training (calibration) R
d
RMSE (°C)
MAE (°C)
R
d
RMSE (°C)
MAE (°C)
MLPNN3
0.984
0.992
1.290
1.014
0.971
0.986
1.690
1.337
MLPNN2 MLPNN1 ANFIS_GP3 ANFIS_GP2 ANFIS_GP1 ANFIS_SC3 ANFIS_SC2 ANFIS_SC1 ANFIS_FC3 ANFIS_FC2 ANFIS_FC1
0.938 0.934 0.984 0.938 0.934 0.976 0.937 0.933 0.981 0.939 0.934
0.967 0.965 0.992 0.967 0.965 0.988 0.967 0.964 0.990 0.968 0.965
2.487 2.579 1.284 2.487 2.576 1.562 2.513 2.585 1.388 2.481 2.575
1.909 2.012 1.002 1.910 2.009 1.245 1.934 2.014 1.098 1.905 2.009
0.932 0.928 0.969 0.933 0.928 0.968 0.932 0.928 0.972 0.933 0.928
0.964 0.962 0.984 0.965 0.962 0.983 0.964 0.962 0.986 0.965 0.962
2.578 2.645 1.770 2.551 2.645 1.789 2.577 2.642 1.685 2.556 2.647
1.999 2.063 1.352 1.976 2.063 1.416 2.001 2.060 1.328 1.976 2.066
month were calculated based on daily Tw values for that same month of the year. For models MLPNN1 (version 1 with only Ta as input variable), local maxima in RMSE are clearly visible in all river stations, and show strong correlation with the seasonal pattern of Q summarized in Fig. 2. In particular, RMSE shows a clear increase during the seasons of higher river flow discharge, except for case 4 (the Rhône River), where they occur just before and after this period. As discussed above, the inclusion of Q in the model (MLPNN2) slightly improves model performance by decreasing RMSE, but does not remove the presence of these local maxima in RMSE during the wet seasons. However, when also CGC is added to the model (MLPNN3), besides a general marked improvement of the prediction capability, one can also appreciate a general flattening of RMSE (particularly for the Dischmabach) that assumes an almost uniform distribution throughout the year. This
Table 5 Performances of different models in modeling water temperature (Tw; °C) for Yvonand station
Validation
Model version
MLPNN3 MLPNN2 MLPNN1 ANFIS_GP3 ANFIS_GP2 ANFIS_GP1 ANFIS_SC3 ANFIS_SC2 ANFIS_SC1 ANFIS_FC3 ANFIS_FC2 ANFIS_FC1
confirms that in the proposed model, Q alone may not be sufficiently informative and that the addition of CGC significantly contributes to better capture the seasonal pattern. This is coherent with previous findings by Piccolroaz et al. (2016), which suggested that in their hybrid air2stream model, the value of adding the role of flow discharge was not much associated to the incorporation of the thermal inertia of the river through the inclusion of water depth, but more to the possibility to account for the effect of upstream and lateral contributing water and heat fluxes. In that model, in fact, besides the dependence on Ta and Q, a sinusoidal annual term with annual periodicity was included to mimic the effect of lateral inflows and heat fluxes, which is analogous to the inclusion of CGC in model MLPNN3. Results at Botovo station are reported in Table 3. A clear increase of model performances can be observed from version
Training (calibration)
Validation
R
d
RMSE (°C)
MAE (°C)
R
d
RMSE (°C)
MAE (°C)
0.991 0.979 0.978 0.984 0.978 0.978 0.987 0.978 0.977 0.986 0.980 0.978
0.995 0.989 0.989 0.992 0.989 0.989 0.993 0.989 0.988 0.993 0.990 0.989
0.790 1.165 1.210 1.024 1.196 1.207 0.937 1.209 1.217 0.962 1.157 1.211
0.610 0.884 0.927 0.790 0.917 0.925 0.731 0.926 0.932 0.753 0.885 0.927
0.988 0.976 0.975 0.980 0.976 0.975 0.984 0.975 0.975 0.983 0.976 0.975
0.994 0.987 0.987 0.990 0.987 0.987 0.992 0.987 0.987 0.991 0.987 0.987
0.913 1.287 1.307 1.166 1.292 1.314 1.054 1.303 1.308 1.080 1.286 1.309
0.685 0.970 0.982 0.878 0.968 0.987 0.790 0.985 0.989 0.820 0.965 0.985
Environ Sci Pollut Res Table 6 Performances of different models in modeling water temperature (Tw; °C) for Sion station
Model version
Training (calibration) R
d
RMSE (°C)
MAE (°C)
R
d
RMSE (°C)
MAE (°C)
MLPNN3
0.966
0.982
0.547
0.422
0.944
0.971
0.763
0.530
MLPNN2 MLPNN1 ANFIS_GP3 ANFIS_GP2 ANFIS_GP1 ANFIS_SC3 ANFIS_SC2 ANFIS_SC1 ANFIS_FC3 ANFIS_FC2 ANFIS_FC1
0.944 0.935 0.963 0.943 0.935 0.952 0.942 0.935 0.959 0.945 0.935
0.970 0.966 0.981 0.970 0.966 0.975 0.969 0.965 0.979 0.971 0.966
0.695 0.744 0.568 0.697 0.743 0.642 0.705 0.748 0.598 0.690 0.744
0.535 0.572 0.437 0.536 0.572 0.490 0.542 0.576 0.462 0.531 0.572
0.939 0.927 0.949 0.938 0.926 0.939 0.937 0.926 0.941 0.939 0.927
0.969 0.962 0.974 0.968 0.962 0.968 0.968 0.962 0.970 0.968 0.962
0.790 0.864 0.723 0.795 0.865 0.793 0.801 0.866 0.779 0.794 0.864
0.582 0.652 0.508 0.582 0.653 0.571 0.585 0.652 0.548 0.584 0.652
1 to version 3, as the R and d values increased gradually and the RMSE and MAE values decreased significantly. During the validation phase, the predicted Tw values correlate generally well with the observed Tw values for most of the proposed models. Using only Ta as input variable, it is clear that all the four models provided the same accuracy. Although including Q as input variable of the models (version 2) decreased the RMSE and MAE values, the percentage of improvement is not as significant (Table 3). Broadly speaking, the four models provided relatively the same accuracy with only very marginal difference. Inclusion of the CGC significantly improves the accuracy of the models, and the most significant improvement is achieved by the MLPNN3 model (RMSE = 1.307 °C, MAE = 1.040 °C), followed by the ANFIS_FC3 (RMSE = 1.368 °C, MAE = 1.076 °C), and then by the ANFIS_SC3 (RMSE = 1.429 °C, MAE = 1.128 °C) and ANFIS_GP3 (RMSE = 1.435 °C, MAE = 1.127 °C) in the validation period. Table 7 Performances of different models in modeling water temperature (Tw; °C) for Davos station
Validation
Model version
MLPNN3 MLPNN2 MLPNN1 ANFIS_GP3 ANFIS_GP2 ANFIS_GP1 ANFIS_SC3 ANFIS_SC2 ANFIS_SC1 ANFIS_FC3 ANFIS_FC2 ANFIS_FC1
The improvement is clearly visible using MLPNN3, and leads to significant decreasing in the RMSE and MAE of the MLPNN1 by 44.38% and 43.36%. ANFIS_FC3 guaranteed the second significant improvement by decreasing the RMSE and MAE of the ANFIS_FC1 by 41.76% and 41.36%, respectively. Finally, the ANFIS_GP3 and ANFIS_SC3 achieved the same improvement accuracy of about 39%. Overall, by comparing the four models, the MLPNN3 is more accurate than the three ANFIS models. The scatterplots and comparison between observed and predicted Tw for the best models (validation phase) at Botovo station are presented in Fig. 6. Table 4 provides the detailed training and validation results for the four models at Donji Miholjac station, which indicates that the daily Tw calculated using only the Ta is in good agreement with the observed values, and the MLPNN1, ANFIS_GP1, ANFIS_SC1, and ANFIS_FC1 models have the same accuracy. The validation results have no significant
Training (calibration)
Validation
R
d
RMSE (°C)
MAE (°C)
R
d
RMSE (°C)
MAE (°C)
0.990 0.966 0.951 0.992 0.966 0.951 0.980 0.962 0.950 0.986 0.967 0.951
0.995 0.983 0.974 0.996 0.983 0.974 0.990 0.980 0.974 0.993 0.983 0.974
0.398 0.743 0.894 0.370 0.742 0.890 0.578 0.783 0.900 0.473 0.735 0.893
0.313 0.559 0.677 0.289 0.560 0.673 0.458 0.590 0.685 0.376 0.555 0.676
0.987 0.964 0.950 0.976 0.965 0.950 0.976 0.963 0.951 0.983 0.964 0.950
0.994 0.981 0.973 0.988 0.982 0.973 0.987 0.981 0.974 0.991 0.981 0.973
0.457 0.759 0.896 0.639 0.750 0.898 0.631 0.775 0.886 0.531 0.768 0.895
0.366 0.571 0.691 0.472 0.562 0.690 0.504 0.588 0.684 0.421 0.585 0.689
Environ Sci Pollut Res Fig. 5 Monthly distribution of RMSE for each version of the MLPNN model and each river station. a Drava at Botovo. b Drava at Donji Miholjac. c Mentue. d Rhône. e Dischmabach
difference for all the four models. For the version 2 using Ta and Q as predictors, the accuracy of the models were only slightly better than version 1, which indicates that the contribution of the Q for the estimation of the Tw is marginal. However, when the CGC was added to Ta and Q (version 3), the performances of the models were significantly improved. The ANFIS_FC3 was the most accurate model with the lowest RMSE and MAE values (RMSE = 1.685 °C, MAE = 1.328 °C) and higher R and d values (R = 0.972, d = 0.986), slightly better than the MLPNN3 (RMSE = 1.690 °C, MAE = 1.337 °C), ANFIS_GP3 (RMSE = 1.770 °C, MAE = 1.352 °C), and
ANFIS_SC3 (RMSE = 1.789 C, MAE = 1.416 °C). The scatterplots and comparison between observed and predicted Tw for the best models at Donji Miholjac station (validation phase) are shown in Fig. 7. The performances of the models for the Yvonand station at Mentue River are summarized in Table 5. The R and d values for the models ranged between 0.975 and 0.988, 0.975 and 0.980, 0.975 and 0.984, and 0.975 and 0.983, for the MLPNN, ANFIS_GP, ANFIS_SC, and ANFIS_FC, respectively. The RMSE and MAE values by the models of the version 3 were much smaller than the values provided by the models of the
Environ Sci Pollut Res 25
Observed Tw (°C)
Predicted Tw (°C)
25
Predicted Tw (°C)
Tw (°C)
20 15 10 5
25
y = 0.9614x + 0.4761 R² = 0.9537
20
20
15
15
10
10
5
2701
0
Observed Tw (°C)
Predicted Tw (°C)
25
Predicted Tw (°C)
20 Tw (°C)
15 10 5
0 0
Time (days) 25
5
(a)
2851
2551
2401
2251
2101
1801
1951
1651
1501
1351
1201
901
1051
601
751
451
301
151
1
0
5 10 15 20 Observed Tw (°C)
25
25
y = 0.9591x + 0.5018 R² = 0.9494
20
20
15
15
10
10
5
5
2701
2551
2401
2251
2101
Observed Tw (°C)
(b)
2851
25
1801
Time (days)
1951
1651
1501
1351
1201
1051
901
751
601
451
151
301
1
0 0
Predicted Tw (°C)
25
Predicted Tw (°C)
20 Tw (°C)
15 10 5
0 0
5 10 15 20 Observed Tw (°C)
25
25
y = 0.957x + 0.5908 R² = 0.9446
20
20
15
15
10
10 5
5
2851
2701
2401
2551
2251
2101
1951
1801
1651
1501
1351
1201
1051
901
751
601
451
301
1
151
0
0 0
Time (days) 25
Observed Tw (°C)
Predicted Tw (°C)
25
Predicted Tw (°C)
20 Tw (°C)
15 10 5
(c) 5
10 15 20 Observed Tw (°C)
0 25
25
y = 0.946x + 0.6428 R² = 0.9446
20
20
15
15
10
10
5
Time (days)
2851
2701
2551
2401
2251
2101
1951
1801
1651
1501
1351
1201
901
1051
751
601
451
301
151
1
0
5
(d)
0 0
5 10 15 20 Observed Tw (°C)
0
25
Fig. 6 Scatterplots and comparison between observed and predicted river water temperature (Tw) for the best models at Botovo station. a MLPNN3. b ANFIS_FC3. c ANFIS_GP3. d ANFIS_SC3
versions 1 and 2. Switching from version 1 to version 2 by the inclusion of the Q as input variable did not improve significantly the performances of the models, especially for the ANFIS_SC model, as the percentage of improvement of the RMSE and MAE was lower than 0.5%. By contrast, the models for the version 3 showed a good accuracy and significant improvement. The MLPNN3 has the highest ratio in decreasing the RMSE and MAE of the MLPNN1 with 30.15% and 30.24%, respectively, compared to 11.26% and
11.24% for the ANFIS_GP3, 19.42% and 20.12 for the ANFIS_SC3, and 17.49% and 16.75% for the ANFIS_FC3, respectively. The scatterplots and comparison between observed and predicted Tw for the best models at Mentue station (validation phase) are reported in Fig. 8. The performances of the models for the Sion station at Rhône River are summarized in Table 6. As a preliminary analysis, we investigated the performance of the four models using only Ta as input variable. The statistical indices clearly show
Environ Sci Pollut Res 30
Observed Tw (°C)
30
Predicted Tw (°C)
25 Predicted Tw (°C)
Tw (°C)
24 18 12 6
20
15
15
10
10
5
2851
2701
2551
2401
2251
2101
1951
1801
1651
1501
1351
1051
1201
901
601
751
451
301
1
151
0
0 0
Predicted Tw (°C)
15 10 5
10 15 20 25 Observed Tw (°C)
20 15
10
10
2851
2701
2551
2401
2251
2101
1951
1801
1651
1351
1501
1201
1051
901
751
601
451
301
1
151
0 0
30
Predicted Tw (°C) Predicted Tw (°C)
Tw (°C)
24
12 6
5
10 15 20 25 Observed Tw (°C)
25
20
20
15
15
10
10
2851
2701
2551
2401
2251
2101
1951
1801
1651
1501
1351
1201
1051
901
751
601
451
301
151
1
0
0 0
Predicted Tw (°C)
30
Predicted Tw (°C)
25 20 15 10 5
5
2851
2701
2551
2401
2251
2101
1951
1801
1651
1501
1351
1201
1051
901
751
601
451
301
151
1
Time (days)
10 15 20 25 Observed Tw (°C)
30
30
y = 0.946x + 0.7048 R² = 0.9366
25
25
20
20
15
15
10
10
5
0
5
(c)
Time (days)
Tw (°C)
30
y = 0.9559x + 0.6401 R² = 0.9384
5
Observed Tw (°C)
0
30
25
0
30
5
(b)
Time (days)
18
25
15
5
Observed Tw (°C)
30
20
0
30
30
y = 0.9637x + 0.4407 R² = 0.944
25 Predicted Tw (°C)
Tw (°C)
5
30
25 20
5
(a)
Time (days) Observed Tw (°C)
25
20
0
30
30
y = 0.9638x + 0.4798 R² = 0.9438
5
(d)
0 0
5
10 15 20 25 Observed Tw (°C)
0 30
Fig. 7 Scatterplots and comparison between observed and predicted river water temperature (Tw) for the best models at Donji Miholjac station. a MLPNN3. b ANFIS_FC3. c ANFIS_GP3. d ANFIS_SC3
that there was no significant difference in the prediction of Tw based on the Ta variable and the models provided similar accuracy with little variation. The RMSE of the MLPNN1, ANFIS_GP1, ANFIS_SC1, and ANFIS_FC1 remains relatively low (0.864 °C to 0.866 °C), MAE between 0.652 °C and 0.653 °C, followed by R and d equal to 0.927 and 0.962, respectively. The obtained modeling results for version 2 clearly show that the MLPNN2 has generally slightly improved performances with respect to the other models. For instance, the R and d are equal to 0.939 and 0.969 for MLPNN2, 0.938 and
0.968 for ANFIS_GP2 and ANFIS_SC2, and 0.939 and 0.968 for ANFIS_FC2. Indeed, the inclusion of Q to the input variable has contributed to an improvement in model accuracy, especially by decreasing the RMSE and MAE values (Table 6); however, the Q provided a lower improvement of Tw prediction compared to the inclusion of the CGC (version 3). MLPNN3 improved the accuracy of the MLPNN1 by decreasing the RMSE and MAE by 11.670% and 18.71%, against 8.56% and 10.74% achieved by MLPNN2. Similarly, ANFIS_GP3 decreased the RMSE and MAE of the ANFIS_GP1 by 16.42% and 22.21%,
Environ Sci Pollut Res 25
Observed Tw (°C)
Predicted Tw (°C)
25
Predicted Tw (°C)
Tw (°C)
20 15 10 5
25
y = 0.955x + 0.4992 R² = 0.9764
20
20
15
15
10
10
5
5
(a)
1081
1021
961
901
841
781
721
601
661
541
481
421
361
301
241
181
61
121
1
0 0
0 0
5
Time (days) 25
15
20
Observed Tw (°C)
Predicted Tw (°C)
25
Predicted Tw (°C)
15 10 5
25
y = 0.9553x + 0.4873 R² = 0.9664
20
20
15
15
10
10 5
5
1081
1021
961
901
841
781
721
661
601
541
481
421
301
361
241
181
121
61
1
0
(b)
0 0
5
Time (days) 25
10
15
20
Observed Tw (°C)
Predicted Tw (°C)
25
25
y = 0.956x + 0.467 R² = 0.9606
20
Predicted Tw (°C)
20
15 10 5
15
15
10
10 5
5
(c)
1081
1021
961
901
841
781
721
661
601
541
481
421
361
301
241
181
61
121
1
0
0
0 0
5
Time (days) 25
10
15
20
25
Observed Tw (°C)
Observed Tw (°C)
Predicted Tw (°C)
25
Predicted Tw (°C)
20 Tw (°C)
15 10 5
25
y = 0.9542x + 0.4901 R² = 0.968
20
20
15
15
10
10
5
5
Time (days)
1081
1021
961
901
841
781
721
601
661
541
481
361
421
301
241
181
61
121
0 1
0
25
Observed Tw (°C)
20 Tw (°C)
25
Observed Tw (°C)
20 Tw (°C)
10
(d) 0
0 0
5
10 15 20 Observed Tw (°C)
25
Fig. 8 Scatterplots and comparison between observed and predicted river water temperature (Tw) for the best models at Yvonand station. a MLPNN3. b ANFIS_FC3. c ANFIS_GP3. d ANFIS_SC3
against 8.09% and 10.87% achieved by ANFIS_GP2. In the same context, ANFIS_SC3 decreased the RMSE and MAE of the ANFIS_SC1 by 8.43% and 12.42%, against 7.51% and 10.28% achieved by ANFIS_SC2. Finally, ANFIS_FC3 decreased the RMSE and MAE of the ANFIS_FC1 by 8.84% and 15.95%, against 8.10% and 10.43% achieved by ANFIS_FC2. The scatterplots and comparison between observed and predicted Tw for the best models at Sion station (validation phase) are presented in Fig. 9.
Results for the Davos station at Dischmabach River are shown in Table 7. It is clear from the results that the four models developed using only the Ta as input variable showed good agreement with the observed Tw, expressed by the high values of R and d (R ≈ 0.950, d ≈ 0.973), and low values of error: RMSE≈0.896 °C, MAE≈0.690 °C. Additionally, the modeling results indicate that the ANFIS_SC1 performed slightly better than the other models. Contrary to the results obtained in the four previous stations (Botovo, Donji
Environ Sci Pollut Res 12
Observed Tw (°C)
Predicted Tw (°C) Predicted Tw (°C)
Tw (°C)
9
12
6 3
12
y = 0.9249x + 0.5362 R² = 0.8905
9
9
6
6
3
3
3601
3421
3241
3061
2701
2881
2341
2521
2161
1981
1801
1441
1621
1261
901
1081
721
541
361
1
181
0
(a)
0 0
3
6 9 Observed Tw (°C)
Time (days) 12
Observed Tw (°C)
Predicted Tw (°C)
y = 0.9117x + 0.6276 R² = 0.8854 Predicted Tw (°C)
Tw (°C)
12
12
9 6 3
9
9
6
6
3
3
3601
3421
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12
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9 Tw (°C)
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y = 0.9234x + 0.5598 R² = 0.901
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0 0
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Time (days) Observed Tw (°C)
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12
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9 Tw (°C)
6 3
6 9 Observed Tw (°C)
3601
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1801
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1
Time (days)
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12
y = 0.9055x + 0.6749 R² = 0.8809
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0 181
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Observed Tw (°C)
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0
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(d) 0
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Fig. 9 Scatterplots and comparison between observed and predicted river water temperature (Tw) for the best models at Sion station. a MLPNN3. b ANFIS_FC3. c ANFIS_GP3. d ANFIS_SC3
Miholjac, Yvonand, and Sion), inclusion of the Q as input variables (version 2) improved significantly the performances of the models. Indeed, MLPNN2 decreased the RMSE and MAE of the MLPNN1 by 15.30% and 17.40%, and ANFIS_GP2 improved the accuracy of the ANFIS_GP1 by decreasing the RMSE and MAE of about 16.50% and 18.55%, respectively. The improvement guaranteed by the ANFIS_SC2 is less than the improvement provide by the MLPNN2 and ANFIS_GP2 and reached
relatively low percentage reduction in RMSE and MAE of 12.53% and 14.04%, respectively. Finally, ANFIS_FC2 improved the accuracy of the ANFIS_FC1 by decreasing the RMSE and MAE of about 14.19% and 15.09%, respectively. The overall accuracy of the four models for the version 3 shows that the MLPNN3 outperformed all the other three models. The scatterplots and comparison between observed and predicted Tw for the best models at Davos station (validation phase) are shown in Fig. 10.
Environ Sci Pollut Res 12
Observed Tw (°C)
Predicted Tw (°C) Predicted Tw (°C)
Tw (°C)
9
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y = 0.9767x + 0.1158 R² = 0.9745
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1081
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1021
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0
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y = 0.9903x + 0.0353 R² = 0.9662
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y = 0.9994x - 0.0271 R² = 0.9526
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y = 0.9379x + 0.3349 R² = 0.9522
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Fig. 10 Scatterplots and comparison between observed and predicted river water temperature (Tw) for the best models at Davos station. a MLPNN3. b ANFIS_FC3. c ANFIS_GP3. d ANFIS_SC3
Conclusions Water temperature is an important indicator which impacts the overall health of rivers, and the accurate prediction of water temperature is one of the most important issues for river management. In this study, MLPNN and three ANFIS models (ANFIS_FC, ANFIS_GP, and ANFIS_SC) were developed to model daily water temperature for rivers. The proposed models were tested in five river stations characterized by
different hydrological conditions. In the validation phase, MLPNN models performed well for the Botovo, Yvonand, and Davos stations with lower RMSE and MAE, and higher R and d values. At Donji Miholjac station, ANFIS_FC3 was more accurate, while the ANFIS_GP3 is the best model at Sion station. Modeling results showed that the inclusion of three inputs as predictors (Ta, Q, and the CGC) yielded the best modeling accuracy among all the developed models, indicating a significant improvement compared to the case when
Environ Sci Pollut Res
only Ta is used as predictor, as typically assumed in most of previous machine learning applications. Results showed that the use of CGC is complementary to the use of Ta and Q, and provides additional relevant information on the seasonality of the river thermal dynamics, possibly mimicking the effect of lateral and upstream water and heat inputs. In addition, the results indicated that for highly regulated river stations with hydropower plants and snowmelt-fed rivers at higher altitudes, the role of flow discharge on river water temperature modeling becomes more important. Overall, modeling performance indicated that the machine learning models developed in this study can be effectively used for river water temperature prediction. Acknowledgements We acknowledge the Swiss Federal Office of the Environment (FOEN), the Swiss Meteorological Institute (MeteoSchweiz), and the Croatian Meteorological and Hydrological Service for providing the water temperature, air temperature, and river flow discharge data used in this study. We thank an anonymous reviewer for the useful comments and suggestions which helped to improve the quality of the study. Funding This work was jointly funded by the National Key R&D Program of China (2018YFC0407203, 2016YFC0401506) and the research project from Nanjing Hydraulic Research Institute (Y118009).
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