




































 
 

 

1 
© 2019 by the authors; licensee Asian Online Journal Publishing Group 
 

Asian Review of Environmental and Earth Sciences 
Vol. 6, No. 1, 1-8, 2019 

ISSN(E) 2313-8173 / ISSN(P) 2518-0134 
DOI: 10.20448/journal.506.2019.61.1.8 

© 2019 by the authors; licensee Asian Online Journal Publishing Group 

    

 
 
 
Water Temperature Prediction Models in Northern Coastal Area, Vietnam 

 
Nguyen Xuan Trinh1   

Tu Quang Trinh2   

Thanh Phuong Phan3    

Tung Nguyen Thanh4   

Bach Nguyen Thanh5    

   
( Corresponding Author)  

1,2,3,4,5Vietnam Institute of Fisheries Economics and  Planning, Vietnam 

 
 

 
Abstract 

This paper presents the results of regression models (linear, nonlinear and stochastic regression) 
and artificial neural network models (ANN) using observed data of daily maximum air and water 
temperature at Bai Chay station in the coastal areas of Northern Delta, Vietnam. The accuracy of 
the models was evaluated and compared by R, RMSE, RMSE% and E indicators. The ANN model 
was highlight results with the RMSE = 1.24; R = 0.98; E = 0.9; RMSE% = 4. The results of the 
study also show that daily water temperature is affected by daily maximum and average air 
temperature of previous 1 and 2 days. The main contribution of this study is to identify the 
appropriate models and time lag factors for water temperature prediction from the air temperature 
applied to neighboring meteorological stations without water temperature monitoring data. The 
results of the study could be used as a basis for determining the spatial distribution of water 
temperature risk to aquaculture in the coastal areas of Northern Delta, Vietnam. 

 
Keywords: Mathematical methods, Environmental issues, Climate, Water, Forecasting models, Model evaluation 

 
Citation | Nguyen Xuan Trinh; Tu Quang Trinh; Thanh Phuong 
Phan; Tung Nguyen Thanh; Bach Nguyen Thanh (2019). Water 
Temperature Prediction Models in Northern Coastal Area, Vietnam. 
Asian Review of Environmental and Earth Sciences, 6(1): 1-8. 
History:  
Received: 12 October 2018 
Revised: 15 November 2018 
Accepted: 17 December 2018 
Published: 25 January 2019 
Licensed: This work is licensed under a Creative Commons 

Attribution 3.0 License  
Publisher:  Asian Online Journal Publishing Group 
 

Contribution/Acknowledgement: The authors gratefully acknowledge all 
the support and assistance of the Program Management Board. The authors 
also wish to thank the referee, the editor, and Sara Lim for helpful comments 
and constructive criticism. 
Funding: This research has been funded by the Government of Vietnam 
under the Program of Scientific and Technological Research for 
Environmental Protection and Disaster Prevention (Code KC08/16-20). 
Competing Interests: The authors declare that they have no conflict of 
interests. 
Transparency: The authors confirm that the manuscript is an honest, 
accurate, and transparent account of the study was reported; that no vital 
features of the study have been omitted; and that any discrepancies from the 
study as planned have been explained. 
Ethical: This study follows all ethical practices during writing.   

 

 

Contents 
1. Introduction ......................................................................................................................................................................................... 2 
2. Data and Methodology ...................................................................................................................................................................... 2 
3. Results and Discussion ...................................................................................................................................................................... 4 
4. Conclusions .......................................................................................................................................................................................... 7 
References ................................................................................................................................................................................................. 8 
 

 
 
 
 
 
 
 

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http://asianonlinejournals.com/index.php/AREES/article/view/709
https://orcid.org/0000-0002-1762-9927
https://orcid.org/0000-0002-9941-104X
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0002-8614-7833
http://asianonlinejournals.com/index.php/AREES/article/view/709
https://orcid.org/0000-0002-1762-9927
https://orcid.org/0000-0002-9941-104X
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0002-8614-7833
http://asianonlinejournals.com/index.php/AREES/article/view/709
https://orcid.org/0000-0002-1762-9927
https://orcid.org/0000-0002-9941-104X
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0002-8614-7833
http://asianonlinejournals.com/index.php/AREES/article/view/709
https://orcid.org/0000-0002-1762-9927
https://orcid.org/0000-0002-9941-104X
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0002-8614-7833
http://asianonlinejournals.com/index.php/AREES/article/view/709
https://orcid.org/0000-0002-1762-9927
https://orcid.org/0000-0002-9941-104X
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0002-8614-7833
http://asianonlinejournals.com/index.php/AREES/article/view/709
https://orcid.org/0000-0002-1762-9927
https://orcid.org/0000-0002-9941-104X
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0002-8614-7833
http://asianonlinejournals.com/index.php/AREES/article/view/709
https://orcid.org/0000-0002-1762-9927
https://orcid.org/0000-0002-9941-104X
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0001-9945-5766
https://orcid.org/0000-0002-8614-7833


Asian Review of Environmental and Earth Sciences, 2019, 6(1): 1-8 

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1. Introduction 
Water temperature plays an important role in aquatic life, including aquaculture species [1, 2]. The water 

temperature affects other environmental parameters such as DO, BOD, algae growth, etc., and gets vulnerable to 
pathogenic bacteria. There are many factors affecting water temperature such as atmospheric conditions, 

topography and water flow [3]. Among atmospheric factors (solar radiation, air temperature, wind speed, humidity 
etc.), air temperature is the most factor affecting the variation in surface water temperature [4] that lead to series 
of water condition change. 

In the northern coastal region of Vietnam, beside natural disasters which directly affect fisheries such as 
storms, floods .etc. every year, the air temperature in summer can reach 39-400C with hot temperature in long 
duration, which makes the water temperature too high for the tolerance of aquatic species. On the other hand, when 
the water temperature rises, aquatic species tend to be active in water of deeper level, leading to an increase in 
oxygen demand [4] increasing the risk for intensive aquaculture ponds, so temperature is a particularly important 
factor threatening the stable development of aquaculture sector. Therefore, when studying disaster risks for 
aquaculture, it is indispensible to consider the risks of maximum daily water temperature to determine the viability 
of aquatic species [5]. 

However, water temperature prediction is still a complexity [4] because water temperature depends on many 
factors. There are number of different application for water temperature predition model Loubna, et al. [6]. Caissie 
[3] divided into 3 main categories: regression, stochastic, and deterministic models. Otherwise, Caissie [3] and 
Zhu, et al. [2] gave two categories deterministic and statistical models that they have advantages and drawback. 

The deterministic model applies simulations of water temperature using an approach that relates to the total 
amount of solar energy reaching the earth and the interrelated factors for determining water temperature (eg 
Sinokrot and Stefan [7]; Webb and Nobilis [8]). This approach is often impractical, complex and time-consuming 
in collecting and processing input data of many of the explanatory variables which are often difficult to collect such 
as solar radiation, wind, atmospheric energy [4, 6]. 

Statistical models could be classified in two categories including parametric and non-parametric models. 
Parametric models can also be decomposed into regression and stochatic models.  

 The regression model simulating water temperature based on air temperature is commonly used in many 
studies due to the simplicity of the collected data and applied for weekly, monthly and annual time steps of data. 
The regression models including: single and multi-variabe linear regression or nonlinear regression. Simple linear 
regression using air temperature (monthly or weekly data) is an explanatory variables to determine water 
temperature [9]. The nonlinear regression model proposed by Mohseni, et al. [10] provided the base to many 
successful studies [11, 12]. However, regression simulation (linear or nonlinear) is less suitable to apply for shorter 
time steps such as daily data (due to autocorrelation in time series of water temperature) [6]. 

The stochastic model [13, 14] was developed from the regression model, proposed by Kothandaraman [15] 
based on statistics of continuous time series of air temperature and water temperature to act as a basis for defining 
relationships through parameters. The stochastic model is generally applied to relatively short time data (hourly or 
daily data) and takes into account the time lag of the relevant factors. 

None-parametric models (k-Nearest Neighbour, Artificial Neural Network model-ANN, etc.) use the structure 
of availble data [6]. Artificial Neural Network model (ANN) has recently been developed with 3 basic layers of 
multi-layer backpropagation network model [2, 4]: the input layer, one or more hidden layers, and the output 
layer. The model always uses input data divided into two categories, namely training  and testing data set. 
Application of ANN method has been successfully proved by some studies for water temperature predition (ex: 
Anamarija [4]; Marijana, et al. [16]; Sahoo, et al. [17]; Zhu, et al. [2]; DeWeber and Wagner [18]). However, 
the comparison bettween models showed, in some cases ANN models provided better results, while in other case, 
some regression models provide higher accuracy  of results [2]. Their resluts may depend on data quality and 
study areas, variables of time lags of the daily mean air temperature in multilayer perception ANN models. 
Therefore,the purpose of this study is to collect the appropriate model of water temperature prediction from air 
temperature data applying for the meteorological stations without  observed water temperature and serving for 
determining the risk thresholds to aquaculture Northern coastal areas Vietnam. 
 

2. Data and Methodology 
2.1. Data 

Data of Bai Chay station, Quang Ninh province was used to evaluate the accuracy of the models. 10-years data 
(2008-2017) of daily air temperature and water temperature including maximum air temperature(Ta_max); 
maximum water temperature(Tw-max); average air temperature(Ta_tb); average water temperature(Tw_tb) of Bai 
Chay station is collected. 

 

 
Figure-1. Variation of water and air temperature 

                Source: Data collected from Bai Chay station (e.g. of  year 2008) 



Asian Review of Environmental and Earth Sciences, 2019, 6(1): 1-8 

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Figure 1 shows the correlation between the maximum water and the air temperature at Bai Chay station with 
the data 2008, points out that the water temperature always changes linearly depending on the maximum and 
average air temperature. During the year, the maximum water temperature is always lower than the maximum, but 
higher than the average air temperature. In some case, When fluctuation of day and night temperature suddenly 
change,the maximum water temperature may be higher than that ones of air temperature (in summer). Thus, the 
maximum water temperature in a period of time always changes slowly and is not synchronized with the maximum 
air temperature and it creates a delay time between Ta_max and Tw-max  

 
2.2. Methodology 
A. Simple Linear Regression Model  

A simple linear regression model used a linear function with a single explanatory variable. The regression 
model simulates the variation of water temperature determined by the correlation with air temperature. 

Simple linear regression equation:  

(1) 
Tw(t): water temperature in time t 
Ta(t): air temperature in time t; a0, a1 is the coefficient of the regression equation 

ε(t): Error [6] 

 
B. Nonlinear Regression Model 

Most common nonlinear regression methods involve air and water temperatures [6] with 5 parameters.. 

    
 

             (2) 

Where  Tw: Daily maximum water temperature predition 
Ta: Air temperature measured by day t  

, , β: The coefficient of the model, calculated by using the nonlinear regression model under the 
condition of minimum sum of squared difference (SSD). 

C. Stochastic Model 
Stochastic model proposed by Kothandaraman [15] and Cluis [19]. In the model, water temperature TW is 

simulated by 2 basic components: (i) air temperature in long periods of time and water temperature in short time 
period. 

 

                           (3) 

              
  

   
              (4) 

sin () function in Equation (4) shows the trend of variation of water temperature by season or year cycle. 
TA(t): Seasonal air temperature; a,b, t0: The correlation coefficient of the model which can be identified by 

nonlinear regression model. 
Rw(t): Water temperature over short period of time  
The stochastic model is used based on the development of a model proposed by Kothandaraman [15] that 

determines the time lag between water temperature and air temperature 

                                      (5) 

Where: β1, β2 and β3 are the correlation coefficients of the model, calculated by using the nonlinear regression 
model under the condition of the minimum sum of squared differences. 

Ra(t), Ra(t – 1) and Ra(t – 2) is the air temperature at time t, (t – 1), (t – 2). 

              
  

   
                                     (6) 

In model (6), the water temperature at time t is determined based on the dependence of daily air temperature by 
the sine function in Equation (4) and the lag over time (lag = 1 and lag = 2), corresponding to time t-1 (1 day 
before) and t-2 (2 days before) of air temperature Equation (5). 
 

D. Artificial Neural Networks -ANN 
In recent years, ANN has been applied quite widely in many areas related to estimation and forecasting due to 

high accuracy when complex nonlinear models are difficult to achieve by conventional mathematical equations [3, 
17, 20]. In this study, ANN model are used to identify the daily maximum water temperature with the neurons as 
input data of the maximum and average air temperature in a time period to determine the time lag between air and 
water temperature. 

Figure 2 show the basic structure of ANN consisting of three basic layers: (i) Input layer (data layer entered - 
Input layer) are neurons X1, X2, ... Xn; (ii) One or more hidden layers - (processing data layer -Hidden layer); and 
(iii) output data layer (output data layer created - Output layer). Each layer in ANN consists of nodes (neurons), 
each neuron connects to another neuron of the previous layer and moves from the data layer into the hidden layer 
to the output layer. In an ANN there might be multiple hidden layers, each neuron in the hidden layer consists of 
three components, including weights; bias and activation function. The activation function mainly used is sigmoid 
function (including logsig, tansig- Nonlinear function) or purelin - linear function. 
 



Asian Review of Environmental and Earth Sciences, 2019, 6(1): 1-8 

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Figure-2. Structure of ANN model 

                                                Source: Modified from Srivastav, et al. [21] 

 
According to Marijana, et al. [16] mathematically, neuron is calculated by the equation: 

 
Y= (v) 
Where:   W[w1, w2…wn]  Vector of the weight 
    X[x1, x2…xn]  Vector of input signal 
    Wn+1   Bias 

    (v)   Activation function 
ANN associated with machine learning methods, in which input data is divided into 2 parts: training (80%) and 

testing (20%) data. The training data was used to determine the parameters of the proposed models then the model  
adjust the weight of each neuron and the error. The quality of the resulting models was assessed using the test 
dataset. The entire process performed by dedicated software. 

 

E. Model Evaluation 
The accuracy of the output is the factor deciding the model's efficiency and is usually done by evaluating some 

parameters. 
 

      √
 

 
∑       ̂   

  
      (7) 

      
   

 ̅ 
√

 

 
∑       ̂   

  
     (8) 

    
∑       ̂   

  
   

∑       ̅    
   

    (9) 

  
∑       ̅    ̂     ̅̂    

   

√∑       ̅   ∑   ̂     ̅̂    
   

 
   

   (10) 

 ̂  : water temperature prediction in day i 

   : Observed water temperature in day i  

 ̅̂ : Average value of  ̂   

 ̅ : Average value of     
n: Size of data set 
Root mean square error – RMSE: The parameter describes the error between observed and calculated data  It 

could be standardized by the percentage% (RMSE%) to describe relativity to the mean value. 
Correlation coefficient R: provides information about the linear relationship between the calculated value and 

the observed value. R value ranges from 0-1. The closer the R=1 value is, the closer the correlation is. 
Nash and Sutcliffe [22]: determine the effectiveness of the model. E assesses the relative difference between 

simulation value and observation value. E has a value of - to 1. The minimum E value of 0.9 specifies an 
acceptable model. 

 

3. Results and Discussion 
In the study, the daily data including air and water observation at Bai Chay station of 10 years (2008-2017) are 

used and divided into 2 data sets: the data set from 2008-2014 is used as learning data (training data); The data set 
from 2015-2017 is used as testing data.  

The training data (air and water temperature data) are used for coefficient identifiation of regression models 
including: Simple linear (Equation 1); nonlinear regression model (Equation 2); Stochastic model (Equation 5); 
artificial neural network model (Variables in Table 1). In the testing data, air temperature data and outputs of 
models identifying from training data were used to simulate water temperature. Then, the results of comparision 
between simulated and observed water temperature were implemented   through parameters RMSE, R, E, 
 
 
 

  

 

Lớp dữ liệu vào Lớp ẩn Lớp dữ liệu ra 

 

Input 

layers 
Hidden 

layer 

Output  
layer 



Asian Review of Environmental and Earth Sciences, 2019, 6(1): 1-8 

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 Simple Linear Regression Model  
The coefficients of a simple linear regression model are identified by training data set  from 2008-2014 in Excel 

software. The results determine parameters as follows: 
 

Tw (t)=2.986+0.874*Ta(t) 
Figure 3 depicts the difference between the observed and the simulated data of the model. The evaluation of 

accuracy results are shown in Table 2. In which, the correlation coefficient between water temperature and air 
temperature at Bai Chay station are R = 0.89; RMSE = 1.68. However, NashSutcliffe coefficient E = 0.89 <0.9 
shows, this model has a poor accuracy. 
 

 Nonlinear Regression Model 
Nonlinear regression model is applied similarly to linear regression model with logistic nonlinear regression in 

solver function in Excel software for training data 2008-2014 . The output of model enable to identify parameter of 
Equation (2) as follows: 

   
      

                 
 

Figure 4 depicts the difference between observed and simulated data of nonlinear regression models. The 
results of the model implementation are shown in Table 2. In which, the correlation coefficient between water and 
air temperature at Bai Chay station is R = 0.9; Root Mean Square Error RMSE = 1.6 and NashSutcliffe coefficient 
E = 0,9 shows that this model could be applied for the calculation of water temperature from air temperature 
values. 
 

 Stochastic Model  
By using the 2-day time lag (t-1) and (t-2), parameters of the Stochastic model are calculated: 

 

                  [
  

   
        ]                                    

In the Table 2, the accracy indicators of model R = 0.94; RMSE = 1.4; NashSutcliffe coefficient E = 0.92, show 
the stochastic model is the outperform of these regression model. Figure 5 describes the correlation coefficient 
between water and air temperature at the Bai Chay station. It also show that the water temperature is not only 
influenced by the daily maximum air temperature but it is also greatly influenced by the temperature value of the 
previous 2 days. This means that when the air temperature rises or falls suddenly, the water temperature continues 
to fluctuate more slowly in about 2 days (48 hours). 
 

 Artificial Neural Network Model 
The calculation of network neurals is done by NNTOOL of MATLAB 2018a software, through 3 steps 

 
Step 1 : Network Training 

Network training is done through a training data set. Each MLP network configuration is performed with the 
maximum number of iterations 1000 times (1000 epoch). In the training set, input variables are neurons from 
MLP1 to MLP10 (Table 1). Through training data set, bias and weights through each loop are identified and 
adjusted. In this study, the algorithm used is Feed-forward back drop, LevenbergMarquardt (LMA) algorithm–
TrainML in Matlap software. 
 

Table-1. Variables in the Artificial neural network model 

No Neuron in the network Interpretation 

1 MLP1: Ta_max Consider the effect of daily maximum air temperature 
2 MLP2: Ta_max, Ta_tb Consider the effect of maximum and average daily air temperature 
3 MLP3: Ta_max, Ta_tb , Ta_tb -1 Consider the correlation of 1 day lag of water temperature with air 

temperature 
4 MLP4: Ta_max, Ta_tb, Ta_tb -1, Ta_tb -2 Consider the correlation of the 2-day lag of the average air 

temperature with the water temperature 
Ta_tb -2: Daily average air temperature in 2 day before 

5 MLP5: Ta_max, Ta_tb, Ta_tb -1, Ta_tb -2, 
Ta_max -1 

Consider the relation of  1-2 day lag of average air temperature, 
Maximum air temperature with water temperature 

6 MLP6: Ta_max, Ta_tb, Ta_tb -1, Ta_tb-2, 
Ta_max -1, Ta_max -2 

7 MLP7: Ta_max, Ta_tb, Ta_max (0,1,2), 
Ta_tb (0,1,2) 

Consider the correlation of Ta_max variation in 3 days, 1-2 day lag of 
average air temperature, Maximum air temperature with water 
temperature 

8 MLP8: Ta_max, Ta_tb, Ta_max (0,1,2), 
Ta_tb (0,1,2), Ta_tb -1, Ta_tb -2, Ta_max -1, 
Ta_max -2 

Considering the correlation of the average progress in 3 days  
 

9 MLP9: Ta_max, Ta_tb, Ta_max (0,1,2), 
Ta_max -1, Ta_max -2 

Considering the correlation between variation of Ta_max in 3 days, 1-
2 day lag of air temperature, Max air temperature with water 
temperature 

10 MLP10: Ta_max, Ta_max (0,1,2), Ta_max -
1, Ta_max -2 

Consider the correlation of the progress and latency of Max air 
temperature with water temperature 

Source: Defined by the author  

 
 
 



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Step 2: Testing 
When the result of performing network training that satisfies the requirements of the number of iterations 

produces, the computer software will record the entire process with the weights, errors and adjustment coefficients 
of each iteration. This process then apply for target data to calculate water temperature prediction and to produce 
model results 

 
Step 3: Output Evaluation 

Evaluation of the accracy results is done by comparing the water temperature data measured and the water 
temperature generated from the model's testing data to identify the accuracy of the model. 

 
Where:  
Ta_max: Daily maximum air temperature  
Ta_tb: Daily average air temperature  
Ta_max (0,1,2): Average of daily maximum air temperature of 3 days (present and 2 previous days); (0:present day; 

1: 1 day before; 2: 2 day before)   
Ta_tb (0,1,2): Average of daily average air temperature of 3 days’ average (present and 2 previous days); 

(0:present day; 1: 1 day before; 2: 2 days before) 
Ta_tb -1: Daily average air temperature of 1 day before  
Ta_tb -2: Daily average air temperature of 2 previous days 
Ta_max -1: Daily maximum air temperature of 1 day before 
Ta_max -2: Daily maximum air temperature of 2 previous days  
The aim of the study is to find the best model for identifying the maximum water temperature through air 

temperature. Therefore, the daily maximium and average air temperature are included in all models. MLP4, MLP5, 
MLP6 models additionally consider the correlation between the water temperature and air temperature with t-1 
values: 1 day lag; t-2: 2-day lag; MLP7 and MLP8 models added elements of the effect of air temperature variation 
in 3 consecutive days (current day and 2 days before). 

The results of evaluation in each neuron network structure shown in the parameters in Table 2, Figure 6 show 
that MLP4 network model with MLP4 neurals: Ta_max, Ta_tb, Ta_tb -1, Ta_tb -2 give the outperform  results with 
indicators RMSE = 1.24, RMSE% = 4.5%; correlation coefficient R=0.988 and E = 0.94. 

The comparison of RMSE, R, E indicators show that the stochastic model and artificial neural network model 
with the same variables Ta_max, Ta_tb, Ta_tb -1 Ta_tb -2 give better results. From the output of the models, it can be 
seen that the daily maximum water temperature depends on:  the daily average, maximum, and the average 
temperature of the 2 previous days. This also shows that the time lag of water temperature compared to air 
temperature is 2 days. 
 

  Table-2. Indicators of accuracy models  
 Models RMSE RMSE% R E 

1 simple linear regression 1,68 6,1 0,89 0,89 
2 Nonlinear regression 1,6 5,8 0,90 0,90 
3 Stochastic 1,4 5,1 0,94 0,92 
4 ANN     

 MLP1 2 7,3 0,9 0,84 
 MLP2 1,759 6,4 0,97 0,88 
 MLP3 1,62 5,9 0,97 0,89 
 MLP4 1,24 4,5 0,988 0,94 
 MLP5 1,579 5,7 0,98 0,90 
 MLP6 1,558 5,7 0,98 0,90 
 MLP7 1,58 5,7 0,981 0,90 
 MLP8 1,556 5,7 0,987 0,90 
 MLP9 1,585 5,8 0,989 0,90 
 MLP10 1,59 5,8 0,98 0,90 

      Source: Authors’ calculation  
 

 
Figure-3. Simulated and observed water temperature in simple linear regression model 

                            Source: Data collected from Bai Chay station (e.g. of  year 2008) 
 



Asian Review of Environmental and Earth Sciences, 2019, 6(1): 1-8 

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Figure-4. Simulated and observed water temperature in nonlinear regression model 

                    Source: Data collected from Bai Chay station (e.g. of  year 2008) 
 

 
Figure-5. Simulated and observed water temperature in stochastic regression model 

                   Source: Data collected from Bai Chay station (e.g. of  year 2008) 

 

 
Figure-6. Simulated and observed water temperature in ANN-MLP4 model 

                      Source: Data collected from Bai Chay station (e.g. of  year 2008) 
 

4. Conclusions 
The study used the daily average, maximum air and water temperature data of Bai Chay station to assess 

output accuracy by implementing 03 regression models (linear regression, Nonlinear, stochastic regression) and 
artificial neural network models. In particular, artificial neural network model was built with 10 network structures 
(MLP1-MLP10) to determine some factors of air temperature affecting variation and time lag of water 
temperature. The results of 14 models identified that ANN-MLP4 model with 4 parameters  Ta_max, Ta_tb, Ta_tb -1, 
Ta_tb -2 gave the best results with values of RMSE = 1.24; R = 0.98; E = 0.94. The study allows to identify 
that:The maximum temperature of water (Tw_max) depends greatly on the daily average and maximum air 
temperature . 

The time lag between the daily maximum air and water temperature in this sutdy applying for the coastal area 
of the Northern Delta, Vietnam is 2 days. Daily average temperature is important factors because it It take values 
of daily minimum and day and night temperature fluctuations. 

Stochastic model examines seasonal and short-term fluctuations between air and water temperature. This 
model gave the best results in the regression methods implemented. ANN model allows using complex input 
variables. This model should be considered for water temperature prediction as a base on disaster risk and climate 
change to aquaculture in coastal Northern areas, Vietnam. 

 



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[2] S. Zhu, E. K. Nyarko, and M. Hadzima-Nyarko, "Modelling daily water temperature from air temperature for the Missouri River," 

Peer Journal, vol. 6, p. e4894, 2018. 
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