Modeling of River Water Temperatures using Feed-forward Artificial

Neural Networks

Cindie Hébert

, Daniel Caissie

, Mysore G. Satish

and Nassir El-Jabi

Faculty of Engineering, Dalhousie University, Halifax, NS, B3J 2X4, Canada

Fisheries and Oceans, Moncton, NB, E1C 9B6, Canada

Faculty of Engineering, Université de Moncton, Moncton, NB, Canada

Keywords: River/Streams, Modeling, Temperature, Artificial Neural Network.

Abstract: Water temperature influences most physical, chemical and biological processes of the river environment. It

plays an important role in the distribution of fishes and on the growth rates of many aquatic organisms. It is

therefore important to develop water temperature models in order to effectively manage aquatic habitats, to

study the thermal regime of rivers and to have effective tools for environmental impact studies. The

objective of the present study was to develop a water temperature model based on artificial neural networks

(ANN) for two thermally different watercourses. The ANN model performed best in summer and autumn

and showed a poorer (but still good) performance in spring. The many advantages of ANN models are their

simplicity, low data requirements, their capability of modelling long-term series as well as have an overall

good performance.

1 INTRODUCTION

Water temperature has both economic and

ecological significance when considering issues such

as water quality and biotic conditions in rivers

(Caissie, 2006). As such, fish habitat suitability is

highly dependent on stream water temperatures. It is

therefore important to use adequate water

temperature modeling approaches to effectively

predict water temperature variability.

Since the 1990’s, artificial neural networks

(ANN) have been widely used in the field of

hydrology, namely in modeling of precipitation and

runoff, water demand predictions, groundwater, and

water quality modeling (Govindaraju, 2000). One of

the main reasons was the fact that ANN has the

capacity to recognize relations between input and

output variables without necessarily requiring any

physical explications. This approach can be very

useful in hydrology because most relationships are

non-linear, very complex, and sometimes unknown.

Although ANNs have been applied in many

hydrological studies in recent decades, very few of

these studies have dealt with the modeling of river

water temperatures (Risley et al., 2003); (Bélanger et

al., 2005); (Sivri et al., 2007); (Chenard and Caissie,

2008), especially at the hourly time step (Risley et

al., 2003).

Therefore, the objective of this component of the

study was to develop an ANN model to predict

hourly river water temperatures using minimal and

accessible input data. This model was applied to two

thermally different watercourses and its performance

was compared to other water temperatures models.

2 METHODOLOGY

2.1 Study Area

The two study sites were located on the Miramichi

river system (New Brunswick, Canada), which is

world renowned for its population of Atlantic

salmon. The first study site was located on the Little

Southwest Miramichi River (LSWM) at

approximately 25 km from the river mouth. The

drainage area of this basin is 1190 km

(Johnston,

1997). The LSWM has a river width of

approximately 80 m, with a depth of 0.55 m on

average during mean flow conditions. No lateral

variation of water temperatures were observed due

to the well-mixed nature of the river (Caissie et al.,

2007). The canopy closer was less than 20%.

The second study site was located on Catamaran

Brook (Cat Bk) approximately 8 km upstream of the

558

Hébert C., Caissie D., G. Satish M. and El-Jabi N..

Modeling of River Water Temperatures using Feed-forward Artiﬁcial Neural Networks.

DOI: 10.5220/0004158005580562

In Proceedings of the 4th International Joint Conference on Computational Intelligence (NCTA-2012), pages 558-562

ISBN: 978-989-8565-33-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

mouth. It is the site of a 15-year multidisciplinary

hydrobiological research study aimed at quantifying

stream ecosystem processes and the impact of timber

harvesting (Cunjak, Caissie and El-Jabi, 1990).

Catamaran Brook has a drainage area of 27 km

the study site, an average stream width of 9 m and a

depth of 0.21 m. Catamaran Brook is well-mixed

due to high turbulence, similar to LSWM, but the

brook is more sheltered by streamside vegetation

and upland slopes. The canopy closer for Catamaran

was estimated at 55%-65%.

2.2 Water Temperature Model

Water temperature data for the ANN were collected

for the period of April 15 (day 105) to October 31

(day 304) and for years between 1998 and 2007 at

both CatBK and LSWM. This period corresponded

approximately to the period of the year without ice

cover, i.e., open water condition. Some years had

missing data for a few days and these days were not

included in the ANN model. Data were separated

into two samples: training data (1998-2002) and

validation data (2003-2007).

The developed hourly ANN model of this study

used six input nodes: air temperature (°C) of the

present and previous hour, time of day (hour), the

time of year (day), daily mean water temperature

(simulated) (°C), and the mean daily water level (m).

The selection of air temperature, as input data, was

based on the availability of data and their strong

correlation to water temperatures (Cluis, 1972);

(Song and Chien, 1977); (Stefan and Preud’Homme,

1993); (Mohseni and Stefan, 1999); (Bélanger et al.,

2005); (Chenard and Caissie, 2008). Daily mean

water temperatures were first predicted from a daily

ANN model (using air temperature (°C) of the

present and previous day (°C), daily water level (m),

and time of year (day)). The air temperature of the

previous day was used as input because air and

water temperature are strongly correlated

(Kothandaraman, 1971); (Cluis, 1972). These daily

mean water temperatures were then used as input

data into the hourly ANN water temperature model.

During the training, the observed daily mean water

temperatures were used; however during the

validation the simulated daily mean water

temperatures were used to simulate the hourly

temperatures. The output of the developed ANN

model was hourly water temperature at both Cat Bk

and LSWM.

The feed-forward backpropagation ANN model

was created using Matlab Student 7.1. For the

application within the present study, the supervised

learning process was used. The ANN model was

adjusted for the minimum difference between

predicted and observed water temperatures. The

ANN model achieved optimal six input nodes, five

hidden nodes in one hidden layer and only one

output node. The transfer function (f(n)) used

between each node was the hyperbolic tangent

sigmoid transfer function, described as follows:









 n

(1)

This function also represents well the non-linear

processes usually found in hydrology (Smith, 1993);

(Jain et al., 1996).

2.3 Modeling Performance Criteria

Three criteria were used to compare modeling

performances: the root-mean-square error (RMSE),

the coefficient of determination (R

), and the bias

(Bias). They were selected because they are often

used in modeling studies and results from these

performance criteria were also available for other

water temperature models at Cat Bk and LSWM.

The root-mean-square error (RMSE) represents the

mean errors associated to the model. The coefficient

of determination (R

) represents the percentage of

variability that can be explained by the model. The

bias is an indication of the overestimation or

underestimation of the water temperature model and

represents the mean of errors.

3 RESULTS

Results of the ANN models (RMSE, R

, and bias)

are represented in Table 1. The ANN model

generally provided the best results at Cat Bk with a

root-mean-square error (RMSE) of 0.63°C for the

training and 1.19°C for the validation period. At Cat

Bk, the coefficient of determination (R

) was 0.986

(training) and 0.948 (validation). The bias was at

0.00°C for the training period and -0.28°C for the

validation period. For the LSWM, the ANN model

performed comparably well, especially during the

training (RMSE = 0.69°C and R

= 0.989).

However, during the validation period, the RMSE

was higher at 1.62°C and a correspondingly lower

at 0.930. The bias for LSWM was 0.00°C

(training) and 0.05°C (validation). Overall (all

years), the ANN model performed well for both

watercourses with RMSE of 0.94°C (Cat Bk) and

1.23°C (LSWM) and with R

of 0.967 (Cat Bk) and

ModelingofRiverWaterTemperaturesusingFeed-forwardArtificialNeuralNetworks

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0.962 (LSWM). Water temperatures were slightly

underestimated at Cat Bk with bias of –0.13°C and

the overall bias for LSWM was very low (0.02°C).

Table 1: Results of the ANN water temperature models.

Training Validation All years

(1998- 2002) (2003-2007) (1998-2002)

Cat. Bk

RMSE 0.63 1.19 0.94

0.986 0.948 0.967

Bias 0.00 -0.28 -0.13

LSWM

RMSE 0.69 1.62 1.23

0.989 0.930 0.962

Bias 0.00 0.05 0.02

Table 2: Results of the seasonal analysis.

Training Validation All years

(1998-2002) (2003-2007) (1998-2002)

Spring

Cat. Bk

RMSE 0.70 1.38 1.06

0.979 0.920 0.951

Bias 0.01 -0.02 -0.01

LSWM

RMSE 0.85 1.76 1.38

0.979 0.922 0.947

Bias 0.02 0.78 0.39

Summer

Cat. Bk

RMSE 0.64 1.02 0.85

0.942 0.865 0.901

Bias 0.00 -0.32 -0.16

LSWM

RMSE 0.67 1.61 1.23

0.961 0.776 0.868

Bias -0.02 -0.20 -0.11

Autumn

Cat. Bk

RMSE 0.47 1.25 0.94

0.979 0.856 0.915

Bias 0.00 -0.53 -0.27

LSWM

RMSE 0.52 1.39 1.00

0.985 0.890 0.943

Bias 0.02 -0.47 -0.19

Table 2 shows the performance of the model on a

seasonal basis. Spring was between April 15 and

June 21 (day 105-171), summer between June 22

and September 20 (day 172-263) and autumn

between September 22 and October 31 (day 264-

305). For the training period, autumn showed the

best performance with a RMSE of 0.47°C (Cat Bk)

and 0.52°C (LSWM). Spring (training period)

showed a poorer performance with RMSE of 0.70°C

(Cat Bk) and 0.85°C (LSWM). RMSEs during the

summer were similar at Cat Bk and LSWM with

values of 0.64°C and 0.67°C. Coefficients of

determination (R

) were similar in autumn and

spring with values over 0.979; however, lower

values were observed in summer (0.942-0.961). The

biases were generally small for both watercourses

for the training period with seasonal values less than

±0.02°C.

Seasonal results were similar during the

validation period, although RMSEs and biases were

generally higher with lower R

. Highest RMSEs

were observed during the spring (1.38°C Cat Bk and

1.76°C LSWM) and best performances were in

summer in Cat Bk (1.02°C) and autumn in LSWM

(1.39°C). Summer had the lowest R

(0.776),

whereas spring had the highest R

(0.922). Spring

showed a general overestimation of predicted water

temperature in LSWM with a bias of 0.78°C. In

general (all years), the ANN model showed similar

seasonal performances in Cat Bk and a better

performance in summer and autumn for LSWM.

4 DISCUSSION

Most ANN models have estimated daily mean water

temperatures. The modeling of hourly stream water

temperature in this study was found to be as good as

the modeling of daily mean stream water

temperatures. For example, Chenard and Caissie

(2008), who modeled daily mean stream

temperatures in Catamaran Brook using an ANN,

achieved similar results with overall RMSE of

0.96°C and R

of 0.971. Bélanger et al. (2005)

calculated an overall RMSE of 1.06°C when

applying an ANN model at Catamaran Brook (daily

mean temperatures). The study by Bélanger et al.

(2005) used only air temperature and water level as

input parameters. Risley et al. (2003) have

developed a more complex ANN model for 148 sites

in western Oregon on a short-term period (June 21 to

September 20, 1999). Three different ANN models

were developed to estimate hourly water

temperatures along 1

, 2

, and 3

order streams

using meteorological data (air temperature, dew-

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point temperature, short-wave solar radiation, air

pressure, and precipitation), riparian habitat

characteristics (stream bearing, gradients, depth,

substrate, wetted widths, and canopy cover), and

basins landscape characteristics (topographic and

vegetative), acquired by using a geographic

information system (GIS). Their results showed

RMSEs ranging between 0.05°C and 0.59°C and

with R

ranging from 0.88 to 0.99.

Comparison of seasonal performance showed

that the ANN model performed best in summer or

autumn, which is consistent with other temperature

models (Caissie et al., 1998); (Caissie et al., 2005);

(Chenard and Caissie, 2008). It could suggest the

potential role of discharge in the modeling

performance, as low water levels are usually

observed in autumn and mid-summer, resulting in

more effective thermal exchange and giving better

performances. The poorer but still good performance

in spring could be explained by the higher discharge

caused by snowmelt, resulting in a poorer air to

water temperature relationship (Caissie et al., 1998).

The performance of the model was closely linked to

water levels, meaning that the performance was

better when water levels were low. At LSWM, the

ANN model performed best in autumn for all the

years, whereas at CatBk, some years had their best

performance during summer. These results suggest

that the thermal exchange is more efficient for less

sheltered river under low flow (autumn at LSWM).

CatBk is more sheltered and could potentially be

influenced by other factors (ex., groundwater)

reducing the efficiency of the thermal exchange. For

example, Hébert, Caissie, Satish, and El-Jabi (2011)

showed that the impact of groundwater on hourly

water temperatures was more significant on smaller

streams, like CatBk.

The training period showed better results than

the validation period, which is consistent in

modeling. Daily water levels used in the modeling

were estimated using power functions (Caissie,

2004). Using hourly water levels instead of daily

water levels could potentially improve the modeling,

especially during days that discharge varied

significantly. However, hourly water levels were not

available for the present study.

ANN models have major advantages over more

commonly used water temperature models, as they

do not need many input data. In this case, only air

temperature and water level time series were used to

achieve good predictions. For instance, deterministic

model needs many hydrological and meteorological

parameters that are not always readily available

(e.g., solar radiation). Another major advantage of

ANN is that they are easy to use and very simple in

their application. However, ANN models cannot

give any physical explanation of the relationship

between the input and output data. These models

should therefore be used with caution, especially

when using input data that are outside the range of

the calibration period (Risley et al., 2003).

5 CONCLUSIONS

This study showed that artificial neural network

(ANN) could be an effective tool for the prediction

of hourly stream temperatures. ANN models

achieved comparable or better performances to other

water temperature models reported in the literature,

with RMSE of 0.94°C at Cat Bk and 1.23°C at

LSWM. ANN models showed a good generalization

capability by modeling well water temperature time-

series. ANN was effectively applied on two

thermally different streams and provides similar

results and performances. As such, ANN models can

be considered as effective modeling tool in water

resources and fisheries management.

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