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Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term
Alexandria Engineering Journal (2017) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term A. Danladi *, M. Stephen, B.M. Aliyu, G.K. Gaya, N.W. Silikwa, Y. Machael Department of Pure and Applied Physics, Adamawa State University, Mubi, Nigeria Received 1 February 2017; revised 15 February 2017; accepted 4 March 2017
KEYWORDS Model; Weather parameters; Forecasting and rainfall
Abstract Rain serves as one of the key components in water cycle and it comes in the form of water droplets that are condensed from atmosphere and then fall on earth surface as rainfall. It has much importance. However, excessive rainfall can cause environmental hazards. This work developed an adaptive neuro – fuzzy inference system (ANFIS) to relate certain weather parameters (temperature and relative humidity) with rainfall in order to forecast the amount of rainfall capable of causing River Yazaram in Mubi town to discharge. It is predicted that, Mubi will experience high rainfall on 7th, 27th and 30th August 2016 as 56 mm, 28.8 mm and 28.8 mm respectively. Furthermore, on 7th August 2016 River Yazaram is likely to discharge. The model developed is validated with mean square percentage error (MAPE) of 4.64% and correlation coefficient of 0.1277 and 0.075 of rainfall with temperature and relative humidity respectively. Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Rainfall is well known in Nigeria as the source of drinking water and water in the stream and used for agricultural purposes. Without rainfall it is impossible to practice agricultural activities in Nigeria today. On the other hand, heavy rainfall can cause rivers to overflow especially River Yazaram in Mubi. This mostly occurs in the month of August, which consequently destroys lives and properties. Therefore, it becomes necessary to constantly or yearly predict the amount of rainfall that will be experienced in the month of August in Mubi. This * Corresponding author. E-mail address: [email protected] (A. Danladi). Peer review under responsibility of Faculty of Engineering, Alexandria University.
will inform people living around the River bank about the danger ahead, so that, they can make adequate preparation. Several authors reported on how to forecast rainfall and causes of River discharge. However, only limited works utilized artificial intelligent tool such as ANFIS. Even though, there are some works carried out by different authors on short and long term forecasting using ANFIS. These include rainfall forecasting [1–7], weather prediction [8], Wind speed [9], river flow estimation [4], multi variable ANFIS using weather parameters [10,11] and simulation for daily temperature [12]. In this work, an ANFIS shall be developed based on the data collected to forecast August 2016 rainfall in Mubi, Adamawa State in order, to estimate the amount of rainfall capable of causing an overflow in River Yazaram. The following objectives shall be realized: Collect appropriate data, classify the data and assign them membership function (MF), formulate rules based
http://dx.doi.org/10.1016/j.aej.2017.03.004 1110-0168 Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
2
A. Danladi et al.
on the data collect, develop ANFIS simulation Model to forecast August 2016 rainfall and finally, recommend the likely days Mubi town will experience heavy rainfall, which may cause River Yazaram to discharge. 1.1. Adaptive neuro-fuzzy inference system ANFIS is developed by integrating fuzzy logic (FL) and artificial neural network (ANN) principles. This is done to improve the performance of the two separate techniques mentioned above. It corresponds to the IF-THEN fuzzy logic rules [12] and has tendency to solve nonlinear functions due to its ability to learn. It is known as the generic algorithms for evaluating different inputs. However, in this work, only two inputs will be considered as shown in Fig. 1. Firstly, the input is Multiplexed and sent into the ANFIS plus rules developed by the expert. Secondly, rules in the ANFIS act on the input and produce an output (forecasted).
Part of River Yazaram.
Figure 2
60
Relative Humidity Actual Rainfall
Forecasting is a method of making future prediction using previous or present information. Forecasting can be done in terms of long, medium or short based on the need. Hence in this work, short term forecasting will be adopted since only the rainfall in the month of August, 2016 will be forecasted.
Weather Parameter
1.2. Short term forecasting
Temperature
40
20
0
2. Study area
0
5
10
15
20
25
30
35
Days
Mubi is located on latitude 10°140 N and longitude 13°150 E and it has many Rivers around its environment but River Yazaram divides the town into almost two equal parts. It is noticed and reported by the Adamawa State University metrological center that, in the month of August River Yazaram discharges when Mubi town experiences heavy rainfall in the order of 45– 60 mm. This prompted us to conduct the study. Fig. 2 depicts River Yazaram and Fig. 3 depicts rainfall, temperature and relative humidity.
Figure 3a
Rainfall, temperature and relative humidity.
2.1. Method of data collection and presentation Three sets of data: Temperature (T), Relative humidity (H) and rainfall (R) for the month of August were collected from the metrological center of Adamawa State University, Mubi, and are presented as depicted in Figs. 3a and 3b. Figure 3b Input1
MUX
ANFIS
Output
ANFIS input/output interface.
Fig. 3b shows the relationship between input (Temperature and Relative humidity) and output data (Rainfall) on ANFIS interface. 2.2. Fuzzification
Input2
Figure 1
Rules
Block diagram of the ANFIS structure.
As earlier mentioned, ANFIS is the combination of FL and ANN. Fuzzification of the input/output data needs to be first considered. Usually, the input/output are fuzzified based on
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
Assessing the influence of weather parameters
3
the data range (maximum and minimum) for the prediction to be realized.
2.4. Formulation of rules and implementation of ANFIS simulation model
2.3. Classification of input/output data and membership function
Since there are two inputs and one output, the ANFIS network model is developed as shown in Fig. 4.
T and H can be classified as input and R as the output. There are several types of MF(s) but in this work generic MF (gbell) was adopted because of its suitability to handle all kinds of data. It consists of a vector say x and other nonlinear parameters a, b, c, referred to as antecedents of the ANFIS rules given by lA ðxÞ ¼
1þ
1 xc2b
ð1Þ
a
a, b, c change the generic bell shape if altered accordingly and x can be T, H or R [ ].
Table 3
Linguistic term
H1 H2 H3 H4 H5
Table 4
L4
L1 L2
L3
a1
H
1
π
T
TH
1
N
1 1
a2
L5
Linguistic terms and intervals of Relative humidity. Intervals a
b
c
3.125 3.105 3.130 3.126 3.125
2.001 1.999 2.011 1.999 2.000
32.00 38.20 44.49 50.75 57.00
Linguistic terms and intervals of rainfall.
Linguistic terms
Intervals
R1 R2 R3 R4 R5
508.10 23.30 100.20 2.64 3.94
R
∑ b1 π
N 2 2
2
b2 TH
Figure 4
ANFIS network model.
Table 1 Comparison of block diagram and equivalent network model of ANFIS. Fig. 1
Fig. 2
Inputs Multiplexing ANFIS/rules Output
LI L2–L3 L4 L5
Table 2
MF of the temperature.
Linguistic terms and intervals of temperature.
Linguistic term
T1 T2 T3 T4 T5
Figure 5
Intervals a
b
c
0.936 0.910 0.948 0.975 0.955
2.001 2.011 2.007 1.978 1.998
19.00 20.87 22.82 24.62 26.49
Figure 6
MF of the relative humidity.
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
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A. Danladi et al.
ANFIS equivalent two input networks a1, a2, b1 and b2 represents the fuzzy sets. The MF for a and b is defined by the generalized bell MF given in Eq. (1). In correspondence with Fig. 1, L1 represents the inputs, L2-L3 represent multiplexer, L4 represents ANFIS/rules and L5 represents the output (see Table 1).
Figure 7
Based on this network model shown in Fig. 3, rules are developed. First rule: IF T is a1 and H is b1, THEN R1 ¼ p1 T þ q1 H r1
ð2Þ
Second rule: IF T is a2 and H is b2, THEN
Simulated ANFIS network model.
Figure 8
Rule viewer.
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
Assessing the influence of weather parameters
5
R2 ¼ p2 T þ q2 H r2
ð3Þ
The average weight is obtained as given in (4) Ra ¼
w1 f1 þ w2 f2 w1 þ w2
ð4Þ
L1: Every node in L1 auto-generates a member grade of linguistic value a1, a2, b1, and b2 and these are used to define the MF as given in (5) and (6) called nonlinear functions. yi;1 ¼ lðai ÞT for; i ¼ 1; 2; 3
ð5Þ
yi;1 ¼ lðbi1 ÞH for; i ¼ 1; 2; 3
ð6Þ
where ai or bi2 is a linguistic term sometimes referred to as HIGH, LOW or MODERATE and T or H is the input at the ith node. L2: All the nodes in this layer are labeled as p, which multiply the two incoming signals. For example, a1b1 or a2b2 multiplexed, and the firing strength of a rule may be expressed as in (7). yi;2 ¼ wi ¼ lai ðTÞlbi ðHÞ:
ð7Þ
L3: Each node in this layer is labeled N. ith node determines the ith rule firing strength as given in Eq. (8) wi i ¼ 1; 2; 3 ð8Þ yi;3 ¼ wi ¼ w1 þ w2 L4: Here each node is an adaptive node as given in (9) yi;4 ¼ wi Ri ¼ wi pi YðtÞ þ qi Yðt 1Þ þ r1
ð9Þ
where wi is the output of L3 while, p1, q1 and r1 are the antecedents. L5: The final consequence is obtained as P wi Ri R¼ P ð10Þ wi 2.5. Error analysis
MAPE ¼
n1 X AF 100% A i¼1
ð11Þ
P P P n TR ð TÞð RÞ r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r¼ h ih P i P P P n T2 ð TÞ2 n R2 ð RÞ2
ð12Þ
P P P n HR ð HÞð RÞ r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h P ih P i P P n H2 ð HÞ2 n R2 ð RÞ2
ð13Þ
where R represents rainfall and T or H represents temperature or humidity, n represents the days in month of August, and A and F represent the actual and forecasted rainfall respectively. 3. Result and discussion 3.1. Linguistic terms and intervals Tables 2–4 present the linguistic terms and the intervals of the MFs of T, H and R, while Figs. 5 and 6 present the MF of the input parameters that correspond to MF intervals. 3.2. Simulated result The network in Fig. 6 is simulated using one sample data selected randomly. For instance, T = 25.5 °C and H = 46%. It produced R = 3.8 mm as displayed in Fig. 8 and all the other values of R are obtained in the same manner (see Fig. 7). 3.3. Model validation The model is validated based on what is seen in Fig. 9. The MAPE is obtained as 4.64% with corresponding efficiency of 95.36%. Rainfall and Temperature are positively related to correlation coefficient (r) = 0.1277 while rainfall
The measure of prediction accuracy is considered using the following indicators: Mean Absolute Percentage Error (MAPE) and coefficient of Correlation as is given in Eqs. (11) and (12) respectively.
60
Predicted Rainfall Actual Rainfall
Rainfall (mm)
50 40 30 20 10 0
0
5
10
15
20
25
30
35
Days
Figure 9
Actual and forecasted rainfall.
Figure 10
Parameters surface viewer.
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
6 and humidity are also, positively related to (r) = 0.075. Usually, r ranges between 1 and +1. As r approaches +1, the relationship between the two variables examined is positive. When r, indicates zero means there is no correlation between the variables and negative signifies negative correlation. On 1st, 4th–9th, 16th, 20th, 24th and 26th of August 2016, the amount of rainfall predicted is the same as that of August 2015. While on the other days the rainfall is higher except on 3rd, 13th, 21st, 25th and 28th where the rainfall is expected to be less than what was experienced in August 2015. It is also noticed that 7th, 27th, and 30th have the highest rainfall in the month. However, on 7th, River Yazaram is likely to discharge. Fig. 10 depicts the surface viewer of the three parameters. 4. Conclusion A model of an ANFIS is developed to forecast August 2016 rainfall. It is observed that, the overall rainfall forecasted for the year 2016 is higher than the actual rainfall measured in August 2015 by 0.002 mm. Also observed a significant increase in the amount of rainfall predicted on 7th, 27th, and 30th August 2016. And it is recommended that, on 7th August, River Yazaram is likely to discharge. In addition, Long term forecasting may be used instead of the short term forecasting where the data measured are not sufficient for efficient prediction. References [1] E. Aldrian, Y.S. Djamil, Application of multivariate Anfis for daily rainfall prediction, Influences Train. Data Size, Makara, Sains 12 (1) (2008) 7–14.
A. Danladi et al. [2] S. Banik, M. Anwer, A.F.M.K. Khan, R.A. Rouf, F.H. Chanchary, Forecasting Bangladeshi monsoon rainfall using neural network and genetic algorithm approaches, Int. Technol. Manage. Rev. 2 (1) (2009) 1100–1107. [3] C. Jeong, S. Ju-Young, T. Kim, H. Jun-Haneg, Monthly precipitation forecasting with neuro-fuzzy model, Water Resour. Manage. 26 (2012) 4467–4483. [4] O.E. Jaafer, S.A. Akrami, Adaptive neuro-fuzzy inference system based model for rainfall forecasting in Klang River, Malaysia, Int. J. Phys. Sci. 6 (12) (2011) 2875–2888. [5] J.O. Folorunsho, Application of adaptive neuro fuzzy inference system (Anfis) in river Kaduna discharge forecasting, Res. J. Appl. Sci., Eng. Technol. 4 (21) (2012) 4275–4283. [6] A.H. Agboola, A.J. Gabriel, A.E.O Aliyu, B.K. Alese, Development of a fuzzy logic based rainfall prediction model, Int. J. Eng. Technol. 3 (4) (2013) 100–109. [7] D.N.A. Mahapatra, P. Mishra, A Survey on rainfall prediction using artificial neural network, Int. J. Comput. Appl. 72 (16) (2013). [8] C. Fernando, J. Nickel, Average hourly wind speed forecasting with ANFIS, in: 11th Americas Conference on wind Engineering – San Jaun Puerto Rico, 2009. [9] Y.W. Khun, A study on soft computing approach in weather forecasting. Masters thesis, Universiti Teknologi Malaysia, Faculty of Computer Science and Information Systems, 2010. [10] S. Gyanesh, K. Sanjeev, K.K. Manoj, Application of artificial neural network in weather forecasting a comprehensive literature review, Int. J. Comput. Appl. (2012) 0975–8887. [11] M. Ricardo, J.P. Trigo, P. Palutik, Simulation of Daily Temperatures for Climate Change Scenarios over Portugal: A Neural Network Model Approach, University of East Anglia, Norwich, NR4 7TJ, United Kingdom, climate research (Clim., Res.). vol. 13, 1999, pp. 45–59. [12] J. Yen, R. Langari, Fuzzy Logic, Intelligence, Control, and Information, Prentice Hall, 1999.
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term A. Danladi *, M. Stephen, B.M. Aliyu, G.K. Gaya, N.W. Silikwa, Y. Machael Department of Pure and Applied Physics, Adamawa State University, Mubi, Nigeria Received 1 February 2017; revised 15 February 2017; accepted 4 March 2017
KEYWORDS Model; Weather parameters; Forecasting and rainfall
Abstract Rain serves as one of the key components in water cycle and it comes in the form of water droplets that are condensed from atmosphere and then fall on earth surface as rainfall. It has much importance. However, excessive rainfall can cause environmental hazards. This work developed an adaptive neuro – fuzzy inference system (ANFIS) to relate certain weather parameters (temperature and relative humidity) with rainfall in order to forecast the amount of rainfall capable of causing River Yazaram in Mubi town to discharge. It is predicted that, Mubi will experience high rainfall on 7th, 27th and 30th August 2016 as 56 mm, 28.8 mm and 28.8 mm respectively. Furthermore, on 7th August 2016 River Yazaram is likely to discharge. The model developed is validated with mean square percentage error (MAPE) of 4.64% and correlation coefficient of 0.1277 and 0.075 of rainfall with temperature and relative humidity respectively. Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Rainfall is well known in Nigeria as the source of drinking water and water in the stream and used for agricultural purposes. Without rainfall it is impossible to practice agricultural activities in Nigeria today. On the other hand, heavy rainfall can cause rivers to overflow especially River Yazaram in Mubi. This mostly occurs in the month of August, which consequently destroys lives and properties. Therefore, it becomes necessary to constantly or yearly predict the amount of rainfall that will be experienced in the month of August in Mubi. This * Corresponding author. E-mail address: [email protected] (A. Danladi). Peer review under responsibility of Faculty of Engineering, Alexandria University.
will inform people living around the River bank about the danger ahead, so that, they can make adequate preparation. Several authors reported on how to forecast rainfall and causes of River discharge. However, only limited works utilized artificial intelligent tool such as ANFIS. Even though, there are some works carried out by different authors on short and long term forecasting using ANFIS. These include rainfall forecasting [1–7], weather prediction [8], Wind speed [9], river flow estimation [4], multi variable ANFIS using weather parameters [10,11] and simulation for daily temperature [12]. In this work, an ANFIS shall be developed based on the data collected to forecast August 2016 rainfall in Mubi, Adamawa State in order, to estimate the amount of rainfall capable of causing an overflow in River Yazaram. The following objectives shall be realized: Collect appropriate data, classify the data and assign them membership function (MF), formulate rules based
http://dx.doi.org/10.1016/j.aej.2017.03.004 1110-0168 Ó 2017 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
2
A. Danladi et al.
on the data collect, develop ANFIS simulation Model to forecast August 2016 rainfall and finally, recommend the likely days Mubi town will experience heavy rainfall, which may cause River Yazaram to discharge. 1.1. Adaptive neuro-fuzzy inference system ANFIS is developed by integrating fuzzy logic (FL) and artificial neural network (ANN) principles. This is done to improve the performance of the two separate techniques mentioned above. It corresponds to the IF-THEN fuzzy logic rules [12] and has tendency to solve nonlinear functions due to its ability to learn. It is known as the generic algorithms for evaluating different inputs. However, in this work, only two inputs will be considered as shown in Fig. 1. Firstly, the input is Multiplexed and sent into the ANFIS plus rules developed by the expert. Secondly, rules in the ANFIS act on the input and produce an output (forecasted).
Part of River Yazaram.
Figure 2
60
Relative Humidity Actual Rainfall
Forecasting is a method of making future prediction using previous or present information. Forecasting can be done in terms of long, medium or short based on the need. Hence in this work, short term forecasting will be adopted since only the rainfall in the month of August, 2016 will be forecasted.
Weather Parameter
1.2. Short term forecasting
Temperature
40
20
0
2. Study area
0
5
10
15
20
25
30
35
Days
Mubi is located on latitude 10°140 N and longitude 13°150 E and it has many Rivers around its environment but River Yazaram divides the town into almost two equal parts. It is noticed and reported by the Adamawa State University metrological center that, in the month of August River Yazaram discharges when Mubi town experiences heavy rainfall in the order of 45– 60 mm. This prompted us to conduct the study. Fig. 2 depicts River Yazaram and Fig. 3 depicts rainfall, temperature and relative humidity.
Figure 3a
Rainfall, temperature and relative humidity.
2.1. Method of data collection and presentation Three sets of data: Temperature (T), Relative humidity (H) and rainfall (R) for the month of August were collected from the metrological center of Adamawa State University, Mubi, and are presented as depicted in Figs. 3a and 3b. Figure 3b Input1
MUX
ANFIS
Output
ANFIS input/output interface.
Fig. 3b shows the relationship between input (Temperature and Relative humidity) and output data (Rainfall) on ANFIS interface. 2.2. Fuzzification
Input2
Figure 1
Rules
Block diagram of the ANFIS structure.
As earlier mentioned, ANFIS is the combination of FL and ANN. Fuzzification of the input/output data needs to be first considered. Usually, the input/output are fuzzified based on
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
Assessing the influence of weather parameters
3
the data range (maximum and minimum) for the prediction to be realized.
2.4. Formulation of rules and implementation of ANFIS simulation model
2.3. Classification of input/output data and membership function
Since there are two inputs and one output, the ANFIS network model is developed as shown in Fig. 4.
T and H can be classified as input and R as the output. There are several types of MF(s) but in this work generic MF (gbell) was adopted because of its suitability to handle all kinds of data. It consists of a vector say x and other nonlinear parameters a, b, c, referred to as antecedents of the ANFIS rules given by lA ðxÞ ¼
1þ
1 xc2b
ð1Þ
a
a, b, c change the generic bell shape if altered accordingly and x can be T, H or R [ ].
Table 3
Linguistic term
H1 H2 H3 H4 H5
Table 4
L4
L1 L2
L3
a1
H
1
π
T
TH
1
N
1 1
a2
L5
Linguistic terms and intervals of Relative humidity. Intervals a
b
c
3.125 3.105 3.130 3.126 3.125
2.001 1.999 2.011 1.999 2.000
32.00 38.20 44.49 50.75 57.00
Linguistic terms and intervals of rainfall.
Linguistic terms
Intervals
R1 R2 R3 R4 R5
508.10 23.30 100.20 2.64 3.94
R
∑ b1 π
N 2 2
2
b2 TH
Figure 4
ANFIS network model.
Table 1 Comparison of block diagram and equivalent network model of ANFIS. Fig. 1
Fig. 2
Inputs Multiplexing ANFIS/rules Output
LI L2–L3 L4 L5
Table 2
MF of the temperature.
Linguistic terms and intervals of temperature.
Linguistic term
T1 T2 T3 T4 T5
Figure 5
Intervals a
b
c
0.936 0.910 0.948 0.975 0.955
2.001 2.011 2.007 1.978 1.998
19.00 20.87 22.82 24.62 26.49
Figure 6
MF of the relative humidity.
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
4
A. Danladi et al.
ANFIS equivalent two input networks a1, a2, b1 and b2 represents the fuzzy sets. The MF for a and b is defined by the generalized bell MF given in Eq. (1). In correspondence with Fig. 1, L1 represents the inputs, L2-L3 represent multiplexer, L4 represents ANFIS/rules and L5 represents the output (see Table 1).
Figure 7
Based on this network model shown in Fig. 3, rules are developed. First rule: IF T is a1 and H is b1, THEN R1 ¼ p1 T þ q1 H r1
ð2Þ
Second rule: IF T is a2 and H is b2, THEN
Simulated ANFIS network model.
Figure 8
Rule viewer.
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
Assessing the influence of weather parameters
5
R2 ¼ p2 T þ q2 H r2
ð3Þ
The average weight is obtained as given in (4) Ra ¼
w1 f1 þ w2 f2 w1 þ w2
ð4Þ
L1: Every node in L1 auto-generates a member grade of linguistic value a1, a2, b1, and b2 and these are used to define the MF as given in (5) and (6) called nonlinear functions. yi;1 ¼ lðai ÞT for; i ¼ 1; 2; 3
ð5Þ
yi;1 ¼ lðbi1 ÞH for; i ¼ 1; 2; 3
ð6Þ
where ai or bi2 is a linguistic term sometimes referred to as HIGH, LOW or MODERATE and T or H is the input at the ith node. L2: All the nodes in this layer are labeled as p, which multiply the two incoming signals. For example, a1b1 or a2b2 multiplexed, and the firing strength of a rule may be expressed as in (7). yi;2 ¼ wi ¼ lai ðTÞlbi ðHÞ:
ð7Þ
L3: Each node in this layer is labeled N. ith node determines the ith rule firing strength as given in Eq. (8) wi i ¼ 1; 2; 3 ð8Þ yi;3 ¼ wi ¼ w1 þ w2 L4: Here each node is an adaptive node as given in (9) yi;4 ¼ wi Ri ¼ wi pi YðtÞ þ qi Yðt 1Þ þ r1
ð9Þ
where wi is the output of L3 while, p1, q1 and r1 are the antecedents. L5: The final consequence is obtained as P wi Ri R¼ P ð10Þ wi 2.5. Error analysis
MAPE ¼
n1 X AF 100% A i¼1
ð11Þ
P P P n TR ð TÞð RÞ r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r¼ h ih P i P P P n T2 ð TÞ2 n R2 ð RÞ2
ð12Þ
P P P n HR ð HÞð RÞ r ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h P ih P i P P n H2 ð HÞ2 n R2 ð RÞ2
ð13Þ
where R represents rainfall and T or H represents temperature or humidity, n represents the days in month of August, and A and F represent the actual and forecasted rainfall respectively. 3. Result and discussion 3.1. Linguistic terms and intervals Tables 2–4 present the linguistic terms and the intervals of the MFs of T, H and R, while Figs. 5 and 6 present the MF of the input parameters that correspond to MF intervals. 3.2. Simulated result The network in Fig. 6 is simulated using one sample data selected randomly. For instance, T = 25.5 °C and H = 46%. It produced R = 3.8 mm as displayed in Fig. 8 and all the other values of R are obtained in the same manner (see Fig. 7). 3.3. Model validation The model is validated based on what is seen in Fig. 9. The MAPE is obtained as 4.64% with corresponding efficiency of 95.36%. Rainfall and Temperature are positively related to correlation coefficient (r) = 0.1277 while rainfall
The measure of prediction accuracy is considered using the following indicators: Mean Absolute Percentage Error (MAPE) and coefficient of Correlation as is given in Eqs. (11) and (12) respectively.
60
Predicted Rainfall Actual Rainfall
Rainfall (mm)
50 40 30 20 10 0
0
5
10
15
20
25
30
35
Days
Figure 9
Actual and forecasted rainfall.
Figure 10
Parameters surface viewer.
Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004
6 and humidity are also, positively related to (r) = 0.075. Usually, r ranges between 1 and +1. As r approaches +1, the relationship between the two variables examined is positive. When r, indicates zero means there is no correlation between the variables and negative signifies negative correlation. On 1st, 4th–9th, 16th, 20th, 24th and 26th of August 2016, the amount of rainfall predicted is the same as that of August 2015. While on the other days the rainfall is higher except on 3rd, 13th, 21st, 25th and 28th where the rainfall is expected to be less than what was experienced in August 2015. It is also noticed that 7th, 27th, and 30th have the highest rainfall in the month. However, on 7th, River Yazaram is likely to discharge. Fig. 10 depicts the surface viewer of the three parameters. 4. Conclusion A model of an ANFIS is developed to forecast August 2016 rainfall. It is observed that, the overall rainfall forecasted for the year 2016 is higher than the actual rainfall measured in August 2015 by 0.002 mm. Also observed a significant increase in the amount of rainfall predicted on 7th, 27th, and 30th August 2016. And it is recommended that, on 7th August, River Yazaram is likely to discharge. In addition, Long term forecasting may be used instead of the short term forecasting where the data measured are not sufficient for efficient prediction. References [1] E. Aldrian, Y.S. Djamil, Application of multivariate Anfis for daily rainfall prediction, Influences Train. Data Size, Makara, Sains 12 (1) (2008) 7–14.
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Please cite this article in press as: A. Danladi et al., Assessing the influence of weather parameters on rainfall to forecast river discharge based on short-term, Alexandria Eng. J. (2017), http://dx.doi.org/10.1016/j.aej.2017.03.004