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Mathematical Model for Flood Forecasting of the Chi River
Basin
Kantima Meeyaem1and Pattarawit Polpinit
2+
1Department of Electrical and Computer Engineering, Kasetsart University Chalermphrakiat
SakonNakhon Province Campus, SakonNakhon, Thailand 2Department of Computer Engineering, Faculty of Engineering, KhonKaen University, KhonKaen, Thailand
Abstract.Accurate flood forecasting is desirable in order to have lead-time for taking appropriate
prevention measures so as to minimize the damage caused. In this paper, a hybrid model, which combines three mathematical concepts, namely, drainage density, Gumbel distribution function and Muskingum
method, are employed for flood foresting in the Chi River Basin. All three concepts have been shown to be
generally effective with the areas in Thailand [1]-[3]. The model is applied to the area called Phra Lap district
that is very close to KhonKaen city, Thailand. Data of monthly water levels and geological data of the Chi
River basin are used. The experimental results show that the hybrid model has overall good accuracy
performance.
Keywords: mathematical flood modelling, flood forecasting, Gumbel distribution, drainage density,
Muskingum method
1. Introduction
Flood is a worldwide problem that is difficult to predict because there are many natural and unnatural
factors that can cause flood. Numerical models for flood prediction have been studied extensively and
cangenerally be classified into two main categories, namely conceptual model and empirical model based on
system analysis [for example 4-6].Usually the conceptual models require huge amount of data in order to
calibrate the model. Hence the empirical model may be preferred for its simplicity. Many mathematical
concepts have been applied in those empirical models including Gumbel distribution, drainage density, and
Muskingum method.
Gumbel distribution function is generally effective when applied to flood flows with respect to the
criteria required [7]. Md. AbdusSabur[1] conducted a flood frequency analysis of the divided flood regions
in order to determine the best probability distributions of annual flood peaks in Thailand and found that the
best probability distribution function for fitting the empirical frequency distribution of annual flood peaks
series in Thailand is Gumbel distribution. Natural Environmental Research Council of the United Kingdom
[2] also recommended that Gumbel distribution is the first choice among distributions of the annual flood
peaks, when only a small sample is available and the distribution to be fitted if an estimate based on the
sample data along is required.Drainage density (Dd) was defined by Horton [8] as the ratio of the total length
of rivers in a watershed over its contributing area. It describes the degree of drainage network development
and was recognized by many authors to be significantly effective on the area where flood frequently occurs
[9, 10]. The data of drainage density is useful to help evaluate the risk of flood as many works have
incorporated the concept for flood analysis in Thailand [11]-[13]. Muskingum method is one of the best
known method for flood routing (works using Muskingum method are for example [14, 15]).
Corresponding author. Tel.: +66-4336-2160
Email address: [email protected]
5
2014 International Conference on Intelligent Agriculture
IPCBEE vol.63 (2014 ) © (2014 ) IACSIT Press, Singapore
DOI: 10.7763/IPCBEE. 2014 . V63. 2
The method is based on an assumed linear relationship between a channel’s storageand inflow and
outflow discharge and consequently, it accounts for prism and wedge storage.
In this paper, a hybrid algorithm that includes parameters from Gumbel distribution, drainage density,
and Muskingum method will be applied to the study area, namely, Ban Phue that is a village located at the
center of PhraLupdistrict as shown in Fig 1. The area has the Chi River as the boundary on the south and is
next to KhonKaen city that is one of the most important cities in the northeast region of Thailand. The
parameters of Gumbel distribution and drainage density will be from the results presented in [6] where
Polpinit and Meeyaem applied Gumbel distribution and drainage density to the studied area.In addition,
Muskingum method implementation will be analyzed here. There has been no system for flood forecasting or
flood warning to prevent flood within the district.
Fig. 1 (a) Map of Phra Lap district (b) Map of hydrological stations E.16A and E.1
2. Hybrid Flood Model
Each concept is analyzed individually using water of the past five years to calibrate parameter to the
study area.
2.1. Gumbel distribution function [6]
The analysis of the past monthly water level data using Gumbel distribution function in order to obtain
the period of occurrence of the flood is described here. The data are water level of the past five years
measured at the upstream hydrological water station (E.16A shown in Figure1(b)).The average water level
and the standard deviation of the data are obtained. Then the parameters of moment estimation (α0 and β0)
can be obtained as follows:
𝛼0 =𝜋
𝑆 6 (1)
𝛽0 = 𝑥 − 0.45𝑆 (2)
where S is the standard deviation of the yearly maximum water level and x is the average water level.
The water level (QTr) attimeTr can be obtained by solving the following equation:
𝑄𝑇𝑟= 𝛽𝑂 − 𝛼𝑂 𝑙𝑛 −𝑙𝑛 1 −
1
𝑇𝑟 (3)
Then we simulate water level in order to analyze the period of the recurrence of the flood water level
which show that the minimum water level from the generated data is152 m. (MSL.). Using the minimum, we
obtain the period of reoccurrence with the following relation between Gumbel reduced variant and the period
of recurrence
6
𝑒−𝑒−𝑦= 1 −
1
𝑇𝑟 (4)
2.2. Drainage density [6]
Drainage density can be obtained by following Equation.
𝐷𝑑 = ∑𝐿
𝐴 (5)
where 𝐷𝑑 is drainage density
𝐿 is the length of the river
𝐴 is the size of area basin The study area is divided into four sub-regions by used the height and the distance from the Chi River,
namely A1, A2, A3 and A4, as show in Fig. 2.
Fig. 2 Four sub regions of the studied area
Each sub-region shows the size of area that flood flow to the Chi River and the distance from the Chi
River that the water in the river flow to area at time that predict. By use the rainfall and the water level in the
Chi River are basis for decide and choose the sub region. The result of the analysis is shown in Table 1.
Table 1: The results of the Drainage Density analysis
The sub
region
The size of
area
(km2)
The summation of the
length of the river (km.) The 𝑫𝒅 values
(km-1
)
A1 7.31 36.58 5.0041
A2 13.14 43.71 3.3265
A3 20.99 49.93 2.3788
A4 28.53 54.69 1.9169
2.3. Muskingum method
To analyze the flow routing of the Chi River close to the study area, the Muskingum method is used. The
downstream (O) of the Chi River can be calculated as follows
𝑂𝑛 = 𝑐𝐼𝑛−1 + (1 − 𝑐)𝑂𝑛−1 (6)
where O is downstream
𝐼 is upstream of water obtained from the hydrological water station E.16A
𝑐 is constant which can be computed from 𝑐 =𝑣
𝑣+1.7where 𝑣is the cross-sectional average
velocitythat can be computed from Manning equation
𝑣 = 1
𝑛𝑅
2
3𝑆1
2 (7)
where 𝑅 is hydraulic radius
𝑆is slope of water surface 1.329 meter
𝑛 is the Manning coefficient which is 0.025
7
We are interested in peak time delay between upstream and downstream in the graph of flow routing that
can be interpreted as water that could leakage to the surrounded area. Figure 3 shows the graph of flow
routing during the flood period in 2011.
Fig. 3 water flow of the study area
3. Model Concept
The model studied in this paper combines the concepts of Gumbeldistribution function, drainage density
and Muskingum method to forecast flood in the study area. Using parameters calibrated in the analysis step,
we set the function for the flood prediction as follows:
Percent chance of flood = 𝑤1𝑥1+𝑤2𝑥2+𝑤3𝑥3
𝑤1+𝑤2 +𝑤3 (8)
where 𝑥1 = 100
𝑑∗ 𝑇𝑟 where 𝑑is the total number of days mornitored and 𝑇𝑟 is the number of
days from the predicted recurrence of maximum water level using Gumbel distribution
𝑥2 = 100
152.6∗ 𝐸 where 𝐸 is the water level at the hydrological water station E.16A
𝑥3 = 100
550.0∗ 𝐸where𝐸 is the water flow calculated in the study area using Muskingum
method.
𝑤1, 𝑤2 and 𝑤3 are weight for Gumbel distribution, drainage density and Muskingum
method respectively.
Using the water data of the study area from the year 2007-2011 for flood simulation, we set the
parameters w1 , w2 and w3 to be 1.0, 2.0 and 2.0 respectively. The percent chance of flood presents the
chance that the study area will have flood. It can also approximate the damage of the flood i.e. for all the
heavy flood during the period of experimental simulation the equation presents the number of higher of 90%.
We evaluate the model using past water data from the year 2002-2006 and found that the model gave an
accurate prediction. All heavy flood occurrences during that period were reported in the model with the
percent chance of flood of over 90%. Almost all flash flood occurrences were also be detected with the
chance of flood shown ranged from around 60%-80%.
4. Conclusion
In this paper, a hybrid model is proposed for flood prediction and tested in the case study area. The
model contains three mathematical concepts, namely, Gumbel distribution function, drainage density and
Muskingum method. Each of these concepts has their own characteristic and represents a difference view to
water data. Each concept was calibrated to optimize parameters individually and together using past water
Peak attenuation
Peak time delay
Downstream
Upstream
Water flo
w (m
3/s)
Days
Peak attenuation
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data. The evaluation shows that the hybrid model givesfairly accurate prediction. The model could be
suitable for real time flood prediction system due to its less complexity and small amount of data required.
One of the possible future works would be to investigate the correlation between the percent chance of flood
and the damage level.
5. Acknowledgements
The authors would like to thank Department of Royal Irrigation, Khon Kaen province, for the data of
monthly water levels from the hydrological station in the Chi River to use in this research and also the
Faculty of Engineering, Khon Kaen University for providing financial support for this project.
6. References
[1] M. Sabur, (1982). Regional Flood Frequency Analysis of Thailand. Asian Institute of Technology Thesis No. Wa-
82-19 Bangkok, Thailand.
[2] Natural Environment Research. Council.1975. Flood Studies Report Vol. 1 The United Kingdom.
[3] C. Thaweesuk (2003). Flood Forecasting in River Basin: The Chi River Study Case.KhonKaen University Thesis
ISBN: 974-435-414-3. KhonKaen, Thailand, 2003.
[4] K. Chau and Y. Jiang, (2001). 3D Numerical Model for Pearl River Estuary. J. Hydraul. Eng., 2001, 127(1): 72–
82.Technical Note.
[5] C. Wu and K. Chau, (2006). Evaluation of Several Algorithms in Forecasting Flood.In Advances in Applied
Artificial IntelligenceLecture Notes in Computer Science. 2006, 4031: 111-116.
[6] P. Polpinit and K. Meeyaem, (2012). Flood Modeling using Gumbel Distribution and Drainage Density for Flood
Forecasting in the Chi River: AmphurMuang, KhonKaen, Thailand Case. In Proceedings of The 4thKKU
International Engineering Conference. pp. 99-10.
[7] R. Ward and M. Robinson (1999). Principle of Hydrology. McGraw-Hill Publishing, USA.
[8] R. Horton, (1945). Erosional Development of Streams and their Drainage Basins. Hydrophysical Approach to
Quantitative Morphology, Geol. Soc. Am. Bull., 56, pp. 275–370.
[9] V. Gardiner and K. Gregory, (1982) Drainage density in rainfall-runoffmodelling, in: Rainfall-runoff
Relationships, edited by: V. P. Singh, Water Resources Publications, Littleton (Colorado), pp. 449–76.
[10] B. Pallard, A. Castellarin, and A. Montanari, (2008). A look at the links between drainage density and flood
statistics. Hydrol. Earth Syst. Sci. Discuss., 2008, 5:2899–2926.
[11] T. Tussaporn and C. Mongkolsawat, (2009). Spatial Characteristics of Floods over the Sub-watershed of the
Mekong River in Northeast Thailand using Multi–temporal RADARSAT DATA. In Proceedings of the 30th Asian
Conference on Remote Sensing. pp. 18-23 October 2009. Beijing, China.
[12] T. Charlchai, Y. Chao, B. Abdollah, and D. Omthip, (2004) Assessment of flood risk in Hat Yai Municipality,
Southern Thailand, using GIS. Journal of Natural Disaster Science, 2004, 26(1): 1-14.
[13] S. Nutchanart and T. Wisuwat (2011). Estimation of the IHACRES Model Parameters for Flood Estimation of
Ungauged Catchments in the Upper Ping River Basin. Kasetsart J. (Nat. Sci.) 2011, 45: 917 – 931.
[14] B. Miroslav, D. Michaela, and S. Ján, On the use of the Muskingum method for the simulation of flood wave
movements. Slovak Journal of Civil Engineering, 2010/3, pp.14-20.
[15] S. Elbashir, (2011) Flood Routing in Natural Channels Using Muskingum Methods. Dissertation submitted in
partial fulfillment of the requirements for the Dublin Institute of Technology’s Master of Engineering
Computation.2011.
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