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Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

SYNTHETIC SIMULATION OF STREAMFLOW AND RAINFALL DATA

USING DISAGGREGATION MODELS

Nurul Adzura Ismail

1

,

Sobri Harun

1

, Zulkifli Yusop

2

1

Department of Hydraulics and Hydrology, Faculty of Civil Engineering,

Universiti Teknologi Malaysia, Skudai 81310, Johor, Malaysia.

2

Institute of Environmental and Water Resources Management, Faculty of Civil Engineering,

Universiti Teknologi Malaysia, Skudai 81310, Johor, Malaysia.

Abstract: Synthetic hydrological series is useful for evaluating water supply

management decision and reservoir design. This paper examines stochastic

disaggregation models that are capable of reproducing statistical characteristics

especially mean and standard deviation of historical data series. Simulation was

carried out on both transformed and untransformed streamflow and rainfall series of

Sungai Muar. The Synthetic Streamflow Generation Software Package (SPIGOT)

model was found to be the most robust for streamflow simulation. On the other hand,

the Valencia-Schaake (VLSH) model is more superior for generating rainfall series.

Keywords: Streamflow; Rainfall; Simulation; Disaggregation.

Abstrak: Siri hidrologi sintetik ialah satu kaedah yang berguna untuk menilai

keputusan dalam pengurusan bekalan air dan rekabentuk empangan. Kertas kerja ini

bertujuan menguji model disaggregasi stokastik yang berupaya menghasilkan semula

ciri-ciri statistik terutama min dan sisihan piawai ke atas siri bulanan aliran sungai

dan hujan. Simulasi telah dilakukan dengan kaedah transformasi dan tanpa

transformasi menggunakan data aliran sungai dan hujan tadahan Sungai Muar. Model

Synthetic Streamflow Generation Software Package (SPIGOT) dipilih sebagai model

yang paling baik untuk simulasi aliran sungai manakala model Valencia-Schaake

(VLSH) memberi keputusan yang terbaik dalam menjana siri hujan.

Katakunci: Aliran Sungai; Hujan; Simulasi; Disaggregasi.

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

57

1. Introduction

The streamflow and rainfall sequences to be analyzed may be thought of as

one particular realisation, produced by underlying probability mechanism of

the phenomenon. In other words, in analysing streamflow and rainfall

sequences many hydrologists regard it as a realisation of a stochastic process.

The generated data sequences, particularly monthly time series such as

streamflow or rainfall are widely used in water resources planning and

management to understand the variability of future system performance.

Stochastic data generation aimed at generating synthetic data sequences that

are statistically similar to the observed data sequences. Therefore, the

generated data is important for more accurate solution of various complex

planning, design and operational problems in water resources development

(Yevjevich, 1989). Typically, stochastic simulation of hydrologic time series

such as streamflow and rainfall are based on mathematical models (Salas,

1993; Hipel and McLeod, 1994). Simulation methods for the hydrologic time

series can be classified into disaggregation and aggregation methods (Harun,

1999). Valencia and Schaake (1973) proposed the so-called disaggregation

model that subsequently becomes a major technique for modeling hydrologic

series. Further modification and applications of disaggregation model have led

to the development of other models such as Mejia - Rouselle, SPIGOT and

Lane.

The main objective of this study was to develop and test various stochastic

models capable of reproducing the historical statistical characteristics

especially mean and standard deviation of monthly streamflow and rainfall

series. The streamflow and rainfall records of Sungai Muar were obtained

from the Department of Irrigation and Drainage (DID), Malaysia. Ten data

sets were simulated from the historical records and each set consists of one

hundred years of flow and rainfall sequences. The model performance for

untransformed and transformed data series was compared.

2. Methodology

Several disaggregation models namely Valencia-Schaake model (Valencia and

Schaake, 1973), Mejia-Rouselle model (Mejia and Rouselle, 1976), Lane

(Lane, 1979) and Synthetic Streamflow Generation Software Package

(Grygier and Stedinger, 1991) were tested. The basic form of Valencia-

Schaake model (VLSH) can be written in a matrix form as:

ttt

BεAQY

(1)

for the case of disaggregating annual flows into seasonal flows, Y

t

,

y,.....y,y Y

m,t2,t1,t

i

t

is a column matrix containing the seasonal flow

values which sum to Q

t

, and for the same time Q and Y are referred as flow

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

58

values. Q

t

is a 1 x 1 matrix of the annual streamflow value of year t, m is taken

as 12 month,

t

is the m x 1 matrix of independent standard normal deviates,

and A and B are the parameters matrices with dimensions of m x 1 and m x m,

respectively. The Mejia-Rouselle (MJRS) model takes the following form:

1tttt

Y C ε B Q AY

(2)

in which Y

t

, Q

t

,

t

, A and B are similar to the Valencia-Schaake model and C

is the additional (m x m ) parameter matrix. The Lane model (LANE) for a

single site can be written as:

(3)

in which Y

ν, t

is the seasonal streamflow vector; Q

v

is the annual streamflow

vector;

v,t

is the vector of normally distributed noise term with mean zero and

the identity matrix as its variance – covariance matrix. The noises

v, t

are

independent in time and space; v denotes the number of year and t is for

season (month). The condensed disaggregation procedures are based on

Synthetic Streamflow Generation Software Package (SPIGOT). The model

takes the following form:

(4)

where t is for month; ν is for year; Y

ν,t

is the seasonal streamflow vector;

tν,1tν, ttν,

ε E CE

is the normally distributed innovations of

v,t

, the

independent zero-mean normal random vectors; and Q

v,t

is the generated

annual streamflow vector.

For the case of rainfall simulation, the VLSH model can be written as:

ttt

ε B Z AX

(5)

where X

t

,

,

2,1,

,.....,

mt

tt

xxxX

i

t

is a column matrix containing the seasonal

rainfall values which sum to Z

t

, and for the same time Z and X represent

rainfall values. Z

t

is a 1 x 1 matrix of the annual rainfall value of year t, m is

taken as 12 month,

t

is the m x 1 matrix of independent standard normal

deviates, and A and B are the parameters matrices with dimensions m x 1 and

m x m, respectively. For the case of MJRS model, the rainfall series

simulation reads:

1tttt

XCε BZ AX

(6)

tν,tν,ttt ν,

E Q B AY

1tν, τtν,tνttν,

Y C ε B Q AY

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

59

where the X

t

, Z

t

, A, B and

t

are similar with equation (5) and C is the

additional (m x m) parameter matrix. The LANE model for rainfall series can

be written as:

1tν,ttν,tν

t

tν,

XCε BZ

A

X

(7)

The development of streamflow and rainfall simulation model involves

three procedures; statistical analysis of data, fitting a stochastic model, and

generating a synthetic series. The simulation models used in this study are

based on work by Toa and Delleur (1976) and Grygier and Stedinger (1991).

The quality of the data was examined by performing time series plotting,

distribution plot and descriptive analyses. The statistical characteristics of the

observed data series are important factors in selecting the type of model.

Basically, a streamflow and rainfall series can be characterised by their mean,

standard deviation, skewness coefficient and season-to-season correlation

coefficient.

In the case of non-normally distributed monthly streamflow and rainfall

series the data was first transformed. Logarithmic, Box-Cox and power

transformation techniques were generally sufficient to obtain normal

distribution. The use of normally distributed series (after transformation) is

preferred because their statistical properties are well established compared to

the original series (non normal distribution). The generated series were then

compared with the historical records for the untransformed and transformed

cases. The normality of the data was tested using the skewness of normality

(Valencia and Schaake, 1973). The descriptive analysis consists of parameter

estimation and model testing to ensure that the model can fit the data well. The

parameter estimation step was done after the type of model(s) was selected.

The model parameters were estimated either by the method of moments

(MOM) or by the least squares methods (LSM).

The parameter estimations of the stochastic model were tested to ensure

that the model comply with the model requirement. The goodness of fit test

involved checking the residuals and comparing the model with the historical

properties. The basic assumptions about the residual are that they are normal

and independent. For testing whether the residuals are independent, two

approaches were used. The first compute the correlation coefficient and check

whether the values are statistically equal to zero. The second approach used

the Porte Manteau lack of fit test as described by Valencia and Schaake (1973)

and Grygier and Stedinger (1991).

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

60

3. Results and Discussion

This analysis used 26 years of streamflow and 59 years of rainfall data of

Sungai Muar. The statistics of the historical and generated streamflow and

rainfall sequences were computed and compared. Figures 1 and 2 show that all

disaggregation candidate models can adequately preserve the historical mean

for transformed and untransformed streamflow. However, the SPIGOT model

preserves the historical standard deviation better than the other candidate

models (Figures 3 and 4). VLSH is obviously the best model for flow

simulation as it consistently preserve the statistical properties of most of the

mean monthly values for both untransformed and transformed flow series.

Nevertheless, all the tested models failed to preserve the skewness coefficient

for both untransformed and transformed streamflow and rainfall series.

In addidition, Box and Whisker plots of the annual flow for each model are

shown in Figures 5 and 6. The candidate models consistently demonstrate a

good reproduction of the historical properties (annual mean) for the

transformed flow sequences (Figure 5). The tested models, however, are less

promising in preserving the historical annual standard deviation except for the

VLSH model (Figure 6).

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

0

20

40

60

80

100

120

140

MEAN (mcm)

HISTORICAL VLSH MJRS LANE SPIGOT

Figure 1: Mean monthly streamflow obtained by various

disaggregation models (transformed flow)

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

61

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

0

20

40

60

80

100

120

140

MEAN(mcm)

HISTORICAL VLSH MJRS LANE SPIGOT

Figure 2: Mean monthly streamflow obtained by various

disaggregation models (untransformed flow)

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

0

20

40

60

80

STD DEVIATION

HISTORICAL VLSH MJRS LANE SPIGOT

Figure 3: Mean monthly standard deviation of streamflow obtained by

various disaggregation models (transformed flow)

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

0

20

40

60

80

100

STD DEVIATION (mcm)

HISTORICAL VLSH MJRS LANE SPIGOT

Figure 4: Mean monthly standard deviation of streamflow obtained by

various disaggregation models (untransformed flow)

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

62

VLSH MJRS LANE SPIGOT

450

550

650

750

MEAN (mcm)

Mean

±SD

±1.96*SD

Box & Whisker Plot

Historical mean = 518.61mcm

Figure 5: Annual mean streamflow obtained by various

disaggregation models (transformed flow)

VLSH MJRS LANE SPIGOT

300

500

700

STD. DEVIATION (mcm)

Mean

±SD

±1.96*SD

Box & Whisker Plot

Historical Std. Deviation = 322.35 mcm

Figure 6: Annual standard deviation of streamflow obtained by

various disaggregation models (transformed flow)

Similar comparisons were made for the rainfall simulation. In Figures 7 and

8, all the disaggregation models are able to produce very similar mean

monthly with the historical mean for both transformed and untransformed

rainfall series. Similar results were obtained for the preservation of mean

monthly standard deviation (Figure 9). As for the annual data, the candidate

models are successful in preserving the historical annual mean for transformed

rainfall series (Figure 10). However, the MJRS and LANE models slightly

underestimated the historical standard deviation (Figure 11). In overall, the

VLSH model is the most robust for preserving the historical annual standard

deviation for the transformed rainfall sequences.

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

63

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

50

100

150

200

250

300

MEAN (mm)

HISTORICAL VLSH MJRS LANE

Figure 7: Mean monthly rainfall generated by various

disaggregation models (transformed series)

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

50

100

150

200

250

300

MEAN (mcm)

HISTORICAL VLSH MJRS LANE

Figure 8: Mean monthly of rainfall obtained by various

disaggregation models (untransformed series)

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

MONTH

0

40

80

120

160

200

STD.DEVIATION

(mm)

HISTORICAL VLSH MJRS LANE

Figure 9: Mean monthly standard deviation of rainfall obtained by

various disaggregation models (transformed series)

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

64

VLSH MJRS LANE

1700

1900

2100

2300

2500

MEAN (mm)

Mean

±SD

±1.96*SD

HISTORICAL MEAN = 1806.92 mm

Box & Whisker Plot

Figure 10: Annual mean of rainfall obtained by various

disaggregation models (transformed series)

VLSH MJRS LANE

800

1000

1200

1400

1600

STD. DEVIATION (mm)

Mean

±SD

±1.96*SD

HISTORICAL STD. DEVIATION = 981.98 mm

Box & Whisker Plot

Figure 11: Annual standard deviation of rainfall obtained by various

disaggregation models (transformed series)

Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)

65

4. Conclusion

The tested disaggregation models have successfully preserved the historical

mean and standard deviation of streamflow and rainfall series of Sungai Muar.

Nevertheless, the models failed to preserve the skewness coefficient. VLSH

model was found to be the best stochastic disaggregation technique as it

produces very similar properties to the historical streamflow and rainfall

series. These findings, however, must be considered preliminary as the models

were only tested on one site. Due to variability of hydrological data, this study

must be replicated to a number of rivers in Malaysia before any generalization

can be made.

Acknowledgements

This research has been supported by RMC-UTM Vote No 75034 and financial

support provided by NSF Ministry of Science and Technology. The

Department of Irrigation and Drainage (DID) is gratefully acknowledged for

providing the data.

References

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Software Package User’s Manual V2.6, School of Civ. and Envir. Eng., Cornell

Unversity, Ithaca, N.Y.

Harun, S. (1999) Forecasting and Simulation of Net Inflows for Reservoir Operation

and Management. Ph.D. Thesis, University Teknologi Malaysia, 220 pp.

Hipel, K.W., and McLeod, A.I. (1994) Time Series Modeling of Water Resources and

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Mejia, J.M., and Rouselle, J. (1976). Disaggregation models in hydrology revisited.

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