Hydrology of Humid Tropical Regions with Particular Reference to the Hydrological Effects of Agriculture and Forestry Practice (Proceedings of the Hamburg Symposium, August 1983). IAHS I'ubl. no. 140.

Simulating flood hydrographs from storm rainfalls in Venezuela

RICARDO R. PONTE RAVIREZ Instituto de Geografla, Unlversidad de Los Andes, Mêrida, Venezuela ELIZABETH M. SHAW Department of Civil Engineering, Imperial College, London SW7 2BU, UK

ABSTRACT The research programme VIMHEX (Venezuela Inter­national Meteorological and Hydrological Experiment) produced valuable rainfall and streamflow data during two summer seasons for selected drainage basins in Venezuela. Applying VIMHEX data, the forecasting of flood flows from heavy rainstorms has been investigated for the predomin­antly rural Guanipa River basin (4324 km2) in the eastern plains and for the small tributary basin of the Caris River (329 km 2). The nonlinear runoff routing model (RORB), with areal rainfall inputs computed by the Thiessen method, after calibration, simulated a test flood hydrograph with an overall goodness-of-fit of 93% for the Guanipa and 94% for the Caris. Operated in the design mode, using only the storm rainfall data, there were errors of 4% and 1% in the simulated peak discharges for the drainage basins. Effects of the spatial distribution of storm rainfalls on the resultant stream hydrographs were also studied for the Caris basin. The areal rainfalls for six storms sampled by three rain recorders were derived by different tech­niques and characteristics of the output hydrographs from the RORB model were compared.

La simulation des hydrogrammes de crues provenant d'averses orageuses au Venezuela RESUME La programme de recherche VIMHEX (Venezuela International Meteorological and Hydrological Experiment) a fourni des données importantes concernant les précipit­ations et les écoulements dans le réseau hydrographique pendant deux saisons des pluies pour quelques bassins versants choisis au Venezuela. D'après les données VIMHEX, la prévision des crues produites par des averses intenses a ete étudiée pour le bassin rural de la riviere

2

Guanipa (4324 km ) qui se trouve dans les plaines de l'est et aussi pour le bassin du petit tributaire Caris (329 km ). Un modèle non-lineaire de la propagation des crues et des écoulements (RORB), a ete calibre pour simuler 1'hydrogramme de crue en se servant des données des précipitations sur des superficies données, qui ont été calculées par la méthode de Thiessen. La simulation de 1'hydrogramme d'une crue-test présentait pour l'ensemble de l'ajustement 93% de 1'hydrogramme observé pour la

435

436 Ricardo R.Ponte Ramirez & Elizabeth M.Shaw

Guanipa et 91% pour la Caris. Le debit de pointe de chaque bassin a été calculé dans les conditions de calcul du projet avec une erreur de 4% par le modèle RORB, n' utilisant que les données de précipitation. Une etude sur l'influence de la distribution spatiale des averses intenses a été faite pour le bassin Caris. Les précipit­ations sur des superficies données, mesurées par trois pluviomètres, ont été calculées pour six averses en se servant de procédés différents. Les hydrogrammes simulés avec ces données par le modèle RORB ont été comparés.

INTRODUCTION

In ail parts of the world where man is endeavouring to develop the environment to improve the quality of life, the forecasting of flood discharges in the rivers is a prime necessity. Whether the develop­ment is for industrial or urban water supplies , for the enhancement of agricultural production or merely for bridge construction in the design of improved land communications, it is a function of the hydrologist to provide the civil engineer with the required infor­mation on the incidence of peak flows. The need for such information is paramount in the developing economy of Venezuela.

Any study of river behaviour is dependent on a good series of discharge measurements and the most satisfactory results are obtained from continuous records. In addition, for individual flood events, a representative network of raingauges over the drainage basin is essential in order to give prior warning of increasing river flows. During the rainy seasons (May-September) of 1969 and 1972 in north­east and central Venezuela, the Venezuela International Meteorol­ogical and Hydrological Experiment (VIMHEX) established networks of recording raingauges and streamgauges, The meteorological objectives of the experiment were to study the local structure of the mesoscale convective systems and their relationship to the synoptic (macro) scale situations. About 75% of the rainfall comes from mesoscale systems (local showers and thunderstorms) and on the macroscale , the rainy season results from the northward migration of the Inter­tropical Convergence Zone (ITCZ). Results from the meteorological studies of the VIMHEX data have been published by many workers in the field (e.g. Riehl, 1973; Betts et al., 1976; Cruz, 1973). In this study, some of the river flow records, together with the recording raingauge measurements in the corresponding drainage basins, have been analysed with the aim of simulating flood hydrographs from storm rainfalls with particular attention to forecasting the peak flows.

THE DRAINAGE BASIN

A drainage basin in the eastern plains of Venezuela was selected from the VIMHEX area where the storm development is unaffected by the orographic effects of the high Andes mountains. Figure 1 shows the location of the Guanipa River basin defined by the streamgauging station no. 35 at the crossing of the Temblador to Maturin road. The headwaters with the tributaries, Tonoro and Caris, drain a rocky area which rises to a maximum height of 300 m above sea level and

Simulating flood hydrographs in Venezuela 437

A^VsM

FIG.l Topography oi study area.

the total drainage basin area is 4324 km . Vegetation is scarce over the upland area due to the acidic soil and only becomes extensive along the river valleys where it is controlled by the water table. In the lower parts of the drainage basin, sandy alluvial soils also support sparse vegetation except adjacent to the streams. The Guanipa basin is predominantly rural. Situated in the savanna climatic belt, temperatures are high, annual average 26 C, and of the average annual rainfall (1000 to 1300 mm), the maximum falls are in the summer, June to August, with monthly totals of around 200 mm.

Rainfall and streamflow data were taken from the VIMHEX 1969 records for the 20 recording raingauges at the sites shown in Fig.2 and for the three marked streamgauging stations. Stations 33 and 34 define the drainage basins of the tributaries Caris and Tonoro respectively. In this paper only the results of the hydrological studies for the Guanipa (4324 ki') and the Caris (329 km ) are presented to give the greatest contrast in drainage basin area (Ponte Ramirez, 1981).

Particulars of 11 storm events for the two drainage basins are given in Table 1. The total rainfall for each storm is the areal rainfall value derived by the Thiessen method from the recorded data; the appropriate polygons are shown in Fig.2. The discharge data were abstracted from the published 2-h values (Simons et al., 1971). The storm hydrographs were plotted on semilogarithmic paper; the times of the start, peak and end of the storm flows were identified. The baseflow separations were made consistently for each event by extending the pre-storm baseflow recession to the time of the peak and joining this point to the end of the stormflow.

THE RUNOFF ROUTING MODEL

The ability to forecast the peaks of flood flows is dependent on the size of the drainage basin and on the availability of hydrometric

438 Ricardo R.Ponte Ramirez & Elizabeth M.Shaw

FIG.2 Guanipa basin: raingauge distribution, Thiessen polygon network, streamgauging stations and subareas.

TABLE 1 Rainfall and discharge for the selected storms

Drainage Storm; basin Date No.

Total Rainfall rain duration (mm) (h)

Peak discharge

Antecedent baseflow

Guanipa 14 26 11 28 23

12 14 11 16 28 23

07 07 08 08 09

07 07 08 08 08 09

69 69 69 69 69

69 69 69 69 69 06

Gl G2 G3 G4 G5

CI C2 C3 C4 C5 C6

25 8

35 16 19

20 32

5 17 20 17

3 3 8 4 8

7 6 4 3 6 8

24 26 23

6 35

4 5 3 5 5 8

O 0 0 0 0

0 0 0

.0 0

.0

68.76 78.95 78.40 61.46 94.35

23.6 27.4 13.9 30.0 13.O

Caris 88.34 79. lO 68.08 48 .07 40.65 34. lO

4.69 5.31 0.40 3.33 1.90 l.OO

measurements. For a large drainage basin observations of river levels in the headwaters may be used to forecast maximum levels at strategic downstream points on the river. Failing upstream river levels and in small basins , rainfall measurements are necessary on which to base forecasts of flood peaks. There are many methods developed by hydrologists for relating rainfall quantities to river discharges; for short term events a deterministic method has much to recommend it.

For the Venezuelan basins, the runoff routing method initiated in Australia (Laurenson, 1965) and developed further for flood estimation (Mein et al., 1974) has been applied to the available rainfall and river flow data. The computer package of the runoff-routing model,

Simulating flood hydrographs in Venezuela 439

RORB, was made available at Imperial College (Laurenson & Mein, 1978). The rainfall data first enter a loss model which produces rainfall-excess which then passes into a basin storage model to produce a surface runoff hydrograph. If there is significant baseflow it is estimated separately and added to the surface runoff hydrograph.

The loss model comprises an initial loss (I.L.) followed by a constant loss rate (<f>); for urban basins with impervious areas, an initial loss may be followed by a proportional loss related to the impervious area. The drainage basin storage effects are represented by the nonlinear expression of the form:

S = 3600 KQm (1)

3

where S is the volume of water in storage (m ) , Q is the outflow 3 — 1

discharge (m s ), K is the storage-discharge coefficient related to the travel time in the area of storage, and m is the discharge component usually in the range 0.6 to 0.8.

The runoff routing model is applied to selected basins of the total area to be studied. For the Guanipa basin 11 appropriate sub­divisions labelled A to K are shown in Fig. 3. Model nodes are sited at the following selected points:

(a) at the point on the stream nearest to the centroid of each sub-basin;

(b) at the downstream limit of each sub-basin; (c) at the confluence of streams from different sub-basins; and

finally, (d) at the outlet of the main drainage basin.

A sub-basin, with model nodes at the "centroid" streampoint and the sub-basin outlet, may be defined for any point on the river or tributaries where flow data are required.

FIG.3 Basin storage model: Guanipa basin.

440 Ricardo R.Ponte Ramirez S Elizabeth M.Shaw

The model operates on the sequence of nodes as displayed diagram-atically in Fig.3. For each of the sub-basins, the areal rainfall quantities are evaluated for the chosen time intervals (t) from the pluviograph data. In fitting the model the rainfall inputs are subjected to the "loss model" calibrated so that the total rainfall excess for the basin is equivalent to the volume of observed surface runoff. The rainfall excess hyetograph for sub-basin A (mm h_ ) is

3 — 1

converted to a rainfall excess hydrograph (m s ) which is then assumed to enter the stream at centroid A, node 1. This is routed to node 2 via the storage model, equation (1). Expressing the continuity equation

1 dS

3600 dt

in finite difference form, gives:

*t + It+1 _ Qt + Qt+1 _ st+l ~ St 2 2 3600At

and the solution of the equations by an iterative technique proceeds until two successive estimations of Q differ by less than 1%. The rainfall excess hydrograph for sub-basin B is then added at node 3 and the combined hydrographs routed to node 4. The sequence continues down the mainstream to be joined at node 6 by the runoff routed down the Caris tributary with the Tonoro tributary contribution joining at node 11. The total drainage basin hydrograph is produced at node 19 from the 11 subareas.

MODEL PARAMETERS

There are two main parameters K and m to be evaluated for the model. The storage-discharge coefficient K is regarded as the product of

two factors:

K = KcKr

Kr is a dimensionless ratio, the relative delay time for a given model storage determined from the physical characteristics of the stream channel.

It is defined in the RORB package for each sub-basin (i) by:

Kri = di/ daV R

distance (km), the distance from the centroid of the whole basin to the outlet; and R is a channel condition factor and equals 1 for natural channels. Kr is determined therefore from drainage basin and channel characteristics.

Kc is the principal parameter to be determined in calibrating the model. Kc and m are interdependent; changes in m in its range 0.6 to 0.8 cause changes in Kc.

The RORB package has been assembled to run in three modes

Simulating flood hgdrographs in Venezuela 441

according to the information required and the existing knowledge of the parameters. Table 2 sets out the combinations of the various states and the type of run prescribed.

TABLE 2 RORB model run modes

FIT DESIGN

Hydrograph Parameters Purpose, of run

Known Unknown To determine parameters

Known Unknown Known Known To test To determine model design hydrograph

The program is designed for interactive operation from a computer terminal. The basic data, rainfall and hydrograph values and drain­age basin data are read from a preprepared data file. Parameters are punched in while running the program. The loss model is chosen, the initial loss is given by the user for FIT and TEST runs and the constant loss rate is evaluated by the program. In DESIGN runs, the user must supply both loss model parameters and they are assumed constant for the whole drainage basin. The drainage basin storage parameters m and Kc are then supplied to serve the whole drainage basin; the predetermined Kr values in the drainage basin data modify Kc to give a separate storage coefficient K for each sub-basin area.

The output from the program comprises on-line plots of the observed and simulated hydrographs from FIT and TEST runs and the simulated hydrograph only from DESIGN runs together with the numerical data at the prescribed time intervals. The rainfall excess is also plotted and numerous other statistics produced and printed.

APPLICATION TO THE GUANIPA AND CARIS BASINS

For the fitting or calibration of the model, four storm events were used for the Guanipa basin and five for the Caris basin. Storm numbers G3 and C3 were set aside for independent testing of the model. The results are shown in Table 3. It will be noted that the value of m has been kept constant at 0.75. The simulated peaks (Qp) fit the observed peaks very well; the larger discrepancies erring on the positive side with higher simulations and any differences in the times to peak (Tp) erring on the early side; an acceptable fault in practical forecasting. The goodness-of-fit criterion represented

2

by R is a measure of the overall fit of the hydrographs.

R2 = l - (F2/F„2) If q0 are the observed hydrograph ordinates with mean q0 and qs are the simulated hydrograph ordinates,

F2 = Z° (qs - q 0):

442 Ricardo R.Ponte Ramirez S Elizabeth M.Shaw

TABLE 3 Fitting RORB to the Guanipa and Caris basins

Storm no.

GUANIPA Gl G2 G4 G5

Average

CARIS CI C2 C4 C5 C6

Average

Loss I.L. (mm)

0.0 O.O 1.0

10.53

2.0 29.1

1.0 17.2

5.0

Model :

* (mm h x)

24.5 3.8

19.9 6.0

10.06 0.04

11.65 1.09

12.9

Model parame Kc

68.9 57.5 56.4 67.0

62.5

11.0 10.4 17.1

4.3 8.0

10.2

ter s : m

0.75 0.75 0.75 0.75

0.75

0.75 0.75 0.75 0.75 0.75

0.75

Qp (m3s Obs.

68.76 78.95 61.46 94.35

88.34 79.10 48.07 40.65 34.10

- 1 ) : Sim.

69.70 78.70 61.70 94.30

88.16 79.28 48.97 40.61 34.19

T (hi Obs.

31 32 21 34

4 6 7 7

13

\ ; Sim.

30 32 21 33

4 6 7 7

13

Error in peak(%)

0.5 0.3 0.4 0.1

0.33

0.2 0.2 1.9 0.1 0.3

0.54

R1

92. 85. 77. 97.

88.

93. 90, 95, 98, 95

94.

.3 4

.0

.4

.0

.3

.1

.6

.2

.4

.5

and

= £• 1=1 < %

Although the simulated peaks on the smaller drainage basin show the larger error on average, the overall fit of the simulated hydrographs is better than that for the large Guanipa drainage basin where the storm G4 brought down the average for R2. The variability of the storm patterns over the large basin is a factor which provides difficulties in the evaluation of the loss model parameters.

The RORB model was then applied to the two test storms using the mean values obtained for K from the FIT runs with the value of m fixed at 0.75. The results of the TEST runs are given in Table 4.

TABLE 4 Test results for the Guanipa and Caris basins

Storm no. Loss model: Model Q (m3s~1): T (h): Error R2

I.L, (J) parameters: Obs. Sim. Obs. Sim. in

Kc m peak (%)

GUANIPA

G3 24.8 5.96 62.5 0.75 78.4 77.4 28 29 1.2 93.4 CARIS C3 0.0 0.30 10.2 0.75 68.1 69.2 5 4 1.7 93.7

The calculated peak flows of the simulated hydrographs compare very well with the observed flows with errors of only 1.2% and 1.7% in the Guanipa and Caris basins respectively. The overall fit of the simulated hydrograph of the large basin, 93.4% is similar to that for the small tributary, 93.7%.

The model was then run in the DESIGN mode for the test storms. Only the rainfall data are used in this mode with the same average

Simulating flood hydrographs in Venezuela 443

model parameters derived in the fitting runs but with estimated loss model parameters. The peak of the simulated hydrograph obtained in the design run differed by 4% from the observed peak for the Guanipa and only 1% for the Caris basin.

One of the main objectives of the simulation studies is to derive a discharge hydrograph using only the rainfall data. The simulated peak discharges for the test storms are highly satisfactory. The times to peak, 29 h for the Guanipa and 4 h for the Caris, were also acceptable. Such results would be valuable in forecasting flood peaks in practice. A further application of the simulation technique is the estimation of extreme floods with long return periods for civil engineering design purposes. Some indication of such high peak discharges may be derived by simulating the hydrographs from design storms taken from rainfall depth-duration-frequency data published by the Ministry of Public Works.

AREAL RAINFALL VARIABILITY

One of the particular interests in this investigation was the quantification of areal rainfall variability. This is particularly important in regions with scattered rainfall from irregular convective systems. An attempt was made to assess the areal rainfall differences by deriving the areal rainfalls by two methods and observing the hydrograph variations from respective runs of the RORB model.

For the experiments, the data for the six storms on the Caris basin were abstracted from the records of raingauge stations 6, 10 and 19. These are shown more clearly in Fig.4. The subareas A, B

FIG.4 Caris sub-basin: three subareas and the Thiessen polygon network.

and C for the Caris basin are also defined. The areal rainfalls for the subareas were obtained from the area proportions of the relevant Thiessen polygon rainfalls. Thus the rainfall of subareaA

444 Ricardo R.Ponte Ramirez S Elizabeth M.Shavj

was totally defined by the measurements at gauge 19, rainfall of subarea B required the measurements of all three gauges and sub-area C needed only gauges 6 and 10. A second determination of the areal rainfall values for each subarea was made by the multiquadric method (Lee et al., 1974) which provides for a gradient of the rainfall quantities between measuring sites. The percentage differences between the areal rainfalls for the total drainage basin and the three subareas derived by the two methods is given in Table 5.

TABLE 5 Comparison of areal rainfall by multiquadric and Thiessen methods

Storm Percentage differences multiquadric to Thiessen:

Basin area Subarea A Subarea B Subarea C

Cl C2 C3 C4 C5 C6

Average

-16 -34

+1 -31 +16 +10

-14.3

-32 -37

+3 -33 +24

+1

12.3

-9 -10

+5 -12 +11 -14

-4.8

+14 -43

-9 -40 +24 -28

-13

The multiquadric method on average gives a lower areal rainfall value than the Thiessen weighting method. This is due to less areal weighting on the high rainfalls, particularly noticeable for storm Cl which was centred on subarea A. Although the rainfall differences are considerable for four of the storms, the errors in the simulated peak discharges from the observed values were all under 1% for both sets of rainfall data. The overall fit of the hydrographs given by R showed little difference on average, 93.1% with the multiquadric method and 90.7% with the Thiessen method. Storm Cl however, provided a 90.1% fit with the multiquadric and only 75.0% with the Thiessen method.

The variability in the represented rainfall distributions is damped by the drainage basin response modelled by the storage relationships. Some smoothing of the differences is also provided by the loss model.

It is not advisable to draw firm conclusions from this limited experiment with only six storms represented by measurements from only three raingauge stations. Further investigations should be carried out with a larger raingauge network on basins with other hydrological regimes.

In conclusion, it has been demonstrated that the nonlinear runoff routing model (RORB) can be applied satisfactorily to simulate the rainfall-runoff relationship and to produce flood hydrographs from storm rainfalls in Venezuela. Given good rainfall measurements, peak flows can be forecast and design floods can be derived from extreme

Simulating flood hydrographs in Venezuela 445

rainfall intensities.

ACKNOWLEDGEMENTS The research was carried out at Imperial College by the first author with the financial support of the Universidad de Los Andes, Mérida, Venezuela. The RORB program was run on the Imperial College CDC 6400 computer. Mr A.Robson very kindly drafted the resume.

REFERENCES

Betts, A.K., Grover, R.M. & Moncrieff, M.W. (1976) Structure and motion of tropical squall lines over Venezuela. Quart. J. Roy. Met. Soc. 102, 395-404.

Cruz, L.A. (1973) Venezuelan rainstorms as seen by radar. J. Appl. Met. 12, 119-126.

Laurenson, E.M. (1965) A catchment storage model for runoff routing. J. Hydrol. 2, 141-163.

Laurenson, E.M. & Mein, R.G. (1978) General runoff routing computer program. RORB Version 2 - User Manual.

Lee, P.S. , Lynn, P.P. & Shaw, E.M. (1974) Comparison of multiquadric surfaces for the estimation of areal rainfall. Hydrol. Sci . Bull. 19 (3), 303-317.

Mein, R.G., Laurenson, E.M. & McMahon, T.A. (1974) Simple nonlinear model for flood estimation. J. Hydraul. Div. ASCE HY11, 1507-1518.

Ponte Ramirez, R.R. (1981) Storm rainfall and runoff in Venezuela. Unpublished M.Phil, thesis, Imperial College, University of London.

Riehl, H. (1973) Controls of the Venezuela rainy season. Bull. Am. Met. Soc. 54, 9-12.

Simons, D.B., Richardson, E.V., Stevens, M.A., Duke, J.H. & Duke, V.C. (1971) VIMHEX Hydrology Report II. Streamflow, groundwater, and ground response data. Civil Engineering Dept, Colorado State Univ., Fort Collins, USA.