Hidrologia

Proceedings of 2013 IAHR World Congress

ABSTRACT: Unare River Basin with an area of about 23 000 Km2es constantly affected by the overflow of floods, threatening the development of economic and social activities in the region. Hydro meteorological information is scarce and only recently has been implemented measurement stations. Consequently, using the data collected so far, it is necessary to calibrate the rainfall-runoff models (P (Q)) to further zoning floodplains and evaluate hydrological risks involved. The objective of the research is to calibrate the models of rainfall-runoff process and determine water levels in rivers for flood of different return periods. For calibration of the models digitized 1:100,000 national charts were used, as well as observations of 29 rainfall sensors and two sensors of water levels in the river. The hydrological parameters were obtained by combining the databases of physiography, soil types and land uses and synthetic storms for return periods (Tr) of 2, 10, 25, 50 and 100 years. Three P (Q) models were validated based on physical processes and used to generated flood zone maps. Statistical autoregressive models adjust well to the observations of 63% of the rainfall sensors (R2> 0.5). The observed rainfall intensities fit well to previously calibrated IDF curves models. Maximum flood levels for Tr 2/100 years are in the order of 0.42/1.06 m. for Guanape river; 1.25/2.29 for Guaribe river, 0.19/ 0.25 m. for Guere river, 0.29/ 0.5 m. for Ipire river ands 0.78/1.21 m. for Tamanaco river. For each case a floodplain map was developed. KEY WORDS: Model P (Q), Floodplains, Hydrological processes, Zoning, Models based on physical processes, Runoff. 1 INTRODUCTION

Unare River Basin is annually affected by extreme hydrological events, causing flooding in the plains during the rainy season. It is composed of five basins of the rivers: Guanape, Guaribe, Gere, Ipire and Tamanaco. These sub-basins are characterized by low slopes of land, causing flooding of large areas near rivers mentioned. Generally, these areas are located settlements omitting legislation restricting the occupation of these. Additionally, there are limitations to the application of the rules because of the lack of instruments, such as floodplain zoning maps. The zoning of flood events involves large uncertainties because of poor monitoring of variables such as, rain and runoff. These variables must correspond to extreme events based on the occurrence of maximum values. Statistical analysis of these events leads to the estimation of the frequency with which these can be matched or exceeded, known as the return period. As the period of return increases, the magnitude of hydrologic event also increases.

In basins that lack of continuous observations of runoff is required to apply flood estimation models. These are isolated events, represented by a rapidly varied flow. Isolation and flow variation characteristics are related to frequency of occurrence and variation within rain events, respectively. From the foregoing, it is evident that there is a relationship between rainfall and runoff. This relationship may be influenced by

Rainfall-Runoff Model Calibration for the Floodplain Zoning of Unare River Basin, Venezuela

Adriana Mrquez Professor, Carabobo University, Carabobo, Venezuela. Email: [email protected]

Edilberto Guevara Professor, Carabobo University, Carabobo, Venezuela. Email: [email protected]

physical factors such as: the topography, geomorphology, soil type and land use (Diez-Herrero et al, 2009). The influence of these factors can be considered explicitly or implicitly (Zhang and Govindaraju, 2000), according to the modeling technique that is used, which can be based on deterministic models or black box, respectively. The first are explained by physical processes while the latter are not, such as those based on statistical regressions (Martinez and Martinez, 2002) and the use of tools such as artificial neural networks (Eberhart and Dobbins, 1990, Bishop, 1994; Jain and Srinivasulu, 2004).

Also, the rainfall-runoff modeling based on physical processes over time has tended to be represented in a distributed manner over the space in which it occurs. Some models represent a simplified space (Jetten et al. 2003). The Stanford Watershed Model (Crawford and Linsley, 1962; Crawford and Linsley, 1966), the USDAHL-series of models (Holtan and Lopez, 1971; Holtan et al., 1975) and more recently the black box models mentioned above. Since the 1980s several major hydrological research groups have been developing distributed process-based hydrological models for simulating the transport of water, soil, nutrients and pollutants. Examples are groundwater transport models (e.g. Zheng, 1990; Harbaugh and McDonald, 1996; AQUA3D, 2001), rainfall-runoff models (e.g. SHE, Abbott, 1986a,b; TOPMODEL, Beven, 1997; LISFLOOD, De Roo et al., 2000), rainfall-runoff models including erosion (e.g. Grayson et al., 1992; EUROSEM, Morgan et al., 1998; Tucker et al., 1999), and rainfall-runoff models with nutrient or pollutant transport (e.g. Mackay and Ban, 1997). Clearly, hydrologists have a continuing need for new and better models, because concepts on how to represent hydrological processes in computer simulation models are still evolving. This change of ideas in modelling is being driven by new observation techniques, including remote sensing, and data storage and presentation technology such as geographical information systems (GIS), which provide larger volumes of useful data than ever before. The purpose of this research is to model the rainfall-runoff process during isolated events by the estimation of hydrological model parameters contained in the package HEC-HMS (USACE, 2000) Unare River Basin, Venezuela.

2 THEORETICAL FUNDAMENT

2.1 IDF CURVES MODEL

Many types of hydrologic analyses require estimates of rainfall intensities (or rainfall depths) for certain durations and frequencies of occurrence. Rainfall IDF data are generally available in the form of tables, graphs, or maps on which isohyetal lines are drawn. In specifying a design rainfall, it is necessary to specify its depth, the duration, and the frequency of occurrence of the storm event. Alternatively, IFD curves can be mathematically specified since Intensity I, duration D and Depth P are related as:

P = I D; or I = P/D (1)

The IDF relationship for point rainfall has been expressed by the general relationship:

I = K Tm / (D + to)n (2)

where I is the rainfall intensity in mm/h; T the return period in years; D the duration of rainfall in hours; m, n and to are parameters obtained by fitting by least squares method.

2.2 PHYSICAL PROCESSES BASED MODELS

Models based on physical processes (MBPP) investigated are structured in three modes. The first type consists of the following models of processes: MBPP1: loss model and rainfall-runoff transformation of the Soil Conservation Service (SCS) of the United States, Muskingum model, and flow recession model. The second type consists of the following process models: MBPP2: SCS loss model, Clarks unit hydrograph (UH) model, Muskingum model; model flow recession. The third type consists of the following process models: MBPP3: SCS loss model, Snyders UH model, Muskingum model and flow recession model.

2.2.1 SCS CURVE NUMBER LOSS MODEL

2

The Curve Number (CN) of the Soil Conservation Service (SCS) model estimates the precipitation excess as a function of cumulative rainfall, soil cover, land use, and antecedent moisture, using the following equation:

= ( )2 + (2) where Pe is the accumulated precipitation excess at time t, P accumulated rainfall depth at time, Ia the initial abstraction (initial loss) and S potential maximum retention, a measure of the ability of a watershed to abstract and retain storm precipitation. Until the accumulated rainfall exceeds the initial abstraction, the precipitation excess, and hence the runoff, will be zero.

From analysis of results from many small experimental watersheds, the SCS developed an empirical relationship of Ia and S. Therefore, the excess accumulated over time t is:

= (0.2)2+0.8 (3) The maximum retention, S, and watershed characteristics are related by an intermediate parameter,

the curve number as:

= 25400 254 (4) Values curve number ranging from 100 (bodies of water) to about 30 to permeable soils with high

infiltration rate.

2.2.2 DIRECT RUNOFF MODEL

SCS UH MODEL The Soil Conservation Service (SCS) proposed a parametric UH model; this is based upon averages

of UH derived from gaged measure rainfall and runoff for a large number of small agricultural watersheds. The U.S. Technical Report 55, (1986) and the National Engineering Handbook, (1971) describe in detail.

The SCS HU model is dimensionless. The components are expressed as: Ut is UH discharge, as a

ratio to the HU peak discharge, Up, for any time t, a fraction of Tp, the time to HU peak. Research by the SCS suggests that the UH peak and time of UH peak are related by:

= (5) where A is the area of the basin, and C a constant conversion (2.08 in SI). The time to peak is related to the precipitation surplus unit as follows:

= 2 + (6) in which t is the excess precipitation duration, and tlag basin lag, defined as the time difference between the center of mass of rainfall excess and the peak of HU (USACE, 1998).

Estimating the SCS UH model parameters

The SCS HU lag can be estimated via calibration, using procedures described below, for basins with level measurements. For ungaged watershed, the SCS suggests that HU lag time may be related to the time of concentration tc, as:

= 0.6 (7) The time of concentration is a physical parameter that can be estimated as: = + + (8)

3

where tsheet is the sum of travel time in sheet flow segments over the watershed land surface estimated based on kinematic wave approximations (Chow, 1959); tshallow the sum of the travel time in shallow flow segments, down streets, or in shallow rills; and tChannel sum of travel time in channel segments estimated using Manning's equation (Chaudhry, 1993).

CLARKS UH MODEL

Clarks model derives a watershed UH by explicit representing two critical processes in the transformation of excess precipitation to runoff:

Translation: or movement of the excess from its origin throughout the drainage to the watershed outlet.

Attenuation: or reduction of the magnitude of the discharge as the excess is stored throughout the watershed.

Short-term storage of water throughout a watershed -in the soil, on the surface and in the channels-

plays an important role in the transformation of precipitation excess to runoff. The linear reservoir model is a common representation of the effects of this storage. That model begins with the continuity equation:

= (9)

in which dS/dt is the time rate of change of water in storage at time t; It average inflow to storage at time t; and Ot outflow from storage at time t. With a linear reservoir model, storage time t is related to outflow as: = (10)

where R is a constant linear reservoir parameter. By combining and solve the equations using simple finite difference approximation occurs:

= + 1 (11) where CA, CB are the routing coefficients. The coefficients are calculated from:

= + 0,5 (12)

= 1 (13) The average effluent during the period t is:

= 1 + 2 (14)

Estimating Model Parameters Clark HU Application of the Clarks model requires: Properties of the time-area histogram; The storage coefficient, R. The linear routing model properties are defined implicitly by a time-area histogram. Studies of HEC

have shown that, even though a watershed-specific relationship can be developed, a smooth function fitted to a typical specific time-area relationship represents the temporal distribution adequately for HU derivation for most watershed. That typical time-area relationship, which is included in HEC-HMS is:

4

=

1.414

1.5 2

1 1.414 1

1.5 2

(15)

where at is the cumulative time contributor area at time t, A the total area of the basin, and tc the time of concentration of the basin. For use in HEC-HMS only tc parameter is important. This can be estimated by calibration. The basin storage coefficient r is an index over the temporary storage of precipitation in the watershed as it drains it to a point of departure. It can also be determined by calibration if the runoff and precipitation data as are available.

SNYDERS UH MODEL

In 1938, Snyder published a description of a parametric UH developed for analysis of ungaged watershed. He provided relationships for estimating the UH parameters from watershed characteristics. Snyder selected lag, peak flow, and total time base as the critical characteristics of a HU. He defined a standard UH as one whose rainfall duration, tr, is related to the basin lag, tp, by:

= 5.5 (16) Thus, if the duration is specified, the lag of Snyders standard UH can be found. Otherwise, the

following relationship is used to define the relationship of UH peak time and UH duration.

= 4 (17) in which tR is the desired duration of UH; and tpR lag of desired UH.

For the standard case, UH lag and the peak per unit of excess precipitation per unit area of the watershed is related by:

=

(18)

where Up is the peak of standard HU, A watershed drainage area, Cp UH peaking coefficient, and C the conversion constant. For other durations, peak HU, QPR, is defined as:

=

(19)

Snyders HU model requires specifying the standard lag, tp, and the coefficient, Cp.

Estimating parameters Snyder HU The HU lag is estimated as:

= ()0.3 (20) where Ct is the basin coefficient; L the length of the main stream from the outlet to the divide; Lc the length along the main stream from the outlet to a point nearest the watershed centroid, and C conversion constant (0.75 for SI). The Ct and Cp parameters are best found via calibration. Bendient and Huber (1992) reported that Ct typically ranges between 1.8 and 2.2, although it has been found to vary from 0.4 in mountainous areas to 8.0 along the Gulf of Mexico. They also reported that Cp ranges from 0.4 to 0.8, where the larger value of Cp are associated with smaller values of Ct.

5

2.2.3 MODELING CHANNEL FLOW

MUSKINGUM MODEL The Muskingum routing model, uses a simple finite difference approximation of the continuity

equation:

1 + 2 1 + 2 = 1 + (21)

Storage in the reach is modeled as the sum of prism storage and wedge storage. The volume of the prism storage is the outflow rate, O, multiplied by the travel time through the reach, K. The volume of wedge is a weighted difference between inflow and the outflow, multiplied by the travel time K. Thus, the Muskingum model defines the storage as:

= + ( ) (22) where K is the travel time of the flood wave through routing reach; and X a dimensionless weight (0 X

0.5).

Parameter estimation of Muskingum model Parameter restrictions: the feasible range for the parameter X is (0, 0.5). However, these other

constraints apply to selection of X and K parameter. The accurate solution requires selection of appropriate time steps, distance steps, and parameters to

ensure accuracy and stability of the solution. x / t is selected to approximate c, where c is the average wave speed over a distance increment x.

The parameters K, X and the computational time step t also must be selected to ensure that the Muskingum model is rational. The values of X and K should be chosen so that the combination fall in the range x (0, 0.5) and t / k (0, 2) (Cunge, 1969).

3 MATERIALS AND METHODS

The research was conducted in Unare river basin. The basin is located in the northeastern region and the plains of Venezuela. It is located between 8 44 '07 "-10 05' 31" north latitude and 66 12 '37' - 64 09 '29 "west longitude. The rainfall intensities information used corresponds to 29 weather stations, two level sensors and rating curves. The land use in Unare river basin is averaged as follows: 50% agriculture, 40% natural vegetation, 4% residential, and 6% other (Figures 1 and 2).

Figure 1 Land use in Unare river basin, Venezuela.

6

Figure 2 Land use in the Unare river basin, Venezuela

Calibration includes: a regional model curves intensity-duration-frequency (IDF) of rainfall, three

models based on physical process (MBPP) of rainfall-runoff (loss, rainfall-runoff transformation, channel flow and flow recession). MBPP1: loss and rainfall-runoff transformation models of the Soil Conservation Service (SCS) of the United States, Muskingum model, and flow recession model. The second type consists of the following process models: MBPP2: SCS loss model, Clarks unit hydrograph (UH) model, Muskingum model; model flow recession. The third type consists of the following process models: MBPP3: SCS loss model, Snyders UH model, Muskingum model and flow recession model.

The Ipire and Unare river sub-basins have been selected as observation points to calibrate rainfall-runoff models. These are equipped with a level sensor, which provides measurements every 5 minutes from 2011 and discharge vs. level curve, allowing the runoff can be observed compared with the estimated. The validation was performed by comparing the estimated values with those observed. The observations were obtained from discharge vs. level curves measured between 2011 and 2012 (Figure 3). From the curves have been transformed water levels provided by electromagnetic sensors flow every 5 minutes, getting the hydrographs in the middle and lower basin of the Unare river (Figure 4). Found calibration parameters were applied to river basins: Guanape, Gere, Guaribe and Tamanaco for the simulation of rainfall-runoff process.

Figure 3 Curves of Discharge vs. Level: (a) Curacao Bridge Station. Unare river middle basin. Guarico State. Venezuela (b) Clarines bridge station. Unare river basin outlet point. Anzoategui State. Venezuela

7

Figure 4 Unare river hydrograph: (a) Curacao Bridge Station. Zaraza. Unare river middle basin. Guarico State. Venezuela (b) Clarines bridge station. Unare river basin outlet point. Anzoategui State. Venezuela.

4 RESULTS AND DISCUSSION

IDF model parameters for Unare river basin vary as follows: K between 28.6878 and 54.2202; between 3.9581 and 5.5157 m, n between 0.6664 and 1.1635, t0 between 0.0655 and 0.6243, respectively (Table 1). The IDF model statistics indicate values that are satisfactory (Table 2).

Table 1 IDF model parameters for Unare river basin, Venezuela.

Basin Statistical K m n to

Minimum 28.6878 0.2473 0.6664 0.0655

Unare River Maximo 54.2202 0.3677 1.1635 0.6243

Average 41.4540 0.2959 0.9150 0.3449

Table 2 Performance criteria of IDF model for Unare river basin, Venezuela.

Station R2 (R2)adj AAE AARE AE ARE

Unare River 0.88 0.88 6.98 82.22 -0.23 -66.80

R2: determination coefficient; (R2)adj.: adjusted determination coefficient; AAE: average absolute error; AARE: average absolute relative error (%); AE: average error; ARE: average relative error (%).

The estimated intensity by the IDF curve model for the unare river basin approaches to observed satisfactorily. Residues indicate that most of the values estimated by the model have been three standard deviations below the values observed (Figure 5).

8

Figure 5 Model adjusted for IDF curves. Clarines bridge Station. Unare River Basin. Venezuela. Table 3 shows the estimated parameters for the application of MBPF 1 to Ipire River sub-basin. These vary

according to the models as follows: Model of losses: Ia between 20 and 100 mm, CN between 55.53 and 78.24, impermeability between 24.14 and 40.05 %. Model transformation: tlag between 14.34 and 89.02 h. Flow recession model: equal to 3 m3/s. Transit model: K between 3.23 and 11.16 h, X equal to 0.5.

Figure 6 shows a comparison of observed and estimated peak discharges of the Ipire river sub-basin. The observed peak discharge (dotted black line), Qp (obs) = 59.70 m3/s estimated peak flow Qp (est) = 43.5 m3/s (blue line).

Table 3 Parameters for MBPF1 application, Ipire River sub-basin.

Sub Basin

Losses Transformation Flow

Reccesion Transit

Ia (mm) CN Impermeability(%) tlag (h) Q (m3/s) River K (h) X W4120 20.00 78.24 24.14 14.34 3.00 R4030 3.23 0.50 W4130 87.85 66.55 30.28 45.34 3.00 R4040 11.16 0.50 W4140 91.99 62.74 33.59 43.56 3.00 R4050 3.58 0.50 W4150 93.87 60.84 35.09 89.02 3.00 R4080 37.66 0.50 W4160 99.58 55.92 39.67 41.85 3.00 R4060 6.27 0.50 W4170 100.00 55.53 40.00 14.70 3.00 R4070 4.88 0.50 W4180 99.83 55.61 39.87 61.47 3.00 R4100 4.57 0.50 W4190 100.00 55.53 40.05 57.09 3.00 R4110 29.23 0.50 W4200 91.51 66.57 28.90 69.89 3.00 R4090 11.19 0.50

Obs

erve

d In

tens

ity (m

m/h

)

Stan

dard

ized

Res

idua

l

Estimated Intensity

9

Figure 6 Results of MBPF1model calibration. Observed and estimated flow. Ipire river Sub-basin. Unare river basin, Venezuela.

Table 4 shows the estimated parameters for the application of MBPF 2 to Ipire River sub-basin. These vary

according to the models as follows: Model of losses: Ia between 20 and 100 mm, CN between 55.53 and 78.24, impermeability between 24.14 and 40.05 %. Model transformation: tc between 6.37 and 28.23 h. Flow recession model: equal to 3 m3/s. Transit model: K between 3.23 and 11.16 h, X equal to 0.5.

Table 4 Parameters for MBPF2 application, Ipire River sub-basin.

Sub Basin

Losses Transformation Flow

Reccesion Transit

Ia (mm) CN Impermeability(%) tc (h) R Q (m3/s) River K (h) X

W4120 20.00 78.24 24.14 7.37 4.42 3.00 R4030 3.23 0.50

W4130 87.85 66.55 30.28 15.48 9.29 3.00 R4040 11.16 0.50

W4140 91.99 62.74 33.59 11.97 7.18 3.00 R4050 3.58 0.50

W4150 93.87 60.84 35.09 19.20 11.52 3.00 R4080 37.66 0.50

W4160 99.58 55.92 39.67 6.37 3.82 3.00 R4060 6.27 0.50

W4170 100.00 55.53 40.00 2.74 1.64 3.00 R4070 4.88 0.50

W4180 99.83 55.61 39.87 15.60 9.36 3.00 R4100 4.57 0.50

W4190 100.00 55.53 40.05 15.59 9.36 3.00 R4110 29.23 0.50

W4200 91.51 66.57 28.90 28.23 16.94 3.00 R4090 11.19 0.50

Figure 7 Results of MBPF2 model calibration. Observed and estimated flow. Ipire river Sub-basin. Unare river basin, Venezuela.

Flow

(m3 /s

)

Legend:

Observed Flow (m3/s)

Estimated Flow

Flow

(m3 /s

)

Legend:

Observed Flow (m3/s)

Estimated Flow

10

Figure 7 shows a comparison of observed and estimated peak discharges of the Ipire river sub-basin. The observed peak discharge (dotted black line), Qp (obs) = 59.70 m3/s estimated peak flow Qp (est) = 64.3 m3/s (blue line).

Table 5 shows the estimated parameters for the application of MBPF 2 to Ipire River sub-basin. These vary according to the models as follows: Model of losses: Ia between 20 and 100 mm, CN between 55.53 and 78.24, impermeability between 24.14 and 40.05 %. Model transformation: tp between 7.10 and 33.5 h and Cp equal to 0.8. Flow recession model: equal to 3 m3/s. Transit model: K between 3.23 and 11.16 h, X equal to 0.5.

Figure 8 shows a comparison of observed and estimated peak discharges of the Ipire river sub-basin. The observed peak discharge (dotted black line), Qp (obs) = 59.70 m3/s estimated peak flow Qp (est) = 63.1 m3/s (blue line).

Table 5 Parameters for MBPF3 application, Ipire River sub-basin.

Sub Basin

Losses Transformation Flow

Reccesion Transit

Ia (mm) CN Impermeability(%) tp (h) Cp Q (m3/s) River K (h) X

W4120 20.00 78.24 24.14 7.60 0.80 3.00 R4030 3.23 0.50

W4130 87.85 66.55 30.28 10.00 0.80 3.00 R4040 11.16 0.50

W4140 91.99 62.74 33.59 33.50 0.80 3.00 R4050 3.58 0.50

W4150 93.87 60.84 35.09 12.00 0.80 3.00 R4080 37.66 0.50

W4160 99.58 55.92 39.67 7.10 0.80 3.00 R4060 6.27 0.50

W4170 100.00 55.53 40.00 19.70 0.80 3.00 R4070 4.88 0.50

W4180 99.83 55.61 39.87 15.30 0.80 3.00 R4100 4.57 0.50

W4190 100.00 55.53 40.05 22.30 0.80 3.00 R4110 29.23 0.50

W4200 91.51 66.57 28.90 13.90 0.64 3.00 R4090 11.19 0.50

Figure 8 Results of MBPF3 model calibration. Observed and estimated flow. Ipire river Sub-basin. Unare river basin, Venezuela.

In Figures 9a, 9b and 9c shows the comparison of the observed and estimated flow through transformation models:

SCS, Clark and Snyder, respectively. In Figure 9a, the linear function having a slope of 2.2017 and the coefficient of determination (R2) has a value of 0.7136. In Figure 9b, the trend line has a slope of 1.0182 and the R2 has a value of 0.6972. In Figure 9c, the trend line has a slope of 1.1878 and R2 has a value of 0.7888.

Flow

(m3 /s

)

Legend:

Observed Flow (m3/s)

Estimated Flow

11

Figure 9 Adjusted Physical Processes based models to observations in the calibration step for the following models of rainfall-runoff transformation: (a) Soil Conservation Service (SCS), (b) Clark Unit Hydrograph. (c) Snyder unit hydrograph.

Table 6 shows the peak flows of the sub-basins of the rivers: Guanape, Guaribe, Gere, Ipire and Tamanaco,

which shows that the flow rate increases as the return period increases from 2 to 100 years, as follows: Guanape river from 18.5 to 21 m3/s; Guaribe river from 30.6 to 42.1 m3/s; Gere river from 89 to 89.3 m3/s; Ipire river from 28.3 to 34.6 m3/s, Tamanaco river, from 92.3 to 92.9 m3/s. Shows that the variation is low in return periods.

Table 6 Peak flow sub-basins of the rivers: Guanape, Guaribe, Gere, Ipire and Tamanaco. Unare River basin, Venezuela.

Sub-Basin Peak Flow (m3/s)

Tr=2 year Tr=10 year Tr =25 year Tr =50 year Tr =100 year

Guanape 18.5 20.1 20.2 20.6 21.0

Guaribe 30.6 31.0 36.2 38.8 42,1

Gere 89.0 89.0 89.0 89.1 89.3

Ipire 28.3 29,7 31.2 33.0 34.6

Tamanaco 92.3 92,6 92.7 92.8 92.9

5 DISCUSSION OF RESULTS. It was found that the observed intensities fit IDF curves models calibrated to Guevara and Marquez

(2009), Marquez et al, (2012), corresponding to rainfall return period of 2 years. The MBPF 3 is the selected model, which includes: SCS loss and rainfall-runoff transformation Snyder models (R2 between 0.4 and 0.78.) In this model, the parameter Cp is equal to 0.8 according Bendient and Huber, (1992). The parameter X is equal to 0.5 according Cunge (1969).

Estimated Flow (m3/s)

Obs

erve

d Fl

ow (m

3 /s)

SCS

(a)

Estimated Flow (m3/s)

Obs

erve

d Fl

ow (m

3 /s)

Clark

(b)

Estimated Flow (m3/s)

Obs

erve

d Fl

ow (m

3 /s)

Snyder

(c)

12

6 CONCLUSIONS The range of the interval of the parameters in Unare river basin is influenced by local parameters

found for the rainfall stations ubicated in floodplains. These were significantly different, which could be associated with the influence of topography on climate.

The IDF model fit to the observed values is satisfactory in terms of the coefficient of determination (R2> 0.7).

In Unare river Subbasin floodplain: Guanape, Guaribe, Gere, Ipire, Tamanaco with Tr = 2 and 100 years, the maximum depths varied between 0.42 and 1.06 m, 1.25 and 2.29 m , 0.19 and 0.25 m, 0.29 to 0.5, 0.78 and 1.21 m.

ACKNOWLEDGEMENTS The research was conducted at the center for water research and environmental (CIHAM-UC), with financial support from the ministry of popular power for science and technology (FONACIT) and Ministry of Popular Power for the Environment.

References Abbott M.B., Bathurst J.C., Cunge J.A., OConnel P.E., and Rasmussen J. (1986a). An introduction to the European

Hydrological SystemSysteme Hydrologique SHE, 1: history and philosophy of a physically-based distributed modelling system. Journal of Hydrology 87: 4559.

Abbott M.B., Bathurst J.C., Cunge J.A., OConnel P.E., and Rasmussen J. (1986b). An introduction to the European Hydrological SystemSysteme Hydrologique SHE, 2: structure of a physically-based distributed modelling system. Journal of Hydrology 87: 6177.

AQUA3D. 2001. AQUA3D, Groundwater Flow and Contaminant Transport Model. Vatnaskil Consulting Engineers. http://www.vatnaskil.is/aqua3d.htm (Access date: 02/10/2001.)

Beven K.J. (ed.). 1997. Distributed Modelling in Hydrology: Applications of TOPMODEL. Wiley: Chichester. Bishop, C. M. (1994). Neural networks and their applications. Rev. Sci. Instrum., 65, 18031832. Chaudhry, H.C. (1993). Open-channel hydraulics. Prentice Hall N.Y. Chow, V.T. (1959). Open channel flow. McGraw Hill, New York. Crawford, N. H. and Linsley R. K. (1962). The synthesis of contnuos streamflow hydrographs on a digital computer.

Technical Report 12, Department of civil Engineering, Standford University. 121 p. Crawford, N. H. and Linsley R. K. (1966). Digital simulation in hydrology: Standford Watershed Model IV. Technical

Report 12, Department of civil Engineering, Standford University. 210 p. Cunge, J. A. (1969). On the subject of the flood propagation computation method (Muskingum Method). Journal of

Hydraulic Research, 7 (2), 205-230. De Roo A.P.J, Wesseling C.G., and Van Deursen W.P.A. (2000). Physically based river basin modelling within a GIS;

the LISFLOOD model. Hydrological Processes 14: 19811992. Dez-Herrero, A.; Lain-Huerta, L. and Llorente-Isidro, M. (2009). A Handbook on Flood Hazard Mapping

Methodologies. Publications of the Geological Survey of Spain (IGME), Series Geological Hazards /Geotechnics No. 2, 190 pp., Madrid. ISBN 978-84-7840-813-9

Eberhart, R. C., and Dobbins, R. W. (1990). Neural network PC tools: A practical guide, Academic, San Diego. Guevara E. and Mrquez A. (2008). Regional Modeling of IDF Curves for Venezuela. 11th International Conference

on Urban Drainage, Edinburgh, Scotland, UK. Harbaugh A.W., and McDonald M.G. (1996). Users Documentation for MODFLOW-96, an Update to the U.S.

Geological Survey Modular Finitedifference Ground-water Flow Model. U.S. Geological Survey: Denver, Colorado, USA.

Holtan, H.N., and Lopez N.C., (1971). USDAHL-70 model of watershed hydrology. Technical Bulletin 1435, Agricultural Research Service, U.S. Department of Agriculture. 85 p.

Holtan, H.N., Stiltner, G.J., y Lopez N.C., (1975). USDAHL-74 revised model of watershed hidrology. Technical Bulletin 1518, Agricultural Research Service, U.S. Department of Agriculture. 99 p.

Grayson R.B., Moore I.D., and McMahon T.A. (1992). Physically based hydrologic modelling 1. a terrain-based model for investigative purposes. Water Resources Research 28(10): 26392658.

Jain, A. and Srinivasulu, S. (2004). Development of eective and ecient rainfall-runo models using integration of deterministic, real coded genetic algorithms and articial neural network techniques, Water Resour. Res., 40, W04302, doi:10.1029/2003WR002355.

Mackay D.S., and Ban L.E. (1997). Forest ecosystem processes at the watershed scale: dynamic coupling of distributed hydrology and canopy growth. Hydrological Processes 11: 11971217.

Martinez, W. L., and Martinez, A. R. (2002). Computational statistics handbook with MATLAB, Chapman & Hall, London.

Mrquez, A., Guevara E., Daz E., and Romero A., (2012). Parametrizacin de modelo para curvas intensidad-duracin-frecuencia de lluvia. casos: cuencas del embalse Pao-Cachinche y ro Unare, Venezuela. XXV Congreso latinoamericano de Hidrulica. San Jos. Costa Rica.

13

Morgan R.P.C., Quinton J.N., Smith R.E., Govers G., Poesen J.W.A., Auerswald K., Chisci G., Torri D., and Styczen M.E. (1998). The European soil erosion model (EUROSEM): a dynamic approach for predicting sediment transport from fields and small catchments. Earth Surface Processes and Landforms 23: 527544.

Tucker G., Gasparini N., Bras R.L., and Rybarczyk S. (1999). An object-oriented framework for distributed hydrologic and geomorphic modeling using triangulated irregular networks. In Proceedings of GeoComputation 99, 4th International GeoComputation Conference, Fredericksburg, USA, 2528 July. http://www.geovista.psu.edu/geocomp/geocomp99 (Access date: 14/11/2000.)

USACE, (1998). HEC-1 flood hydrograph package users manual. Hydrological Engineering Center. Davis, C.A. USACE, (2000). Hydrological Modeling System, HEC-HMS. Hydrological Engineering Center. Davis, C.A. WMO (1983). Guide to Hydrological Practice. Vol. II. Analysis, Forecasting and Applications, WMO No. 168, 4th.

Ed.. Geneve, Switzerland Zhang, B., and Govindaraju, S. (2000). Prediction of watershed runoff using Bayesian concepts and modular

neural networks. Water Resour. Res., 36(3), 753762. Zheng, C. (1993). Extension of the method of characteristics for simulation of solute transport in three dimensions.

Ground Water 31(3): 456465.

14