[ Introduction ]  [ Background ]  [ Methodology ]   [ Data Analysis ]  [ GDUH Model Application ]  [ Summary and Conclusions ]  [ References ]  • 


Gustavo Ariza



APPLICATION OF THE GENERAL DIMENSIONLESS UNIT HYDROGRAPH

USING CALIFORNIA WATERSHED DATA


Luis Gustavo Ariza Trelles


SPRING 2017


ABSTRACT

This study validates the general dimensionless unit hydrograph (GDUH) model using California watershed/basin data. A unit hydrograph is the hydrograph produced by a unit depth of runoff uniformly distributed over the entire watershed/basin and lasting a specified unit duration. The general dimensionless unit hydrograph (GDUH) is a dimensionless formulation of the unit hydrograph, effectively associating the convolution technique with the model of cascade of linear reservoirs (CLR).

Ten (10) California watersheds/basins are selected for analysis. The basins encompass a wide range in the values of geomorphological parameters (drainage area, average land surface slope, and stream channel slope). For each basin, a set of maps are produced and related geomorphological parameters are calculated using GIS. For each basin, average measured and predicted unit hydrographs are calculated following the GDUH methodology. Conceptual and statistical analyses are used to develop a strategy for the prediction of unit hydrographs on the basis of local/regional geomorphology.

A predictive methodology for the calculation of unit hydrographs based on geomorphology has been validated and tested. The avowed strength of the methodology is its conceptual basis, being founded on the time-tested theory of the cascade of linear reservoirs. The central focus on the general dimensionless unit hydrograph (GDUH) as a unifying theory enhances the validation exercise.


1.  INTRODUCTION

[ Background ]  [ Methodology ]   [ Data Analysis ]  [ GDUH Model Application ]  [ Summary and Conclusions ]  [ References ]  •  [ Top ] 

1.1  Introduction

The concept of unit hydrograph is well established in hydrologic engineering research and practice. The unit hydrograph is defined as the hydrograph produced by a unit depth of runoff uniformly distributed over the entire catchment (watershed or basin) and lasting a specified unit duration. The concept has been used since the 1930s for the simulation of flood flows around the world (Sherman, 1932).

The general dimensionless unit hydrograph (GDUH), developed by Ponce (2009a, 2009b), is a dimensionless formulation of the unit hydrograph. The GDUH effectively associates the convolution technique (of the unit hydrograph) with the model of cascade of linear reservoirs (CLR), originally due to Nash (1957). The CLR model constitutes the routing component of several hydrologic models that have since been developed around the world, notably the SSARR model (U.S. Army Engineer North Pacific Division, 1972).

This study attempts to validate the GDUH model using California watershed/basin data. Geographic and rainfall-runoff data is readily available online in the State of California, thus facilitaling collection and analysis. Digital elevation maps (DEM) are available from the USGS virtual platforms Earth Explorer and Alaska Satellite Facility. Rainfall data is available from the NOAA virtual platform National Centers for Environmental Information. Runoff data is available from the USGS virtual platform National Water Information System.

This study selects ten (10) California watersheds/basins for analysis. To enable the proper study of unit hydrograph diffusion, the basins encompass a wide range in the values of geomorphological parameters (drainage area, average land surface slope, and stream channel slope). Conceptual and statistical analyses are used to develop a methodology for the accurate prediction of unit hydrographs on the basis of local/regional geomorphology. Given the prospect of global warming and its magnifying effect on flood flows, the timeliness of this endeavor cannot be overemphasized.

1.2  Objectives

The objectives of this study are:

General

  • To validate and test the general dimensionless unit hydrograph (GDUH) model using suitable geomorphological parameters.

Specific

  1. To select ten (10) watersheds/basins in California for detailed conceptual and statistical analysis.

  2. For each basin:

    • To produce a set of maps and calculate related suitable geomorphological parameters using GIS.

    • To calculate average measured and predicted unit hydrographs following the GDUH methodology.

  3. To identify a diffusion parameter to better characterize unit hydrograph diffusion.

  4. To use statistical correlations to develop a predictive tool for unit hydrograph analysis based on local/regional geomorphology.

1.3  Scope

This study encompasses the development and validation of a predictive methodology to calculate unit hydrographs based on local/regional geomorphology. The avowed strength of the methodology is its conceptual basis, being based on time-tested cascade of linear reservoirs theory. The central focus on the general dimensionless unit hydrograph (GDUH) as a unifying theory enhances the validation exercise.


2.  BACKGROUND

[ Methodology ]   [ Data Analysis ]  [ GDUH Model Application ]  [ Summary and Conclusions ]  [ References ]  •  [ Top ]  [ Introduction ] 

2.1  The unit hydrograph

Over the past century, the unit hydrograph (UH) has been used as a methodology to generate flood flows for midsize and large basins (Ponce, 1989; Ponce, 2014a). In 1930, the Committee on Floods of the Boston Society of Civil Engineers, after a study of New England flood hydrographs, concluded the following (referenced by Hoyt et. al., 1936, p. 123):

"...that a flood hydrograph once determined for a given river, even for an ordinary flood, will serve as a basis for the estimation of greater flood run-off, due to the fact that the base of the flood hydrograph (or time-of-flood period) appears to be approximately constant for different floods."

This statement may be interpreted as follows: For a certain basin of drainage area A, given a single rainfall event of effective depth d and duration tr, which covers the entire area, the volumen of runoff Vr and consequently the peak flow Qp, are proportional to the effective rainfall intensity d/tr. In other words, the hydrograph response (Q) is linear with respect to the intensity and, therefore, independent of the time base Tb.

Sherman (1932) built on this concept to develop the unit hydrograph for flood studies in large basins. The word unit is normally understood to refer to a unit depth of effective rainfall or runoff. However, it should be noted that Sherman first used the word to describe a unit depth of runoff (1 cm or 1 in.) lasting a unit increment of time, i.e., an indivisible increment. The unit increment of time can be either 1-h, 3-h, 6-h, 12-h, 24-h, or any other suitable duration (Ponce, 2014a).

The unit hydrograph is defined as the hydrograph produced by a unit depth of runoff uniformly distributed over the entire catchment (watershed or basin) and lasting a specified unit duration. To illustrate the concept of unit hydrograph, assume that a certain storm produces 1 cm of runoff and covers a 50-km2 catchment over a period of 2 h. The hydrograph measured at the catchment outlet would be the 2-h unit hydrograph for this 50-km2 catchment (Fig. 2.1).

Concept of a unit hydrograph

Figure 2.1  Concept of a unit hydrograph.

Two assumptions are crucial to the development of the unit hydrograph: (1) linearity, and (2) superposition. Given a unit hydrograph, a hydrograph for a runoff depth other than unity can be obtained by simply multiplying the unit hydrograph ordinates by the indicated runoff depth (linearity), as shown in Fig. 2.2 (a). This, of course, is possible only under the assumption that the time base remains constant regardless of runoff depth.

Concept of linearity

Figure 2.2 (a)  The property of linearity.

The time base of all hydrographs obtained in this way is equal to that of the unit hydrograph. Therefore, the procedure can be used to calculate hydrographs produced by a storm consisting of a series of runoff depths, each lagged in time one increment of unit hydrograph duration, as shown in Fig. 2.2 (b).

Concept of linearity

Figure 2.2 (b)  Lagging of the unit hydrograph.

The summation of the corresponding ordinates of these hydrographs (superposition) allows the calculation of the composite hydrograph, as shown in Fig. 2.2 (c). The procedure depicted in Fig. 2.2 is referred to as the convolution of a unit hydrograph with an effective storm pattern (hyetograph). In essence, the procedure amounts to stating that the composite hydrograph ordinates are a linear combination of the unit hydrograph ordinates.

Concept of linearity

Figure 2.2 (c)  The property of superposition.

The assumption of linearity has long been considered one of the limitations of unit hydrograph theory. In nature, it is unlikely that catchment response will always follow a linear function. For one thing, discharge and mean velocity are nonlinear functions of flow depth and stage. In practice, however, the linear assumption provides a convenient means of calculating runoff response without the complexities associated with nonlinear analysis.

The upper limit of applicability of the unit hydrograph is not very well defined. Sherman (1932) used it in connection with basins varying from 1300 to 8000 km2. Linsley et. al. (1962) mention an upper limit of 5000 km2 in order to preserve accuracy. More recently, the unit hydrograph has been linked to the concept of midsize catchment, i.e., greater than 2.5 km2 and less than 250 km2. This certainly does not preclude the unit hydrograph technique from being applied to catchments larger than 250 km2, although overall accuracy is likely to decrease with an increase in catchment size (Ponce, 2014a).

2.2  Storage routing and linear reservoirs

As shown in Section 2.3, the concepts of unit hydrograph and cascade of linear reservoirs are intrinsically connected. The cascade is effectively a series of linear reservoirs, and the latter is a way of performing storage routing. Therefore, this section addresses storage routing and linear reservoirs.

The techniques for storage routing are invariably based on the differential equation of water storage. This equation is founded on the principle of mass conservation, which states that the change in flow per unit length in a control volume is balanced by the change in flow area per unit time. In partial differential form it is expressed as follows:

 ∂Q        ∂A
____  +  ____  =  0
 ∂x         ∂t
(2-1)

in which Q = flow rate, A = flow area, x = space (length), and t = time.

The differential equation of storage is obtained by lumping spatial variations. For this purpose, Eq. 2-1 is expressed in finite increments:

 ΔQ         ΔA
_____  +  _____  =  0
 Δx           Δt
(2-2)

With ΔQ = O - I, in which O = outflow and I = inflow; and ΔS = ΔA Δx , in which ΔS = change in storage volume, Eq. 2-2 reduces to:

             ΔS
I - O = _____
              Δt
(2-3)

in which inflow, outflow, and rate of change of storage are expressed in L3T -1 units. Furthermore, Eq. 2-3 can be expressed in differential form, leading to the differential equation of storage:

               dS
I - O  =  _____
                dt
(2-4)

Equation 2-4 implies that any difference between inflow and outflow is balanced by a change of storage in time (Fig. 2.3). In a typical reservoir routing application, the inflow hydrograph (upstream boundary condition), initial outflow and storage (initial conditions), and reservoir physical and operational characteristics are known. Thus, the objective is to calculate the outflow hydrograph for the given initial condition, upstream boundary condition, reservoir characteristics, and operational rules.

Inflow, outflow, and change of storage in a reservoir

Figure 2.3  Inflow, outflow, and change of storage in a reservoir.

Equation 2-4 can be solved by analytical or numerical means. The numerical approach is usually preferred because it can account for an arbitrary inflow hydrograph. The solution is accomplished by discretizing Eq. 2-4 on the x-t plane, a graph showing the values of a certain variable in discrete points in time and space (Fig. 2.4).

Figure 2.4 shows two consecutive time levels, 1 and 2, separated between them an interval Δt, and two spatial locations depicting inflow and outflow, with the reservoir located between them. The discretization of Eq. 2-4 on the x-t plane leads to:

  I1 + I2          O1 + O2         S2 - S1
_________  -  __________  =  _________
       2                  2                   Δt
(2-5)

in which I1 = inflow at time level 1; I2 = inflow at time level 2; O1 = outflow at time level 1; O2 = outflow at time level 2; S1 = storage at time level 1; S2 = storage at time level 2; and Δt = time interval. Equation 2-5 states that between two time levels 1 and 2 separated by a time interval Δt, average inflow minus average outflow is equal to change in storage (Ponce, 2014a).

Discretization of storage equation in the <i>x-t</i> plane

Figure 2.4  Discretization of storage equation in the x-t plane.

For linear reservoirs, the relation between storage and outflow is linear. Therefore:

S1 = K O1 (2-6a)

and

S2 = K O2 (2-6b)

in which K = storage constant, in T units.

Substituting Eqs. 2-6 into 2-5, and solving for O2:

O2 = C0 I2  +  C1 I1  +  C2 O1 (2-7)

in which C0, C1 and C2 are routing coefficients defined as follows:

                 Δt /K
C0 = ________________
            2  +  ( Δt /K )
(2-8a)

C1 = C0 (2-8b)

            2  -  ( Δt /K )
C2 = _________________
            2  +  ( Δt /K )
(2-8c)

Since C0 + C1 + C2 = 1, the routing coefficients are interpreted as weighting coefficients. These routing coefficients are a function of Δt /K, the ratio of time interval to storage constant. Values of the routing coefficients as a function of Δt /K are given in Table 2.1.

Table 2.1  Linear reservoir routing coefficients.
(1) (2) (3) (4)
Δt /K C0 C1 C2
1/8 1/17 1/17 15/17
1/4 1/9 1/9 7/9
1/2 1/5 1/5 3/5
3/4 3/11 3/11 5/11
1 1/3 1/3 1/3
5/4 5/13 5/13 3/13
3/2 3/7 3/7 1/7
7/4 7/15 7/15 1/15
2 1/2 1/2 0
4 2/3 2/3 -1/3
6 3/4 3/4 -1/2
8 4/5 4/5 -3/5

A reservoir exerts a diffusive action on the flow, with the net result that the peak flow is attenuated and consequently, the time base is increased. For the case of a linear reservoir, the amount of attenuation is a function of Δt/K. The smaller this ratio, the greater the amount of attenuation exerted by the reservoir; conversely, large values of Δt/K cause less attenuation. Note that values of Δt/K > 2 will lead to negative attenuation (observe the negative values of C2 in Col. 4, Table 2.1). This amounts to amplification; therefore, values of Δt/K > 2 are not used in reservoir routing (Ponce, 2014a).

2.3  The cascade of linear reservoirs

The cascade of linear reservoirs is a widely used method of hydrologic catchment routing. As its name implies, the method is based on the connection of several linear reservoirs in series. For N such reservoirs, the outflow from the first would be taken as inflow to the second, the outflow from the second as inflow to the third, and so on, until the outflow from the (N - 1)th reservoir, is taken as inflow to the N th reservoir. The outflow from the N th reservoir is taken as the outflow from the cascade of linear reservoirs.

Each reservoir in the series provides a certain amount of diffusion and associated lag. For a given set of parameters Δt/K and N, the outflow from the last reservoir is a function of the inflow to the first reservoir. In this way, a one-parameter linear reservoir method (Δt/K) is extended to a two-parameter catchment routing method. The addition of the second parameter (N) provides considerable flexibility in simulating a wide range of diffusion and associated lag effects. The method has been widely used in catchment simulation, primarily in applications involving large gaged river basins. Rainfall-runoff data can be used to calibrate the method, i.e., to determine a set of parameters Δt/K and N that produces the best fit to the measured data.

The solution of the cascade of linear reservoirs can be accomplished in two ways: (1) analytical, and (2) numerical. The analytical version is due to Nash (1957), who originated the concept of instantaneous unit hydrograph (IUH) (Section 2.4). According to Nash, the instantaneous unit hydrograph is obtained when the duration tr  of the unit hydrograph is reduced indefinitely, i.e., tr ⇒ 0. Nash assumed that the IUH could be represented as the cascade of linear reservoirs.

The numerical version of the cascade of linear reservoirs is featured in several hydrologic simulation models developed in the United States and other countries. Notable among them is the Streamflow Synthesis and Reservoir Regulation (SSARR) model, which uses it in its watershed, stream channel routing, and baseflow modules. The SSARR model has been in the process of development and application since 1956. The model was developed to meet the needs of the U.S. Army Corps of Engineers North Pacific Division in the area of mathematical hydrologic simulation for planning, design, and operation of water-control works. (U.S. Army Engineer North Pacific Division, 1972).

The SSARR model was first applied to operational flow forecasting and river management activities in the Columbia River System. Later, it was used by U.S. Army Corps of Engineers, National Weather Service, and Bonneville Power Administration. Numerous river systems in the United States and other countries have been modeled with SSARR.

To derive the routing equation for the method of cascade of linear reservoirs, Eq. 2-7 is reproduced here in a slightly different form:

Q j+1 n+1 = C0 Q j n+1 + C1 Q j n + C2 Q j+1 n (2-9)

in which Q represents discharge, whether inflow or outflow and j and n are space and time indexes, respectively (Fig. 2.5).

Space-time discretization in the method of cascade of linear reservoirs

Figure 2.5  Space-time discretization in the method of cascade of linear reservoirs.

As with Eq. 2-7, the routing coefficients C0, C1 and C2 are a function of the dimensionless ratio Δt /K. This ratio is properly a Courant number (C = Δt /K). In terms of Courant number, Eqs. 2-8 are expressed as follows:

               C
C0  =  _______
            2 + C
(2-10a)

C1  =  C0 (2-10b)

            2 - C
C2  =  _______
            2 + C
(2-10c)

For application to catchment routing, it is convenient to define the average inflow as follows:

            Q j n  +  Q j n+1
j = __________________
                      2
(2-11)

Substituting Eqs. 2-10b and 2-11 into Eq. 2-9 gives the following:

Q j+1n+1 = 2 C1 j  +  C2 Q j+1n (2-12)

or, alternatively, through some algebraic manipulation:

                       2 C
Q j+1n+1 =   _________ [ j  -  Q j+1n ]  +  Q j+1n
                      2 + C
(2-13)

Equations 2-12 and 2-13 are in a form convenient for catchment routing because the inflow is usually a rainfall hyetograph, that is, a constant average value per time interval. Note that Eqs. 2-12 and 2-13 are identical. Equation 2-12 was presented by Ponce in his version of the cascade of linear reservoirs (Ponce, 2014a). Equation 2-13 is the routing equation of the SSARR model (U.S. Army Engineer North Pacific Division, 1972).

Smaller values of C lead to greater amounts of runoff diffusion. For values of C > 2, the behavior of Eq. 2-12 (or Eq. 2-13) is highly dependent on the type of input. For instance, in the case of a unit impulse (rainfall duration equal to the time interval), Eq. 2-12 (or Eq. 2-13) results in negative outflow values, i.e., numerical instability. In practice, Eq. 2-12 (or Eq. 2-13) are restricted to C ≤ 2.

The cascade of linear reservoirs provides a convenient mechanism for simulating a wide range of catchment routing problems. Furthermore, the method can be applied to each runoff component (surface runoff, subsurface runoff, and baseflow) separately, and the catchment response can be taken as the sum of the responses of the individual components.

For instance, assume that a certain basin has 10 cm of runoff, of which 7 cm are surface runoff, 2 cm are subsurface runoff, and 1 cm is baseflow. Since surface runoff is the less diffused process, it can be simulated with a high Courant number, say C = 1, and a small number of reservoirs, say N = 3. Subsurface runoff is much more diffused than surface runoff; therefore, it can be simulated with C = 0.4 and N = 5. Baseflow, being very diffused, can be simulated with C = 0.1 and N = 7 (Ponce, 2014a).

2.4  The instantaneous unit hydrograph

Nash (1957) defined the instantaneous unit hydrograph (IUH) as that obtained when the duration tr of the effective rainfall is decreased indefinitely. Furthermore, Nash represented the IUH as a series of n linear reservoirs, i.e., a cascade of linear reservoirs.

According to Nash, the general equation for the instantaneous unit hydrograph is:

                V
u   =   _________  e - t / K ( t / K ) n -1   
             K Γ(n)
(2-14)

in which u = unit hydrograph ordinate, and t = time. In this equation: V = unit hydrograph volume; K = storage constant, in time units; n = number of reservoirs in the series; and Γ(n) = gamma function.

Equation 2-14 is the analytical version of the IUH or cascade of linear reservoirs. The numerical version is represented by either Ponce's model (Eq. 2-12) or the SSARR model (Eq. 2-13).

2.5  The geomorphologic instantaneous unit hydrograph

Rodríguez-Iturbe and Valdés (1979) pioneered in establishing the relation of the instantaneous unit hydrograph with the geomorphologic characteristics of the catchment; see also the companion papers (Valdés et. al. 1979; Rodríguez-Iturbe et. al. 1979).

The geomorphologic characteristics are expressed in terms of the following basin parameters:

  1. The bifurcation ratio (law of stream numbers) RB:

    RB = Nw / Nw+1 (2-15a)

    In any basin, Nw is the number of streams of order w, and Nw+1 is the number of streams of order w+1. In Nature, values of RB are normally between 3 to 5.

  2. The length ratio (law of stream lengths) RL:

    RL = w / w-1 (2-15b)

    In any basin, w is the mean hydraulic length of order w, and w-1 is the mean hydraulic length of order w-1. In Nature, values of RL are normally between 1.5 to 3.5.

  3. The area ratio (law of stream areas) RA:

    RA = w / w-1 (2-15c)

    In any basin, w is the mean area of order w, and w-1 is the mean area of order w-1. In Nature, values of RA are normally between 3 to 6.

  4. The internal scale parameter LΩ, defined as the hydraulic length of a basin of order Ω.

  5. The dynamic parameter v, defined as the velocity corresponding to the peak discharge for a given rainfall-runoff event in a basin.

According to Rodríguez-Iturbe and Valdés (1979), the equations to calculate the geomorphologic instantaneous unit hydrograph (GIUH) are:

qp = θ v (2-16)

tp = k / v (2-17)

In which qp = peak discharge, in T -1 units; and tp = time-to-peak, in T units.

The parameters θ and k are a function of the basin parameters RA, RB, RL, and LΩ, as follows:

θ = ( 1.31 / LΩ ) RL  0.43 (2-18)

k = 0.44 LΩ RB 0.55 / ( RA 0.55 RL 0.38 ) (2-19)

The parameters θ and k have dimensions of L -1 and L, respectively.

Equations 2-18 and 2-19 assume the basin order Ω = 3, and the hydraulic length of the first-order subbasin L1 = 1000 m.

2.6  The concept of runoff diffusion

The unit hydrograph seeks to calculate runoff diffusion, i.e., the spreading of the hydrograph in time and space. In practice, the amount of runoff diffusion depends on whether the flow is through: (a) a reservoir, (b) a stream channel, or (c) a catchment.

Flow through a reservoir always produces runoff diffusion. Flow in stream channels may or may not produce runoff diffusion, depending on the relative scale of the flood wave, provided the Vedernikov number is less than 1. The relative scale of the flood wave relates to whether the wave is: (a) kinematic, (b) diffusion, or (c) mixed kinematic-dynamic. In catchment flow, diffusion is produced: (1) for all wave types, when the time of concentration exceeds the effective rainfall duration, or (2) for all effective rainfall durations, when the wave is a diffusion wave (Ponce, 2014b).

2.6.1  Runoff diffusion in reservoirs

Reservoirs are natural or artificial surface-water hydraulic features that provide runoff diffusion. Runoff diffusion is depicted by the sizable attenuation of the inflow hydrograph, as shown in Fig. 2.6.

Reservoir routing example

Figure 2.6  Runoff diffusion through a reservoir.

2.6.2  Runoff diffusion in stream channels

Stream channels, i.e., channels or canals, are surface-water hydraulic features which may or may not provide runoff diffusion, depending on the relative scale of the disturbance (flood wave). The amount of wave diffusion is characterized by the dimensionless wavenumber σ, as shown in Fig. 2.7. The dimensionless wavenumber is defined as:

           2 π
σ  =  _______  Lo
             L
(2-20)

in which L = wavelength of the disturbance, and Lo = the length of channel in which the equilibrium flow drops a head equal to its depth (Lighthill and Whitham, 1955):

             do
Lo  =  ______
             So
(2-21)

Four types of waves are identified:

  1. Kinematic waves,

  2. Diffusion waves,

  3. Mixed kinematic-dynamic waves, and

  4. Dynamic waves.

Kinematic waves lie on the left side of the wavenumber spectrum, featuring constant dimensionless relative wave celerity and zero attenuation. Dynamic waves lie on the right side, featuring constant dimensionless relative wave celerity and zero attenuation. Mixed kinematic-dynamic waves lie in the middle of the spectrum, featuring variable dimensionless relative wave celerity and medium to high attenuation. Diffusion waves are intermediate between kinematic and mixed kinematic-dynamic waves, featuring mild attenuation. In hydraulic engineering practice, dynamic waves are commonly referred to as Lagrange or "short" waves, while the mixed kinematic-dynamic waves are commonly referred to as "dynamic waves," fueling a semantic confusion.

Celerity of wave propagation in open-channel flow

Fig. 2.7  Celerity of wave propagation in open-channel flow (Ponce and Simons, 1977).

For flood routing computations, the governing equations of continuity and motion, commonly referred to as the Saint Venant equations, may be linearized and combined into a convection-diffusion equation with discharge Q as the dependent variable (Hayami, 1951; Dooge, 1973; Dooge et al., 1982; Ponce, 1991a ; Ponce, 1991b):

  ∂Q              dQ        ∂Q                 Qo                             ∂2Q
______  +  ( ______ ) ______  =  [ ( ________ ) ( 1 - V 2 ) ] _______
   ∂t               dA         ∂x               2 T So                          ∂x2
(2-22)

in which V = Vedernikov number, defined as the ratio of relative kinematic wave celerity to relative dynamic wave celerity (Ponce, 1991b):

             (β - 1) Vo   
V  =  ______________
              (g do)1/2
(2-23)

in which β = exponent of the discharge-flow area rating Q = Aβ, Vo = mean flow velocity, do = mean flow depth, and g = gravitational acceleration.

In Eq. 2-22, for V = 0, the coefficient of the second-order term reduces to the kinematic hydraulic diffusivity, originally due to Hayami (1951). On the other hand, for V = 1, the coefficient of the second-order term reduces to zero, and the diffusion term vanishes. Under this latter flow condition, all waves, regardless of scale, travel with the same speed, fostering the development of roll waves (Fig. 2.8).

Roll waves in a steep irrigation canal

Fig. 2.8  Roll waves in a steep canal, Cabana-Mañazo irrigation, Puno, Peru.

2.6.3  Runoff diffusion in catchments

Surface runoff in catchments may be one of three types (Ponce, 1989a; 2014a):

  1. Concentrated flow, when the effective rainfall duration is equal to the time of concentration,

  2. Superconcentrated flow, when the effective rainfall duration is longer than the time of concentration, and

  3. Subconcentrated flow, when the effective rainfall duration is shorter than the time of concentration.

Figure 2.9 shows a typical open-book schematization for overland flow modeling. Input is effective rainfall on two planes adjacent ot a channel. Output is the outflow hydrograph at the catchment outlet.

Open-book catchment schematization

Fig. 2.9  Open-book catchment schematization.

Figure 2.10 shows dimensionless catchment outflow hydrographs for the three cases described above (Ponce and Klabunde, 1999). The maximum possible peak outflow is: Qp = Ie A, in which Ie = effective rainfall intensity, and A = catchment area. By definition, the maximum possible peak outflow is reached for superconcentrated and concentrated flow. However, in the case of subconcentrated flow, the peak outflow fails to reach the maximum possible value. Effectively, this amounts to runoff diffusion, because the flow has actually been spread in time (and space).

Thus, runoff diffusion is produced for all waves when the time of concentration exceeds the effective rainfall duration. This is typically the case of midsize and large basins, for which the catchment slope (along the hydraulic length) is sufficiently mild (small). The time of concentration is directly related to catchment hydraulic length and bottom friction, and inversely related to bottom slope and effective rainfall intensity (Ponce, 1989b; 2014b).

Celerity of wave propagation in open-channel flow

Fig. 2.10  Dimensionless catchment runoff hydrographs (Ponce and Klabunde, 1999).

Figure 2.11 shows dimensionless rising overland flow hydrographs for a kinematic wave model (labeled KW) and for several storage-concept models, for the discharge-area rating exponent m ranging from m = 1, corresponding to a linear reservoir, to m = 3, corresponding to laminar flow (Ponce et al., 1997). The kinematic wave time-to-equilibrium, akin to the time of concentration, is theoretically equal to one-half of the time of concentration of the storage-based models (Ponce, 1989; 2014). It is seen that the storage models spread the hydrograph and, consequently, produce diffusion, while the kinematic wave model lacks runoff diffusion altogether. The kinematic time-to-equilibrium is the shortest possible value of time of concentration, resulting, in the aggregate, in the largest peak flows. Thus, under pure kinematic flow, runoff diffusion vanishes.

Dimensionless rising hydrographs of overland flow

Fig. 2.11  Dimensionless rising hydrographs of overland flow (Ponce et al., 1997).

In actual numerical computations, a kinematic wave model may not be entirely devoid of diffusion, due to the appearance of numerical diffusion (Cunge, 1969; Ponce, 1991a). In fact, first-order schemes of the kinematic wave equation produce numerical diffusion. This diffusion, however, is uncontrolled, not based on physical parameters and, therefore, unrelated to the true diffusion of the physical problem.

2.7  The general dimensionless unit hydrograph

The cascade of linear reservoirs (CLR) (Section 2.3) and the instantaneous unit hydrograph (IUH) (Section 2.4) are essentially the same. A general dimensionless unit hydrograph (GDUH) may be generated using the CLR method for a basin of drainage area A and unit hydrograph duration tr. The resulting dimensionless unit hydrograph can be shown to be solely a function of Courant number C and number of reservoirs N, and therefore, to be independent of either A or tr. Thus, for a given set of C and N, there exists a unique GDUH, of global applicability (Ponce, 2009).

The dimensionless time t* is defined as follows:

t* = t / tr (2-20)

in which t = time, and tr = unit hydrograph duration.

The dimensionless discharge Q* is defined as follows:

Q* = Q / Qmax (2-21)

in which Q = discharge, and Qmax = maximum discharge, i.e., that attained in the absence of runoff diffusion (Ponce, 2014):

Qmax = i A (2-22)

in which:

i = effective rainfall intensity, in L T -1 units; and A = basin drainage area, in L2 units.

Therefore:

Q* = Q / (i A) (2-23)

In SI units, for a unit rainfall depth of 1 cm:

i = 0.01 (m) / [ 3,600 (s/hr) × tr (hr) ] (2-24)

Thus:

Q* = 0.36 Q tr / A (2-25)

in which Q is in m3/s, tr  in hr and A in km2.

In practice, a set of C and N are chosen such that the runoff diffusion properties of the basin are properly represented in the GDUH. Steeper basins required a large C and a small N; conversely, milder basins required a small C and a large N. The practical range of parameters is:  0.1 ≤ C ≤ 2; and 1 ≤ N ≤ 10. Within this range, the pair C = 2 and N = 1 provides zero diffusion, while the pair C = 0.1 and N = 10 provides a very significant amount of diffusion. Note that the case of zero diffusion is equivalent to the assumption of runoff concentration only, which is inherent in the rational method (Ponce, 2014).

Once the GDUH is chosen, the ordinates of the unit hydrograph may be calculated from Eq. 2-25 as follows:

Q = 2.7778 Q* A / tr (2-26)

Likewise, the abscissa (time) may be calculated from Eq. 2-20 as follows:

t = t* tr (2-27)

The unit hydrograph thus calculated may be convoluted with the effective storm hyetograph to determine the composite flood hydrograph (Ponce, 2014).

The GDUH has the following significant advantages:

  1. The GDUH is solely a function of C and N, and is of global applicability.

  2. Unlike other established unit hydrograph procedures such as the Natural Resources Conservation Service (NRCS) unit hydrograph, the GDUH is a two-parameter model; therefore, it is able to simulate a wider range of runoff diffusion effects (Ponce, 2014).

The GDUH cascade parameters (C and N) are estimated based on the runoff diffusion properties of the basin under consideration. The runoff diffusion properties are largely dependent on the overall terrain's topography and geomorphology. Steep basins have little or no diffusion; conversely, mild basins have substantial amounts of diffusion. The case of zero diffusion is modeled with C = 2 and N = 1. Conversely, the case of great diffusion may be modeled with C = 0.1 and N = 10 (Ponce, 1980).

In Nature, basins are classified with regards to runoff diffusion on the basis of mean land surface slope. A preliminary classification is shown in Table 2.2 (Ponce, 2009). This table shows the various geomorphologic classes and the associated range in mean land surface slope, with the estimated cascade parameters and corresponding GDUH peak values (discharge Q*p and time t*p). Table 2.2 may be used as a reference for the preliminary appraisal of C and N for a given basin.

Table 2.2  Basin classification with regards to runoff diffusion.
Class Mean land surface slope
(m/m)
Cascade parameters GDUH peak values
C N Q*p t*p
(1) (2) (3) (4) (5) (6)
Very steep > 0.1 2 1 1 1
Steep 0.1 - 0.01 1.5 2 0.472 2
Average 0.01 - 0.001 1 4 0.224 4
Mild 0.001 - 0.0001 0.5 6 0.088 11
Very mild 0.0001 - 0.00001 0.2 8 0.03 36
Extremely mild < 0.00001 0.1 9 0.014 81


3.  METHODOLOGY

[ Data Analysis ]  [ GDUH Model Application ]  [ Summary and Conclusions ]  [ References ]  •  [ Top ]  [ Introduction ]  [ Background ]  

3.1  Overview

The methodology for this study aims to develop a relation between the GDUH cascade parameters C and N and the respective basin geomorphologic characteristics. For this purpose, several suitable basins are selected in California, encompassing a broad range in geomorphologic features, in particular stream channel slope and land surface slope. For daily data, the time interval of analysis is one day; therefore, the corresponding duration of the unit hydrograph is 1 day (tr = 1 day).

The selected methodology depends on the temporal storm characteristics. The following two situations are considered:

  • Simple storms, featuring a one-day precipitation impulse (a one-day predominant precipitation event may be used in practice); and

  • Complex storms, with a precipitation event distributed over several days.

3.1.1  Simple storms

For simple storms, the following steps are required:

  1. Assemble the rainfall-runoff data

    Assemble corresponding sets of rainfall-runoff data for each watershed/basin, and identify three (3) suitable infrequent events for analysis.

  2. Calculate the unit hydrograph runoff volume

    Calculate the runoff volume corresponding to 1 cm of effective rainfall.

  3. For each event:

    1. Use the straight line technique of baseflow separation to determine the direct runoff storm hydrograph.

    2. Calculate the runoff volume corresponding to the direct runoff storm hydrograph obtained in Step 3(a), and compare with the runoff volume obtained in Step 2.

    3. Based on the results of Step 3(b), multiply the direct runoff storm hydrograph ordinates by the appropriate factor to establish the unit hydrograph ordinates. Confirm that it corresponds to 1 cm of runoff. When warranted, perform minor volumetric corrections.

    4. Calculate the dimensionless unit hydrograph (DUH) using Eqs. 2-20 and 2-23 for the abscissas and ordinates, respectively.

  4. Calculate the unit hydrograph

    Average the three (3) dimensionless unit hydrographs obtained in Step 3 (d) to obtain the watershed/basin's dimensionless unit hydrograph (DUH). Confirm that it corresponds to 1 cm of runoff.

  5. Calculate the cascade parameters C and N

    Match the dimensionless unit hydrograph peak flow Q*p and time-to-peak t*p to a suitable general dimensionless unit hydrograph (GDUH) featuring paired cascade parameters C and N.

3.1.2  Complex storms

For complex storms, the follow steps are required:

  1. Assemble the rainfall-runoff data

    Assemble corresponding sets of rainfall-runoff data for each watershed/basin, and identify three (3) suitable infrequent events for analysis.

  2. For each event:

    • Use the straight line technique of baseflow separation to determine the direct runoff storm hydrograph.

    • Calculate the runoff volume corresponding to the direct runoff storm hydrograph.

    • Apply the φ-index procedure to the total storm hyetograph to determine the effective storm hyetograph (Ponce, 2014a).

    • Apply the inverse convolution technique to the direct runoff storm hydrograph obtained in Step 2 (b) and the effective storm hyetograph obtained in Step 2 (c) to calculate the unit hydrograph (Section 3.2).

    • Calculate the dimensionless unit hydrograph (DUH) using Eqs. 2-20 and 2-23 for the abscissas and ordinates, respectively.

  3. Calculate the unit hydrograph

    Average the three (3) dimensionless unit hydrographs obtained in Step 2 (e) to obtain the watershed/basin's unit hydrograph (UH). Confirm that it corresponds to 1 cm of runoff.

  4. Calculate the cascade parameters C and N

    Match the dimensionless unit hydrograph peak flow Q*p and time-to-peak t*p to a suitable general dimensionless unit hydrograph (GDUH) featuring paired cascade parameters C and N.

For each of the basins analyzed, the set of thus found paired C and N cascade parameters are related to primary basin geomorphologic characteristics such as channel/land slope.

In a practical application, once the average stream channel slope and land surface slope are determined, the appropriate values of C and N are used to calculate the dimensionless unit hydrograph (DUH). The latter is used, together with the basin area A and unit hydrograph duration tr (Eqs. 2-26 and 2-27, respectively), to calculate the unit hydrograph (UH).

3.2  Convolution and inverse convolution

Convolution is the procedure by which a certain unit hydrograph and an effective storm hyetograph are used to calculate the corresponding flood hydrograph. Conversely, inverse convolution is the procedure by which a certain flood hydrograph and an effective storm hyetograph are used to calculate the corresponding unit hydrograph.

[Click on figure to enlarge]
Convolution and inverse convolution

Fig. 3.1  Convolution and inverse convolution.

3.2.1  Convolution

The convolution procedure is based on the principles of linearity and superposition. The volume under the composite hydrograph is equal to the total volume of the effective rainfall. Given Tbu = time base of the X-hour unit hydrograph, and a storm consisting of n X-hour intervals, the time base of the composite (flood) hydrograph Tbc is equal to:

Tbc = Tbu + (n - 1)X(3-1)

The convolution procedure is illustrated by the following example. Assume that the following 1-h unit hydrograph has been derived for a certain watershed:

Time (h) 0 1 2 3 4 5 6 7 8 9
Flow (m3/s) 0 100 200 400 800 600 400 200 100 0

A 6-h storm with a total of 5 cm of effective rainfall covers the entire watershed and is distributed in time as follows:

Time (h) 0 1 2 3 4 5 6
Effective rainfall (cm) 0.1 0.8 1.6 1.2 0.9 0.4

The composite (flood) hydrograph is calculated using the convolution technique, as follows (Table 3.1):

  • Column 1 shows the time in hours.

  • Column 2 shows the unit hydrograph ordinates in cubic meters per second.

  • Column 3 shows the product of the first-hour rainfall depth times the unit hydrograph ordinates.

  • Column 4 shows the product of the second-hour rainfall depth times the unit hydrograph ordinates, lagged 1 h with respect to Col. 3.

  • The computational pattern established by Cols. 3 and 4 is the same for Cols. 5 to 8.

  • Column 9, the sum of Cols. 3 through 8, is the composite hydrograph for the given storm pattern.

Table 3.1  Composite hydrograph by convolution.
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Time
(h)
UH
( m3/s)
0.1 ×
UH
0.8 ×
UH
1.6 ×
UH
1.2 ×
UH
0.9 ×
UH
0.4 ×
UH
Composite
hydrograph
( m3/s)
0 0 0 __ __ __ __ __ 0
1 100 10 0 __ __ __ __ 10
2 200 20 80 0 __ __ __ 100
3 400 40 160 160 0 __ __ 360
4 800 800 320 320 120 0 __ 840
5 600 60 640 640 240 90 0 1670
6 400 40 480 1280 480 180 40 2500
7 200 20 320 960 960 360 80 2700
8 100 10 160 640 720 720 160 2410
9 0 0 80 320 480 540 320 1740
10 __ __ 0 160 240 360 240 1000
11 __ __ __ 0 120 180 160 460
12 __ __ __ __ 0 90 80 170
13 __ __ __ __ __ 0 40 40
14 __ __ __ __ __ __ 0 0
Sum 2800 14,000

The sum of Col. 2 is 2800 m3/s and is equivalent to 1 cm of net rainfall. The sum of Col. 9 is verified to be 14,000 m3/s, and, therefore, the equivalent of 5 cm of effective rainfall. The time base of the composite hydrograph is Tbh = 9 + (6 - 1) × 1 = 14 h.

3.2.2  Inverse convolution

The inverse convolution procedure enables the calculation of a unit hydrograph based on an effective storm hyetograph and a composite (flood) hydrograph. The procedure is referred to as method of forward substitution (Ponce, 2014).

The unit hydrograph can be calculated directly due to the banded property of the convolution matrix (see Table 3.1). With m = number of nonzero unit hydrograph ordinates, n = number of intervals of effective rainfall, and N = number of nonzero storm hydrograph ordinates, the following relation holds:

N = m + n - 1 (3-1)

Therefore:

m = N - n + 1 (3-2)

By elimination and back substitution, the following formula is developed for the unit hydrograph ordinates ui as a function of storm hydrograph ordinates qi  and effective rainfall depths rk , for i varying from 1 to m:

                    k = 2, n
           qi  _   Σ     uj rk
                    j = i - 1, 1
ui  =  _______________________
                         r1
(3-3)

In the summation term of Eq. 3-3, j decreases from j -1 to 1, and k increases from 2 up to a maximum of n.

This recursive Eq. 3-3 allows the direct calculation of a unit hydrograph based on a hydrograph from complex storm. In practice, however, it is not always feasible to arrive at a solution because it may be difficult to get a perfect match of composite (flood) hydrograph and effective storm hyetograph (due to noise in the data). Note that the (measured) storm hydrograph would have to be separated into direct runoff and baseflow before attempting to use Eq. 3-3.

The inverse convolution procedure is illustrated by applying Eq. 3-3 to the example of Table 3-1. Using Eq. 3-2, with number of nonzero storm hyetograph ordinates N = 13, and number of intervals of effective rainfall n = 6, the number of nonzero unit hydrograph ordinates is: m = 8. Therefore:

  1. u1 = q1/ r1 = 10 / 0.1 = 100

  2. u2 = (q2 - u1r2) / r1 = (100 - 100 × 0.8) / 0.1 = 200

  3. u3 = [q3 - (u2r2 + u1r3)] / r1 = [360 - (200 × 0.8 + 100 × 1.6)] / 0.1 = 400

  4. u4 = [q4 - (u3r2 + u2r3 + u1r4) ] / r1 = [840 - (400 × 0.8 + 200 × 1.6 + 100 × 1.2)] / 0.1 = 800

  5. u5 = [q5 - (u4r2 + u3r3 + u2r4 + u1r5) ] / r1

    u5= [1670 - (800 × 0.8 + 400 × 1.6 + 200 × 1.2 + 100 × 0.9)] / 0.1 = 600

  6. u6 = [q6 - (u5r2 + u4r3 + u3r4 + u2r5 + u1r6) ] / r1

    u6= [2500 - (600 × 0.8 + 800 × 1.6 + 400 × 1.2 + 200 × 0.9 + 100 × 0.4)] / 0.1 = 400

  7. u7 = [q7 - (u6r2 + u5r3 + u4r4 + u3r5 + u2r6) ] / r1

    u7= [2700 - (400 × 0.8 + 600 × 1.6 + 800 × 1.2 + 400 × 0.9 + 200 × 0.4)] / 0.1 = 200

  8. u8 = [q8 - (u7r2 + u6r3 + u5r4 + u4r5 + u3r6) ] / r1

    u8= [2410 - (200 × 0.8 + 400 × 1.6 + 600 × 1.2 + 800 × 0.9 + 400 × 0.4)] / 0.1 = 100

This result confirm the ordinates of the unit hydrograph shown in Col. 2 of Table 3-1.

3.3  General dimensionless unit hydrograph

The theory of the general dimensionless unit hydrograph (GDUH) was developed by Ponce (2009). A GDUH can be generated using the cascade of linear reservoirs (CLR) method (Section 2.3) for a basin of drainage area A and unit hydrograph duration tr. The resulting set of Q* vs t* unit hydrograph paired values (Section 2.7) can be shown to be solely a function of the cascade parameters Courant number C and number of linear reservoirs N, and to be independent of either A or tr. Thus, for a given set of C and N values, there is a unique GDUH, of global applicability.

An online version of the GDUH as a function of C and N is given in ponce.sdsu.edu/online_general_uh_cascade. Figure 3.2 shows a sample output for C = 1 and N = 3. This program is used in Section 5.1 to match measured and predicted dimensionless unit hydrographs.

Table C N 01.

Fig. 3.2  Dimensionless unit hydrograph for C = 1 and N = 3.

An online version of a GDUH series for a given C (recommended range 0.1 ≤ C ≤ 2.0) and for all N in the range 1 ≤ N ≤ 10 is given in ponce.sdsu.edu/online_series_uh_cascade. Figure 3.3 shows a sample output for C = 1. Compare the discharge values of Fig. 3.3 for N = 3 with those of Fig. 3.2.

Table C N 02.

Fig. 3.3  Dimensionless unit hydrograph for C = 1 and 1 ≤ N ≤ 10.

An online version of a GDUH series for six (6) C values covering the recommended range (2.0, 1.5, 1.0, 0.5, 0.2, and 0.1), and for all N values in the range 1 ≤ N ≤ 10, is given in ponce.sdsu.eduonline_all_series_uh_cascade. Figure 3.2 shows a summary table of dimensionless peak discharge Qp* and time of occurrence tp*. Compare the result for Courant number C = 1 and N = 3 in Fig. 3.4 with that of Fig. 3.3 (t* = 3; Q* = 0.272).

Table C N 03.

Fig. 3.4  Summary table of dimensionless unit hydrographs for 2 < C ≤ 0.1, and 1 ≤ N ≤ 10.


3.4  Series of dimensionless unit hydrographs

Figures 3.5 (a) to (f) show the series of dimensionless unit hydrographs (DUHs) for cascade parameters C with values of 2, 1.5, 1, 0.5, 0.2 and 0.1; and N varying between 1 and 10. The examination of these figures enables the following conclusions:

  1. Hydrograph diffusion increases with a decrease in the value of C.

  2. Hydrograph diffusion increases as N increases from 1 to 10.

  3. The hydrograph's positive skewness increases with a decrease in the value of C.


DUH C=2.

Fig. 3.5 (a)  Dimensionless unit hydrograph for C = 2.


DUH C=1.5.

Fig. 3.5 (b)  Dimensionless unit hydrograph for C = 1.5.


DUH C=1.

Fig. 3.5 (c)  Dimensionless unit hydrograph for C = 1.


DUH C=0.5.

Fig. 3.5 (d)  Dimensionless unit hydrograph for C = 0.5.


DUH C=0.2.

Fig. 3.5 (e)  Dimensionless unit hydrograph for C = 0.2.


DUH C=0.1.

Fig. 3.5 (f)  Dimensionless unit hydrograph for C = 0.1.

Figures 3.6 (a) to (f) show the series of dimensionless unit hydrographs (DUHs) for cascade parameters N with values of 1, 2, 3, 4, 5 and 6; and C varying between 2 and 0.1 as indicated. The examination of these figures enables the following conclusions:

  1. Hydrograph diffusion increases as N increases from 1 to 6.

  2. Hydrograph diffusion increases with a decrease in the value of C.

  3. The hydrograph's positive skewness increases with a decrease in the value of C.


DUH N=1

Fig. 3.6 (a)  Dimensionless unit hydrograph for N = 1.


DUH N=2

Fig. 3.6 (b)  Dimensionless unit hydrograph for N = 2.


DUH N=3.

Fig. 3.6 (c)  Dimensionless unit hydrograph for N = 3.


DUH N=4.

Fig. 3.6 (d)  Dimensionless unit hydrograph for N = 4.


DUH N=5

Fig. 3.6 (e)  Dimensionless unit hydrograph for N = 5.


DUH N=6

Fig. 3.6 (f)  Dimensionless unit hydrograph for N = 6.


3.5  GDUH, CLR and convolution

The cascade of linear reservoirs (CLR) (Section 2.3) and the convolution of the unit hydrograph with the effective storm hyetograph (Section 3.2.1) lead to the same composite flood hydrograph, provided the cascade parameters (GDUH) are used to develop the unit hydrograph for the convolution. These propositions are substantiated with an example.

Assume the 6-hr effective storm hyetograph shown in Table 3.2.

Table 3.2  Effective storm hyetograph.
Time (hr) 1 2 3 4 5 6
Effective rainfall (cm) 1 2 4 3 2 1

Assume the basin drainage area:  A = 432 km2. The applicable unit hydrograph duration tr is the same as the [effective] storm hyetograph time interval (Table 3.2), i.e., tr = Δt = 1 hr. Assume that the basin has a relatively steep relief, with cascade parameters C = 1 and N = 2. An online version of the GDUH as a function of C and N is given in ponce.sdsu.edu/online_general_uh_cascade. The corresponding DUH is shown in Fig. 3.7.

Table C N 04.

Fig. 3.7  Dimensionless unit hydrograph for C = 1 and N = 2.

Given the reservoir storage constant K:

K = Δt / C = tr / C = 1(3-4)

and time

t = t* tr(3-5)

and discharge

Q = 2.777778 Q* A / tr(3-6)

the program ponce.sdsu.edu/online_dimensionless_uh_cascade gives the unit hydrograph and dimensionless unit hydrograph shown in Fig. 3.8.

Table C N 05.

Fig. 3.8  Unit hydrograph and dimensionless unit hydrograph for C = 1 and N = 2.

With C = 1 (i.e., K = 1), N = 2, and the given effective storm hyetograph (Table 3.2), the program ponce.sdsu.edu/online_routing_08 calculates the composite flood hydrograph by the cascade of linear reservoirs (Ponce 1989). The composite flood hydrograph is shown in Fig. 3.9.

Table C N 06.

Fig. 3.9  Composite flood hydrograph by the cascade of linear reservoirs (CLR).

The convolution of the unit hydrograph (Fig. 3.8, Cols. 2 and 3) with the effective storm hyetograph (Table 3.2) is accomplished using the program ponce.sdsu.edu/online_convolution. For this example, an effective storm hyetograph is applicable; therefore, the curve number is:  CN = 100. The composite flood hydrograph is shown in Fig. 3.10. Remarkably, it is confirmed that the results of Figs. 3.9 and 3.10 are essentially the same.

Table C N 07.

Fig. 3.10  Composite flood hydrograph by convolution.

In summary, given a set of cascade parameters C and N, and an effective storm hyetograph, the method of cascade of linear reservoirs (CLR) can be used to calculate a composite flood hydrograph. Likewise, the convolution of a unit hydrograph derived with the GDUH method, using the same set of cascade parameters (C and N), can be used to calculate a composite flood hydrograph. It is shown that these two flood hydrographs are the same.


4.  DATA ANALYSIS

[ GDUH Model Application ]  [ Summary and Conclusions ]  [ References ]  •  [ Top ]  [ Introduction ]  [ Background ]   [ Methodology ] 

4.1  Rationale

Several basins in California are selected, with wide ranging geomorphological features. The basins meet the following requirements:

  1. A wide range in drainage areas, from approximately 100 to 60,000 km2.

  2. A wide range of main stream channel slopes, from approximately 0.0001 to 0.05 m/m.

  3. Corresponding precipitation and discharge data for three (3) suitable infrequent events.

  4. A minimum of manmade storage features (reservoirs).

4.2  Data sources

The hydrometeorological and geomorphological data was collected from the following sources:

  1. Digital elevation maps (DEM) from the following USGS virtual platforms: (a) Earth Explorer and (b) Alaska Satellite Facility.

  2. Rainfall data from the following NOAA virtual platform: National Centers for Environmental Information.

  3. Runoff data from the following USGS virtual platform: National Water Information System.

4.3  Geomorphological parameters

4.3.1  Drainage area

The drainage area determines the potential runoff volume, provided the storm covers the whole area. The catchment divide is the loci of points delimiting two adjacent catchments, i.e., the collection of high points (peaks and saddles) separating catchments draining into different outlets. In this study, catchment areas were obtained with the aid of GIS.

4.3.2  Drainage perimeter

The perimeter of the drainage area is the sum of the length delineating the catchment. Catchment perimeters were obtained with the aid of GIS.

4.3.3  Catchment hydraulic length

The hydraulic length is the length measured along the principal watercourse. The principal watercourse (or main stream) is the central and largest watercourse of the catchment and the one conveying the flow to the outlet. Hydraulic lengths were obtained with the aid of GIS.

4.3.4  Form ratio

The form ratio is defined as follows:

              A
Kf  =  _______
             L 2
(4-1)

in which Kf = form ratio, A = catchment area, and L = catchment length, measured along the longest watercourse. Area and length are given in consistent units such as square kilometers and kilometers, respectively.

4.3.5  Compactness ratio

An alternate morphological description is based on catchment perimeter rather than area. For this purpose, an equivalent circle is defined as a circle of area equal to that of the catchment. The compactness ratio is the ratio of the catchment perimeter to that of the equivalent circle. This leads to:

             0.282 P
Kc  =  ____________
                A 1/2
(4-2)

in which Kc = compactness ratio, P = catchment perimeter, and A = catchment area, with P and A given in any consistent set of units.

4.3.6  Maximum and minimum elevation

The maximum elevation is the highest point in the catchment divide, while the minimum elevation is the catchment outlet. The difference between these two reference points is the catchment relief. Catchment elevations were obtained with the aid of GIS.

4.3.7  Average land surface slope

Grid methods are often used to obtain measures of land surface slope for runoff evaluations. For instance, the USDA Natural Resources Conservation Service (NRCS) determines average surface slope by overlaying a square grid pattern over the topographic map of the watershed. The maximum surface slope at each grid intersection is evaluated, and the average of all values calculated. This average is taken as the representative value of land surface slope. The procedure was performed with the aid of GIS, and the average land surface slope referred to as S0.

4.3.8  Stream channel slope

The channel gradient of a principal watercourse is a convenient indicator of catchment relief. A longitudinal profile is defined by its maximum (upstream) and minimum (downstream) elevations, and by the horizontal distance between them. The channel gradient obtained directly from the upstream and downstream elevations is referred to as the S1 slope.

An alternate stream channel slope is obtained by calculating the slope between two points in the profile, located at 10% and 85% from the mouth, respectively. This procedure is recommended by the U.S. Geological Survey (Ponce, 2014a). This stream channel slope is referred to as S2.

4.3.9  Total stream channel length

The total stream channel length is the sum of all stream channels defined inside the cachtment. This procedure was performed with the aid of GIS.

4.3.10  Drainage density

The catchment's drainage density is the ratio of total stream length to catchment area. A high drainage density reflects a fast and peaked runoff response, whereas a low drainage density is characteristic of a delayed runoff response.

4.3.11  Mean annual precipitation

Rainfall varies not only temporally but also spatially, i.e., the same amount of rain does not fall uniformly over the entire catchment. Isohyets are used to depict the spatial variation of rainfall. An isohyet is a contour line showing the loci of equal rainfall depth. Isohyetal analysis was performed with the aid of GIS.

4.4  Selection of basins

Ten (10) basins located in California were selected for analysis. The basins are listed in Table 4.1.

Table 4.1  Basins selected for this study.
(1) (2) (3) (4)
No. Basin / Location Area
(km2)
Counties
1 Campo Creek near Campo, CA 218 San Diego, CA; Baja California, Mexico
2 Whitewater River near Mecca, CA 3,849 Riverside and San Bernardino, CA
3 Mojave River near Victorville, CA 56,583 Los Angeles, San Bernardino, Kern and Inyo in California; and Pahrump, Amargosa Valley, Beaty, Goldfield and Yucca Flat in Nevada
4 Amargosa River near Tecopa, CA 8,315 Inyo in California; Beaty, Amargosa Valley, Pahrump and Yucca Flat in Nevada
5 Petaluma River near Petaluma, CA 93 Marin and Sonoma, CA
6 Russian River near Guerneville, CA 3,463 Mendocino and Sonoma, CA
7 Los Gatos Creek near Coalinga, CA 247 Fresno, CA
8 Cottonwood Creek near Cottonwood, CA 2,435 Shasta and Tehama, CA
9 Salinas River near Spreckels, CA 11,777 Monterrey, San Benito, San Luis Obispo and Kern, CA
10 Shasta river near Montague, CA 1,737 Siskiyou, CA

4.4.1 Campo Creek near Campo, CA

The headwaters of Campo Creek are located near the community of Live Oak Springs, in southeast San Diego County, California (Fig. 4.1). The stream flows in a predominantly southwestern direction toward the community of Campo (Fig. 4.2). The National Weather Service (NWS) meteorological station is located in Campo (Fig. 4.3). The USGS streamgaging station is located at the intersection of Campo Creek with California State Route 94 (Fig. 4.4).

Downstream view of Campo Creek subbasin.

Fig. 4.1  Downstream view of Campo Creek near its headwaters.


Upstream view of Campo Creek subbasin.

Fig. 4.2  Upstream view of Campo Creek in Campo valley, California.


Downstream view of Campo Creek subbasin.

Fig. 4.3  NOAA NWS raingage at Campo, California.


Upstream view of Campo Creek subbasin.

Fig. 4.4  USGS streamgaging station at the intersection of Campo Creek with SR 94.


Figure 4.5 shows the outline of the Campo Creek subbasin. Most of the basin is located in southeast San Diego County; however, a very small fraction is located in Baja California, Mexico. The main ecosystem is the Mediterranean chaparral, which corresponds to Koppen's warm summer Mediterranean climate (Csa). The mean annual precipitation is 400 mm (15.78 in). Figure 4.6 shows the hydrologic map of the Campo Creek subbasin.

After crossing into Mexico, Campo Creek is renamed Cañada Joe Bill, which flows into Tecate Creek at Tecate. In turn, Tecate Creek flows into the Tijuana River, the latter eventually discharging into the Pacific Ocean at Imperial Beach, California.

Aerial view of Campo Creek subbasin.
Google Earth®

Fig. 4.5  Aerial view of the Campo Creek subbasin.

[Click on figure to enlarge]
Campo Creek subbasin map.

Fig. 4.6  Hydrologic map of the Campo Creek subbasin.


Table 4.2 shows precipitation and streamgaging data sources from the Campo Creek subbasin. Table 4.3 shows hydrologic and geomorphologic parameters calculated for the Campo Creek subbasin.

Table 4.2   Data sources for the Campo Creek subbasin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 041424 Campo 3237'24'' 11628'22'' 801.6
Discharge USGS 11012500 Campo Creek near Campo 3235'28'' 11631'29'' 667

Table 4.3   Hydrologic and geomorphologic parameters of the Campo Creek subbasin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 218.04
2 Perimeter of drainage area P km 101.25
3 Catchment hydraulic length L km 34.83
4 Form ratio Kf - 0.18
5 Compactness ratio Kc - 1.93
6 Maximum elevation Emax m (msl) 1406
7 Minimum elevation Emin m (msl) 667
8 Average land surface slope S0 m/m 0.171
9 Stream slope (from 0 to 100%) S1 m/m 0.021
10 Stream slope (from 10 to 85%) S2 m/m 0.018
11 Total stream channel length L km 72.98
12 Drainage density D km/km2 0.33
13 Mean annual precipitation Pma mm 400

Figure 4.7 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 1983.

Fig. 4.7 (a)  Campo Creek near Campo, California: Flood hydrograph No. 1 - Year 1983.


Flood hydrograph measured in 1993.

Fig. 4.7 (b)  Campo Creek near Campo, California: Flood hydrograph No. 2 - Year 1993.


Flood hydrograph measured in 1998.

Fig. 4.7 (c)  Campo Creek near Campo, California: Flood hydrograph No. 3 - Year 1998.


4.4.2 Whitewater river near Mecca, CA

The headwaters of Whitewater river at located near San Gorgonio Mountain, in southeast Forest Falls, California. The stream flows in a predominantly southeastern direction toward the community of Whitewater (Fig. 4.8), flowing into the Salton Sea (Fig. 4.9). The National Weather Service (NWS) meteorological stations are located in Palm Springs, Palm Desert and Indio. The USGS streamgaging station is located near its mouth at the Salton Sea.

Whitewater river  canyon.
Google Earth®

Fig. 4.8  The Whitewater river canyon.


Whitewater river.

Fig. 4.9  Mouth of the Whitewater river at the Salton Sea.

Figure 4.10 shows the outline of the Whitewater river basin. Most of the basin is located in Riverside County; however, a very small fraction is located in San Bernardino County. This basin has been one of southern California's most important agricultural regions, which corresponds to Koppen's winter/hot summer climate. The mean annual precipitation is 112 mm (4.41 in). Figures 4.11 and 4.12 show the hydrologic map and the mean annual precipitation map of the Whitewater river basin.

Aerial view of Whitewater river basin.
Google Earth®

Fig. 4.10  Aerial view of the Whitewater river basin.


[Click on figure to enlarge]
Whitewater river basin map.

Fig. 4.11  Hydrologic map of the Whitewater river basin.


[Click on figure to enlarge]
Whitewater river basin mean annual precipitation map.

Fig. 4.12  Mean annual precipitation map of the Whitewater river basin.


Table 4.4 shows precipitation and streamgaging data sources from the Whitewater river basin. Table 4.5 shows hydrologic and geomorphologic parameters calculated for the Whitewater river basin.

Table 4.4   Data sources for the Whitewater river basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 048892 Desert Resorts RGNL AP 3338'10'' 11610'00'' -36
Precipitation NWS 044259 Indio Fire STN 3342'31'' 11612'55'' -6.4
Precipitation NWS 042327 Deep Canyon LAB 3339'05'' 11622'35'' 366
Precipitation NWS 046635 Palm Springs 3349'39'' 11630'35'' 130
Discharge USGS 10259540 Whitewater river near Mecca 3331'29'' 11604'36'' -69

Table 4.5   Hydrologic and geomorphologic characteristics of the Whitewater river basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 3,849
2 Perimeter of drainage area P km 461.82
3 Catchment hydraulic length L km 126.92
4 Form ratio Kf - 0.24
5 Compactness ratio Kc - 2.10
6 Maximum elevation Emax m (msl) 3490
7 Minimum elevation Emin m (msl) -69
8 Average land surface slope S0 m/m 0.268
9 Stream slope (from 0 to 100%) S1 m/m 0.028
10 Stream slope (from 10 to 85%) S2 m/m 0.012
11 Total stream channel length L km 294.48
12 Drainage density D km/km2 0.08
13 Mean annual precipitation Pma mm 112

Figure 4.13 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 2008.

Fig. 4.13 (a)  Whitewater river near Mecca, California: Flood hydrograph No. 1 - Year 2008.


Flood hydrograph measured in 2008.

Fig. 4.13 (b)  Whitewater river near Mecca, California: Flood hydrograph No. 2 - Year 2008.


Flood hydrograph measured in 2015.

Fig. 4.13 (c)  Whitewater river near Mecca, California: Flood hydrograph No. 3 - Year 2015.


4.4.3 Mojave river near Victorville, CA

The headwaters of the Mojave river are located near the highlands of Indian Wells, Cantil, Peasonville, Darwin, Afton Canyon (Fig. 4.14), Blanco Mountain, Sylvana Mountain, Gold Mountain, Palmer Mountain, Beatty, Amargosa Valley, Clark Mountain and Baker. The stream flows in a predominantly southern direction toward the community of Helendale (Fig. 4.15). The National Weather Service (NWS) meteorological stations are located in Pearblossom, Palmdale, Lancaster, Mojave, Barstow, Randsburg, China Lake, Trona and Stovepipe wells. The USGS streamgaging station is located at the intersection of National Trails Highway with Mojave Heights.

Whitewater river.
Google Earth®

Fig. 4.14  The Mojave river at Afton Canyon, California.


Whitewater river.

Fig. 4.15  The Mojave river at Helendale, California.


Figure 4.16 shows the outline of the Mojave river basin. The basin is located in Kern, Los Angeles, San Bernardino and Inyo Counties of California; and Goldfiel, Beatty, Yucca Flat, Amargosa Valley and Pahrump Counties of Nevada. The weather corresponds to Koppen's desert climate (BWk). The mean annual precipitation is 109 mm (4.29 in). Figures 4.17 and 4.18 show the hydrologic map and the mean annual precipitation map of the Mojave river basin.

Aerial view of Mojave river basin.
Google Earth®

Fig. 4.16  Aerial view of the Mojave river basin.


[Click on figure to enlarge]
Mojave river basin map.

Fig. 4.17  Hydrologic map of the Mojave river basin.

[Click on figure to enlarge]
Mojave river basin mean annual precipitation map.

Fig. 4.18  Mean annual precipitation map of the Mojave river basin.

Table 4.6 shows precipitation and streamgaging data sources from the Mojave river basin. Table 4.7 shows hydrologic and geomorphologic parameters calculated for the Mojave river basin.

Table 4.6   Data sources for the Mojave river basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 046624 Palmdale 3435'18'' 11805'38'' 796
Precipitation NWS 042941 Fairmont 3442'18'' 11825'47'' 933
Precipitation NWS 003159 Lancaster 3444'28'' 11812'42'' 713
Precipitation NWS 046773 Pearblossom 3430'09'' 11753'49'' 945
Precipitation NWS 045756 Mojave 3502'57'' 11809'43'' 834
Precipitation NWS 093104 China Lake NAF 3541'15'' 11741'35'' 680
Precipitation NWS 049035 Trona 3545'49'' 11723'27'' 517
Precipitation NWS 040521 Barstow 3453'34'' 11701'19'' 677
Precipitation NWS 053139 Stovepipe Wells 1 SW 3636'07'' 11708'42'' 26
Precipitation NWS 047253 Randsburg 3522'09'' 11739'09'' 1088
Discharge USGS 10261500 Mojave river near Victorville 3434'23'' 11719'11'' -83

Table 4.7   Hydrologic and geomorphologic characteristics of the Mojave river basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 56,583
2 Perimeter of drainage area P km 1787.72
3 Catchment hydraulic length L km 511.81
4 Form ratio Kf - 0.22
5 Compactness ratio Kc - 2.12
6 Maximum elevation Emax m (msl) 3351
7 Minimum elevation Emin m (msl) -83
8 Average land surface slope S0 m/m 0.164
9 Stream slope (from 0 to 100%) S1 m/m 0.0038
10 Stream slope (from 10 to 85%) S2 m/m 0.00014
11 Total stream channel length L km 6067.17
12 Drainage density D km/km2 0.11
13 Mean annual precipitation Pma mm 109

Figure 4.19 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 2010.

Fig. 4.19 (a)  Mojave river near Victorville, California: Flood hydrograph No. 1 - Year 2010.


Flood hydrograph measured in 2017.

Fig. 4.19 (b)  Mojave river near Victorville, California: Flood hydrograph No. 2 - Year 2017.


Flood hydrograph measured in 2017.

Fig. 4.19 (c)  Mojave river near Victorville, California: Flood hydrograph No. 3 - Year 2017.


4.4.4 Amargosa river near Tecopa, CA

The headwaters of the Amargosa river at located near Beatty, Timber Mountain, Black Mountain, Shoshone and Amargosa Valley (Fig. 4.20). The stream flows in a predominantly southeastern direction toward the communities of Beatty, Amargosa Valley, Evelyn, Shoshone and Tecopa (Fig. 4.21). The National Weather Service (NWS) meteorological station is located in Shoshone. The USGS streamgaging station is located near Tecopa, California.

Amargosa river upstream.
Google Earth®

Fig. 4.20  Upstream view of Amargosa river.


Amargosa river near shoshone.
Google Earth®

Fig. 4.21  View of Amargosa river near Shoshone, California.


Figure 4.22 shows the outline of the Amargosa river basin. The basin is located in Inyo County of California; and Beatty, Yucca Flat, Amargosa Valley and Pahrump Counties of Nevada. The weather corresponds to Koppen's cold desert climate (BWk). The mean annual precipitation is 110 mm (4.32 in). Figures 4.23 and 4.24 show the hydrologic map and the mean annual precipitation map of the Amargosa river basin.

Aerial view of Amargosa river basin.
Google Earth®

Fig. 4.22  Aerial view of the Amargosa river basin.

[Click on figure to enlarge]
Amargosa river basin map.

Fig. 4.23  Hydrologic map of the Amargosa river basin.

Table 4.8 shows precipitation and streamgaging data sources from the Amargosa river basin. Table 4.9 shows hydrologic and geomorphologic parameters calculated for the Amargosa river basin.

Table 4.8   Data sources for the Amargosa river basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 048200 Shoshone 3558'18'' 11616'15'' 471
Discharge USGS 10251300 Amargosa river near Tecopa 3550'55'' 11613'45'' 389

Table 4.9   Hydrologic and geomorphologic characteristics of the Amargosa river basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 8,315
2 Perimeter of drainage area P km 657.70
3 Catchment hydraulic length L km 190.54
4 Form ratio Kf - 0.23
5 Compactness ratio Kc - 2.03
6 Maximum elevation Emax m (msl) 2414
7 Minimum elevation Emin m (msl) 389
8 Average land surface slope S0 m/m 0.151
9 Stream slope (from 0 to 100%) S1 m/m 0.011
10 Stream slope (from 10 to 85%) S2 m/m 0.007
11 Total stream channel length L km 597.63
12 Drainage density D km/km2 0.07
13 Mean annual precipitation Pma mm 110

Figure 4.24 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 2007.

Fig. 4.24 (a)  Amargosa river near Tecopa, California: Flood hydrograph No. 1 - Year 2007.


Flood hydrograph measured in 2008.

Fig. 4.24 (b)  Amargosa river near Tecopa, California: Flood hydrograph No. 2 - Year 2008.


Flood hydrograph measured in 2010.

Fig. 4.24 (c)  Amargosa river near Tecopa, California: Flood hydrograph No. 3 - Year 2010.


4.4.5  Petaluma river near Petaluma, CA

The headwaters of the Petaluma river at located near Sonoma Mountain. The stream flows in a predominantly southweastern direction toward the communities of Penngrove and Petaluma (Fig. 4.25). The National Weather Service (NWS) meteorological station is located in Petaluma (Fig. 4.26). The USGS streamgaging station is located near Petaluma, California.

Whitewater river.
Google Earth®

Fig. 4.25  The Petaluma river at Petaluma, California.


Whitewater river.
Google Earth®

Fig. 4.26  The Petaluma river at the USGS streamgaging station.


Figure 4.27 shows the outline of the Petaluma river basin. The basin is located in Sonoma County of California. The weather corresponds to Koppen's mild Mediterranean climate. The mean annual precipitation is 624 mm (24.57 in). Figure 4.28 shows the hydrologic map of the Petaluma River basin.

Aerial view of Petaluma river basin.
Google Earth®

Fig. 4.27  Aerial view of the Petaluma river basin.


[Click on figure to enlarge]
Petaluma river basin map.

Fig. 4.28  Hydrologic map of the Petaluma river basin.

Table 4.10 shows precipitation and streamgaging data sources from the Petaluma river Basin. Table 4.11 shows hydrologic and geomorphologic parameters calculated for the Petaluma river basin.

Table 4.10   Data sources for the Petaluma river basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 046826 Petaluma Airport 3815'28'' 12236'28'' 6.10
Discharge USGS 11459150 Petaluma river at Copland Pumping Station 3814'18'' 12238'21'' 5

Table 4.11   Hydrologic and geomorphologic characteristics of the Petaluma river basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 93
2 Perimeter of drainage area P km 68.81
3 Catchment hydraulic length L km 17.64
4 Form ratio Kf - 0.30
5 Compactness ratio Kc - 2.01
6 Maximum elevation Emax m (msl) 648
7 Minimum elevation Emin m (msl) 5
8 Average land surface slope S0 m/m 0.099
9 Stream slope (from 0 to 100%) S1 m/m 0.036
10 Stream slope (from 10 to 85%) S2 m/m 0.025
11 Total stream channel length L km 20.98
12 Drainage density D km/km2 0.23
13 Mean annual precipitation Pma mm 624

Figure 4.29 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 2000.

Fig. 4.29 (a)  Petaluma river near Petaluma, California: Flood hydrograph No. 1 - Year 2000.


Flood hydrograph measured in 2002.

Fig. 4.29 (b)  Petaluma river near Petaluma, California: Flood hydrograph No. 2 - Year 2002.


Flood hydrograph measured in 2010.

Fig. 4.29 (c)  Petaluma river near Petaluma, California: Flood hydrograph No. 3 - Year 2010.


4.4.6  Russian river near Guerneville, CA

The headwaters of the Russian river at located near Saint Helena Mountain, Red Mountain, and the highlands of Potter and Redwood valleys. The stream flows in a predominantly southeastern direction toward the communities of Potter Valley, Redwood Valley, Ukiah, El Roble, Largo, Hopland, Pieta, Preston, Cloverdale, Asti, Geyserville (Fig. 4.30), Healdsburg and Guerneville (Fig. 4.31). The National Weather Service (NWS) meteorological stations are located in Potter Valley, Ukiah and Cloverdale. The USGS streamgaging station is located near Guerneville.

Russian river.
Google Earth®

Fig. 4.30  The Russian river at Gerseyville, California.


Russian river.
Google Earth®

Fig. 4.31  The Russian river at Guerneville, California.


Figure 4.32 shows the outline of the Russian river basin. The basin is located in Mendocino and Sonoma Counties in California. The weather corresponds to Koppen's hot-summer Mediterranean climate (Csa). The mean annual precipitation is 1072 mm (42.20 in). Figures 4.33 and 4.34 show the hydrologic map and the mean annual precipitation map of the Russian river basin.

Aerial view of Petaluma river basin.
Google Earth®

Fig. 4.32  Aerial view of the Russian river basin.


[Click on figure to enlarge]
 Russian river basin map.

Fig. 4.33  Hydrologic map of the Russian river basin.


[Click on figure to enlarge]
 Russian river basin mean annual precipitation map.

Fig. 4.34  Mean annual precipitation map of the Russian river basin.

Table 4.12 shows precipitation and streamgaging data sources from the Russian River basin. Table 4.13 shows hydrologic and geomorphologic parameters calculated for the Russian River basin.

Table 4.12   Data sources for the Russian river basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 041838 Cloverdale 3847'59'' 12301'03'' 100
Precipitation NWS 049126 Ukiah 4 WSW 3907'36'' 12316'19'' 556
Precipitation NWS 047109 Potter Valley P H 3921'43'' 12307'43'' 310
Discharge USGS 11467000 Russian river near Guerneville 3830'31'' 12255'36'' 6

Table 4.13   Hydrologic and geomorphologic characteristics of the Russian river basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 3,463
2 Perimeter of drainage area P km 610.32
3 Catchment hydraulic length L km 161.20
4 Form ratio Kf - 0.13
5 Compactness ratio Kc - 2.92
6 Maximum elevation Emax m (msl) 1425
7 Minimum elevation Emin m (msl) 8
8 Average land surface slope S0 m/m 0.242
9 Stream slope (from 0 to 100%) S1 m/m 0.005
10 Stream slope (from 10 to 85%) S2 m/m 0.002
11 Total stream channel length L km 911.41
12 Drainage density D km/km2 0.26
13 Mean annual precipitation Pma mm 1072

Figure 4.35 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 1994.

Fig. 4.35 (a)  Russian river near Guerneville, California: Flood hydrograph No. 1 - Year 1994.


Flood hydrograph measured in 1995.

Fig. 4.35 (b)  Russian river near Guerneville, California: Flood hydrograph No. 2 - Year 1995.


Flood hydrograph measured in 1998.

Fig. 4.35 (c)  Russian river near Guerneville, California: Flood hydrograph No. 3 - Year 1998.


4.4.7  Los Gatos Creek near Coalinga, CA

The headwaters of Los Gatos Creek at located near Santa Rita and Condon Peak. The stream flows in a predominantly southeastern direction toward the community of Coalinga (Fig. 4.36). The National Weather Service (NWS) meteorological station is located in Coalinga. The USGS streamgaging station is located upstream at Coalinga (Fig. 4.37).

Los Gatos Creek.
Google Earth®

Fig. 4.36  Los Gatos Creek near Coalinga, California.


Los Gatos Creek upstream.
Google Earth®

Fig. 4.37  Los Gatos Creek upstream of Coalinga, California.


Figure 4.38 shows the outline of Los Gatos Creek basin. The basin is located in Fresno County in California. The weather corresponds to Koppen's cold/summer Mediterranean climate. The mean annual precipitation is 394 mm (15.51 in). Figure 4.39 shows the hydrologic map of Los Gatos Creek basin.

Aerial view of Los Gatos Creek basin.
Google Earth®

Fig. 4.38  Aerial view of Los Gatos Creek basin.


[Click on figure to enlarge]
 Los Gatos Creek basin map.

Fig. 4.39  Hydrologic map of Los Gatos Creek basin.

Table 4.14 shows precipitation and streamgaging data sources from Los Gatos Creek basin. Table 4.15 shows hydrologic and geomorphologic parameters calculated for Los Gatos Creek basin.

Table 4.14   Data sources for the Los Gatos Creek basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 041869 Coalinga 14 WNW 3613'59'' 12034'01'' 500
Discharge USGS 11224500 Los Gatos Creek near Coalinga 3612'53'' 12028'11'' 325

Table 4.15   Hydrologic and geomorphologic characteristics of Los Gatos Creek basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 247
2 Perimeter of drainage area P km 103.25
3 Catchment hydraulic length L km 30.88
4 Form ratio Kf - 0.26
5 Compactness ratio Kc - 1.85
6 Maximum elevation Emax m (msl) 1496
7 Minimum elevation Emin m (msl) 325
8 Average land surface slope S0 m/m 0.328
9 Stream slope (from 0 to 100%) S1 m/m 0.037
10 Stream slope (from 10 to 85%) S2 m/m 0.015
11 Total stream channel length L km 62.25
12 Drainage density D km/km2 0.25
13 Mean annual precipitation Pma mm 394

Figure 4.40 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 1977.

Fig. 4.40 (a)  Los Gatos Creek near Coalinga, California: Flood hydrograph No. 1 - Year 1977.


Flood hydrograph measured in 1978.

Fig. 4.40 (b)  Los Gatos Creek near Coalinga, California: Flood hydrograph No. 2 - Year 1978.


Flood hydrograph measured in 1978.

Fig. 4.40 (c)  Los Gatos Creek near Coalinga, California: Flood hydrograph No. 3 - Year 1978.


4.4.8  Cottonwood Creek near Cottonwood, CA

The headwaters of Cottonwood Creek at located near Lazyman Butte, North Yolla Bolly and highlands of Platina. The stream flows in a predominantly northeastern direction toward the communities of Platina, Ono and Cottonwood (Fig. 4.41). The National Weather Service (NWS) meteorological station is located in the highlands of Platina. The USGS streamgagin station is located near Cottonwood.

Cottonwood Creek.
Google Earth®

Fig. 4.41  Cottonwood Creek at Cottonwood, California.


Figure 4.42 shows the outline of Cottonwood Creek basin. The basin is located in Shasta and Tehama Counties in California. The weather corresponds to Koppen's warm-summer Mediterranean climate (Csa). The mean annual precipitation is 876 mm (34.49 in). Figure 4.43 shows the hydrologic map of the Cottonwood Creek basin.

Aerial view of Cottonwood Creek basin.
Google Earth®

Fig. 4.42  Aerial view of Cottonwood Creek basin.


[Click on figure to enlarge]
 Cottonwood creek basin map.

Fig. 4.43  Hydrologic map of Cottonwood Creek basin.

Table 4.16 shows precipitation and streamgaging data sources from the Cottonwood Creek basin. Table 4.17 shows hydrologic and geomorphologic parameters calculated for the Cottonwood Creek basin.

Table 4.16   Data sources for the Cottonwood Creek basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 043791 Harrison Gulch RS 4021'49'' 12257'54'' 838
Discharge USGS 11376000 Cottonwood Creek near Cottonwood 4023'14'' 12214'15'' 111

Table 4.17   Hydrologic and geomorphologic characteristics of Cottonwood Creek basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 2,435
2 Perimeter of drainage area P km 340.26
3 Catchment hydraulic length L km 106.02
4 Form ratio Kf - 0.22
5 Compactness ratio Kc - 1.94
6 Maximum elevation Emax m (msl) 2462
7 Minimum elevation Emin m (msl) 101
8 Average land surface slope S0 m/m 0.255
9 Stream slope (from 0 to 100%) S1 m/m 0.017
10 Stream slope (from 10 to 85%) S2 m/m 0.010
11 Total stream channel length L km 370.54
12 Drainage density D km/km2 0.22
13 Mean annual precipitation Pma mm 876

Figure 4.44 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 1993.

Fig. 4.44 (a)  Cottonwood Creek near Cottonwood, California: Flood hydrograph No. 1 - Year 1993.


Flood hydrograph measured in 1996.

Fig. 4.44 (b)  Cottonwood Creek near Cottonwood, California: Flood hydrograph No. 2 - Year 1996.


Flood hydrograph measured in 1998.

Fig. 4.44 (c)  Cottonwood Creek near Cottonwood, California: Flood hydrograph No. 3 - Year 1998.


4.4.9  Salinas river near Spreckels, CA

The headwaters of the Salinas river at located near Machesna Mountain, Tassajera Peak; and the hihglands of Atascadero, Paso Robles, King City, Greenfield and Salinas. The stream flows in a predominantly northwestern direction toward the communities of San Ardo (Fig. 4.45), Shandon, Atascadero, Paso Robles (Fig. 4.46), San Miguel, Bradley, San Lucas, King City, Greenfield, Soledad, Gonzales, Chualar and Salinas. The National Weather Service (NWS) meteorological stations are located in Santa Margarita, Paso Robles and King City. The USGS streamgaging station is located near Spreckels, California.

Salinas river at San Ardo.
Google Earth®

Fig. 4.45  Salinas river at San Ardo, California.


Salinas river at Paso Robles.
Google Earth®

Fig. 4.46  Salinas river at Paso Robles, California.


Figure 4.47 shows the outline of the Salinas river basin. The basin is located in San Luis Obispo, San Benito and Monterey Counties in California. The weather corresponds to Koppen's semi-arid and dry steppe and Mediterranean climate (Csb). The mean annual precipitation is 294 mm (11.57 in). Figures 4.48 and 4.49 show the hydrologic map and the mean annual precipitation map of the Salinas river basin.

Aerial view of Salinas River basin.
Google Earth®

Fig. 4.47  Aerial view of Salinas river basin.


[Click on figure to enlarge]
 Cottonwood creek basin map.

Fig. 4.48  Hydrologic map of Salinas river basin.


[Click on figure to enlarge]
 Cottonwood creek basin mean annual precipitation map.

Fig. 4.49  Mean annual precipitation map of Salinas river basin.


Table 4.18 shows precipitation and streamgaging data sources from the Salinas river basin. Table 4.19 shows hydrologic and geomorphologic parameters calculated for the Salinas river basin.

Table 4.18   Data sources for the Salinas river basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 044555 King City 3612'25'' 12108'16'' 98
Precipitation NWS 046742 Paso Robles Muni 3540'11'' 12037'42'' 247
Precipitation NWS 047933 Santa Margarita Booster 3522'27'' 12038'15'' 350
Precipitation NWS 047672 Salinas Dam 3520'14'' 12030'14'' 416
Discharge USGS 111525000 Salinas river near Spreckels 3637'52'' 12140'17'' 6

Table 4.19   Hydrologic and geomorphologic characteristics of Salinas river basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 11,777
2 Perimeter of drainage area P km 1,104.78
3 Catchment hydraulic length L km 334.21
4 Form ratio Kf - 0.11
5 Compactness ratio Kc - 2.87
6 Maximum elevation Emax m (msl) 1783
7 Minimum elevation Emin m (msl) 6
8 Average land surface slope S0 m/m 0.215
9 Stream slope (from 0 to 100%) S1 m/m 0.003
10 Stream slope (from 10 to 85%) S2 m/m 0.0021
11 Total stream channel length L km 1,305.29
12 Drainage density D km/km2 0.22
13 Mean annual precipitation Pma mm 294

Figure 4.50 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 1980.

Fig. 4.50 (a)  Salinas river near Spreckels, California: Flood hydrograph No. 1 - Year 1980.


Flood hydrograph measured in 1983.

Fig. 4.50 (b)  Salinas river near Spreckels, California: Flood hydrograph No. 2 - Year 1983.


Flood hydrograph measured in 1995.

Fig. 4.50 (c)  Salinas river near Spreckels, California: Flood hydrograph No. 3 - Year 1995.


4.4.10  Shasta river near Montague, CA

The headwaters of the Shasta river at located near Mount Shasta and China Mountain. The stream flows in a predominantly northwestern direction toward Edgewood (Fig. 4.51), Gazelle, Grenada and Montague (Fig. 4.52). The National Weather Service (NWS) meteorological station is located in Weed. The USGS streamgaging station is located near Montague, California.

Shasta river at Edgewood.
Google Earth®

Fig. 4.51  Shasta river at Edgewood, California.


Salinas river at Montague.
Google Earth®

Fig. 4.52  Shasta river at Montague, California.


Figure 4.53 shows the outline of Shasta river basin. The basin is located in Siskiyou County in California. The weather corresponds to Koppen's warm-summer Mediterranean climate. The mean annual precipitation is 478 mm (18.82 in). Figure 4.54 shows the hydrologic map of the Shasta river basin.

Aerial view of Shasta River basin.
Google Earth®

Fig. 4.53  Aerial view of Shasta river basin.


[Click on figure to enlarge]
 Shasta river basin map.

Fig. 4.54  Hydrologic map of Shasta river basin.


Table 4.20 shows precipitation and streamgaging data sources from the Shasta river basin. Table 4.21 shows hydrologic and geomorphologic parameters calculated for the Shasta river basin.

Table 4.20   Data sources for the Shasta river basin.
(1) (2) (3) (4) (5) (6) (7)
Variable Agency Code Station name Latitude Longitude Elevation
(m)
Precipitation NWS 049866 Yreka 4142'13'' 12238'27'' 800
Discharge USGS 11517000 Shasta river near Montague 4142'33'' 12232'13'' 749

Table 4.21   Hydrologic and geomorphologic characteristics of Shasta river basin.
(1) (2) (3) (4) (5)
No. Description Symbol Units Value
1 Drainage area A km2 1,737
2 Perimeter of drainage area P km 283.32
3 Catchment hydraulic length L km 67.73
4 Form ratio Kf - 0.38
5 Compactness ratio Kc - 1.92
6 Maximum elevation Emax m (msl) 4305
7 Minimum elevation Emin m (msl) 698
8 Average land surface slope S0 m/m 0.196
9 Stream slope (from 0 to 100%) S1 m/m 0.041
10 Stream slope (from 10 to 85%) S2 m/m 0.013
11 Total stream channel length L km 219.49
12 Drainage density D km/km2 0.13
13 Mean annual precipitation Pma mm 478

Figure 4.55 shows the three (3) flood hydrographs selected for analysis.

Flood hydrograph measured in 2002.

Fig. 4.55 (a)  Shasta river near Montague, California: Flood hydrograph No. 1 - Year 2002.


Flood hydrograph measured in 2015.

Fig. 4.55 (b)  Shasta river near Montague, California: Flood hydrograph No. 2 - Year 2005.


Flood hydrograph measured in 2015.

Fig. 4.55 (c)  Shasta river near Montague, California: Flood hydrograph No. 3 - Year 2015.


5.  GDUH MODEL APPLICATION

[ Summary and Conclusions ]  [ References ]  •  [ Top ]  [ Introduction ]  [ Background ]   [ Methodology ]  [ Data Analysis ] 

5.1  Data analysis

Following Section 3, the data analysis may be based on: (a) simple storms, or (b) complex storms. For the most part, the inherent noisiness of the data precluded application using complex storms. Accordingly, simple storms were chosen for general application as a practical compromise.

Three (3) corresponding event sets of rainfall-runoff data were assembled for each basin. Example results corresponding to Campo Creek are summarized in Tables 5.1 and 5.2. Table 5.1 shows the following:

  • Column 1:  Event number

  • Column 2:  Date (yyyymmdd)

  • Column 3:  Precipitation (in)

  • Column 4:  Precipitation (cm)

  • Column 5:  Discharge (cfs)

  • Column 6:  Direct discharge (cfs), after substracting baseflow

  • Column 7:  Direct discharge (m3/s)

  • Column 8:  Unit hydrograph ordinates, corresponding to 1 cm of runoff volume.


Table 5.1   Example (Campo Creek):  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 19830228 0 0 45 0 0 0
19830301 0 0 68 23 0.65 0.49
19830302 2.91 7.39 399 354 10.02 7.58
19830303 1.27 3.23 347 302 8.55 6.46
19830304 0.74 1.88 305 260 7.36 5.57
19830305 0.11 0.28 179 134 3.79 2.87
19830306 0.23 0.58 121 76 2.15 1.63
19830307 0 0 75 30 0.85 0.64
19830308 0 0 45 0 0 0

Table 5.2 shows the following:

  • Column 1:  Dimensionless time t* (Eq. 2-20).

  • Columns 2-4:  Dimensionless discharge Q* (Eq. 2-23).

  • Column 5:  Average measured dimensionless discharge Q*, the average of Cols. 2-4.

  • Column 6:  Predicted dimensionless discharge Q*, corresponding to the cascade parameters C = 1.2 and N = 2, obtained from GDUH theory by trial and error.


Table 5.2   Example (Campo Creek):  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.2, N = 2)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.12 0.42 0.34 0.29 0.28
2 0.32 0.49 0.46 0.43 0.42
3 0.31 0.07 0.15 0.18 0.19
4 0.16 0.01 0.04 0.07 0.07
5 0.06 0.001 0.01 0.02 0.02
6 0 0 0 0 0

5.1.1  Campo Creek

Following the procedure described in Section 3.1.1, three (3) corresponding event sets of rainfall-runoff data were assembled for Campo Creek. The results are summarized in Tables 5.3 and 5.4.

Table 5.3   Campo creek subbasin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 19830228 0 0 45 0 0 0
19830301 0 0 68 23 0.65 0.49
19830302 2.91 7.39 399 354 10.02 7.58
19830303 1.27 3.23 347 302 8.55 6.46
19830304 0.74 1.88 305 260 7.36 5.57
19830305 0.11 0.28 179 134 3.79 2.87
19830306 0.23 0.58 121 76 2.15 1.63
19830307 0 0 75 30 0.85 0.64
19830308 0 0 45 0 0 0
2 19930106 1.79 4.55 3.3 0 0 0
19930107 3.73 9.47 539 535.7 15.16 10.93
19930108 2.55 6.48 661 657.7 18.61 13.42
19930109 0.22 0.56 34 30.7 0.87 0.63
19930110 0 0 16 12.7 0.36 0.26
19930111 0 0 3.3 0 0 0
3 19980327 0.06 0.15 16 0 0 0
19980328 1.33 3.38 77 61 1.73 7.69
19980329 1.09 2.77 108 92 2.6 11.61
19980330 0.04 0.1 48 32 0.91 4.04
19980331 0 0 31 15 0.43 1.89
19980401 0 0 16 0 0 0

Table 5.4   Campo creek subbasin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.2, N = 2)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.12 0.42 0.34 0.29 0.28
2 0.32 0.49 0.46 0.43 0.42
3 0.31 0.07 0.15 0.18 0.19
4 0.16 0.01 0.04 0.07 0.07
5 0.06 0.001 0.01 0.02 0.02
6 0 0 0 0 0

Figure 5.1 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Campo Creek subbasin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.4, respectively.

Campo Creek subbasin DUH.

Fig. 5.1   Campo Creek subbasin: Average measured vs predicted DUH.


5.1.2  Whitewater River

Following the procedure described in Section 3.1.2, three (3) corresponding event sets of rainfall-runoff data were assembled for Whitewater river. The results are summarized in Tables 5.5 and 5.6.

Table 5.5   Whitewater river basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 20080126 0.06 0.16 75 0 0 0
20080127 1.47 3.73 89 14 0.39 32.9
20080128 0.15 0.37 172 97 2.75 228.6
20080129 0 0 138 63 1.78 148.5
20080130 0 0 90 15 0.43 35.4
20080131 0 0 75 0 0 0
2 20081215 0 0 65 0 0 0
20081216 0.26 0.67 66 1 0.03 1.9
20081217 0.14 0.36 68 3 0.08 5.6
20081218 1.10 2.79 177 112 3.17 209.7
20081219 0.38 0.97 185 120 3.39 224.6
20081220 0 0 65 0 0 0
3 20151029 0 0 51 0 0 0
20151030 0 0 78 27 0.76 69.1
20151031 0 0 81 30 0.85 76.8
20151101 3.56 9 88 37 1.05 94.7
20151102 5.27 13.4 127 76 2.15 194.6
20151103 4.89 12.4 55 4 0.11 10.2
20151104 0 0 51 0 0 0

Table 5.6   Whitewater river basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.77, N = 4)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0 0 0.23 0.08 0.09
2 0 0.45 0.48 0.32 0.32
3 0.28 0.50 0.27 0.36 0.37
4 0.42 0.05 0.02 0.17 0.18
5 0.19 0 0 0.07 0.04
6 0 0 0 0 0

Figure 5.2 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Whitewater river basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.6, respectively.

Whitewater basin DUH.

Fig. 5.2   Whitewater river basin: Average measured vs predicted DUH.


5.1.3  Mojave River

Following the procedure described in Section 3.1.3, three (3) corresponding event sets of rainfall-runoff data were assembled for Mojave river. The results are summarized in Tables 5.7 and 5.8.

Table 5.7   Mojave river basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 20100119 0.40 1.02 114 0 0 0
20100120 0.51 1.30 1170 1056 29.88 1197.7
20100121 0.73 1.86 2310 2196 62.15 2490.7
20100122 0.31 0.79 2550 2436 68.94 2762.9
20100123 0.01 0.01 200 86 2.43 97.5
20100124 0 0 114 0 0 0
2 20170121 0.32 0.82 98 0 0 0
20170122 0.29 0.75 200 102 2.89 232.6
20170123 0.50 1.28 1930 1832 51.85 4177.5
20170124 0.03 0.07 918 820 23.21 1869.8
20170125 0 0 216 118 3.34 269.1
20170126 0 0 98 0 0 0
3 20170205 0 0 85 0 0 0
20170206 0.03 0.07 3400 3315 93.81 3454.2
20170207 0.02 0.04 2680 2595 73.44 2704
20170208 0 0.01 340 255 7.22 265.7
20170209 0 0 153 68 1.92 70.9
20170210 0.05 0.12 137 52 1.47 54.2
20170211 0.17 0.44 85 0 0 0

Table 5.8   Mojave river basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.55, N = 3)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0 0 0.53 0.18 0.17
2 0.28 0.64 0.25 0.40 0.40
3 0.42 0.23 0.18 0.26 0.31
4 0.19 0.08 0.05 0.11 0.10
5 0.07 0.03 0.03 0.04 0.02
6 0 0 0 0 0

Figure 5.3 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Mojave river basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.8, respectively.

Mojave basin DUH.

Fig. 5.3   Mojave river basin: Average measured vs predicted DUH.


5.1.4  Amargosa River

Following the procedure described in Section 3.1.4, three (3) corresponding event sets of rainfall-runoff data were assembled for Amargosa river. The results are summarized in Tables 5.9 and 5.10.

Table 5.9   Amargosa river basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 20070921 0.01 0.03 11 0 0 0
20070922 0.13 0.33 683 672 19.02 414.3
20070923 0.03 0.08 444 433 12.25 267
20070924 0.02 0.05 315 304 8.6 187.4
20070925 0 0 129 118 3.34 72.7
20070926 0 0 39 28 0.79 17.3
20070927 0 0 17 6 0.17 3.7
20070928 0 0 11 0 0 0
2 20080907 0.08 0.20 0.25 0 0 0
20080908 0 0 4.80 4.55 0.13 265.9
20080909 0.03 0.08 12 11.75 0.33 686.6
20080910 0 0 0.38 0.13 0 7.6
20080911 0 0 0.29 0.04 0 2.3
20080912 0 0 0.25 0 0 0
3 20100120 0 0 7.1 0 0 0
20100121 0.10 0.25 45 37.90 1.07 426.1
20100122 0.11 0.28 30 22.90 0.65 257.5
20100123 0 0 25 17.90 0.51 201.2
20100124 0 0 14 6.9 0.20 77.6
20100125 0 0 7.1 0 0 0

Table 5.10   Amargosa river basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.17, N = 2)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.43 0 0.44 0.30 0.27
2 0.24 0.71 0.25 0.42 0.42
3 0.14 0.20 0.14 0.17 0.20
4 0.08 0.06 0.08 0.07 0.08
5 0.05 0.02 0.04 0.04 0.03
6 0 0 0 0 0

Figure 5.4 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Amargosa river basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.10, respectively.

Amargosa basin DUH.

Fig. 5.4   Amargosa river basin: Average measured vs predicted DUH.


5.1.5  Petaluma River

Following the procedure described in Section 3.1.5, three (3) corresponding event sets of rainfall-runoff data were assembled for Petaluma river. The results are summarized in Tables 5.11 and 5.12.

Table 5.11   Petaluma river basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 20000220 0.34 0.86 106 0 0 0
20000221 0.47 1.19 254 148 4.19 2
20000222 0.25 0.64 468 362 10.24 4.8
20000223 0.79 2.01 343 237 6.71 3.2
20000224 0.27 0.69 166 60 1.70 0.8
20000225 0.17 0.43 106 0 0 0
2 20021218 0 0 122 0 0 0
20021219 0.04 0.10 183 61 1.73 0.3
20021220 1.23 3.12 1000 878 24.85 4.8
20021221 0.58 1.47 834 712 20.15 3.9
20021222 0.24 0.61 404 282 7.98 1.5
20021223 0 0 154 32 0.91 0.2
20021224 0 0 122 0 0 0
3 20100204 0.17 0.43 124 0 0 0
20100205 0.68 1.72 531 407 11.52 4.2
20100206 0.49 1.25 719 595 16.84 6.1
20100207 0 0 164 40 1.13 0.4
20100208 0 0 124 0 0 0

Table 5.12   Petaluma river basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.77, N = 3)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.20 0.20 0.34 0.25 0.21
2 0.45 0.45 0.46 0.45 0.45
3 0.29 0.29 0.15 0.24 0.29
4 0.05 0.05 0.04 0.05 0.05
5 0 0 0 0 0

Figure 5.5 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Petaluma river basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.12, respectively.

Amargosa basin DUH.

Fig. 5.5   Petaluma river basin: Average measured vs predicted DUH.


5.1.6  Russian River

Following the procedure described in Section 3.1.6, three (3) corresponding event sets of rainfall-runoff data were assembled for Petaluma river. The results are summarized in Tables 5.13 and 5.14.

Table 5.13   Russian river basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 19941202 0.07 0.18 1350 0 0 0
19941203 0.82 2.09 1980 630 17.83 39.9
19941204 0.86 2.18 4970 3620 102.45 229.2
19941205 0.02 0.04 2990 1640 46.41 103.8
19941206 0.19 0.48 1790 440 12.45 27.9
19941207 0.07 0.18 1350 0 0 0
2 19951229 1.07 2.72 2150 0 0 0
19951230 2.05 5.21 7930 5780 163.57 142.8
19951231 0.03 0.07 9960 7810 221.02 193.0
19960101 0 0 4080 1930 54.62 47.7
19960102 0 0 2850 700 19.81 17.3
19960103 0 0 2150 0 0 0
3 20151029 0 0 2590 0 0 0
20151030 0 0 8620 6030 170.65 118.4
20151031 0 0 11800 9210 260.64 180.9
20151101 0.15 0.38 5730 3140 88.86 61.7
20151102 0.21 0.52 4080 1490 42.17 29.3
20151103 0 0 3130 540 15.28 10.6
20151104 0 0 2590 0 0 0

Table 5.14   Russian river basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.4, N = 2)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.23 0.39 0.33 0.31 0.34
2 0.46 0.48 0.45 0.46 0.46
3 0.28 0.11 0.16 0.18 0.15
4 0.04 0.02 0.05 0.04 0.04
5 0.004 0.003 0.012 0.01 0.01
6 0 0 0 0 0

Figure 5.6 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Russian river basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.14, respectively.

Amargosa basin DUH.

Fig. 5.6   Russian river basin: Average measured vs predicted DUH.


5.1.7  Los Gatos Creek

Following the procedure described in Section 3.1.7, three (3) corresponding event sets of rainfall-runoff data were assembled for Los Gatos Creek. The results are summarized in Tables 5.15 and 5.16.

Table 5.15   Los Gatos creek basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 19971225 0 0 0.39 0 0 0
19971226 0.11 0.28 122 121.61 3.44 21.2
19971227 1.60 4.06 41 40.61 1.15 7.08
19971228 0.74 1.88 2.10 1.71 0.05 0.29
19971229 0 0 0.39 0 0 0
2 19780114 0 0 42 0 0 0
19780115 0.07 0.18 90 48 1.36 1.51
19780116 0.14 0.36 796 754 21.34 23.71
19780117 0 0 129 87 2.46 2.74
19780118 0 0 62 20 0.57 0.63
19780119 0 0 42 0 0 0
3 19780302 0.24 0.61 198 0 0 0
19780303 0.21 0.53 267 69 1.95 2.37
19780304 1.30 3.30 718 520 14.72 17.83
19780305 0.08 0.20 389 191 5.41 6.55
19780306 0 0 252 54 1.53 1.85
19780307 0 0 198 0 0 0

Table 5.16   Los Gatos creek basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.24, N = 1)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.74 0.82 0.67 0.77 0.77
2 0.19 0.15 0.22 0.19 0.18
3 0.01 0.01 0.07 0.03 0.04
4 0.003 0.001 0.03 0.01 0.01
5 0 0 0 0 0

Figure 5.7 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Los Gatos creek basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.16, respectively.

Los Gatos basin DUH.

Fig. 5.7   Los Gatos creek basin: Average measured vs predicted DUH.


5.1.8  Cottonwood Creek

Following the procedure described in Section 3.1.8, three (3) corresponding event sets of rainfall-runoff data were assembled for Cottonwood Creek. The results are summarized in Tables 5.17 and 5.18.

Table 5.17   Cottonwood creek basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 19930119 0.18 0.46 1220 0 0 0
19930120 0.44 1.12 20500 19280 545.62 124.4
19930121 0.03 0.08 13900 12680 358.84 81.8
19930122 0.01 0.03 9250 8030 227.25 51.8
19930123 0 0 4920 3700 104.71 23.9
19930124 0 0 1220 0 0 0
2 19961226 0.02 0.05 8210 0 0 0
19961227 0.06 0.15 17800 9590 271.40 59.2
19961228 1.24 3.15 32300 24090 681.75 148.7
19961229 0 0 19100 10890 308.19 67.2
19961230 0 0 9310 1100 31.13 6.8
19961231 0 0 8210 0 0 0
3 19980320 0.32 0.81 2920 0 0 0
19980321 2.01 5.11 15700 12780 361.67 89.1
19780322 0.03 0.08 14800 11880 336.20 82.9
19780323 0.03 0.08 11300 8380 237.15 58.4
19780324 0 0 8290 5370 151.97 37.5
19780325 0 0 4920 2000 56.60 13.9
19780325 0 0 2920 0 0 0

Table 5.18   Cottonwood creek basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 0.68, N = 1)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.44 0.52 0.31 0.51 0.51
2 0.25 0.12 0.22 0.23 0.25
3 0.14 0.06 0.15 0.14 0.12
4 0.08 0.03 0.10 0.08 0.06
5 0.04 0 0.07 0.05 0.03
6 0 0 0 0 0

Figure 5.8 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Cottonwood creek basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.18, respectively.

Cottonwood basin DUH.

Fig. 5.8   Cottonwood creek basin: Average measured vs predicted DUH.


5.1.9  Salinas River

Following the procedure described in Section 3.1.9, three (3) corresponding event sets of rainfall-runoff data were assembled for Salinas river. The results are summarized in Tables 5.19 and 5.20.

Table 5.19   Salinas river basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 19800217 2.19 5.57 5890 0 0 0
19800218 2.02 5.14 16300 10410 294.60 116.0
19800219 0.83 2.11 31500 25610 724.76 285.3
19800220 0.65 1.65 36200 30310 857.77 337.7
19800221 1.15 2.91 32100 26210 741.74 292.0
19800222 0.02 0.04 26800 20910 591.75 232.9
19800223 0.04 0.09 14800 8910 252.15 99.3
19800224 0 0 5890 0 0 0
2 19830228 0 0 5680 0 0 0
19830301 2.06 5.24 22900 17220 487.33 149.9
19830302 1.14 2.90 43300 37620 1064.65 327.5
19830303 0.68 1.71 59800 54120 1531.60 471.1
19830304 0.31 0.77 37000 31320 886.36 272.6
19830305 0.04 0.09 22000 16320 461.86 142.1
19830306 0.06 0.16 0 0 0 0
3 19950310 4.13 10.50 5800 0 0 0
19950311 3.11 7.91 12700 6900 195.27 76.3
19950312 0.57 1.45 23500 17700 500.91 195.8
19950313 0 0 64000 58200 1647.06 643.9
19950314 0 0 34200 28400 803.72 314.2
19950315 0 0 17800 12000 339.60 132.8
19950316 0 0 5800 0 0 0

Table 5.20   Salinas river basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.36, N = 4)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0.05 0.02 0
1 0.07 0.07 0.05 0.06 0.05
2 0.21 0.26 0.19 0.22 0.20
3 0.26 0.34 0.26 0.30 0.30
4 0.20 0.22 0.25 0.23 0.24
5 0.13 0.08 0.14 0.12 0.12
6 0.07 0.02 0.06 0.05 0.05
7 0 0 0 0 0

Figure 5.9 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Salinas river basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.20, respectively.

Salinas basin DUH.

Fig. 5.9   Salinas river basin: Average measured vs predicted DUH.


5.1.10  Shasta River

Following the procedure described in Section 3.1.10, three (3) corresponding event sets of rainfall-runoff data were assembled for Shasta river. The results are summarized in Tables 5.21 and 5.22.

Table 5.21   Shasta river basin:  Rainfall and runoff data.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Date P
(in)
P
(cm)
Q
(cfs)
Qd
(cfs)
Qd
(m3/s)
Quh
(m3/s)
1 20020127 0.11 0.03 198 0 0 0
20020128 0.03 0.08 621 423 11.97 37.5
20020129 0 0 1130 932 26.38 82.7
20020130 0 0 774 576 16.30 51.1
20020131 0 0 532 334 9.45 29.6
20020201 0 0 198 0 0 0
2 20051229 0.39 0.99 667 0 0 0
20051230 1.12 2.84 1000 333 9.42 18.0
20051231 3.28 8.33 2140 1473 41.69 79.6
20060101 0.73 1.85 1700 1033 29.23 55.8
20060102 0.25 0.64 1550 883 24.99 47.7
20060103 0.19 0.48 667 0 0 0
3 20150124 0.01 0.03 224 0 0 0
20150125 0.46 1.17 540 316 8.94 19.2
20150126 0 0 1340 1116 31.58 67.8
20150127 0 0 990 766 21.68 46.5
20150128 0 0 835 611 17.29 37.1
20150129 0 0 726 502 14.21 30.5
20150130 0 0 224 0 0 0

Table 5.22   Shasta river basin:  Dimensionless unit hydrographs (DUH).
(1) (2) (3) (4) (5) (6)
Measured DUH Average measured
Q*
Predicted Q*

(C = 1.08, N = 2)

t* No. 1 No. 2 No. 3
Q* Q* Q*
0 0 0 0 0 0
1 0.27 0.25 0.19 0.24 0.25
2 0.41 0.40 0.34 0.39 0.39
3 0.20 0.21 0.23 0.22 0.21
4 0.08 0.09 0.13 0.10 0.09
5 0.03 0 0.06 0.03 0.03
6 0 0 0.03 0.01 0.01
7 0 0 0 0 0

Figure 5.10 shows average measured vs predicted dimensionless unit hydrographs (DUH) for the Shasta river basin, obtained by plotting Col. 1 vs Cols. 5 and 6 of Table 5.22, respectively.

Shasta basin DUH.

Fig. 5.10   Shasta river basin: Average measured vs predicted DUH.


5.2  Analysis of results

For illustration purposes, Fig. 5.7 is repeated here. It is shown that all ten (10) cases studied (Section 5.1) show excellent agrement between average measured and predicted DUH. Therefore, the methodology presented in Section 3 may be used to calculate the parameters of the CLR with a reasonable expectation of accuracy, given suitable corresponding rainfall and runoff data. In practice, three infrequent rainfall-runoff events may be used to develop an average measured DUH, from which a predicted DUH may be readily obtained.

Los Gatos basin DUH.

Fig. 5.7   Los Gatos Creek basin: Average measured vs predicted DUH.


5.3  Geomorphological analysis

In this section, measured geomorphological parameters described in Section 4.3 are related to predicted CLR parameters described in Section 5.1. Table 5.23 shows the following:

  • Column 1:  Basin number

  • Column 2:  Basin name

  • Column 3:  Drainage area A (km2)

  • Column 4:  Average land surface slope S0 (m/m)

  • Column 5:  Stream channel slope S1 (from 0 to 100%) (m/m)

  • Column 6:  Stream channel slope S2 (from 10 to 85%) (m/m)

  • Column 7:  Courant number C

  • Column 8:  Number of linear reservoirs N.


Table 5.23   Summary of gemorphological and CLR parameters.
(1) (2) (3) (4) (5) (6) (7) (8)
No. Basin Area
(km2)
S0
(m/m)
S1
(m/m)
S2
(m/m)
C N
1 Campo Creek 218 0.171 0.021 0.018 1.2 2
2 Whitewater river 3,849 0.268 0.028 0.012 1.77 4
3 Mojave river 56,583 0.164 0.0038 0.00014 1.55 3
4 Amargosa river 8,315 0.151 0.011 0.007 1.17 2
5 Petaluma river 93 0.099 0.036 0.025 1.77 3
6 Russian river 3,463 0.242 0.005 0.002 1.4 2
7 Los Gatos Creek 247 0.328 0.037 0.015 1.24 1
8 Cottonwood Creek 2,435 0.255 0.017 0.010 0.68 1
9 Salinas river 11,777 0.215 0.003 0.002 1.36 4
10 Shasta river 1,737 0.196 0.041 0.013 1.08 2

Figure 5.11 shows the calculated C/N pairs for the indicated basins. In general, a lower value of N (N = 1) corresponds to a steeper basin (No. 7), while a higher value of N (N = 4) corresponds to a milder basin (No. 9). As shown in Section 3.4, hydrograph diffusion increases with the number of linear reservoirs.

C/N basins.

Fig. 5.11  C/N pairs for indicated basins.

Figure 5.12 shows the relation between DUH peak discharge Qp* and time-to-peak tp* for the ten (10) basins studied. This graph shows an increase in hydrograph diffusion with a decrease in stream channel slope (compare No. 7 and No. 9).

QpvsTp basins.

Fig. 5.12  Qp* vs tp* for indicated basins.


5.4  Modeling of unit hydrograph diffusion

Section 3.4 shows that hydrograph diffusion increases with an increase in the value of N and a decrease in the value of C. Accordingly, a diffusion number D may be defined as follows:

            N
D  =  ______  
            C
(5-1)

Figures 5.13 to 5.16 show the correlation of the diffusion number D with pertinent geomorphological parameters: (1) drainage basin area A, (2) average land surface slope S0, (3) stream channel slope S1, and (4) stream channel slope S2 (refer to Table 5.23). The results of these correlations are summarized in Table 5.24.

DvsA basins.

Fig. 5.13  Diffusion number D vs drainage basin area A.


DvsS0 basins.

Fig. 5.14  Diffusion number D vs average land surface slope S0.


DvsS1 basins.

Fig. 5.15  Diffusion number D vs stream channel slope S1.


DvsS2 basins.

Fig. 5.16  Diffusion number D vs stream channel slope S2.


Table 5.24   Summary of diffusion number correlations.
(1) (2) (3) (4) (5)
Independent variable α β R 2 R
Drainage basin area A 0.879 0.086 0.261 0.51
Average land surface slope S0 1.016 -0.317 0.106 0.33
Stream channel slope S1 0.904 -0.148 0.191 0.44
Stream channel slope S2 1.215 -0.065 0.09 0.30

Table 5.24 shows that diffusion number D correlates reasonably well with drainage basin area A, and to a lesser extent with stream channel slope S1. In a practical application, given a value of A or S1, the correlations show in this table may be used to calculate D.

Figures 5.17 and 5.18 show the correlation of the number of linear reservoirs N with the following geomorphological parameters: (1) drainage basin area A, and (2) stream channel slope S1. Given the value of A or S1, the correlation shown in these figures may be used to calculate N.

NvsA basins.

Fig. 5.17  Number of linear reservoirs N vs drainage basin area A.


NvsS1 basins.

Fig. 5.18  Number of linear reservoirs N vs stream channel slope S1.


5.5  Example application

Assume a basin of area A = 1,000 km2. Using the methodology derived herein, calculate the unit hydrograph (1 cm) corresponding to a 1-day duration.

Solution.

  1. Using Line 1 of Table 5.24, the diffusion number is:

    D = 0.879 A 0.086

    D = 1.59

  2. Using Fig. 5.17, the number of linear reservoirs is:

    N = 1.126 A 0.086

    N = 2.04

    Assume N = 2.

  3. Using Eq. 5.1:

    C = N / D

    C = 1.26

Figures 5.19 and 5-10 show the DUH and the unit hydrograph for the stated problem, respectively.

DUH example.

Fig. 5.19  Predicted DUH for the example application.


unit hydrograph example.

Fig. 5.20  Predicted unit hydrograph for the example application.


6.  SUMMARY AND CONCLUSIONS

[ References ]  •  [ Top ]  [ Introduction ]  [ Background ]   [ Methodology ]  [ Data Analysis ]  [ GDUH Model Application ] 

6.1  Summary

The present study validates the theory of the general dimensionless unit hydrograph (GDUH) using California watershed/basin data. The GDUH is a dimensionless formulation of the concept of unit hydrograph, of general applicability and of global scope. Given a basin of drainage area A, for which a unit hydrograph of duration tr is sought, the GDUH methodology provides a dimensionless unit hydrograph (DUH) which is solely based on the cascade of linear reservoirs (CLR) parameters C and N, wherein C = Courant number and N = number of linear reservoirs. The methodology is based on matching an average measured DUH with a predicted DUH.

Ten (10) suitable basins were selected in California, covering a broad range of geomorphological parameters, including drainage area, average land surface slope, and stream channel slope. Rainfall-runoff data was analyzed for each basin. Three (3) infrequent flood events were chosen, leading to three (3) unit hydrographs, from which an average measured DUH was obtained. Using the CLR model, a predicted DUH, with parameters C and N, was calculated by trial and error to match the average measured DUH.

A diffusion parameter D was defined to assist in the appropriate modeling of unit hydrograph diffusion. Since the latter increases with an increase in N and a decrease in C, a first approximation for D was taken as: D = N /C. Correlations between D and suitable geomorphological parameters indicated a reasonably good nonlinear fit between the diffusion parameter D and: (a) drainage area A, and (b) stream channel slope S1. In addition, a correlation was performed between the number of linear reservoirs N and: (a) drainage area A, and (b) stream channel slope S1. These two (2) correlations enabled the calculation of the tr-duration unit hydrograph for a watershed/basin of drainage area A.

The methodology developed in this study provides a way to link the shape of the unit hydrograph, i.e., the amount of runoff diffusion, to the geomorphological characteristics of the watershed/basin. It is noted that this objective has been at the center of unit hydrograph research for many decades. Additional applications across the globe ought to provide more information to strengthen the correlations beyond this first attempt at validation of the GDUH theory.

6.2  Conclusions

The following conclusions are derived from this study:

  1. The general dimensionless unit hydrograph (GDUH) model has been validated and tested using California watershed/basin data. The theory is conceptual, of global applicability, and may be used without restrictions across the world. Additional applications should strengthen the model's utility as a predictor of unit hydrographs based on local/regional geomorphology.

  2. In the GDUH model, the characterization of runoff diffusion may be improved using a diffusion parameter D, defined as the ratio of the number of linear reservoirs N and the Courant number C:

                N
    D  =  ______  
                C
    (6-1)

  3. Given a watershed/basin of drainage area A, for which a tr-duration unit hydrograph is sought, the GDUH methodology may be used to develop a unit hydrograph which is consistent with the theory of runoff diffusion. This study confirms the pioneering findings of Hayami (1951), which expressed runoff diffusion is terms of the geomorphological characteristics of the watershed/basin.

6.3  Recommendations

The following recomendations are offered for future work:

  1. Geographical data covering a much wider range of stream channel slopes, varying from as steep as 0.1 to as mild as 0.00001 m/m, is recommended to improve the prediction of the GDUH model.

  2. Additional applications/validations of the GDUH model will contribute to strengthen the model's predictive ability across geographical boundaries.

  3. An increase in the quantity, quality, and online availability of rainfall-runoff data across the world will contribute to enhance the quality of the validation exercise.


REFERENCES

•  [ Top ]  [ Introduction ]  [ Background ]   [ Methodology ]  [ Data Analysis ]  [ GDUH Model Application ]  [ Summary and Conclusions ] 

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