The primarily inputs to the hydrologic model and the governing equations are defined so that the relationship between rainfall intensities, amount of runoff, conditions of the soil, etc. may be understood.
1.0 quantifying the risk of flooding
The standard engineering practice for quantifying the risk of flooding requires that a design storm be selected, that a hydrologic model be used to calculate the peak flow runoff generated by the design storm, and that a hydraulic model be used to calculate the maximum height of water at a particular location. Thus, three separate processes are involved; all of which involve highly subjective judgments.
1.1 Design storm
A 50-year storm has been designated by DPW as an appropriate storm to be used to assess the flood hazard in Topanga Canyon. The term 50-year storm means that a rainstorm of this intensity will occur on average only once in 50 years, or that it has a 2 percent chance of occurring in any one year. As stated in the DPW design manual [2, p 3-1]
ìUsing a 50-year recurrence interval, a frequency larger than typically used by local agencies, the Districtís major channels would be able to accept continually increasing flow demands from local development.î
The selection of a recurrence interval for a design storm is based on the consequences incurred if the design storm is exceeded, and on economic feasibility. The largest possible recurrence interval is desirable in order to minimize damage from floods, but the cost of design and building for a particular design storm must be compared with the value of the averted flood damage. The greater the consequence of the design storm being exceeded, the greater the recurrence interval should be. Conversely, for lesser consequences, a lesser design storm may be used. In situations where facilities and structures already exist, the desired recurrence interval may be reduced because of the difficulty (i.e., in terms of cost and site constraints) of designing to the desired standard (e.g., as was done in Red Rock, Appendix C, Section 1.3.4).
Rainfall intensities for the 50-year storm for the Topanga region have been defined by DPW [2]. The rainfall intensity curve used by DPW for Topanga is shown in Figure M1. Some of these rainfall intensities are listed in Table M-1.
DPWís definition of the ìdesignî or ìCapitalî storm, which is used in Topanga to define the flood hazard, is derived from the rainfall intensities of the 50-year storm, where the storm is presumed to occur over a period of four days with the maximum rainfall occurring on the fourth day. Other occurrence intervals may be used. For example, the FIRM maps used by FEMA are based on a 100 year storm, and a 25-year storm is used by the County in urban areas. The definition of the Capital storm as a four-day event with the maximum intensity on the fourth day is based on the storm which produced the 1938 flood. There is a difference between a 50-year storm and a 50-year flood because soil conditions affect the proportion of rainfall which becomes runoff. For example, a 100-year storm falling on a dry watershed can produce less runoff than a 50-year storm falling on a saturated watershed.
Findings:
The use of a 50-year return interval for the design storm that occurs on the 4th day of a continuous rain is based on the experience with the 1938 flood and represents a ìworst caseî event.
The definition of the flood hazard, applied to property owners along Topangaís creeks is based on a 50-year design storm, while in an urban areaóeven within Topanga Canyon such as at Summit Pointe (Appendix A, Section 2.1)óa 25-year design storm is used.
No cost benefit study was performed for Topanga Canyon to justify the selection of the return interval selected by the County for the Topanga Canyon design storm.
.Figure M-1. Rainfall intensity curve for Topanga (Zone M).
Table M-1. Peak intensity-duration data, M zone.
Rainfall Intensity (in/hr)Duration (Min.)10 Year25 Year50 Year5
6
7
8
9
10
15
20
25
30
40
50
604.680
4.200
3.814
3.506
3.267
3.068
2.470
2.160
1.956
1.8065.760
5.040
4.517
4.125
3.820
3.576
2.836
2.466
2.242
2.0886.540
5.900
5.357
4.913
4.567
4.290
3.440
2.955
2.652
2.44024 hours7.21 - 9.258.81 - 11.6512.01 - 15.00
1.2 Hydrologic model
The hydrologic model provides an estimate of the stream flow (in terms of cubic feet per second, cfs) at various points in the watershed. Portions of the flow model developed by DPW to model the Topanga Watershed are shown in Figure M-2. This figure illustrates how the model for the Topanga watershed is divided into many small sub-regions of generally around 40 acres. For each of the sub-regions, the features (i.e., the soil permeability, slope, etc.) which determine the amount of runoff a sub-region may generated must be defined, typically based on some overall knowledge of the area (e.g., topography maps) and generic test data (e.g., soil infiltration tests). The peak runoff, generally designated with the symbol Q, is determined individually for each of the sub-regions using the following equation:
Q = C Yen I Yen A Eqn (1)
where C = the runoff coefficient for a given combination
of soil and rainfall intensity
I = the rainfall intensity
A = the area of the sub-region
Q = the runoff in cfs, as clear water (i.e., without debris)
The Qs for the sub-regions are then combined to give the accumulated flow along various reaches of the creek.
Figure M-2. A portion of DPW hydrologic model for Topanga: the upper watershed,
mostly to the west of Old Topanga Canyon road.
Usually the computations for the stream flow are performed using a computer code. Using such a code, some results developed by DPW are given in Table M-2 for the 50-year storm. The sub-regions referenced in this table are identified in Figure M-2. The regions are located near the summit of Old Topanga Canyon Road and include Red Rock Canyon, Zuniga Canyon, and portions adjacent to Old Topanga. For each sub-region, its area, the runoff generated by the sub-region, and the accumulated runoff at the exit point of the sub-region (i.e., the summation of the runoff from this sub-region plus any upstream sub-regions) are listed in the table. For example, the table shows that the total flow at the exit point of sub-region 237 (i.e., at the mouth of Zuniga Canyon) is 364 cfs. The magnitude of the flow is primarily related to the rainfall intensity, which is based on the design storm (Figure M-1), and the runoff coefficients selected, which are intended to characterize the ability of the soil to absorb the rainfall. A runoff coefficient of one would indicate a completely impervious surface.
Table M-2. Calculated flow Q for various sub-regions in upper Old Topanga, for the
50year design storm.
Sub-regionArea of sub-region, acresSub-region flow Qr, cfsAccumulated flow Qa, cfs For site 2: in Zuniga Canyon (basin near station 237) 231 25 5454 232 35 65112 233 38 76179 234 39 92235 235 49 105318 236 38 76360 237 40 74364 For site 1: in Red Rock Canyon (basin near station 274) 271 51 193193 272 53 180348 273 30 102446 274 53 128543 275 63 177703 276 23 65723 277 49 118823
Runoff coefficients. One main area of uncertainty in determining stream flow is related to the amount of rainfall absorbed by the soil, which is defined by the runoff coefficient used in Eqn (1). Coefficients are derived experimentally for a variety of soil types which exist in the Santa Monica Mountains. Values for the runoff coefficient, as a function of rainfall intensity, for three different soil types are shown in Figure M-3. As can be seen in the figure different soil types and the amount of rainfall can have a major impact on the amount of water absorbed. In the DPW methodology, the runoff coefficient accounts for the effects of development with the following equation.
CD = (0.9 Yen IMP) + (1.0 - IMP) Yen CU Eqn (2)
where
CD = Developed runoff coefficient
(used in Eqn (1) to compute Q)
CU = Undeveloped runoff coefficient (see Figure M-3)
IMP = Proportion impervious
Typically, CD is supposed to reflect the amount of development that is expected (rather than exists) for a particular sub-region.
Effect of a burned watershed. To account for the effects of a burned watershed on runoff, the DPW design manual [2] recommends that the runoff coefficients be increased to account for the increased imperviousness of the soil caused by a fire. Where the sub-region has recently burned, Eqn (2) would change to:
CíD = (0.9 Yen IMP) + (1.0 - IMP) Yen CB Eqn (3)
where
CB = 1 - K (1 - CU)
CB = the runoff coefficient for a burned sub-region
K = the burn factor (see [2], Appendix G); = around 0.6 for Topanga
Thus, CíD reflects the effect of development and fire on the runoff coefficient.
The DPW methodology usually augments the Q computed by Eqn (1) to account for the added volume of the debris washed out of a burned watershed.
QB = B Yen CíD Yen I Yen A Eqn (4)
where CíD = the runoff coefficient for a given burned region
I = the rainfall intensity
A = the area of the sub-region
QB = the peak runoff in cfs, from a burned area
B = the bulking factor which is used to account for
the increased debris in the water after a fire,
typical values for Topanga are 1.67
For the calculation of the peak runoff, Eqn (4) would be used in most circumstances.
Findings:
DPW uses runoff coefficients based on maximum conditions of saturation, and reduces allowance for infiltration even further by increasing the coefficients to account for a burned watershed. Furthermore, as illustrated by Eqn (2) or Eqn (3) for the developed runoff coefficient, the estimated build out (i.e., proportion impervious) decreases the infiltration and produces a calculated volume of runoff that is even greater. DPW uses coefficients which represent worst case scenarios of build out, soil saturation, and watershed destruction by fire.
The worst case model, when used in a comparative study (e.g., the one cited in Appendix+A, Section 2.1), may bias the determination of the difference in the amounts of runoff generated by a developed and undeveloped property. The DPW methodology treats many undeveloped sites as little different at absorbing runoff than an impervious sites. Thus, the results of the comparative analysis would mask the consequences, in terms of flood hazard increases, of a development (as discussed in Appendix A, Section 2.1).
Without accurate methods to compute runoff, flood hazard protection can not be effectively implemented because it will not be possible to determine the efficacy of the various flood hazard reduction strategies.
The procedure used to calculate runoff in effect holds the property owner to a standard far greater than a 50-year event. DPW has combined several independent events into a single event (i.e., the 50 year storm, the use of a four day storm with the maximum rainfall on the fourth day, a burned watershed, and an amount of debris in the water equal to 2/3 the water volume). This single event has a much higher probability than one would be led to believe given the extensive use of the ì50-year design stormî label. We have estimate that this single event has a return interval of over 500 years.
Using only the Capital storm and the current DPW methodology to evaluate the effect of development is inappropriate because it over estimates the runoff of the undeveloped site, especially for unsaturated and unburned conditions and may underestimate the runoff from the developed site. A variety of storm scenarios are needed to insure that these comparisons produce representative results and can accurately determine the increases in runoff caused by development over a range of major runoff events.
Recommendations:
M1.2-1 Develop a procedure for computing ìbest estimateî values of Q so that comparison studies may evaluate the effect of proposed developments and runoff mitigation measures for a range of storm conditions (e.g., saturated and unsaturated soils, burned/unburned watershed, 1/5/25-year storms and the Capital storm).
M1.2-2 Use runoff coefficients which reflect the consequence of our proposed watershed management plan. These coefficients should either reflect what is presently the case or be lowered to reflect the mitigation efforts of the proposed plan. These efforts are described in Appendix C, Section 1.3.
M1.2-3 Develop an estimate of the actual recurrence interval associated with Countyís 50-year design storm. This is needed so that the decision makers and the public have a clear notion of the standard they are being held to.
M1.2-4 More data is needed concerning the effects on the runoff coefficient from grading, vegetation and fire.
Figure M-3. Variation of runoff coefficient with rainfall intensity.
1.3 Hydraulic model
Using the Qs developed by the hydrologic model as input, another computer code (e.g., HEC II) may be used to generate stream profiles throughout the watershed. These profiles (i.e., surface elevations for the design storm) define the limits and magnitude of the flood hazard. The key variable derived from this model is the velocity and height of the flow, which is related to the destructive force of the water (i.e., its potential to threaten residents; foster erosion; and undermine trees, roadways and structures).
2.0 EVALUATION OF dpw efforts AT QUANTIFYING THE RISK
In 1991, Dr. Dracup, an eminent researcher in the areas of hydrologic and hydraulic modeling and professor at UCLA, assessed DPW estimates of flood hazard in Topanga Canyon [3]. Dr. Dracup found several major flaws in the DPW estimates, including use of inappropriately high rainfall intensities, inappropriate run-off coefficients, and overestimation of the effect of debris on peak stream flow. Also, he pointed out that in a 1985 DPW study for FEMA that formed the basis for the current FIRM map, DPW estimated the peak flow at the mouth of Topanga Canyon at 15,200 cfs for a 100 year event, while only six years later they estimated the peak flow to be 20,600 cfs for a 50 year event. The raising of these issues by Dr. Dracup has lead some residents to question the flood hazard estimates of DPW and highlights the subjective nature of computing runoff.
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