Background for Flood-Loss Reduction Studies

Flood-frequency functions developed following procedures described in the Flood Frequency Studies provide quantitative information about the risk of flooding in a watershed. If the flow-frequency functions are combined with rating and elevation-damage information, expected annual damage can be computed. This computation is the foundation for assessment and comparison of the effectiveness of flood-loss reduction plans. This chapter illustrates how HEC-HMS can be used in the context of such a study.

Authority and Procedural Guidance

USACE activities in flood-loss reduction studies are authorized by:

• The Flood Control Act of 1936.
• Section 206 of the Flood Control Act of 1960.
• Executive Order 11988.
• Section 73 of Public Law 93-251.

In addition to technical guidance identified in earlier chapters, relevant USACE guidance for hydrologic engineering analyses in flood-damage reduction studies includes:

• EP 1110-2-10 (USACE, 1994) provides an overview of flood-damage reduction studies and describes the basic principles of the analyses required throughout a study. It addresses the role of various computer programs in those analyses.
• ER 1110-2-1419 (USACE, 1995) identifies possible damage reduction measures and summarizes typical hydrologic engineering studies required for formulation and evaluation of each.
• EM 1110-2-1619 (USACE, 1996) describes procedures for decision-making under uncertainty - a requirement for all flood-damage reduction studies. It describes how, for example, the impact a lack of gaged flow data has on the frequency function and proposes how this uncertainty can be modeled and accounted for in planning.

Study Objectives

Flood-loss reduction studies are typically undertaken to find the optimal plan to reduce flood damage for a particular watershed - in this case, the optimal plan is the plan that yields the maximum net benefit. As described in EM 1110-2-1419 (USACE, 1995), net benefit, NB, of a proposed plan is computed as:

$//<![CDATA[ \begin{array}{l}\big(4\big) \hspace{5cm} NB = B_{L}+B_{I}+ \big(E[D_{without}]-E[D_{with}]\big)-C\end{array} //]]>$

where:

B_L= annual equivalent location benefit of the plan;
B_I = annual equivalent intensification benefit of the plan;
E[D_without]=EAD in the watershed without the plan;
E[D_with]= EAD with the plan in place;
C= annual equivalent cost of implementing, operating, maintaining, repairing, replacing, and rehabilitating all components of the plan.

The without-plan condition represents existing and future conditions in the absence of the plan, and the with-plan condition represents conditions if a damage reduction plan is implemented.

EM 1110+2+1415 (USACE, 1993) describes how the EAD for an urban area, both without and with a plan, is computed by integrating the appropriate annual damage-frequency function. The damage-frequency function with a rating curve (relationship of flow and elevation), thus yielding an elevation-frequency function. This, in turn, is transformed with an elevation-damage function, yielding the required damage-frequency function.

The flow-frequency, flow-elevation, and elevation damage functions used in the EAD computation are not known with certainty. For example:

• Uncertainty about future hydrologic events and watershed conditions, uncertainty regarding the choice of a statistical distribution, and uncertainty regarding values of parameters of the distribution lead to uncertainty about the frequency function.
• Uncertainty that arises from the use of simplified models to describe complex hydraulic phenomena, from the lack of detailed geometric data, from misalignment of a hydraulic structure, from material variability, and from errors in estimating slope and roughness factors leads to uncertainty about the rating function.
• Economic and social uncertainties, including lack of information about the relationship between depth and inundation damage, lack of accuracy in estimating structure values and locations, and lack of ability to predict how the public will respond to a flood, cause uncertainty about the elevation-damage function.
• Uncertainty about structural and geotechnical performance of water-control measures when these are subjected to rare stresses and loads caused by floods, cause further uncertainty about flood elevations. 

Traditionally in USACE planning studies, these uncertainties have not been considered explicitly in plan formulation and evaluation. Instead, the uncertainties have been accounted for implicitly with factors of safety and freeboard. EM 1110-2-1619 (USACE, 1996) now calls for explicit acknowledgement and description of uncertainties and for quantitative risk analysis in the EAD computation. In simple terms, a description of uncertainty in each of the functions is included in the transformation and integration. Such a distribution might reveal, for example, that the probability is 0.05 that the error in predicting the 0.01 probability discharge is greater than 500 cfs.

With such a description of the error or uncertainty, a description of the uncertainty of the EAD value can also be derived, reported, and weighed in the decision making.

The following table lists damage reduction measures, both structural and nonstructural, and shows how each will alter the frequency, rating, or damage function. Complex plans that include multiple measures will alter more than one of the functions. The impact of measures that alter the frequency function can be evaluated conveniently with HEC-HMS. Evaluation of the impacts of others may require use of other software that is listed in the Other HEC Software that can be used Along with HEC-HMS to Perform a Hydrologic Analysis table.

Damage Reduction Measures and their Impact

Study Procedure

The study procedure is straightforward:

1. Develop the without-plan flow-frequency function, including a description of the uncertainty. HEC-HMS may be used to develop the function.
2. Combine that frequency function with the without-project rating and damage functions, which are also known without certainty. Computer program HEC-FDA can be used for this combination and computation.
3. Select one of the proposed plans and develop the with-project frequency function for that condition, including a description of the uncertainty.
4. Combine that frequency function with the with-project rating and damage functions and compute the with-project damage frequency function, including a description of uncertainty, and EAD for the plan.
5. Determine intensification and location benefits, the cost of the plan, and the net benefit.
6. Compute other indices of plan performance, following guidance in EM 1110-2-1619 (USACE, 1996).
7. Repeat Steps 3, 4, 5, and 6 for all other proposed plans.
8. Compare the results to select the optimal plan.

Note that these steps require significant interaction amongst members of the study team: hydrologic and hydraulic engineers will provide the frequency functions, economists will provide the elevation-damage information, and cost estimators will provide costs of construction.