Methodology for Risk-Based Flood Damage Assessment David R. Maidment CE 394K.2, Spring 1999

Expected Annual Damage, D e Annual maximum flood has exceedance probability, p, 0< p <1, which measures flood severity Return period, T, of an event is given by Expected annual damage, D e, is expected value of the damage which occurs considering floods of all possible severity, p:

Annual Flood Discharge, Q The flood frequency curve, Q(p), is described by the Log Pearson Type III distribution which has parameters, , , C s ,  are uncertain) The flow frequency curve can be generated by flood frequency analysis or by rainfall-runoff modeling There is uncertainty in Q|p which can be specified by f 1 (Q|p) This uncertainty can also be expressed by alternative “realizations” of the flow frequency curve which could exist based on uncertainty in  of Q Realization p Q f 1 (Q|p)

Annual Flood Stage, H Annual flood stage, H, is the highest water surface elevation occurring during the annual maximum flood Flood stage is estimated with –flow program, HEC-RAS –rating curve at gage site Stage height has uncertainty, expressed by probability density, f 2 (H|Q) Selection of a probability level on f 2, yields an alternative realization of the rating curve H datum Q H f 2 (H|Q)

Annual Damage Annual Damage, D, is the flood damage which occurs during the annual maximum flood event as a function of flood stage, H Errors occur in structure values and elevations Uncertainty in the damage is described by the probability density, f 3 (D|H) Selection of a probability level on f 3, yields an alternative realization of the damage-stage curve H D f 3 (D|H)

Computation of Expected Annual Damage Expected annual damage Q H f 2 (H|Q) Q* H* D* For interval,dp, find damage D(H*(Q*(p*))) Integrate over p with (1) Repeat this with sufficient realizations to get stable statistics for mean D e and 25% and 75% values Generate a realization –2 random numbers for ,  for f 1 (Q|p) –1 number for “shift” in f 2 (H|Q) –1 number for “shift” in f 3 (D|H) (1) H D f 3 (D|H) p* Q* dp p Q f 1 (Q|p)

Total Expected Annual Damage for a Project Total annual damage, D T, for a project is found by summing the expected annual damages, in each reach, D i, i=1,2,…,I i=1 i=2 i=3 i=4 i=5

Summing over Floods or Reaches Summing over reaches, then integrating over the flood realizations, the total annual damage is given by: Integrating over flood realizations, then summing over the reaches, the total annual damage is given by: Corps MethodShould this method be used? Currently, the D 25, D 50 and D 75 statistics for a plan are obtained by summing these statistics for each reach

Improvement using GIS GIS-based calculation of flood likelihood and damage at each location Risk-based flood plain boundary zone p* Q* dp p Q f 1 (Q|p) Q H f 2 (H|Q) Q* H*