EARS 5 Problem Set #3 Should I invest in flood insurance? Handed out Friday 1 August Due Friday 8 August

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1 EARS 5 Problem Set #3 Should I invest in flood insurance? Handed out Friday August Due Friday 8 August One of the best strategies for managing floods is through rational land use planning. This requires an analysis of flood hazard, i.e. determining the probability that a certain land area will be flooded. You will carry out such an analysis for two houses located on River X, a river that has discharge characteristics similar to Mink Brook in Hanover. The description below will lead you through the procedure; instructions to construct graphs to be turned in and questions that must be explicitly answered are marked in bold so that you do not miss them. All graphs and tables referred to in the text appear at the end of this description. You should turn in the graphs you construct and your answers to the questions posed. Be sure to explain your answer; credit will not be given for answers with no explanation. To do such this analysis, you will need to do three things. First, you need to determine the recurrence intervals for floods of any given discharge. This requires analysis of annual peak discharge data. Second, you will need to determine the depth of water (stage) required to accommodate a given discharge. Putting this together with the first part will allow you to predict the recurrence interval for floods that will affect the two houses. Third, you will make a decision whether buying flood insurance is a costeffective strategy for the residents of the two houses. Take a look at the two plots of the stream cross section; one cross-section is true to scale (but hard to see detail) and the other is vertically exaggerated (but easy to see detail). The cross-sections show the locations above the stream where the houses are constructed. House s owner chose to have a nice view of the entire stream so positioned her house on the river terrace about 5 meters(horizontally) from the deepest part of the stream. House 2 s owner, on the other hand, was entranced with the idea of living on an island, so placed his house on a high point of land that becomes an island whenever the river stage is greater than about 3/4 meter. Note the elevations above the stream of the two houses and assume that their basements will flood if the stream height reaches those elevations. I. Flood frequency analysis In class we discussed how flood frequency is determined. Annual maximum discharge for n years is ranked from m = (greatest) to m = n (least). The recurrence interval R (in years) corresponding to a given discharge is then R = n + m Annual maximum discharge data for River X (these are real data from Mink Brook) are given in the table at the end of this description. (Electronic files of these data can also

2 be found on Blackboard under Course Documents.) Make a plot of log 0 recurrence interval (on the x-axis) versus discharge (on the y-axis); you may do this by hand or using any suitable graphing program such as Excel. Be sure to label axes and otherwise annotate the graph so anyone looking at it will be able to understand what you are graphing. This plot will allow you to estimate the recurrence interval for any specified discharge. II. Determining flood stage So called rating curves give the relationship between discharge and stream depth (stage). The stage is expressed relative to the deepest part of the stream. A rating curve is unique to a specific section of a stream because it depends on cross-sectional area and slope of the stream (which influences velocity). Below is a rating curve for River X. Based on this, what is the discharge required to flood each house? III. Insurance In its simplest form, flood insurance works like this: Suppose, for illustration purposes only, that an insurance company insures just one house, the house has a value of $50,000, and the recurrence interval for flooding that house is 00 years. If the insurance company charges the homeowner a premium of $50,000/00 years = $500/year, it is likely to break even---i.e. it will most likely collect as much in premiums before the next flood as it is likely to pay the homeowner for the 00 year flood. (This is of course not certain, since there we do not know when the 00 year flood will occur). Actually, the insurance company will do better than break even; it will make a small profit on its one-house insurance pool from interest generated by investing the premiums it collects. In reality, of course, an insurance company insures many houses of varying value and located in zones with varying flood recurrence intervals. Actuarial tables allow insurance premiums to be established so that the company makes a profit overall even if it does not break even on every house (some houses do get flooded long before the homeowner has paid in premiums an amount equivalent to the value of the house). For our purposes, we will assume that both houses are valued at $200,000 (not unrepresentative of Hanover) and that flood insurance costs $2000 per year. Based on your estimate of the flood stage required to flood each home, the corresponding recurrence interval, and the insurance premium, make a recommendation for each homeowner: Should the homeowner buy flood insurance? Or would the homeowner be better off, in the long run, self-insuring---that is, not spending money on insurance premiums but instead putting the money into a bank and assuming that he/she will earn enough to replace the home by the time a flood occurs? Explain your reasoning.

3 River X peak discharge data year discharge (cubic meters per second)

4 7 House River X cross section (vertically exaggerated) 6 height above lowest point in stream (m) House horizontal position (m) height (m) River X cross section horizontal position (m)

5 00 River X rating curve discharge (cubic meters per second) stage (m)