It Rains, But It Might Not Pour
In wet weather monitoring, the collection system manager steps up, metaphorically, to spin the big wheel of weather chance. Too often they will experience the agony of a wet weather flow study budget wasted when there isn't enough rain during the period that the monitors are installed. This risk is best managed by those who recognize the importance of carefully planning wet weather studies and by sharing the risk of inadequate rainfall with the flow monitor service providers.
Important questions can be answered with wet weather flow information. Modelers use actual measured system responses to rain to calibrate hydraulic models. Infiltration and inflow reduction projects require wet weather flow information to quantify the amount of rainwater that finds its way into the collection system. Likewise, wet weather flow information is used to quantify the success of rehabilitation. Overflow abatement projects require wet weather information to determine exactly what magnitude of storm produces overflows. This also becomes an important question when monitoring for discharge compliance.
Characterizing the rainfall-to-sewer-flow relationship is an exercise in sampling. As such, any conclusions are subject to sampling errors. The errors can be fatal when conclusions are based on a pitiful few number of observed rain events. But without a deliberate analysis to quantify sampling error, the victim will be unaware that what may be a major collection system management decision is founded upon a crumb of evidence, akin to playing a game of "Name That Tune" with two notes.
The prevailing procurement methods for wet weather flow studies specify a price based upon the number of monitoring locations and the number of days that flow monitors remain installed. This method works well for flow monitor service providers since their costs are a function of the number of sites and the length of monitoring period. However, this pricing scheme does not always work well for the purchaser whose value is related to the usefulness of the resulting data. The customer must place his or her bet on how many days will be required to capture enough data to support their conclusions. Betting on a short monitoring period can pay off in savings on the study but risks not capturing sufficient rain events. Betting on a long monitoring period increases the odds of capturing rain events but adds cost to the study. We see customers specify wet weather studies as short as 30 days while others specify more than a year. Many are too short. Some are too long. Few are the perfect length.
There are some general boundaries on the number of useful rain events required in a wet weather study. At a minimum, three data points are needed to fit a slope and intercept in a least-squares linear regression. The Combined Sewer Overflow Manual (U.S. Environmental Protection Agency 1993) states that "an adequate number of storm events (usually 5 to 10) should be monitored and used in hydraulic model calibration." To make a sweeping generalization, at least six good storms are desirable for creating linear models of the rainfall-to-flow-volume relationship.
Once there is an idea of the number of events needed, the next question becomes: How long monitors should be installed in order to actually observe that number of storms? The answer requires an appreciation of the rainfall patterns in the study location. Consider, for example, a wet weather monitoring project in the vicinity of the Pueblo, Colo. airport with a hypothetical objective of monitoring rains of 1 inch or more.
There are obvious advantages to conducting the flow monitoring between March and August. By combining the monthly probabilities, we can determine the odds of observing the minimum number of storms desired. For example, the probability of observing at least three 1-inch rain days in an entire year at the Pueblo airport is less than 15 percent. This begins to reveal the special nature of wet weather studies in semi-arid climates. It might require several years of monitoring during the rain season to gather enough data to characterize the rainfall response with sufficient certainty.
Another useful presentation of the rain uncertainties is the cumulative probabilities of observing a given number of system-stressing storms over time. Assuming that the flow monitoring objectives require at least eight storms with 24-hour rainfall totals of 1-inch or more. With this information, the planner can begin to quantify the cost/risk trade-offs of the project-length decision. For example, there is a 50-percent chance that it will take more than 198 days to record eight or more system-stressing storms. There is a 7-percent chance that more than a year will be necessary. As is so often the case in risk management, reducing this risk requires spending more money.
Because all of the risks are borne by the customer under conventional contract arrangements, the length of study is a "how lucky do you feel" decision. When budgets are fixed, the risk minimizing decision may be to monitor fewer locations for a longer period of time. It will usually be better to be certain of the flows in a few locations than unsure about the flows in all locations. Drawing conclusions from non-supporting data is potentially the most damaging outcome, for it is presumed from the outset that the value of the data outweighs the cost of the project.
Roughly 5 to 10 percent of our wet weather flow monitoring projects are extended or repeated due to insufficient rain. The impacts have ranged from a few thousand dollars for a short extension, to several million dollars to repeat an entire large-scale project.
Purchasers of wet weather flow data should consider contract arrangements that share the risk with the flow data provider. Large providers are in a better position to leverage the risk because they monitor in dozens of collection systems over the course of the year. They can diversify rain gambles -- "winning" on some, and "losing" on others. However, the collection system owner who might perform one wet weather study every few years will be subject to the outcome of a single probabilistic event.
Diversification is a common tactic. Portfolio theory promotes diversifying investments rather than placing all holdings in a single stock. Warranty reserves established by equipment manufacturers are based upon covering the cost of repairing a few defective products over the sale of many good products. Insurance is based upon spreading the cost of an extraordinary event, such as a house fire, over many policy holders, most of whom will not experience the event.
Under this new approach -- rain insurance -- warrants that the buyer will receive a data set that contains a specified number of rain events of a specified magnitude. It is flow data for sale on a per-storm basis instead of a per-calendar-day basis. This scheme is much more consistent with the buyer's measure of value.
The actual case illustrated below demonstrates the economics of rain insurance. To guarantee a data set with the prescribed number of storms would cost $395,569 -- 5 percent higher than the risk neutral price of $376,654. In return for this 5-percent premium, the flow-monitoring provider assumes the risk of the project taking longer than expected. In this case, the mean overrun is $88,549. While the actual premium will vary based on the flow-service provider, the point is that the flow service provider can live with a modest risk premium because they will do enough projects to average out the upside and downside of their rain predictions.
For the undiversified purchaser, the benefits may be well worth the premium. In summary, the benefits of rain insurance are as follows.
- Budget certainty -- The flow-monitoring project will cost the same regardless of how long it takes to meet the data objectives. Therefore, the buyer will have no need to reserve funds for repeat monitoring or extensions.
- Reducing the risk of an unusable data set -- The costs of basing decisions on poor-quality data can far exceed the cost of getting good data in the first place. While rain insurance does not absolutely guarantee that the data will have sufficient statistical power, it does guarantee that the data will meet a specified sample size.
- Eliminating the cost of extensions or repeat studies -- A repeat study costs twice what was planned, whereas rain insurance will incur a premium in the neighborhood of 5 to 10 percent.
There are no absolute certainties when it comes to weather prediction. As Alice Hoffman wrote, "When all is said and done, the weather and love are the two elements about which one can never be sure." But extra effort spent in planning, combined with innovative risk-sharing arrangements with flow-data providers will help protect the precious public funds earmarked for purchasing flow-monitor information. .
This article originally appeared in the May/June 2006 issue of Water & Wastewater Products, Vol. 6, No. 3.
This article originally appeared in the August 2007 issue of Occupational Health & Safety.