Rational Method vs OTTHYMO, Comparing Peak Discharge Rates By Alex Nichols, P.Eng.

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1 Rational Method vs OTTHYMO, Comparing Peak Discharge Rates By Alex Nichols, P.Eng. Urban stormwater management for small site is becoming more complex. All of the methods rely upon statistically derived storms representing various return rates (1 in 2 year, 1 in 50 year, etc) acting upon a study area, whose characteristics are represented by a number of variables that in some way are intended to represent the behaviour of a surface type during a storm event. However, the complexity and the end result can vary substantially from method to method. As such, a basic understanding of the differences between methods should be understood prior to their use. In order to show these differences, a comparison will be made between the (Modified) Rational Method and OTTHYMO (software model) as a way of showing the effectiveness and limitations of each method. Probably the most commonly used method for calculating peak discharge rates is the rational method. It is generally used in the design of conveyance systems such as storm sewers. For example, when designing a storm sewer system, contributing catchment areas are allocated a peak discharge rate based on area, a runoff coefficient and the local municipality s design storm (usually a 2 year or 5 year storm event).however, typically the rational method is only used for smaller areas (less than 2.0ha). There are only a few variables that must be known about a study area in order to use the rational method to calculate the peak discharge rate generated during a storm event. As a result the rational method s main advantage is its simplicity. The Rational Method equation is as follows: Q = 2.78 x C x i x A Based on the above equation, all that is required to calculate the peak discharge rate (Q, in m 3 /s) is the runoff coefficient C (a dimensionless coefficient based on the various surface types that make up a study area), intensity i (in mm/hr at a specified time of concentration) and the site area (in hectares). In southern Ontario this method typical uses storms derived using the Chicago distribution. The 2.78 is for the conversion of units. The intensity is calculated based on an intensity-duration-frequency (IDF) curve representing a particular storm event, usually in the form of: i = A / (t + B)^C A, B, and C are specific to a statistically derived storm event (i.e. 5 year event) and t is the time of concentration (in minutes). The initial time of concentration is usually prescribed by the local conservation authority or municipality and is usually given in minutes or it is calculated for large predevelopment areas using methods such as the Airport or Bransby Williams Formulas. If one wants to compare the peak discharge from a 2 year event and a 100 year event for an area with the same runoff coefficient, then calculating the i for the two events using their respective IDF curve equations is typically all that is required. Runoff coefficients lend themselves well to use in the rational method as they are a simplified representation of reality, representing a ratio of volume of runoff generated to actual volume of rainfall. This coefficient may be increased by 25% to represent a 100 year storm event. They also represent the proportion of generated runoff to total rainfall that does not change for the entire duration of any storm event. For example, a runoff coefficient of 0.25 means 25% of rainfall contributing to runoff while a runoff coefficient of 0.90 means 90% of rainfall contributes to runoff. 1 of 7

2 For large study areas or areas that require some representation of complexity, it has become industry practice that computer modeling software be used. While the main advantage of the rational method is its simplicity, for more complex or larger sites this is a disadvantage. The Rational Method, through the use of a runoff coefficient, simplifies the assumed amount of runoff that can be generated by setting a runoff coefficient for a surface with very little regard to soil type, slope and initial abstraction. While the runoff coefficient can be adjusted to better take these factors into account, it can be difficult to do so and cannot represent behaviour such as delayed peaking caused by the site s various characteristics. A good example of this is a surface s Initial Abstraction. Initial Abstraction reflects a surface s inherent ability to physically store rainfall on site. For most surface types, particularly pervious surfaces (landscaping, etc), very little runoff is generated for small frequent events as their initial abstraction is large enough to significantly reduce or eliminate runoff. In the City of Toronto for example, up to 90% of all storms can be considered small or frequent events. As a result the larger storms, which represent only a small fraction of the total rainfall in any given year, will generate any significant amount of runoff. This is especially true of large pervious areas. This behaviour cannot be easily represented with the rational method. Conversely, stormwater management models, such as OTTHYMO, don t have the same inherent simplicity in their calculation of peak flows. While these models are also a simplification of reality, they can take into account a larger variety of surface parameters to more closely represent the actual behaviour of a study area. Their disadvantage is that a fair amount must be known about an area before peak discharge rates can be determined. In some cases there are a number of parameters that must be derived from geotechnical investigations and sets of calculations based on the characteristics of the study area. There is also opportunity to calibrate the models if the real world data exists for flows, etc. When all of these parameters are correctly utilized smaller events generally generate less runoff than that calculated by the rational method and larger events can generate flows closer to or higher than calculated using the rational method. The variance between the methods are attributed to the many characteristics of a study area that are being incorporated into the model during a storm event. The differences between the two methods can be clearly seen in the following table. During smaller storms there is a considerable difference in peak flow, i.e. during the 2 year storm event the OTTHYMO model indicates that the study area would produce 61.2% of the value obtained through the use of the Rational Method. During the larger the events the two methods are closer, however, the OTTHYMO model still produces noticeably smaller flows than what the rational method produces. 2 of 7

3 Peak Discharge Rate Comparison 4 hour Chicago Storm Storm Event Rational Method [L/s] OTTHYMO [L/s] 2 year year year year year year Note: Peak Discharge rates are based on an Area = 10,000m2 (1ha), Runoff Coefficient C =0.40using City of Toronto 4 Hour Chicago Storm Events. Per the MTO Drainage Management Manual, the runoff coefficient for 2, 5 and 10 year storm events are equivalent, while 25 year is increased by 10%, 50 year is increased by 20% and 100 year is increase by 25% over the 2 year value. In OTTHYMO, STANDHYD is used with default parameters. 3 of 7

4 When calculating the required detention storage for a site, usually as the result of the need to reduce post-development flows to pre-development levels, these differences can be further reinforced. When using the rational method, in the form of the modified rational method, for determining detention volumes it is not uncommon to see considerable difference to the OTTHYMO results. This difference is largely a factor or the characteristics of the site and the differences in how peak discharge rates are calculated between the two methods. OTTHYMO generally speaking represents a more conservative (compared to rational method) and when used properly a more realistic, representation of how an area will behave in both smaller and larger storms events. As a result of this conservatism in the smaller events, the use of OTTHYMO will generally result in more storage then the simpler Modified Rational Method approach which if not used properly can underestimate storage requirements. While this may have some cost implications to achieve higher storage volumes, this required volume allows a designer to practice good engineering, to help ensure that the detention storage system being designed is not undersized and is capable of handling real world events. 4 of 7

5 Peak Detention Storage Volume Comparison 4 hour Chicago Storm Storm Event Rational Method [m 3 ] OTTHYMO [m 3 ] 2 year year year year year year Note: Peak Discharge rates are based on an Area = 10,000m2 (1ha), Runoff Coefficient C =0.40 using City of Toronto 4 Hour Chicago Storm Events. Per the MTO Drainage Management Manual, the runoff coefficient for 2, 5 and 10 year storm events are equivalent, while 25 year is increased by 10%, 50 year is increased by 20% and 100 year is increase by 25% over the 2 year value. All discharge rates are being controlled to 50 L/s. In OTTHYMO, STANDHYD is used with default parameters. 5 of 7

6 While the use of the (Modified) Rational Method is an acceptable method for calculating both the peak flows and the peak detention storage requirements for smaller sites in most municipalities or for checking larger sites, any larger area or area with complex hydraulic behaviour is best modelled using OTTHYMO or other acceptable computer modelling software. Though OTTHYMO may have its own limitations and modelling assumptions, it offers a result more in line with how the site may actually behave during an actual storm event. However, it should be noted that this is true for any kind of stormwater management modeling software or method. Modelling software during small events will typically produce less volume and during larger events it has the potential to produce more volume than the (Modified) Rational Method. It is always good when using computer modelling software to check whether the results that are being obtained are reasonable, which is something that the rational method offers as it provides a quick check for the results obtained. Despite the effectiveness in using one method to verify the other, these two methods have very different ways of calculating peak flows, even if the same IDF curve data is used, and as a result it is not always easy to compare the two directly. One is effective as a check for the other in that it can at least give a designer an idea if their numbers make sense. Even if this comparison is hard to make, when it comes to designing stormwater management systems, the tendency is to make use of the method that produces the smaller volume (due to issues with space and costs) required to control a peak discharge rate to an allowable rate. As a result, any stormwater detention system designed with that smaller number obtained by the rational method may be undersized. As this smaller volume is usually the result of the Modified Rational Method (especially in intensified urban environments), this difference only reinforces that an intensified urban environment is in many ways a more complex environment than what the (Modified) Rational Method is capable of representing. For complex environments this leaves the (Modified) Rational Method more appropriate as a checking tool to test the minimum It should be noted that while we might focus on the comparison of the results of two different calculation methods it should be noted there also can be issues with the comparison of the results using the same calculation method. This is something that is usually not considered. Most existing municipal storm sewers were designed decades ago and as a result, that there is a good chance that the IDF curve data that was used to design those old sewers may not be the same IDF curve data that that the local municipality s design manual currently prescribes. It should be noted that this may or may not lead to the system being more or less conservative. Based on our observations, most municipalities accept the following: - OTTHYMO and other modeling software can be helpful in more closely representing the actual behaviour of a study area; - The Rational Method is a quick way to determine peak discharge rates and the accepted method to design conveyance systems (storm sewers); - The Modified Rational Method can be effective for smaller sites to determine detention volume and is a quick way to check that OTTHYMO (or any other modelling software) is calculating a reasonable peak discharge rate or detention volume; - The Rational Method to design storm sewers and allowable peak discharge rates from areas contributing to that storm sewer; - OTTHYMO should not be used to calculate allowable (or pre-development) peak sewer flows; - The Rational Method should not be used to calculate (post-development) peak flows and storage requirements for large and complex sites; and 6 of 7

7 - OTTHYMO, or other modelling software, should be used to calculate (post-development) peak flows and storage requirements for large and complex sites but isn t always accepted as the correct method; Given the various preferences and limitations, perhaps the industry should find a way to reconcile the accepted uses of each calculation method. Similar to the prescriptive methods for wet pond design (MOE SM Manual), it might be time for the industry to consider developing a more prescriptive approach to stormwater management for urban sites, which can accept complexity. Currently we are usually left with only one accepted method or approach, even if there is another that may be more appropriate for the given situation. As a result, if an alternative method is more appropriate sometimes considerable effort must be used to try and justify that method and to show that it follows good engineering practice, even if its merits from that perspective are almost immediately apparent. As we move forward with stormwater management into the future, the designs will become more complex as the design criteria becomes more stringent and refined. The more time spent on trying to support or argue the merits of one method over another, less time is spent on coming up with inventive solutions to stormwater management issues. The industry is in need of an urban method, that follows good engineering practice that clearly prescribes when and where to use each method, eliminating the need to justify the use of the method for every project. 7 of 7