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The effect of runoff adaptation measures is applied in the Adaptation Support Tool (AST), a map table tool to support urban planners by indicating the effectivity of climate adaptation measures that can be applied in urban project areas.

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Separation of storm events

Small rainfall events result in filling the interception storage. Rainfall exceeding the interception storage capacity results in runoff (via SWDS) to open water. Runoff to open water results in discharge from open water to outside the model area. Runoff exceeding the defined discharge capacity of the model area results in storage in the open water part of the model area, where storage in the UWM is defined as a rise of the open water level above the defined target water level.

For determination of the SDF curves of the model area and for determination of the effects of adaptation measures we have to identify separate storm events. To this end we apply fixed periods between storage events and rainfall events. And we prefer using hourly data or even shorter intervals because of the rapid runoff characteristics of urbanized areas. By definition in the UWM, rainfall events are separated by 6 hours without rainfall and storage events are separated by a single time step without increased open water storage.

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Figure 2   Examples of generation of storm events, based on rainfall events (blue) and storage events (red). Each storm Figure 2   Determination of rainfall events (each rainfall event lies between two consecutive event separators (purple vertical lines)

In the AST, we assume that the factor described above is indeed a constant.

The steps to determine this factor are:

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Basically a new storm event starts at the first time step with rainfall after both previous rainfall and storage events are ended. This also goes in case a storage event ends the time step prior to the start of a new rainfall event (i.e. no storage at the first time step of the new rainfall event, like S9 in figure 2). Multiple rainfall events can result in a single storage event (R8 and R9 in figure 2). In case a single rainfall event results in multiple storage events, these storage events are combined to a single storm event (S8 and S9 in figure 2). Event separation lies at the start of each new storm event.

For each defined storm event the following parameters are determined:

• Total rainfall (rain depth)
• Maximum rainfall during a single time step of the event (peak rainfall intensity)
• Total runoff (runoff depth)
• Maximum runoff during a single time step of the event (peak runoff intensity)
• Maximum storage during a single time step of the event (peak storage)
• Total evapotranspiration
• Total groundwater recharge

The event definition is applied in the baseline run, in which the available time series of rainfall and evaporation are applied on the current drainage situation, without any adaptation measures applied. In the baseline run the area discharge capacity is to be set by the model user. In case the area discharge capacity is unknown, a default capacity of 3 to 4 times the average daily rainfall is advised. For calculation of the effect of measures the same event separation is applied as in the baseline run.

Note 1: In case the selected model time step is larger than 6 hours (for instance 1 day), rainfall events are separated by a single time step without rainfall.
Note 2: The area discharge capacity can either be user defined, or a default value can be applied. This default value depends strongly on the climate conditions of the modeled area. A practical value for a default discharge capacity for the base run for event separation is 3 to 4 times the average daily rainfall. In case the actual discharge capacity of the area deviates much from this practical value, it is strongly advised to apply this practical value instead.

Determination of runoff factor

Steps to determine runoff factors for adaptation measures are:

1. Separate events (is automatically done after the baseline run):
   a. Separate

   Separate

   rainfall events by six consecutive hours with no precipitation (Figure 2). Each rainfall event ends when the next rainfall event starts.
   b. Separate storage events by a single time step with no storage in open water (Figure 2). Each storage event ends when the next storage event starts.
   c. Separate combined storage and rainfall events.
   d. The same intervals are applied for the periods of the runoff events.

2. Calculate event-based rainfall depth, event-based baseline runoff depth (baseline is current situation) and event-based uncontrolled runoff depth (situation for situations with applied measure), where uncontrolled applies to measure overflow and normal runoff for the areas without measure.
3. Assign ranks to the data after arranging them in descending order of magnitude, calculate the probability of exceedance of each rank number with the Weibull formula (P=m/(N+1); where m is the rank assigned and N is the number of recordsyears) and calculate the corresponding return period T (T=1/P).
4. Plot the runoff depth against the corresponding return period for all results in a semi-logarithmic graph, where curves are approximate straight lines which facilitate extrapolation and interpolate the points (see examples in Figure 1).
5. Repeat step 2 till 4 for various retention sizes of the measure.
6. As shown in Figure 1 , for a certain runoff depth, implementing a measure reduces its recurrence frequency and increases the return period by a factor, which is approximately constant, especially within lower to medium range of the return value.The curves are approximate parallel within we observe a linear shift of the line on a logarithmic axis, especially within the lower to medium range of the return periods, implying a measure with a certain retention depth reduces the recurrence frequency of certain runoff depth and increases the return period by a constant factor.
7. value indicating a roughly constant factor. They sometimes can diverge, especially for measures with large effective depth and/or within the higher ranges of the return values. In order to make a unified representation of this factorreliable estimate of the shift (= the factor), the model calculates the average of the factors of the changes of return periods for a pre-defined set of runoff depths (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50 mm). Runoff depths that not occur (in some measures) are automatically excluded from the average.
8. The derived factor is only applicable on valid for the measure measure’s inflow area. Multiplying the return period of the normative runoff of the baseline situation , (for which the drainage system is designed, ) by the factor will result in the new return period of the normative runoff. This, however is only valid for the runoff period from the measure inflow area.
9. The return period of the normative runoff from the entire project area is derived in the AST. How this is done, is explained below in a separate section.

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In the Netherlands the normative runoff for urban areas has been defined based on a cost benefit analysis. This has been done several decades ago, resulting in a return time of normative runoff of 2 year. Therefore, we define normative runoff as the runoff event with T=2year runoff depth. From above we know that applying adaptation measures will increase the return time of the normative runoff by a factor. This is how the runoff factor for frequency reduction is defined.

Please note that the runoff frequency reduction factor is not obtained from scientific derivation, but an interesting finding from the empirical graphic method.

From measure inflow area to project area

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