TUFLOW Forum

# Joint probability and time to peak

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There are some guidances available on estimating the joint probability storm events occuring on combined systems (eg. main river and tributary have a joint probability of 2year to 100year). However once the joint probability on the storm event is decided, I am finding it difficult to decide on the coincidence of the time to peak as the catchments would have different time of concentration.

Also because the smaller system(tributary) could peak earlier in relation to the larger system (main river) leading to a two peak scenario thereby resulting in a short duration peak water levels which may not be the worst case flooding situation in the catchment.

Should we manage to forcefit the peaks to occur at the same time on both systems which could be unrealistic (eg. worst case approach) or left to appropriate time to peak for the individual systems?

Any guidance for best practice approach or previous experiences on this topic will be really helpful.

Thanks

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There are some guidances available on estimating the joint probability storm events occuring on combined systems (eg. main river and tributary have a joint probability of 2year to 100year). However once the joint probability on the storm event is decided, I am finding it difficult to decide on the coincidence of the time to peak as the catchments would have different time of concentration.

Also because the smaller system(tributary) could peak earlier in relation to the larger system (main river) leading to a two peak scenario thereby resulting in a short duration peak water levels which may not be the worst case flooding situation in the catchment.

Should we manage to forcefit the peaks to occur at the same time on both systems which could be unrealistic (eg. worst case approach) or left to appropriate time to peak for the individual systems?

Any guidance for best practice approach or previous experiences on this topic will be really helpful.

Thanks

Hi Waterman,

Choice of design storm duration can be fixed through 2 sets of sensitivity tests- utilising same storm duration for individual simulations (say Q100). Check the results that gives you higher water level at your site. It's not a best practice to use seperate storm duration in one simulations. You may find that use of storm duration for tributary and constructing hydrograph for main river gives you the worst peak WL at your site. However, you need to use one storm duration for constructing both the hydrographs for one simulation and repeat the exercise with another storm duration in teh same way to evaluate teh outcome from sensitivity tests.

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Hi Waterman,

There are a lot of different techniques out there. For urban or stormwater flooding, where you are focused on one local catchment, I find most use a similar approach to that which you indicated. Ie, for a localised short duration 100-yr flood, a lower ARI event is used for the receiving water-body. It follows the principle that for a localised short duration rainstorm, there is often some amount of regional rainfall which elevates tailwater levels downstream.

For localised flooding, one method I use is to take the rainfall intensity for the local catchment, and multiply it by the TOC or critical storm duration to calculate your rainfall depth. Then for the receiving catchment or waterbody downstream, calculate its TOC or critical duration, and divide the same rainfall depth by this timeframe to determine which storm to apply downstream.

For example, if a local catchment has a TOC of 50 minutes and the 100-yr ARI intensity is 100mm/hr, the rainfall depth is 83 mm. The TOC for the receiving waterbody is 4 hours. 83 mm over 4 hours gives an intensity of 21mm/hr to be applied to the downstream catchment. When checking your rainfall chart you might find 21 mm/hr at 4 hours to be a 2-yr, 5-yr or even a 10-yr event. It depends purely on the relative TOCs of the catchments and not a fixed rule of thumb. The Queensland Urban Drainage Manual uses this approach among others, where the most conservative approach should be adopted (see Ref 1 below).

Practices in floodplain modelling are quite different. Here you are modelling possibly many rivers and tributaries. Using the above approach would be incredibly time consuming, as you are not conveniently working on just one catchment or system but many. Running through a series of stacked storms, taking an envelope of the maximum water levels and discharges (as described in Mouludul’s post) is the normal approach. This method is also described in Ref 1 as it is easily applied to a local catchment study.

I have found that many authorities use a table similar to that in Ref 2 below. The first problem with this table is that it is based on the ratio of catchment areas between the local catchment and the receiving waterbody. It is possible to have two catchments of the same area, but quite different response times. The coincidence of flooding between adjacent catchments is a function of response time, not area. The second problem I’ve found with this table is that it seems very conservative when applied to some locations.

Cheers,

Paul Ollett.

Ref(1). Queensland Urban Drainage Manual (2007). Coincident Flooding – Section 8.03.4 (page 8-6)

Ref(2). US Federal Highway Urban Drainage Design Manual. Frequencies for Coincidental Occurrence – Table 7-3 (page 7-9)

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PS.

In reading your post again, the question is raised on whether to set both the tributary and receiving waterbody to peak at the same time. If the receiving waterbody experiences some longer duration rainfall, it will be high for some time. The storm-burst for the tributary could really occur at anytime (you can’t put Mother Nature in a box); so if the receiving waterbody is already high-ish, I would tend to make the peaks coincide. Carry out some sensitivity analysis where you stagger the peaks to see what happens. Every system will respond differently. Ultimately you should take a Risk based approach. If the consequences (potential loss of life and/or property damage) are potentially high, then definitely take the conservative approach. There will be other factors outside of modelling that will help you decide.

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