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#### Hydrological Theory

##### Canadian 1-Hour Storm Derivation

From the MIDUSS Version 2 Reference Manual - Chapter 7
(c) Copyright Alan A. Smith Inc.

Recent work by Watt et al (see references) has suggested a simple two parameter design storm which has a linear rising portion followed by an exponentially decreasing recession curve.  Watt et al also suggest the possibility of reversing the linear and exponential segments but this option is not supported by MIDUSS.  Figure 7-5 shows a definition sketch of this design hyetograph.

Figure 7-5 - The Canadian AES 1-hour design storm.

The parameter values which you are prompted to supply for this option are the total depth of rainfall (millimetres or inches), the duration in minutes, the time to peak intensity (minutes) tp and the decay coefficient K.  The decay coefficient K is usually in the range 5 to 7.  As with the other options, the maximum duration and the time step used are as defined in the Hydrology/Time parameters menu command.

It should be noted that the design storm as suggested by Watt et al is intended to be used for storms of 1 hour duration only, since the data used for the work was limited to this duration.  However, MIDUSS allows you to define other values of duration.  Care should be taken if suggested values for the time to peak are taken from Watt et al as these are intended specifically for 60 minute storms.

The rising and falling limbs of the hyetograph suggested by Watt et al are defined by equations [7-11] and [7‑ 12] respectively.

for   t < tp

for   t > tp

For specified values of the parameters td, tp, K and the total depth of rainfall Rtot  the peak intensity  h  (see Fig. 7-5) can be obtained as follows.

The total depth for any time t can then be obtained by integration as shown in equations [7-14] and [7-15].

for   t < tp

for   t > tp

By computing the volumes Vk  and Vk+1  at the beginning and end of a time step, the intensity during the interval is then defined by equation [7-16].

Suggested values for K and tp are shown in two tables referenced below.  These are based on data published by Watt et al.  Values in minutes of the time to peak tp are for 60 minute storms only and should not be used for storms of different duration.   The time to peak as a proportion of duration is provided for guidance.  See the topics listed below.

Suggested K values for Canadian Provinces

 Province K value B.C.(coastal region) 5 Yukon, New Brunswick, Nova Scotia, Newfoundland 6 B.C.(interior), Alberta, Saskatchewan, Manitoba, Ontario, Quebec 7

(from Watt et al - see References)

Suggested tp values for locations in Canada

 Location tp (minutes) tp /Duration Yukon 20 0.33 B.C.(coast) 28 0.47 B.C.(interior), Prince George 13 0.22 Alberta 17-18 0.29 Saskatchewan 23-24 0.39 Manitoba (Brandon, Churchill) 31 0.52 Manitoba (Winnipeg) 25 0.42 Ontario (Timmins, Thunder Bay) 24-25 0.41 Ontario (Ottawa, Kingston, Windsor) 26-27 0.44 Ontario (Toronto, Sudbury) 21 0.35 Quebec (Montreal) 27 0.45 Quebec (Val D'Or, Quebec City) 23 0.38 New Brunswick (Fredericton) 17 0.28 Nova Scotia, Newfoundland 26-28 0.45

(from Watt et al - See References)

Note: These times to peak were obtained from 60 minute duration storms.

(c) Copyright 1984-2010 Alan A. Smith Inc.
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