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I am trying to use the Curve Number Method to calculate the peak flow over an area. The precipitation is provided in a table, with the first column being the time (hr), second column being the incremental rainfall at each time (inch.), and the third being the cumulative rainfall (inch).

If I am calculating the peak flow, should I just go with the highest incremental rainfall during the period (which is 0.75 inch at 1 hr), or the highest cumulative rainfall (which is 2.25 inch.)?

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According to TR-55, here, you use total rainfall. This requires a bit more information about the watershed, namely the time of concentration (which affects the unit peak discharge). Then, from TR-55:

$$\begin{align}q_p &= q_uA_mQF_p\\ \text{where:}\\ q_p &= \text{peak discharge (cfs)} \\ q_u &= \text{unit peak discharge (csm/in)} \\ A_m &= \text{drainage area (mi$^2$)} \\ Q &= \text{runoff (in)} \\ F_p &= \text{pond and swamp adjustment factor}\end{align}$$

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    $\begingroup$ You've indicated the Graphical Peak Discharge Method; the querent is asking about the Curve Number Method. Can you clarify why you're referencing a different method? $\endgroup$ Aug 13, 2021 at 19:11
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Short answer is that you should use the cumulative rainfall in inches (to calculate runoff for each time step) and not the intensity in inch per hour for that time.

Using runoff curve number, we need to account for initial abstraction.

$$\begin{align}Q &= 0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ for~~ P \leq I_a\\ Q &= \frac{(P-I_a)^2}{P-I_a+(\frac{1000}{CN}-10)} ~~~~~~~~~~~~~~~~ for~~ P > I_a\\ \text{where:}\\ Q &= \text{runoff (in)} \\ P &= \text{rainfall (in)} \\ I_a &= \text{initial abstraction (in)} \\ CN &= \text{runoff curve number}\end{align}$$

There is an empirical equation which relates initial abstraction to potential maximum retention (which is also related to curve number).

$$\begin{align}I_a &= 0.2S\\ S &= \frac{1000}{CN}-10\\ \text{where:}\\ S &= \text{potential maximum retention (in)} \\\end{align}$$

Using these equations to replace initial abstraction in the runoff calculation, we get:

$$\begin{align}Q &= 0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ for~~ P \leq I_a\\ Q &= \frac{(P-\frac{200}{CN}+2)^2}{P+\frac{800}{CN}-8} ~~~~~~~~~~~~~~~~~~~~~~~~~ for~~ P > I_a\\\end{align}$$

You can read more here: HEC-HMS Technical Reference Manual

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