The peak data analyses are done on instantaneous peak data, either annual peak or partial duration peaks similar to POT approach.  There are various books that describe these approaches in more detail, such as Handbook of Hydrology, Chow, 1964..  The annual peak series is often used because it is easier to use and explain, but in doing so, some of the detail is lost such as when you have multiple severe floods in one year, the partial duration series would pick up that detail for analysis.  But generally if your goal is perhaps the 100 year storm estimate, either one should give similar results if you have enough data.  

If all you had was mean daily flow, it would be some work to try to convert that to instantaneous peak values from the day(s) with maximum flow.  The USGS collects streamflow data at 15 minute intervals, 96 readings per day in attempts largely to capture form and shape of stream hydrographs.  If you are in snowmelt driven systems, changes are not as abrupt as rainfall driven such as from thunderstorms and cyclonic events.  Warm rain on snow events can be some of the most severe.  

If you have any stream gauging stations with detailed and long term records within your physiographic data of same climate, you may be able to compare your mean daily data with the other station data, and come up with comparison factor to apply to your data to help estimate instantaneous peaks.  There may be time and drainage size differences between two watersheds or basins, so the peak daily flow may not always be the same day on both, even though it was one storm, and also that rainfall is not always well distributed across the landscape, and that is another problem in comparing two systems.  But on the nearby system, if you found that from 30 individual annual peaks, the mean daily flow was 30% of the instantaneous peak, that might be useful to consider.  Of course, if your drainage area is significantly less with flashy response, the mean daily flow might be 25% of instantaneous peak, or if the drainage area is much larger, the value may be 40%, as the peak is not so sharp and spread out over longer duration.  These are not true values, just conceptual.  

If you have detailed rainfall intensity information, you may be able to use that to help reapportion daily flow data back to something that better represents instantaneous values (perhaps using the Unit Hydrograph approach might be helpful to do this).  If you have historic flood marks of severe floods on building, elevations, etc. you maybe able to use that information in trying to estimate peak flows.  Even with some issues to address such as sediment fouling, with the limited expense of transducers today (vented, unvented adjusted by barometric pressure) and ease of install, ability to get detailed time series water levels, which would help substantially in making these calculations, even if your stage discharge relationship is not well developed.  

Also recognize that there are errors in measurement, etc. to consider, even with the best of data.  The annual series of instantaneous peaks is probably the best to use in that it is what others tend to use with the long duration data sets.  For shorter duration data, with ample storm data frequency, the partial duration series may be helpful.  

There are quite a few good books and papers on various aspects of this subject area and analyses possible.  I would suggest that also some of the quality of analysis may also come from experience and ability to understand the individual circumstances, inherent errors and difficulty of measurements or estimates.  Locations of measurement and analysis where streams are actively aggrading or degrading, or have been modified by structures or channelized can have some of their own complexity.  Even with stream stage frequency of 15 minute intervals such as USGS, the instantaneous stage estimate for smaller streams may need to be determined by interpretation and curve fitting.  

POT or AMAX?

From a statistical point of view, I would use POT only if the maximum values can be seen to be iid (independent and identically distributed). This is certainly not the case, if all the extracted maxima belong to one event only. So, please check the maximum values for iid first. However, if you use the AMAX, the maxima can be assumed to be iid, at least there should not be a temporal autocorrelation!

Another suggestion would be to use both, fit the extreme value distributions and compare the results.

Very much appreciate the thought provoking answers so far. To focus on one more specific detail: if the flow data was generated by a rainfall-runoff model with a daily time step then obviously that represents the model estimate of daily mean flow as the input would be daily rainfall totals. Therefore, extracting AMAX/POT series from the rainfall-runoff model output would unfortunately be basing the flood frequency estimation on daily mean flows rather than instantaneous peak flows. Using the paper from William's link, it seems it could be possible to convert mean daily flows to an estimate of peak daily flows using something like the Fuller equation and the catchment's area - but this seems very uncertain. Is it simply not possible to get flood frequency curves unless you have access to high frequency flow data? Is a flood frequency curve based on daily mean flows at all useful?  

I am currently doing something similar , also based on daily mean values. Of course, you underestimate the magnitude, but it is better than nothing.

It also depends a lot on the catchment size and river. For very big rivers, the differences between the mean daily values and the instantaneous peak flow values should not be too large. 

So, yes, I think flood frequency curves based on daily mean values are useful!

Cheers, Patrick 

I would suggest that you carefully consider how the results are to be used, before looking for an answer to your question. Your problem is already tricky because it appears your data is generated from a Hydrologic Model. Which model? Is there an attempt to validate or calibrate? Is a physics based model or a parameterized model? In terms of how the results are to be used, consider the following. If the results are to be used for some type of planning project which includes public/private property, infrastructure, etc., then using MDF for a FFA is dangerous, and not useful. However, if you are interested in the general statistics of MDF, then either a simple flow duration curve, or the focus of this post, FFA, would provide useful information about the data series. It is possible to upscale MDF to an ESTIMATE of maximum daily, or even instantaneous peak IF you have actual data to drive the upscaling. The upscaling commonly occurs through identification of a peaking factor. Dig around in hydrology books and you will find reference to this. I should say though it is more common to apply a peaking factor the maximum daily flow, as opposed to the MDF, the thought being that the maximum daily flow timing was in phase with the instantaneous peak. In summary, carefully consider how the data is to be used, its quality and how it was developed, before thinking about how to use technical procedures to characterize your data.

This is all very interesting.

It seems to me that the crux of the issue is as follows:

• According to extreme value theory, the AMAX or declustered and iid POT series should be based on instantaneous maximum flows;
• It's not possible to measure instantaneous maximum flows so these have to be approximated using sampled measurements;
• The faster the sampling, the better the estimate of the instantaneous peak flows will be;
• In countries with good sampling networks it is possible to get estimates of instantaneous peaks based on 15 minute sampling;
• The underlying sampling rate is not always communicated when expressing flood frequency estimates;
• Substituting daily mean for instantaneous peak daily flow is far from ideal unless you want an estimate of flood frequency for mean daily flow;
• The difference between mean and peak daily flows decreases as the catchment gets larger or the flow variance reduces (for example gradual snow melt);
• It could be possible to estimate instantaneous peak flow from mean daily flow using a Fuller-type relationship such as Qmax=Qmean(2 x area-0.3 + 1) but this would need considerable calibration and testing;
• Obviously any flood frequency analysis based on model output is only as good as the underlying model;
• The model would need to produce flow estimates at a suitable frequency such that an estimate of instantaneous peak flow can be derived, this would require the same frequency for the precipitation input,
• When producing flood frequency curves, it's important to communicate the details of what data was used for the process; finally a question,
• The duration that a design flood can be expected to exceed the stated return period is very rarely given. I would have thought a flow that momentarily exceeds a given threshold will be less damaging than a flow that stays above the threshold for several hours?

There are more issues of course! Many thanks for the fruitful discussion. It's helped me to think through this issue. Please add any more thought if you have any. 

Dr. Dave Rosgen from his extensive work has suggested that for those who know how to read and determine bankfull flow elevations for streams, 2 times bankfull at thalweg has good relationship with approximately 50 year event stage.  I am sure he would not use this for critical needs to protect the public/property from damage, but I have used this on occasion to help suggest flood level and cross section dimension at a flood stage.  It also  helps suggest if stream such as a gully is entrenched (ie, does not have ready access to its or a significant floodplain, or in other words has a terrace rather than a floodplain).  I would suggest anyone become very familiar with his work and measurement detail and avoid just looking and perhaps taking a few quick measures.