The data of an extreme value statistic must be independent random variables. Therefore in my opinion the temporal scale is not the problem in your case but the seasonality which you have by using monthly flows as the data are autocorrelated.

Just an idea which surly is not thought to end. If you remove the seasonality is it then legal to apply standard methods like GEV to the new random data set? I am not sure if/how you can add the seasonality back to the statistics but maybe there is an easy way.

Hi Yang just as a complement to Markus answer, the statistical methods you mention are in principle appropriate for ANY time frame. The limitations are given by the the conditions (usually translated into asumptions) that your data has to meet in order for the methods you mention to give you a meaningfull statistical description. As Markus points out, this methods and the theory behind them have been developed for independent random variables. And it is traditionally assumed (with good reasons) that this independency is assured by taking only the maximum daily peak runoff of a Block (usually a hydrologic year), which is the reason why this is the variable of choice for most extreme data analysis in hydrology.

If for example you are trying to analyse the maximum accumulated rainfall for a 30 day period for a number of years, it is likely that the values are independent from year to year, therefore you may obtain MEANINGFUL (that would be my key word here) statistics from the methods you mention. You do however have to be very carefull on how do you define your blocks (e.g. Calender Years, Hydrologic Years, or some other) in order to remove seasonality effects (Markus already pointed this out). Check the file I have attached.

But you have to take in mind that the longer the time period you analyse, the more difficult it could be to sustain that your data is independent. 

In any case it would be nice to know what exactly you are trying to do, then I could give a more accurate answer.

You may consider spectral singular analysis (SSA)

Your monthly data is usually averaged or added together, so you loose the variance of your daily data. There is NO WAY you can restore the exact nature of your original dataset. Furthermore, extreme events occur in short spans of time, especially flooding and/or rainstorms. So, your monthly data is good for something else but not for what you want. But, there is always a but...There is an unorthodox way to generate a daily dataset from monthly data, using a nearby daily dataset as pivot.

That is something I recently derived for scarce rain data regions of Haiti, for a project I am working for the InterAmerican Development Bank. For each month, you simple multiply each daily value of your pivot station by the quotient of your monthly data for that month over the calculated monthly data of your pivot dataset. That quotient acts like a correction (equivalence) factor between your monthly station and the pivot station. The transformation is statistically robust and adequate if seasonal and long term trends are similar for both stations, something you can easily confirm with cumsum plots and analysis. For your extreme event analysis there is not need of when within the month the "event" occurred, but if it occurred or not and how high it was. After calculating your synthetic daily dataset, you may use University of Oregon methodology for assessing recurrence times etc.

Try it and verify it with known data before ... it's simple, fast and you know exactly the kind of conversion you are applying to derive your synthetic data, not a black box software...

The method has received good peer review and hopefully will be soon published.

As pointed out above, the time period is not an issue, but having iid data is.  For a variety of data sets, I find that removing all discernable fixed effects by multivariate regression leads to a residual time series that for practical applications is suitable for EV analysis (i have tried this for monthly temperature, rainfall and streamflow data in the Australian arid zone, for example). If the extreme is a maximum (which can always be done, by taking reciprocals, for instance), the EV theorem assures that the time series is asymptotically Weibull - I usually use SAS JMP, but R or any decent statistical analysis package will do, even EXCEL. I have typically found that almost (the upper) half of the data is effectively Weibull; but typically, for decent uncertainties on the parameters, one needs almost an order of magnitude more data than for an application of the Central Limit Theorem, for example (same regularity conditions).

If adjacent stations are combined to increase the available data, or there are reasons for regarding the data as having repeated measures, or other random effects, it is important that these are included in the regression analysis. In cases where I have estimated thousands of  random effects, it is often the case that these estimates can be regarded as a random sample from a stationary distribution, in which case the estimates must also be asymptotically Weibull. The use of both  asymptotic estimates allows some quite exquisite analyses of the original data, and the potential detection of "doctored"  data, or changes in the long-term behaviour of the time series.

See, for example, my paper:

Comparison of athletic performances accross disciplines;

a conference paper presented at AUSDM2015 (Brisbane), available for download through ResearchGate.

Study all the Januaries separately, all the Februaries separately, etc.  That makes 12 different time series, each one of length n (the number of years you've got).  If you're only interested in the wettest months (say, the wettest four), you can discard the others and end up with just 4 time series.

There is some auto-correlation in each of your 12 time series, meaning they are not really "i.i.d."  Two reasons at least for this auto-correlation: 1) Low-frequency variability in climate (precipitation and/or temperature), by which some multi-year periods have higher average runoff than other multi-year periods; and 2) A very wet year can carry wet antecedent conditions to the following year (generating a high runoff ratio in the following year), and a dry year can carry dry antecendent conditions to the following year (generating a low runoff ratio).

So, to do this right, you need to study methods that are rarely used, which account for the auto-correlation.  I would look up the publications where Armin Bunde is a co-author and study them.

If you find the auto-correlation in each of your time series (such as the series of n January streamflows, if January is one of your wettest months) to be small, you can decide to neglect it and move on with more commonly used statistical methods.

In that case, you can purchase the book by Stuart Coles (2001) An Introduction to Statistical Modeling of Extreme Values, and read the part where he explains that if the upper tail of an iid random variable is well fitted by a GEV (generalized extreme value distribution) then the peaks over threshold computed from the same data are an iid random variable well fitted by a GPD (Generalized Pareto Distribution); and that it is shown theoretically that the fitted parameters of the GPD have the same values as the GEV.  This is good because then you can use peaks over threshold to fit the GPD and that gives you the GEV parameters.

If you want to study the climatic causes for the variability you see in the streamflows, then you can make the parameters of your GPD become linear functions of climatic variables (the climatic "covariates" of the streamflows).  Then you use the monthly time series of the climatic covariates (which might be, for example, climate variability indices such as those computed by NOAA) and you fit the intercept and slope of each linear function to get parameters of the GPD that are functions of (conditional on) climate variability indices.   I believe Coles (2001) has an example of doing this in his book.

Best wishes.

Mariza

Yang,

Please have a look at these papers. There are many more in my researchgate page.

is there any way to estimate flooding for a specific return period from monthly or annual mea discharge data? It would be very useful for many regions of the world with small amount of data available.

Yes, no problem that would not get its solution

Then, most flood data are non-normal data therefore, one may research on parametric family of models to carry out the analysis or estimate