Here is a nice paper that describes the multifractal nature of rainfall at  temporal scales of 15 mins and 1 day:

http://www.sciencedirect.com/science/article/pii/S0022169499000530#

Another paper is by Dr. Praveen Kumar which describes how to quantify fractal behavior in hydrological processes:

http://personal.cege.umn.edu/~foufoula/papers/efg_065.pdf

I hope you find the following references useful.

Here is a nice paper that describes the multifractal nature of rainfall at  temporal scales of 15 mins and 1 day:

http://www.sciencedirect.com/science/article/pii/S0022169499000530#

Another paper is by Dr. Praveen Kumar which describes how to quantify fractal behavior in hydrological processes:

http://personal.cege.umn.edu/~foufoula/papers/efg_065.pdf

I hope you find the following references useful.

Maybe when u aggregate hydrological signals data into the different scales (…,min ,hour, day ,month, year,…), the process that occurs at the different scales get smoothed into the bigger resolution. Imagine if in the signal of a upper basin river, where fast floods are common. This processes occurs in minutes, and u can see it in the ACF, but when u estimate the ACF at monthly scale u cannot perceive it anymore, because the sampling rate is less than the natural frequency of the process. u can see in the monthly ACF, the rotation around the sun, ENSO oscillations. When u pass to bigger scales like yearly. The ACF look almost random with a short time series, but in a hypothetical scenario where u can have a pretty long series (26000 years ),you ‘ll be able to perceive in the ACF some Milankovitch cycles or solar activity fluctuation. The less process u have registered in the time series, the less complex the algorithm have to be to estimate the future state of the system. But if u don’t have process (cycles) in the time series, like in a short annual series, it will look like a total random, even if there are long period cycles into that scales. Every scale has its own process and we are limited by our measurements.

I like the task, there is meaning. However this question has to be resolved by researcher who has it. Because it is a new one.

Dear Boris can you develope your point a little more? I understood you are saying the posted question is fairly new, right?

Sorry, Efraim,

It took time for me to answer. It is interesting question, and not everybody see it as a question. One might say that fractal analysis will bring the answer (and there are few works in this directions), yes, however, to the point that it was different question.  

 It is hard to say to somebody: you have to do this or this. Just keep thinking and solution actually the methodology of research to answer this question will come. So you sounded it, you have to solve it. 

Best

Dear Boris and Efrain. Sorry if I couldn't express myself clearly, I wasn't intended to tell Efrain what to do, for sure he had been studying a lot this subject and analyzed thousand of hydrological time series, in deferents time scales. what I was trying to say is that the aggregation process is just shortening the power spectrum (that is equal to the acf), by eliminating the oscillations bellow the sampling rate. The open question is not why the acf change when scale change, the question is how it change.  Trying to explain mathematically the properties of the river (basin), and make possible to understand the complex signal that "reflect" the rainfall draining trough it. Does it maybe has to do with the power laws that nature exhibit?.  Fractal and Multifractal Brownian process,  invariants metrics of the shape of the river attractor: fractal, correlation and entropy dimension. Rivers are wonderful investigation subjects given their fractal nature. Rainfall looks like a multi-fractal, and basins have fractals shapes. So it is a vast investigation field to dig on the next years. Free sources of high resolution hydrological data and awareness of the fractal properties of nature are increasing.

Dear Felipe,

I did not criticize anybody. I like your explanations. However, it works for you. I still have my questions about the structure and general model of time series of natural event.  

Thanks Boris and Felipe for the comments about this Question. As Felipe said I have worked with several time series at different time resolution so I arises the question to see the opinion of several researchers in this field. I found that the structure of time series differs among different time scales. As a consequence hydrological analysis requires new methods accounting of that differences so several methods of hydrological design needs updates, specially if we take into account that hypothesis about hydrological and climatological stationarity does not hold any more.

Dear Boris, if there are any of your publications or works about your findings please let me know to find and read.

Efrain,

I put all my publication on my page in ResearchGate.