It is OK to try to make a model with some missing data that you have estimated using a variety of standard type options to do this as long as you document what you are doing and list its potential limits, etc.  I did not necessary follow you on some things like synthetic data.  If you have model based on real data with a few quality controlled estimates on all or good quantifiable supportable values with time, sure a model may help determine relationships or predict or forecast change.  However, if the max rainfall is 250mm in your data, don't expect perfection if you have a storm outside of the boundary with 350mm.  A prediction may be reasonably good, or not.  Sometimes we try things and they work out great, and other times not so good.  But you have the basic elements of the water balance, so you should be in the ballpark as we say sometimes.  As you know, rain can have a lot of spatial variability, and evapotranspiration is not always easy with vegetation and land use changes.  I assume by runoff you mean a recording stream gauge of water entering the lake, and groundwater a good geology map and some wells measuring shallow and deep groundwater.  Don't go adding a bunch more monitoring or data collection points yet, before you try it, but if you come up with abnormalities such as huge losses or entries you cannot figure out, you may have to go to added measures to find out what is happening.   

 Thanks William

Actually, I am not focused on short intervals like Daily, Hourly etc. and for me it is not important to track extreme events like peak floods.

My shortest interval is monthly average values such that they would be used directly or by multiplication with some coefficients in calculation. But the main question is, if statistical models like regression could be done on this type of data. Cause, we are transferring the main statistical properties of data for the next generation of data. Thus, if our model(s) got high R square it is doubtful if it is alright to accept that model results as a well calibrated model.

note: I mean, we previously made some linear and/or nonlinear relationship that may cause in misleading of the model results such that it makes us believe that the model is sufficient but it is not.

Thanks for the PDF, actually one of my main concern is about regeneration of groundwater data (specially for the past). It should be regenerated with respect to lake water level, because it is a coastal aquifer and the lake is a hyper-saline one.

Thankfully

Babak

Hi Babak

I worked on monthly raifall data in Morocco and questioned the problem of the impact of reconstructed values on the persistance of the climatic signal.

It is presented and discussed in these papers.

We found that the major signal is preserved on the reconstructed time series but there are many differences for signals of medium and low frequency 

Hope it is useful

Conference Paper Evolution des relations pluie-débit sur des basins versants du Maroc

Article Evolution of rainfall-runoff relationships in 27 watersheds in Morocco

William,

Thanks for the Pdf but I'd rather working on time series and there is not any detailed information about ground and porosity.

Gil,

Thanks for the PDFs. unfortunately I am not good at reading french!. Anyway, I used a mixed technique of decomposition (Frequency Domain) and time domain analysis cause I need to do some data reconstruction for the past as well as for the feauture. Then I checked for the similarities of patterns and moments of the distribution. For example you can see the similarities of Moments, seasonal Average and standard deviation, auto-correlation, partial auto-correlation and time series of observation versus validation for a runoff time series.

I send you another paper in English where we even reconstructed daily rainfall data .

It is always better to keep close to the observed variability.

Thanks for sending your analysis.

Gil