Coefficient of Determination and Nash-Sutcliffe Efficiency are based on least squares so give greater weight to the peaks. A high CoD can indicate the peaks fit well but not the recessions. You can get a better idea of the fit of the recessions by taking logs. There are other measures you can use if you trawl through the literature however I used a combination of NSE and logNSE to indicate the fit of my models when working on my PhD. However what value to pick is a very good question - the answer to that is dependent on so many factors and is often a case of as good as you can get given the uncertainties involved. Good luck. It is probably good practice to determine your limits of acceptability before you start to model then throw out any models that don't comply - again trawl the literature particularly the work of Keith Beven.

R ^ 2 is not a good indicator because everything that uses the sum of the squared residuals supposes independent and identically distributed uncertainties (not residuals!), Which, we know, is not the case.

Please refer to the following link and the attached file for more details.

https://www.researchgate.net/post/How_do_we_verify_that_a_hydrological_model_is_a_good_model2

Regards

Thanks prof Bachir Achour for all this information, but the 2nd link is not valid, it's a link from a file in a local folder.

Kind regards

Dear Mourad,

Sorry! I've attached the file in my previous comment.

Regards

No problem, thank you prof @bachir achour for your kidness

Kind regards

It is not the coefficient of determination that validates the hydrological model.

Maybe you mean the correlation coefficient. l model. For this coefficient, the minimum acceptable value for validating the hydrological model depends on the significance level (α=5% or 10%) chosen.

coefficient of determination is not a good indicator for validating hydrological models since the relationship between the climatic variables is not always linear. hence, it is recommended that the error values are calculated. non-linear error function remain the best indicator for validation

Coefficient of Determination and Nash-Sutcliffe Efficiency are based on least squares so give greater weight to the peaks. A high CoD can indicate the peaks fit well but not the recessions. You can get a better idea of the fit of the recessions by taking logs. There are other measures you can use if you trawl through the literature however I used a combination of NSE and logNSE to indicate the fit of my models when working on my PhD. However what value to pick is a very good question - the answer to that is dependent on so many factors and is often a case of as good as you can get given the uncertainties involved. Good luck. It is probably good practice to determine your limits of acceptability before you start to model then throw out any models that don't comply - again trawl the literature particularly the work of Keith Beven.

Thanks dear profs: Bachir Achour, Benali Benzater, Rudolph Ilaboya and Ann Kretzschmar for all informations and answers

Kind regards

Mourad

You may find very useful info. in this article.

https://elibrary.asabe.org/abstract.asp??JID=3&AID=23153&CID=t2007&v=50&i=3&T=1

For model fitting to data, the p value corresponding to a given value of adjusted (by number of regression-fitted parameters p) R^2 is a function of n , the number of data points (= number of model simulated points). You can find the standard well-accepted formula for this on-line, together with conditions under which the formula is valid (e.g., normal or near-normal distribution of residuals, etc.). I googled this about a decade ago; should still be available on-line.

Dear Mourad ,

As, all the previous answer mentioned, coefficient of determination is not the best measures to validate the hydrological model, I agreed with this. I just wanted to focus on a very basic point i.e. if the optimisation criteria is NSE, we should validate the model with NSE values not with coefficient of determination.Based on NSE values, you can identified the performance of the model(good/bad).

Two points. One, use not just one parameter, but as many as possible to evaluate model performance. Two, think about the purpose of your modeling.

Hi Mourad,

As Ferdous Ahmed mentioned, the objective of your modelling study is very important when selecting one or more objective function(s). If your interest is particularly in high flows, you might select an objective function at least incorporating the differences between observed and simulated high flows in some way. If your interest is in low flows, very different objective functions should be used, for instance logNSE as Ann Kretzschmar mentioned.

For NSE it is difficult to give a threshold value for acceptable model behavior. Since the squared difference between observed and simulated values is scaled with the observed variability within NSE, its value is dependent on the natural variability (of streamflow). Hence, for catchments with more natural variability it will be easier to obtain higher NSE values than for catchments with less variability.

A good alternative for NSE is the Kling-Gupta Efficiency (KGE), see Article Decomposition of the Mean Squared Error and NSE Performance ...

Good luck,

Martijn

Just as a follow up of Martijn Booij's comment, some of the commercial models such as Mike11 NAM of DHI allow the use of high flow, low flow or the entire spectrum of flow for calibration. I found this feature very useful.