I would suggest that yuu use real stream gauging data to compare models if you have available to you from water agency or University studies.  If you had a number of stream gauging stations, from different physiographic regions, more comparisons would be better than just one to see how models function under varying circumstances such as mountains, hills and coastal plain. How models function at different hydrological scales may also be useful to know.  I think I would stick with relatively undisturbed catchments or watersheds to start, with limited hydrological modifications such as dams, diversions, etc. and then progress if desired to others with degrees of land use change such as urbanization, etc Watersheds with dams, diversions, channelizations can substantially alter flow responses, etc. and are likely to add stress into any model function.  I would avoid interjecting these problems into evaluating how the basic models function.  You could make this as big or small as your project and time allows.  Present graphs of the actual stream measurement data and each model results over a period of time when there are low, moderate and high flows to see how model functions during several ot many storms, hydrographs.  You may want to also develop various tabular comparisons among the models with the real data, such as comparison of time to peak flow, peak flow, recession curve slope with time, baseflow, water yield, correlation coefficients comparing model with the actual data, etc.  If doing multiple stations of real data, each real data station would be an example to present in graph and tabular forms to compare model functions in that circumstance.  The details of each one developed would present the circumstances known, such as catchment or watershed size, land uses, geology, valley/stream type (eg. Rosgen system of classification), gradient, sinuousity, etc.) and any other factors you may want to present to highlight differences.  There may be other or fancier ways to compare data, and some might relate to your specific problem (such as a need to predict peak flows) but these should be a good start.  The visual comparison by plotting the real data over time with each model may say enough in some instances.  You are likely to need log scale graphs of streamflow with time to show comparison detail during low, moderate and high flow periods.  To me, the well presented graphics can tell your story, as many say a picture is worth a thousand words.  I added a visual comparison of stream gauging stations in one vicinity, the first plot shows differences during seasonal thunderstorm period with more localized rainfall and response, and then period when storms are more widespread, affecting all stations as the storms pass over the land.  You can see the differences in units to normalize flows by area with time and present the actual flow detail with log scale graphs.  During peak flow periods, these streams presented would flow over 10,000 cfs, so you can see the advantage of using the log scale if you have high flows to include, but need to also show low flow detail.  

Its very pleasing and educating kind of thoughts and words from  william, which reflects the true physics in back ground, which is inevitable to get understand before switching over to said multi objective functions and their applications/solutions. Yes Stream order and catchment order , can never be avoided at this juncture, so will have to be given a space while framing data and its analysis/churnings.

Hence Florian , You need to give a deep thought , to make your  visionary end product as of more worth and physical significance for real predictions..

All the best .. 

Thanks for the detailed answers. For my models I am using discharge data from the Fulda River in Germany. A moderately sized catchment in Hesse. To visualize the results of the simulated discharge I think I will plot the measured streamflow data together with the upper and lower bounds of all behavioural runs to adress the uncertainty of the predictions (see attachment, sorry for the low resolution). The idea to use a log scale is very good as well and I will try it out.

But the most difficult problem for me so far is to visually compare the values of the three objective functions (logNS, pbias, RSR). As descriped above I already tried using a three dimensional scatter plot but this was not a very good way to display it. I am now thinking about using a spider web plot (see the imgur link). On every axis would be one objective function. This way one could see tradeoffs between the three objective functions. But I am still wondering if there is a better way to visualize it.

https://i.stack.imgur.com/Gr4QN.png

Thank you Ina for your answer. I now settled for the spider plot and was able to make a figure that seems quite comprehandable. I will look into the topic of flow duration curve and if I can add it to my thesis.

comparison of performances of structurally different models can be achieved through an analysis of their residual series on a selected set of validation events (which were not used in the model calibrations). Some years ago in testing the adequacy of a multi-model approach applied for the purpose of flood forecasting I have used to test instead of series of residuals the behaviour of the cumulative series with visualisation of so-called elipse of homogeneity test (Bois, 1976). For more details see Cunge et.al (1992) http://link.springer.com/chapter/10.1007/978-94-011-1630-5_20.

Thanks for your answer Marc. Your approach seems interesing as well, but sadly my university does not have access to the sources you mentioned. Do you have other sources for the topic, not hidden behind a paywall?

I also now tried out the flow duration curves with the results of my model and I am pleased with the results. The graphics allow a new insight for me into my models.

Hi Florian, I would agree that normalizing the fit score such that 0 is a perfect fit and 1 is equivalent to the score you would get if you just used a flat line at the mean of the series, then producing a spider plot will give a good visualization of the results. If you are using, or are familiar with, R software, then there is a package called ggradar that extends the excellent ggplot2 plotting package. While on the subject of R packages there is also a nice package called hydroGOF that calculates approximately 20 acknowledged hydrological goodness-of-fit measures. Also useful is the package hydroTSM (by the same author Mauricio Zambrano-Bigiarini), this has a function called fdc for making nice flow duration curve plots.

Flow duration curves can be a valuable comparison among stations.  I used that to compare various stations in N Georgia, USA on one of my posters in researchgate, and it showed similarities among streams within physiographic areas, differences mostly due to rainfall across the landscape.  I added a trial Stiff Plot in Excel so you can hopefully follow my commands in Excel, appears same as a Spider diagram.  It can be useful, but getting the units of the axis can be a challenge, and the idea of normalizing or rating High, Medium and Low is also sometimes useful.  

Your plot with so much time dependent detail is informative as is, I like it, but if space, consider expanding laterally to cover a full page width or turn page 90 degrees to use length, and more detail will be evident.  I noted that the rainfall showed few instances of low values, so you may need to use narrower lines with a symbol or something to show more of the detail, and not hide the periods of no rain.  I know, its a challenge with daily or more frequent data.  If necessary, with 6 years data, you can stack 3 plots of two years each on a page, and use the same dimensions of each plot (ie, exact replica plots of two years each for your 6 years) so they will be all comparable.  This may better present or highlight the hydrograph response and recession curves by season (growing vs dormant, wet and dry).  You are also using calendar years, and in USA, we often use water years based on Oct 1 is end of summer and generally a low flow period to start each water year.  I would not use that with your data, but something that may apply to help separate water response years.  I think you will find there are many ways to present data and help tell your story to others.

Thanks for the additional answers. For the spider plots I used Python and the wonderful code I found (see Link). The plot one gets look quite nice and are relatively easy to construct.

The hydrograph I will only plot for the few best models, as when used with many models the figure gets confusing as too many lines overlap.

To compare all models that produced behavioural runs I will use the flow duration curve, as in those figures one can see differences quite clear even when many models are used.

http://datascience.stackexchange.com/questions/6084/how-do-i-create-a-complex-radar-chart