Why is evaluating model uncertainty an important part in hydrologic modeling?

The hydrologic system involves complex interactions among the atmospheric, land surface, and subsurface components of the water cycle. Hydrologic models typically conceptualize and represent these complex behaviors using relatively simple mathematical equations in which the (conceptualized) model parameters are aggregate quantities representing spatial and temporal properties of the system and are generally not directly and easily measurable in the field; they must therefore be inferred by indirect methods such as model calibration (Gupta et al., 1998). A variety of model calibration techniques have been developed to ensure consistency between the model simulations of system behavior and their corresponding observations (Duan et al., 2003).

Decision makers are increasingly interested in the uncertainty surrounding model predictions (Loucks et al., 2005), and so modelers are tasked with quantifying and communicating this uncertainty to inform water resources management and policy development (Willems and de Lange, 2007).

It is now generally accepted that the calibration of hydrological models should be approached as a multi-objective problem (Gupta et al., 1998). Uncertainty estimation in hydrological surface and subsurface modeling is today one of the most important subfields of hydrology, according to the numerous contributions in recent scientific literature. In particular, uncertainty estimation is very much related with parameter calibration and model validation. It consists of a verification of the hydrological model appropriateness and performances finalized to providing a quantitative assessment of its reliability.

There are different sources which all of them refer to the uncertainty of hydrological models. I have read the Walker et al., research which revealed that: In a model-based study, uncertainties can arise in (i) model context, (ii) model structure, (iii) forcing data and (iv) identification of parameter values (Walker et al., 2003).

Another study (Mockler et al., 2016) has mentioned that: (i) uncertainty in simulated flow due to uncertainty about the forcing data, here limited to the precipitation data, (ii) uncertainties due to the method of determining model parameters, and iii) uncertainties due to the interactions between the above sources i.e. forcing data and model parameters.

Butts et al., (2004) have stated that four sources of uncertainty occur in deterministic flow modelling; - Random or systematic errors in the model inputs (boundary or initial conditions), - Random or systematic errors in the recorded output data used to measure simulation accuracy, - Uncertainties due to sub-optimal parameter values, and - Uncertainties due to incomplete or biased model structure.

Oudin et al. (2006) studied the impact of corrupted (both random and systematic) inputs (precipitation - P and potential evapotranspiration - PET) on model performance, concluding that random errors in P have potentially the largest effect on model performance. Systematic errors in P may be accounted for in the model calibration if the model structure permits this. However, from the viewpoint of predicting flows at ungauged locations, systematic errors in rainfall are more problematic unless the error does not change significantly between the gauged and ungauged sites.

In hydrology, some of the sources of uncertainty that need to be considered are:

• Observation errors;
• Rating curves, and when these are being extrapolated;
• Spatial interpolation and aggregation, including the spatial resolution of the available data, and the spatial scales of variations in the fields being interpolated.
• Influence of temporal resolution (data time-step)

Only by careful consideration of the sources of uncertainty can valid conclusions be drawn regarding the utility of the data, and the impact the data have on modelled outputs and subsequent conclusions.

The analysis and consideration of uncertainty is particularly important because decisions regarding water resource policy, management, regulation, and program evaluation are increasingly based on hydrologic and water quality modeling (Shirmohammadi et al., 2006). So, if we can't elaborate to decrease the sources of uncertainty then our simulations have face to major problems for making decision and solve the issues related to the different extreme hazard events. Simply speaking, model uncertainty arises from incomplete understanding of the system being modeled and/or the inability to accurately reproduce hydrologic and water quality modeling processes with mathematical and statistical techniques.