# A Critical Review of the Modelling Tools for the Reactive Transport of Organic Contaminants
## 3 Modelling
### Deterministic Models
In recent decades, advances in computing power (more powerful CPUs) and new modelling approaches have enabled the inclusion of more complex geometries for solute transport [573, 574, 575, 576, 577, 578]. In any case, the quality or resolution of the mesh influences how fast the model runs and how accurate it will be. Poor mesh quality leads to further errors in the model [573, 579, 580]. To correct the discretisation of the model, the user should be able to meet certain quality criteria [581; 582]. Furthermore, if the reactive transport calculations include complex reactions such as precipitation, dissolution, oxidation, etc., the model needs a very accurate temporal resolution, i.e., many time steps. 6. The calibration of the numerical model is based on the many model parameters that control the processes that take place along the flow. The parameter set can be adjusted to maximise the fit of the model to a set of experimental data [583]. Therefore, the focus is often on the differences between observed and modelled values, i.e., the residuals. However, calibration must also consider whether the assigned parameters are appropriate (an experienced modeler is a great advantage here). It is therefore important not only to compare the model predictions with the observed data, but also to quantify and explain the uncertainty associated with the model and the data, as calibration and uncertainty analysis are closely linked, and no calibration results should be presented without quantifying the predictive uncertainty of the model [584]. Freyberg [585], for example, conducted an experiment with students who calibrated a groundwater model by trial and error using a series of observed heads. It was found that models with small residuals between simulated and observed data did not make better predictions than models with larger residuals. This problem is of great importance for highly parameterised models, as although they provide an excellent fit, they are also prone to overfitting as the parameter estimation lags behind the noise of the observations [586]. Furthermore, the worst predictions were made by models where the hydraulic conductivity was different in each cell of the model. Therefore, for groundwater flow models, the accuracy of the prediction must be weighed against the complexity of the model, especially the distribution of hydraulic conductivity/transmissivity [587]. The estimation of hydraulic conductivity is extremely important, as it is a key modelling parameter that controls water movement and usually only a fraction of the total investigated area is sampled [588]. The trial-and-error method is monotonous, time-consuming, and also judgmental, as the modeler is responsible for finding an acceptable level of agreement between simulated and observed data. To reduce the time required for calibration and to make this process more systematic and transparent, additional numerical tools can be used [589; 590; 591]. Recently, several calibration methods have been presented, including global optimisation methods [592], Bayesian-based calibration methods using Gaussian process error models [593], and pilot point calibration methods [594; 595]. A promising alternative to the existing optimisation tools included in the modelling software are algorithms written in modern scientific languages such as R and Python, e.g., FloPy [596], ogs5 py [597], RedModRPhree [598], toughie [599], and r2 ogS [600]. It should be emphasised that model calibration can be even more challenging than model construction, as it requires an understanding of phenomena beyond hydrogeology and relies on disciplines such as algebra, geostatistics, geophysics and programming [601; 602; 603; 604; 605; 606; 607; 608; 609; 610; 611; 612; 613; 614; 615; 616; 617; 618; 619; 620; 621; 622; 623; 624; 625; 626; 627; 628; 629; 630; 631; 632; 633;  
Analysing uncertainties, together with calibration and uncertainty reduction, is crucial for the accurate representation and prediction of systems.