EGU General Assembly 2020
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the Creative Commons Attribution 4.0 License.

An extended transfer function model for the prediction of nonpoint-source pollutant travel times

Marialaura Bancheri1, Antonio Coppola2, and Angelo Basile1
Marialaura Bancheri et al.
  • 1Institute for Mediterranean Agricultural and Forestry Systems (ISAFOM), National Research Council (CNR), Ercolano, NA, Italy (
  • 2School of Agricultural, Forestry, Food and Environmental Sciences (SAFE), Hydraulics Division, University of Basilicata, Potenza, Italy

Transfer functions are travel time probability density functions (TT pdfs), which describe the leaching behaviour in a given soil profile. Once they are defined, the output solute concentration at a given time and depth is simply the transfer function convolution with the input concentration signal to the system.

In this work we propose an extended version of Jury's transfer function model (TFM-ext). The proposed model allows to simulate the spatio-temporal distribution of nonpoint-source solutes along the unsaturated zone that: i) integrates a simplified statistical approach with the physically-based soil hydrological parameters; ii) is valid for wide range of applications, both in space and time; iii) is standard and easily replicable; iv) is easy to interpret.

With the assumptions of a) a gravity induced water flow, b) a conservative and nonreactive solute and c) a purely convective flow, ignoring the convective mixing of solute flowing at different velocities and the molecular diffusion, the TT pdf were calculated as functions of the unsaturated hydraulic conductivity k(θ). The strength of the model, despite its important assumptions, is that it derives the TT pdf from a physical quantity, i.e. the hydraulic conductivity function. Moreover, the model extends the transport process to the generic depth z, where information on the hydraulic properties could not be available, assuming a lognormal travel time pdf, whose parameters are scaled according to the generalized transfer function model.

A sensitivity analysis, based on Monte Carlo simulations, to evaluate to which parameters the TFM-ext is more sensitive, was performed. Results shown that θs and τ, of the van Genuchten-Mualem model, are the parameter affecting more the mean travel times.

Moreover, in order to validate TFM-ext, an application in the Telesina Valley, a hilly area of 200 km2 in Southern Italy, was performed. Forty-six soil profiles, completely characterized from the hydrological point of view, were used to evaluate the mean travel times and then compared with the results obtained with a notable physically based model, Hydrus 1D. Two distinct applications were performed: the first with constant upper boundary conditions equal to those applied to the TFM-ext exercise, and the second with real daily variable upper boundary conditions. Results of both cases gave very high correlation coefficients (above 0.8) and mean absolute errors of 30 and 40 days, respectively.

Eventually, the model was implemented as an operative tool for the groundwater vulnerability assessment within the geospatial Decision Support System developed for LANDSUPPORT H2020 project.

How to cite: Bancheri, M., Coppola, A., and Basile, A.: An extended transfer function model for the prediction of nonpoint-source pollutant travel times , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3819,, 2020

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  • CC1: Comment on EGU2020-3819, Horst H. Gerke, 06 May 2020

    Very nice work! I would be interested in the reasons for deviations in results between those obtained with Hydrus and those with your transfer function. Hydrus could also produce some numerical errors or is it caused by model simplifications?  

    • AC1: Reply to CC1, Marialaura Bancheri, 06 May 2020

      Dear Horst,

      Thank you for your comment. Besides the possible Hydrus 1D numerical errors, which we still consider our benchmark reference, we think that the deviations are mainly due to our model simplifications (e.g, the steady state assumption). 



  • CC2: Comment on EGU2020-3819, Horst H. Gerke, 06 May 2020

    Thanks, have you compared cumulative drainage between models?

    • AC2: Reply to CC2, Marialaura Bancheri, 06 May 2020

      No we didn't compute the drainage comparison since TFM-ext assumes steady state condition along the entire soil profile. But your suggestion could help to disentangle the water mass from the solute trasport process, within Hydrus, to better understand the differences between the two models.

      Or did you mean something different?

      Thank you


  • AC3: Comment on EGU2020-3819, Marialaura Bancheri, 06 May 2020

    Just few clarifications, after the interesting live chat:

    • It is important to stress that with the TFM-ext we do not want to describe in details local scale transport behavior (e.g., macropore or preferential flows), but our aim is looking for a simplified model to be used at large scales, providing estimations of mean travel times of the NPS, by also taking in consideration the spatial variability of the soils. TFM-ext model, in fact, was conceived to be integrated within the web-based geo-spatial decision support system LandSupport, which requires real-time answers ranging from few to thousand pixels (runs).


    •  Results of the sensitivity analysis applied to the model was performed starting from a dateset of 46 fully characterised soil profiles, from the hydraulic point of view. It showed that a variation in the saturated soil water content completely modifies the position of the hydraulic conductivity curve in the k(θ) plane with significant effects on the derivative of the k(θ) and thus on the size of the pores involved in the transport at a given top boundary flux. Similar conclusions can be drawn for the parameter τ, with the additional effect of a very high CV, which has itself consequences on the variability of the travel time pdf.


    • The hydraulic properties of the soil profiles in the study area were obtained from laboratory measurements on undisturbed soil samples, then scaled to field conditions (e.g., for those soils with high stone content). Soil profiles were digged in selected points (representative soil profiles chosen after a preliminary pedological study of the area).


    • The model considers a stream-tube approach, where no lateral or small-distance overland transport flow were considered. As regards the solute transport we are considering a stochastic-convective model.


    • The deviations between TFM-ext and Hydrus 1D are mainly due to our model simplifications (e.g, the steady state assumption) and also to the solute transport model assumed. We are in fact considering a stochastic-convective model while in Hydrus 1D the process is convective-dispersive. This determines a difference in the output breakthrough curves and then in the mean travel times, which are partially damped by the way we computed the first and second moments.