[1] Many details about the flow of water in soils in a hillslope are unknowable given current technologies. One way of learning about the bulk effects of water velocity distributions on hillslopes is through the use of tracers. However, this paper will demonstrate that the interpretation of tracer information needs to become more sophisticated. The paper reviews, and complements with mathematical arguments and specific examples, theory and practice of the distribution(s) of the times water particles injected through rainfall spend traveling through a catchment up to a control section (i.e., "catchment" travel times). The relevance of the work is perceived to lie in the importance of the characterization of travel time distributions as fundamental descriptors of catchment water storage, flow pathway heterogeneity, sources of water in a catchment, and the chemistry of water flows through the control section. The paper aims to correct some common misconceptions used in analyses of travel time distributions. In particular, it stresses the conceptual and practical differences between the travel time distribution conditional on a given injection time (needed for rainfall-runoff transformations) and that conditional on a given sampling time at the outlet (as provided by isotopic dating techniques or tracer measurements), jointly with the differences of both with the residence time distributions of water particles in storage within the catchment at any time. These differences are defined precisely here, either through the results of different models or theoretically by using an extension of a classic theorem of dynamic controls. Specifically, we address different model results to highlight the features of travel times seen from different assumptions, in this case, exact solutions to a lumped model and numerical solutions of the 3-D flow and transport equations in variably saturated, physically heterogeneous catchment domains. Our results stress the individual characters of the relevant distributions and their general nonstationarity yielding their legitimate interchange only in very particular conditions rarely achieved in the field. We also briefly discuss the impact of oversimple assumptions commonly used in analyses of tracer data.

Article (refereed) -postprintTipping, E.; Benham, S.; Boyle, J.F.; Crow, P.; Davies, J.; Fischer, U.; Guyatt, H.; Helliwell, R.; Jackson-Blake, L.; Lawlor, A.J.; Monteith, D.T.; Rowe, E.C.; Toberman, H. 2014. Atmospheric deposition of phosphorus to land and freshwater. Environmental Science: Processes and Impacts, 16 (7). 1608-1617. 10.1039/c3em00641g Contact CEH NORA team at noraceh@ceh.ac.ukThe NERC and CEH trademarks and logos ('the Trademarks') are registered trademarks of NERC in the UK and other countries, and may not be used without the prior written consent of the Trademark owner. Oceania, and South-Central America. The deposition rates are log-normally distributed, 30 and for the whole data set the geometric mean deposition rates are 0.027, 0.019 and 31 0.14 g m -2 a -1 for TP, FTP and PO 4 -P respectively. At smaller scales there is little 32 systematic spatial variation, except for high deposition rates at some sites in Germany, 33 likely due to local agricultural sources. In cases for which PO 4 -P was determined as well 34 as one of the other forms of P, strong parallels between logarithmic values were found. 35Based on the directly-measured deposition rates to land, and published estimates of P 36 deposition to the oceans, we estimate a total annual transfer of P to and from the 37 atmosphere of 3.7 Tg. However, much of the phosphorus in larger particles (principally 38 primary biological aerosol particles) is probably redeposited near to its origin, so that 39 long-range transport, important for tropical forests, large areas of peatland and the 40 oceans, mainly involves fine dust from deserts and soils, as described by the simulations 41of Mahowald et al. (Global Biogeochemical Cycles 22, GB4026, 2008). We suggest that 42 local release to the atmosphere and subsequent deposition bring about a pseudo-43 diffusive redistribution of P in the landscape, with P-poor ecosystems, for example 44 ombrotrophic peatlands and oligotrophic lakes, gaining at the expense of P-rich ones. 45Simple calculations suggest that atmospheric transport could bring about significant local 46 redistribution of P among terrestrial ecosystems.Although most atmospherically 47 transported P is natural in origin, local transfers from fertilised farmland to P-poor 48 ecosystems may be significant, and this requires further research. 49 50

As any model of real-world phenomena, soil erosion models must be tested against empirical evidence to have their performance evaluated. This is critical to develop knowledge and confidence in model predictions. However, evaluating soil erosion models is complicated due to the uncertainties involved in the estimation of model parameters and measurements of system responses. Here, we undertake a term co-occurrence analysis to investigate how model evaluation is approached in soil erosion research. The analysis illustrates how model testing is often neglected, and how model evaluation topics are segregated from current research interests. We perform a meta-analysis of model performance to understand the mechanisms that influence model predictive accuracy. Results indicate that different models do not systematically outperform each other, and that calibration seems to be the main mechanism of model improvement. We review how soil erosion models have been evaluated at different temporal and spatial scales, focusing on the methods, assumptions, and data used for model testing. We discuss the implications of uncertainty and equifinality in soil erosion models, and implement a case study of uncertainty assessment that enables models to be tested as hypotheses. A comment on the way forward for the evaluation of erosion models is presented, discussing philosophical aspects of hypothesis testing in environmental modelling. We refute the notion that soil erosion models can be validated, and emphasize the necessity of defining fit-for-purpose tests, based on multiple sources of data, that allow for a broad investigation of model usefulness and consistency.

[1] There is still a need for catchment hydrological and transport models that properly integrate the effects of preferential flows while accounting for differences in velocities and celerities. A modeling methodology is presented here which uses particle tracking methods to simulate both flow and transport in multiple pathways in a single consistent solution. Water fluxes and storages are determined by the volume and density of particles and transport is attained by labeling the particles with information that may be tracked throughout the lifetime of that particle in the catchment. The methodology allows representation of preferential flows through the use of particle velocity distributions, and mixing between pathways can be achieved with pathway transition probabilities. A transferable 3-D modeling methodology is presented for the first time and applied to a unique step-shift isotope experiment that was carried out at the 0.63 ha G1 catchment in Gårdsjön, Sweden. This application highlights the importance of combining flow and transport in hydrological representations, and the importance of pathway velocity distributions and interactions in obtaining a satisfactory representation of the observations.