[1] In hydrological tracer studies, the gamma distribution can serve as an appropriate transit time distribution (TTD) as it allows more flexibility to account for nonlinearities in the behavior of catchment systems than the more commonly used exponential distribution. However, it is unclear which physical interpretation can be ascribed to its two parameters (a, b). In this study, long-term tracer data from three contrasting catchments in the Scottish Highlands were used for a comparative assessment of interannual variability in TTDs and resulting mean transit times (MTT = ab) inferred by the gamma distribution model. In addition, spatial variation in the long-term average TTDs from these and six additional catchments was also assessed. The temporal analysis showed that the b parameter was controlled by precipitation intensities above catchment-specific thresholds. In contrast, the a parameter, which showed little temporal variability and no relationship with precipitation intensity, was found to be closely related to catchment landscape organization, notably the hydrological characteristics of the dominant soils and the drainage density. The relationship between b and precipitation intensity was used to express b as a time-varying function within the framework of lumped convolution integrals to examine the nonstationarity of TTDs. The resulting time-variant TTDs provided more detailed and potentially useful information about the temporal dynamics and the timing of solute fluxes. It was shown that in the wet, cool climatic conditions of the Scottish Highlands, the transit times from the time-variant TTD were roughly consistent with the variations of MTTs revealed by interannual analysis.

We use high‐resolution tracer data from an experimental site to test theoretical approaches that integrate catchment‐scale flow and transport processes in a unified framework centered on selective age sampling by streamflow and evapotranspiration fluxes. Transport processes operating at the catchment scale are reflected in the evolving residence time distribution of the catchment water storage and in the age selection operated by out‐fluxes. Such processes are described here through StorAge Selection (SAS) functions parameterized as power laws of the normalized rank storage. Such functions are computed through appropriate solution of the master equation defining formally the evolution of residence and travel times. By representing the way in which catchment storage generates outflows composed by water of different ages, the main mechanism regulating the tracer composition of runoff is clearly identified and detailed comparison with empirical data sets are possible. Properly calibrated numerical tools provide simulations that convincingly reproduce complex measured signals of daily deuterium content in stream waters during wet and dry periods. Results for the catchment under consideration are consistent with other recent studies indicating a tendency for natural catchments to preferentially release younger available water. The study shows that power law SAS functions prove a powerful tool to explain catchment‐scale transport processes that also has potential in less intensively monitored sites.

Abstract:Empirically based understanding of streamflow generation dynamics in a montane headwater catchment formed the basis for the development of simple, low-parameterized, rainfall-runoff models. This study was based in the Girnock catchment in the Cairngorm Mountains of Scotland, where runoff generation is dominated by overland flow from peaty soils in valley bottom areas that are characterized by dynamic expansion and contraction of saturation zones. A stepwise procedure was used to select the level of model complexity that could be supported by field data. This facilitated the assessment of the way the dynamic process representation improved model performance. Model performance was evaluated using a multicriteria calibration procedure which applied a time series of hydrochemical tracers as an additional objective function. Flow simulations comparing a static against the dynamic saturation area model (SAM) substantially improved several evaluation criteria. Multi-criteria evaluation using ensembles of performance measures provided a much more comprehensive assessment of the model performance than single efficiency statistics, which alone, could be misleading. Simulation of conservative source area tracers (Gran alkalinity) as part of the calibration procedure showed that a simple two-storage model is the minimum complexity needed to capture the dominant processes governing catchment response. Additionally, calibration was improved by the integration of tracers into the flow model, which constrained model uncertainty and improved the hydrodynamics of simulations in a way that plausibly captured the contribution of different source areas to streamflow. This approach contributes to the quest for low-parameter models that can achieve process-based simulation of hydrological response.

Abstract:Catchment travel time distributions reflect how precipitation from different storms is stored and mixed as it is transported to the stream. Catchment travel time distributions can be described by the mean travel time and the shape of the distribution around the mean. Whereas mean travel times have been quantified in a range of catchment studies, only rarely has the shape of the distribution been estimated. The shape of the distribution affects both the short-term and long-term catchment response to a pulse input of a soluble contaminant. Travel time distributions are usually estimated from conservative tracer concentrations in precipitation and streamflow, which are analyzed using time-domain convolution or spectral methods. Of these two approaches, spectral methods are better suited to determining the shape of the distribution. Previous spectral analyses of both rainfall and streamflow tracer time series from several catchments in Wales showed that rainfall chemistry spectra resemble white noise, whereas the stream tracer spectra in these same catchments exhibit fractal 1/f scaling over three orders of magnitude. Here we test the generality of the observed fractal scaling of streamflow chemistry, using spectral analysis of long-term tracer time series from 22 catchments in North America and Europe. We demonstrate that 1/f fractal scaling of stream chemistry is a common feature of these catchments. These observations imply that catchments typically exhibit an approximate power-law distribution of travel times, and thus retain a long memory of past inputs. The observed fractal scaling places strong constraints on possible models of catchment behavior, because it is inconsistent with the exponential travel time distributions that are predicted by simple mixing models.

Abstract:Although the importance of riparian forest in moderating stream temperature variability is recognized, most previous research focuses on conifer harvesting effects and summer maximum temperature with highly variable findings. This article compares stream temperature, microclimate and heat exchange dynamics between semi-natural forest and moorland (no trees) reaches in the Scottish Cairngorms over two calendar years to provide a longer-term perspective. Mean daily water column temperature is warmer for moorland than forest in late winter-early spring, but cooler in summer. Daily water column temperature range is greater for moorland than forest. Streambed temperature dynamics are markedly different between reaches, reflecting contrasting groundwater-surface water (GW-SW) interactions. Mean, minimum and maximum daily air temperature is cooler, humidity is lower, and wind speed is much higher for moorland than forest on average. Net radiation is the dominant heat sink in autumn-winter and major heat source in spring-summer for moorland and summer for forest. Net radiation is greater in summer and lower in winter for moorland than forest. Sensible heat is an energy source in autumn-winter and sink in spring-summer, with loss (gain) greater in summer (winter) for moorland than forest. Latent heat is predominantly a sink for both reaches, with magnitude and variability higher for moorland than forest. Streambed heat flux is much smaller than fluxes at the air-water interface, with moorland and forest illustrating seasonal and between-reach differences attributable to different GW-SW interactions. Seasonal patterns in stream energy budget partitioning are illustrated schematically. To our knowledge, this is the first such study of mixed woodland, which generates notably different results to work on coniferous forest. This research provides a process basis to model stream thermal impact of changes in forest practice, and so inform decision making by land and water resource managers.