James W. Kirchner

Fractal stream chemistry and its implications for contaminant transport in catchments

The time it takes for rainfall to travel through a catchment and reach the stream is a fundamental hydraulic parameter that controls the retention of soluble contaminants and thus the downstream consequences of pollution episodes. Catchments with short flushing times will deliver brief, intense contaminant pulses to downstream waters, whereas catchments with longer flushing times will deliver less intense but more sustained contaminant fluxes. Here we analyse detailed time series of chloride, a natural tracer, in both rainfall and runoff from headwater catchments at Plynlimon, Wales. We show that, although the chloride concentrations in rainfall have a white noise spectrum, the chloride concentrations in streamflow exhibit fractal 1/f scaling over three orders of magnitude. The fractal fluctuations in tracer concentrations indicate that these catchments do not have characteristic flushing times. Instead, their travel times follow an approximate power-law distribution implying that they will retain a long chemical memory of past inputs. Contaminants will initially be flushed rapidly, but then low-level contamination will be delivered to streams for a surprisingly long time.

Moving beyond heterogeneity and process complexity: A new vision for watershed hydrology

Field studies in watershed hydrology continue to characterize and catalogue the enormous heterogeneity and complexity of rainfall runoff processes in more and more watersheds, in different hydroclimatic regimes, and at different scales. Nevertheless, the ability to generalize these findings to ungauged regions remains out of reach. In spite of their apparent physical basis and complexity, the current generation of detailed models is process weak. Their representations of the internal states and process dynamics are still at odds with many experimental findings. In order to make continued progress in watershed hydrology and to bring greater coherence to the science, we need to move beyond the status quo of having to explicitly characterize or prescribe landscape heterogeneity in our (highly calibrated) models and in this way reproduce process complexity and instead explore the set of organizing principles that might underlie the heterogeneity and complexity. This commentary addresses a number of related new avenues for research in watershed science, including the use of comparative analysis, classification, optimality principles, and network theory, all with the intent of defining, understanding, and predicting watershed function and enunciating important watershed functional traits.

Spatially Averaged Long-Term Erosion Rates Measured from in Situ-Produced Cosmogenic Nuclides in Alluvial Sediment

Spatially averaged erosion rates of small catchments can be accurately inferred from the concentrations of cosmogenic nuclides in stream sediment. Here we test this technique at two catchments by comparing erosion rates inferred from cosmogenic nuclides with rates of alluvial fan deposition over the past 16,000 years. These two independent estimates agree within one standard error, demonstrating that cosmogenic nuclide signatures of stream sediment can be used to measure spatially averaged long-term erosion rates. Using this technique, we show that long-term erosion rates are an exponential function of average hillslope gradient at these sites.

Mountain erosion over 10 yr, 10 k.y., and 10 m.y. time scales

We used cosmogenic 10 Be to measure erosion rates over 10 k.y. time scales at 32 Idaho mountain catchments, ranging from small experimental watersheds (0.2 km 2 )t o large river basins (35 000 km 2 ). These long-term sediment yields are, on average, 17 times higher than stream sediment fluxes measured over 10‐84 yr, but are consistent with 10 m.y. erosion rates measured by apatite fission tracks. Our results imply that conventional sediment-yield measurements—even those made over decades—can greatly underestimate long-term average rates of sediment delivery and thus overestimate the life spans of engineered reservoirs. Our observations also suggest that sediment delivery from mountainous terrain is extremely episodic, sporadically subjecting mountain stream ecosystems to extensive disturbance.

EVOLUTIONARY DYNAMICS OF PATHOGEN RESISTANCE AND TOLERANCE

Abstract Host organisms can respond to the threat of disease either through resistance defenses (which inhibit or limit infection) or through tolerance strategies (which do not limit infection, but reduce or offset its fitness consequences). Here we show that resistance and tolerance can have fundamentally different evolutionary outcomes, even when they have equivalent short-term benefit for the host. As a gene conferring disease resistance spreads through a population, the incidence of infection declines, reducing the fitness advantage of carrying the resistance gene. Thus genes conferring complete resistance cannot become fixed (i.e., universal) by selection in a host population, and diseases cannot be eliminated solely by natural selection for host resistance. By contrast, as a gene conferring disease tolerance spreads through a population, disease incidence rises, increasing the evolutionary advantage of carrying the tolerance gene. Therefore, any tolerance gene that can invade a host population will tend to be driven to fixation by selection. As predicted, field studies of diverse plant species infected by rust fungi confirm that resistance traits tend to be polymorphic and tolerance traits tend to be fixed. These observations suggest a new mechanism for the evolution of mutualism from parasitism, and they help to explain the ubiquity of disease. Corresponding Editor: L. Nunney

Catchment-scale advection and dispersion as a mechanism for fractal scaling in stream tracer concentrations

Time series of chemical tracers in rainfall and streamflow can be used to probe the internal workings of catchments. We have recently proposed that catchments act as fractal filters for inert chemical tracers like chloride, converting ‘white noise’ rainfall chemistry inputs into fractal ‘’ chemical time series in runoff [Nature 403 (2000) 524]. This implies that catchments have long-tailed travel-time distributions, and thus retain soluble contaminants for unexpectedly long timespans. Here we show that these long-tailed travel-time distributions, and the fractal tracer time series that they imply, can be generated by advection and dispersion of spatially distributed rainfall inputs as they travel toward a channel. Tracer pulses that land close to the stream reach it promptly, with relatively little dispersion. Tracer pulses that land farther upslope must travel farther to reach the stream, and undergo more dispersion. The tracer signal in the stream will be the integral of the contributions from each point along the length of the hillslope, with a peak at short lag times (reflecting tracers landing near the stream) and a long tail (reflecting tracers landing farther from the stream). Here we integrate the advection–dispersion equation for rainfall tracers landing at all points on a simple model hillslope, and show that it yields fractal tracer behavior, as well as a travel-time distribution nearly equivalent to that found empirically [Nature 403 (2000) 524]. However, it does so only when the dispersion length scale approaches the length of the hillslope, implying that subsurface transport is dominated by large conductivity contrasts related to macropores, fracture networks, and similar large-scale heterogeneities in subsurface conductivity. Thus, the 1/f scaling observed at our study sites indicates that these catchments are dominated by flowpaths that exhibit macro-dispersion over the longest possible length scales.

Strong tectonic and weak climatic control of long-term chemical weathering rates

The relationships among climate, physical erosion, and chemical weathering have remained uncertain, because long-term chemical weathering rates have been difficult to measure. Here we show that long-term chemical weathering rates can be measured by combining physical erosion rates, inferred from cosmogenic nuclides, with dissolution losses, inferred from the rock-to-soil enrichment of insoluble elements. We used this method to measure chemical weathering rates across 22 mountainous granitic catchments that span a wide range of erosion rates and climates. Chemical weathering rates correlate strongly with physical erosion rates but only weakly with climate, implying that, by regulating erosion rates, tectonic uplift may significantly accelerate chemical weathering rates in granitic landscapes.

Longitudinal Profile Development into Bedrock: An Analysis of Hawaiian Channels

Analysis of topographic maps of rivers incised into dated Hawaiian lava flows shows that the long term average bedrock erosion rate along certain reaches is linearly related to stream power. Field observations suggest that two processes may control Hawaiian channel downcutting: (1) stream power-dependent erosion, including abrasion of the channel bed by transported particles, and (2) step-wise lowering caused by knickpoint propagation. Modeling results indicate that a simple stream power-dependent erosion law predicts the straight to weakly convex longitudinal profiles characteristic of Kauai channels but is insufficient to predict two other characteristic features: the upslope propagation of knickpoints and the straight 5-8° channel slopes below the knickpoints; thus more than this single transport law is apparently required to model bedrock channel incision. Field surveys also indicate that significant portions of the channel lengths below the knickpoints are mantled with large boulders. We propose that the boulder mantling of long channel reaches inhibits channel incision, reducing downcutting to a rate set by boulder weathering, breakdown and transport of the material, and perhaps by knickpoint propagation sweeping under the boulder armor. Partial boulder mantling of bedrock-dominated channels is common in mountainous regions, and a theory which takes boulder armoring into account will have broader applications than one which ignores these limiting effects.

Minimal climatic control on erosion rates in the Sierra Nevada, California

Climate is widely thought to regulate erosion rates, but the relationships among precipitation, temperature, and erosion rate have remained speculative, because long-term erosion rates have been difficult to measure. We used cosmogenic nuclides to measure long-term erosion rates at climatically diverse sites in the Sierra Nevada, California, spanning 20‐180 cm/yr in annual precipitation and 4‐15 8C in mean annual temperature. Average erosion rates vary by only 2.5 fold across these sites and are not correlated with climate, indicating that climate only weakly regulates nonglacial erosion rates in mountainous granitic terrain.

Friction angle measurements on a naturally formed gravel streambed: Implications for critical boundary shear stress

We report the first measurements of friction angles for a naturally formed gravel streambed. For a given test grain size placed on a bed surface, friction angles varied from 10o to over 100o; friction angle distributions can be expressed as a function of test grain size, median bed grain size, and bed sorting parameter. Friction angles decrease with increasing grain size relative to the median bed grain size, and are a systematic function of sorting, with lower friction angles associated with poorer sorting. The probability distributions of critical shear stress for different grain sizes on a given bed surface, as calculated from our friction angle data, show a common origin, but otherwise diverge with larger grains having narrower and lower ranges of critical shear stresses. The potential mobility of a grain, as defined by its probability distribution of critical shear stress, may be overestimated for larger grains in this analysis, because our calculations do not take into account the effects of grain burial and altered near-bed flow fields.