[1] Water fluxes in catchments are controlled by physical processes and material properties that are complex, heterogeneous, and poorly characterized by direct measurement. As a result, parsimonious theories of catchment hydrology remain elusive. Here I describe how one class of catchments (those in which discharge is determined by the volume of water in storage) can be characterized as simple first-order nonlinear dynamical systems, and I show that the form of their governing equations can be inferred directly from measurements of streamflow fluctuations. I illustrate this approach using data from the headwaters of the Severn and Wye rivers at Plynlimon in mid-Wales. This approach leads to quantitative estimates of catchment dynamic storage, recession time scales, and sensitivity to antecedent moisture, suggesting that it is useful for catchment characterization. It also yields a first-order nonlinear differential equation that can be used to directly simulate the streamflow hydrograph from precipitation and evapotranspiration time series. This single-equation rainfall-runoff model predicts streamflow at Plynlimon as accurately as other models that are much more highly parameterized. It can also be analytically inverted; thus, it can be used to ''do hydrology backward,'' that is, to infer time series of whole-catchment precipitation directly from fluctuations in streamflow. At Plynlimon, precipitation rates inferred from streamflow fluctuations agree with rain gauge measurements as closely as two rain gauges in each catchment agree with each other. These inferred precipitation rates are not calibrated to precipitation measurements in any way, making them a strong test of the underlying theory. The same approach can be used to estimate whole-catchment evapotranspiration rates during rainless periods. At Plynlimon, evapotranspiration rates inferred from streamflow fluctuations exhibit seasonal and diurnal cycles that agree semiquantitatively with Penman-Monteith estimates. Thus, streamflow hydrographs may be useful for reconstructing precipitation and evapotranspiration records where direct measurements are unavailable, unreliable, or unrepresentative at the scale of the landscape.

Abstract:Concentration-discharge relationships have been widely used as clues to the hydrochemical processes that control runoff chemistry. Here we examine concentration-discharge relationships for solutes produced primarily by mineral weathering in 59 geochemically diverse US catchments. We show that these catchments exhibit nearly chemostatic behaviour; their stream concentrations of weathering products such as Ca, Mg, Na, and Si typically vary by factors of only 3 to 20 while discharge varies by several orders of magnitude. Similar patterns are observed at the inter-annual time scale. This behaviour implies that solute concentrations in stream water are not determined by simple dilution of a fixed solute flux by a variable flux of water, and that rates of solute production and/or mobilization must be nearly proportional to water fluxes, both on storm and inter-annual timescales. We compared these catchments' concentration-discharge relationships to the predictions of several simple hydrological and geochemical models. Most of these models can be forced to approximately fit the observed concentration-discharge relationships, but often only by assuming unrealistic or internally inconsistent parameter values. We propose a new model that also fits the data and may be more robust. We suggest possible tests of the new model for future studies. The relative stability of concentration under widely varying discharge may help make aquatic environments habitable. It also implies that fluxes of weathering solutes in streams, and thus fluxes of alkalinity to the oceans, are determined primarily by water fluxes. Thus, hydrology may be a major driver of the ocean-alkalinity feedback regulating climate change.