Catchments as simple dynamical systems: Catchment characterization, rainfall‐runoff modeling, and doing hydrology backward

Abstract

[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.

Investigating storage‐discharge relations in a lowland catchment using hydrograph fitting, recession analysis, and soil moisture data

“…[21] In this method, the parameters are not optimized globally, but obtained from discharge data from selected periods, following the approach of Kirchner [2009]. From the total data set, periods without P and ET were selected.…”

“…This has been a hydrological research topic for many decades. Brutsaert and Nieber [1977] investigated discharge recession curves, Kirchner [2009] used system parameters obtained with recession analysis in a simple hydrological model, and Teuling et al [2010] used this model to obtain system parameters by means of calibration. There are many other studies in which storage-discharge relations have been found by means of discharge (recession) analysis, but a more obvious approach, namely using storage data directly, is not known to the authors.…”

“…Lowland catchments cover an extensive part of the world's most densely populated areas and, therefore, adequate discharge forecasts in these catchments are of large societal and economic value. Kirchner [2009] used the Plynlimon catchment (runoff ratio ¼ 0.79) to illustrate his simple dynamical systems approach, in which a nonlinear reservoir model is based on the storage-discharge relation. Teuling et al [2010] applied this approach to the slightly less humid Rietholzbach catchment (runoff ratio ¼ 0.73), where the approach worked well during wet conditions, but failed during dry summers.…”

Concentration–discharge relationships reflect chemostatic characteristics of US catchments

“…However, because b 0 is usually close to zero for different solutes, it is possible that the variation in p may be small. Another parameter, b 1 , has been shown to relate storage and discharge in catchments, and is expressed as a function of the parameters k and (Kirchner, 2009; and see Appendix, Equation A12 and A13). The two log-log slopes b 0 and b 1 are not sufficient to uniquely constrain the three parameters k , and p , so the individual e-folding depths (as well as values of the reactivity parameter k R for each solute, see Appendix) could only be determined by direct measurement.…”

Estimation of Active Stream Network Length in a Hilly Headwater Catchment Using Recession Flow Analysis

“…The backward difference approximation of dQ/dt (=(Qt-t − Qt)/ t) was calculated using consecutive daily flows and plotted against the arithmetic mean ((Qt-t + Qt)/2) of the corresponding flows [1]. Next, along with simulated actual daily evapotranspiration (AET) from the soil, and infiltration (AI) into the soil-both calculated by the GSFLOW model-recession stream flows were selected according to the following criteria [27][28][29]: (1) data points with no positive values of dQ/dt, and (2) data points when the absolute ratio of (AI-AET) to observed Q is smaller than 0.1. As a result, 51 individual recessions with at least four continuous days' length were derived.…”