The falling limb of the hydrograph - the streamflow recession - is frequently well approximated by power law functions, in the form dq/dt = -aqb, so that recessions are often characterized in terms of their power law parameters (a, b). The empirical determination and interpretation of the parameter a is typically biased by the presence of a ubiquitous mathematical artifact resulting from the scale-free properties of the power law function. This reduces the information available from recession parameter analysis and creates several heretofore unaddressed methodological "pitfalls." This letter outlines the artifact, demonstrates its genesis, and presents an empirical rescaling method to remove artifact effects from fitted recession parameters. The rescaling process reveals underlying climatic patterns obscured in the original data and, we suggest, could maximize the information content of fitted power laws.

In seasonally dry climates, a distinct rainy season is followed by a pronounced dry season during which rainfall often makes a negligible contribution to soil moisture. Using stochastic analytical models of soil moisture to represent the effects of this seasonal change has been hindered by the need to mathematically represent the stochastic influence of wet season climate on dry season soil water dynamics. This study presents a simple process-based stochastic model for soil moisture dynamics, which explicitly models interseasonal transient dynamics while accounting for carry over soil moisture storage between the wet and dry seasons, and allows a derivation of an analytical expression for the dry season mean first passage time below a soil moisture threshold. Such crossing times pose controls on both vegetation productivity and water stress during dry summers. The new model, along with an existing model that incorporates nonzero dry season rainfall but not variability in the soil moisture condition at the start of the dry season, are tested against data from the Tonzi Ranch Ameriflux site. Both models predict first passage times well for high soil moisture thresholds, but the new model improves prediction at lower thresholds. The annual soil moisture probability distribution function (PDF) from the new model also compares well with observations.

The linearized hillslope Boussinesq equation, introduced by Brutsaert (1994), describes the dynamics of saturated, subsurface flow from hillslopes with shallow, unconfined aquifers. In this paper, we use a new analytical technique to solve the linearized hillslope Boussinesq equation to predict water table dynamics and hillslope discharge to channels. The new solutions extend previous analytical treatments of the linearized hillslope Boussinesq equation to account for the impact of spatiotemporal heterogeneity in water table recharge. The results indicate that the spatial character of recharge may significantly alter both steady state subsurface storage characteristics and the transient hillslope hydrologic response, depending strongly on similarity measures of controls on the subsurface flow dynamics. Additionally, we derive new analytical solutions for the linearized hillslope-storage Boussinesq equation and explore the interaction effects of recharge structure and hillslope morphology on water storage and base flow recession characteristics. A theoretical recession analysis, for example, demonstrates that decreasing the relative amount of downslope recharge has a similar effect as increasing hillslope convergence. In general, the theory suggests that recharge heterogeneity can serve to diminish or enhance the hydrologic impacts of hillslope morphology.

Flow duration curves (FDC) display streamflow values against their relative exceedance time. They provide critical information for watershed management by representing the variation in the availability and reliability of surface water to supply ecosystem services and satisfy anthropogenic needs. FDCs are particularly revealing in seasonally dry climates, where surface water supplies are highly variable. While useful, the empirical computation of FDCs is data intensive and challenging in sparsely gauged regions, meaning that there is a need for robust, predictive models to evaluate FDCs with simple parameterization. Here, we derive a process-based analytical expression for FDCs in seasonally dry climates. During the wet season, streamflow is modeled as a stochastic variable driven by rainfall, following the stochastic analytical model of Botter et al. (2007a). During the dry season, streamflow is modeled as a deterministic recession with a stochastic initial condition that accounts for the carryover of catchment storage across seasons. The resulting FDC model is applied to 38 catchments in Nepal, coastal California, and Western Australia, where FDCs are successfully modeled using five physically meaningful parameters with minimal calibration. A Monte Carlo analysis revealed that the model is robust to deviations from its assumptions of Poissonian rainfall, exponentially distributed response times and constant seasonal timing. The approach successfully models period-of-record FDCs and allows interannual and intra-annual sources of variations in dry season streamflow to be separated. The resulting median annual FDCs and confidence intervals allow the simulation of the consequences of interannual flow variations for infrastructure projects. We present an example using run-of-river hydropower in Nepal as a case study. Key Points Probabilistic derivation of flow distribution in seasonally dry climate Successfully applied in Nepal, California, and Western Australia Disentangles inter- and intra-annual streamflow variations © 2014. American Geophysical Union. All Rights Reserved.

Seasonally dry ecosystems exhibit periods of high water availability followed by extended intervals during which rainfall is negligible and streamflows decline. Eventually, such declining flows will fall below the minimum values required to support ecosystem functions or services. The time at which dry season flows drop below these minimum values (Q∗), relative to the start of the dry season, is termed the "persistence time" (). The persistence time determines how long seasonal streams can support various human or ecological functions during the dry season. In this study, we extended recent work in the stochastic hydrology of seasonally dry climates to develop an analytical model for the probability distribution function (PDF) of the persistence time. The proposed model accurately captures the mean of the persistence time distribution, but underestimates its variance. We demonstrate that this underestimation arises in part due to correlation between the parameters used to describe the dry season recession, but that this correlation can be removed by rescaling the flow variables. The mean persistence time predictions form one example of the broader class of streamflow statistics known as crossing properties, which could feasibly be combined with simple ecological models to form a basis for rapid risk assessment under different climate or management scenarios.

A broad class of soil fungi form the annular patterns known as 'fairy rings' and provide one of the only means to observe spatio-temporal dynamics of otherwise cryptic fungal growth processes in natural environments. We present observations of novel spiral and rotor patterns produced by fairy ring fungi and explain these behaviors mathematically by first showing that a well known model of fairy ring fungal growth and the Gray-Scott reaction-diffusion model are mathematically equivalent. We then use bifurcation analysis and numerical simulations to identify the conditions under which spiral waves and rotors can arise. We demonstrate that the region of dimensionless parameter space supporting these more complex dynamics is adjacent to that which produces the more familiar fairy rings, and identify experimental manipulations to test the transitions between these spatial modes. These same manipulations could also feasibly induce fungal colonies to transition from rotor/spiral formation to a set of richer, as yet unobserved, spatial patterns.

The study of single streamflow recession events is receiving increasing attention following the presentation of novel theoretical explanations for the emergence of power law forms of the recession relationship, and drivers of its variability. Individually characterizing streamflow recessions often involves describing the similarities and differences between model parameters fitted to each recession time series. Significant methodological sensitivity has been identified in the fitting and parameterization of models that describe populations of many recessions, but the dependence of estimated model parameters on methodological choices has not been evaluated for event-by-event forms of analysis. Here, we use daily streamflow data from 16 catchments in northern California and southern Oregon to investigate how combinations of commonly used streamflow recession definitions and fitting techniques impact parameter estimates of a widely used power law recession model. Results are relevant to watersheds that are relatively steep, forested, and rain-dominated. The highly seasonal mediterranean climate of northern California and southern Oregon ensures study catchments explore a wide range of recession behaviors and wetness states, ideal for a sensitivity analysis. In such catchments, we show the following: (i) methodological decisions, including ones that have received little attention in the literature, can impact parameter value estimates and model goodness of fit; (ii) the central tendencies of event-scale recession parameter probability distributions are largely robust to methodological choices, in the sense that differing methods rank catchments similarly according to the medians of these distributions; (iii) recession parameter distributions are method-dependent, but roughly catchment-independent, such that changing the choices made about a particular method affects a given parameter in similar ways across most catchments; and (iv) the observed correlative relationship between the power-law recession scale parameter and catchment antecedent wetness varies depending on recession definition and fitting choices. Considering study results, we recommend a combination of four key methodological decisions to maximize the quality of fitted recession curves, and to minimize bias in the related populations of fitted recession parameters.

Quantifying evapotranspiration is critical to accurately predict vegetation health, groundwater recharge, and streamflow generation. Hillslope aspect, the direction a hillslope faces, results in variable incoming solar radiation and subsequent vegetation water use that influence the timing and magnitude of evapotranspiration. Previous work in forested landscapes has shown that equator-facing slopes have higher evapotranspiration due to more direct solar radiation and higher evaporative demand. However, it remains unclear how differences in vegetation type (i.e., grasses and trees) influence evapotranspiration and water partitioning between hillslopes with opposing aspects. Here, we quantified evapotranspiration and subsurface water storage deficits between a pole- and equator-facing hillslope with contrasting vegetation types within central coastal California. Our results suggest that cooler pole-facing slopes with oak trees have higher evapotranspiration than warmer equator-facing slopes with grasses, which is counter to previous work in landscapes with singular vegetation types. Our water storage deficit calculations indicate that the pole-facing slope has a higher subsurface storage deficit and a larger seasonal dry down than the equator-facing slope. This aspect difference in subsurface water storage deficits may influence subsequent deep groundwater recharge and streamflow generation. In addition, larger root-zone storage deficits on pole-facing slopes may reduce their ability to serve as hydrologic refugia for oaks during periods of extended drought. This research provides a novel integration of field-based and remotely-sensed estimates of evapotranspiration required to properly quantify hillslope-scale water balances. These findings emphasize the importance of resolving hillslope-scale vegetation structure within Earth system models, especially in landscapes with diverse vegetation types.

Abstract: Quantifying evapotranspiration (ET) is critical to accurately predict vegetation health, groundwater recharge, and streamflow generation. Hillslope aspect, the direction a hillslope faces, results in variable incoming solar radiation and subsequent vegetation water use that drive ET. Previous work in watersheds with a single dominant vegetation type (e.g., trees) have shown that equator‐facing slopes (EFS) have higher ET compared to pole‐facing slopes (PFS) due to higher evaporative demand. However, it remains unclear how differences in vegetation type (i.e., grasses and trees) influence ET and water partitioning between hillslopes with opposing aspects. Here, we quantified ET and root‐zone water storage deficits between a PFS and EFS with contrasting vegetation types within central coastal California. Our results suggest that the cooler PFS with oak trees has higher ET than the warmer EFS with grasses, which is counter to previous work in landscapes with a singule dominant vegetation type. Our root‐zone water storage deficit calculations indicate that the PFS has a higher subsurface storage deficit and a larger seasonal dry down than the EFS. This aspect difference in subsurface water storage deficits may influence the subsequent replenishment of dynamic water storage, groundwater recharge and streamflow generation. In addition, larger subsurface water deficits on PFS may reduce their ability to serve as hydrologic refugia for oaks during multi‐year droughts. This research provides a novel integration of field‐based and remotely‐sensed estimates of ET required to properly quantify hillslope‐scale water balances. These findings emphasize the importance of resolving hillslope‐scale vegetation structure within Earth system models, especially in landscapes with diverse vegetation types.