David N. Dralle

Analytical model for flow duration curves in seasonally dry climates

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

Dry season streamflow persistence in seasonal climates

PUBLICATIONS Water Resources Research RESEARCH ARTICLE Dry season streamflow persistence in seasonal climates 10.1002/2015WR017752 David N. Dralle 1 , Nathaniel J. Karst 2 , and Sally E. Thompson 1 Key Points: Derived probabilistic model for the persistence time of dry season high flow conditions Successfully predicts mean, but not variance; attributed to inter-annual recession model variation Proposed framework for using crossing statistics (e.g., persistence time) to forecast ecologic risk Supporting Information: Supporting Information S1 Figure S1 Figure S2 Correspondence to: D. N. Dralle, dralle@berkeley.edu Citation: Dralle, D. N., N. J. Karst, and S. E. Thompson (2015), Dry season streamflow persistence in seasonal climates, Water Resour. Res., 51, doi:10.1002/2015WR017752. Received 26 JUN 2015 Accepted 8 DEC 2015 Accepted article online 13 DEC 2015 C 2015. American Geophysical Union. V All Rights Reserved. DRALLE ET AL. Department of Civil and Environmental Engineering, University of California, Berkeley, California, USA, 2 Division of Mathematics and Science Division, Babson College, Wellesley, Massachusetts, USA Abstract 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 sea- son flows drop below these minimum values (Q * ), relative to the start of the dry season, is termed the ‘‘persistence time’’ (T Q ). 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 stochas- tic 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 persist- ence 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. 1. Introduction Pronounced variability in precipitation is the defining characteristic of seasonally dry ecosystems (SDE) [Fati- chi et al., 2012; Vico et al., 2014], which cover nearly 30% of the planet and contain about 30% of the Earth’s population [Peel and Finlayson, 2007; CIESIN, 2012]. In these regions, a distinct rainy season is followed by a pronounced dry season during which rainfall makes a small or negligible contribution to the water balance. As a consequence, the availability of dry season surface water resources depends strongly on streamflow, which is generated primarily from the storage and subsequent discharge of antecedent wet season rainfall in the subsurface [Brahmananda Rao et al., 1993; Samuel et al., 2008; Andermann et al., 2012]. Because these transient stores are strongly influenced by the characteristics of the wet season climate, dry-season water availability can be highly variable from year to year in many SDE’s [Samuel et al., 2008; Andermann et al., 2012]. This hydroclimatic variability leaves SDE’s, considered important ‘‘hot spots’’ of biodiversity [Miles et al., 2006; Klausmeyer and Shaw, 2009], and the human populations that depend upon them susceptible to threats, such as soil erosion, deforestation, and water diversions [Miles et al., 2006; Underwood et al., 2009]. Future climate scenarios are projected to further intensify wet season rainfall variability in many SDEs [e.g., Gao and Giorgi, 2008; Garc ia-Ruiz et al., 2011; Dominguez et al., 2012], necessitating models which can pre- dict the response of water resources to climatic change in order to measure the corresponding risk to local ecosystems and human populations [Vico et al., 2014; M€ uller et al., 2014]. Stochastic methods have a 30 year history of use in deriving simple, process-based models for the probabil- ity distributions of hydrologic variables, such as soil moisture, streamflow, and associated ecological responses [Milly, 1993; Szilagyi et al., 1998; Rodriguez-Iturbe et al., 1999; Laio, 2002; Botter et al., 2007; Thomp- son et al., 2013, 2014]. To date, the majority of stochastic analytical models for hydrology have been devel- oped under conditions where the climatic forcing does not exhibit strong seasonality [Rodriguez-Iturbe et al., 1999; Porporato et al., 2004; Botter et al., 2007]. Those studies that have considered the effects of sea- sonality in rainfall or evaporative demand have either focused on the mean dynamics of the variable of interest [Laio, 2002; Feng et al., 2012, 2015] or excluded a treatment of the transient dynamics between the wet and dry seasons [D’odorico et al., 2000; Miller et al., 2007; Kumagai et al., 2009]. This is problematic in DRY SEASON STREAMFLOW PERSISTENCE IN SEASONAL CLIMATES

High Time for Conservation: Adding the Environment to the Debate on Marijuana Liberalization

The liberalization of marijuana policies, including the legalization of medical and recreational marijuana, is sweeping the United States and other countries. Marijuana cultivation can have significant negative collateral effects on the environment that are often unknown or overlooked. Focusing on the state of California, where by some estimates 60%–70% of the marijuana consumed in the United States is grown, we argue that (a) the environmental harm caused by marijuana cultivation merits a direct policy response, (b) current approaches to governing the environmental effects are inadequate, and (c) neglecting discussion of the environmental impacts of cultivation when shaping future marijuana use and possession policies represents a missed opportunity to reduce, regulate, and mitigate environmental harm.

A minimal probabilistic model for soil moisture in seasonally dry climates

PUBLICATIONS Water Resources Research TECHNICAL REPORTS: METHODS 10.1002/2015WR017813 Key Points: Develops a model for analytic soil moisture PDFs and crossing times in seasonally dry regions Presents a novel representation of soil moisture conditions at the beginning of the dry season Successful test using AmeriFlux soil moisture data from Tonzi Ranch Correspondence to: D. N. Dralle, dralle@berkeley.edu Citation: Dralle, D. N., and S. E. Thompson (2016), A minimal probabilistic model for soil moisture in seasonally dry climates, Water Resour. Res., 52, doi:10.1002/2015WR017813. A minimal probabilistic model for soil moisture in seasonally dry climates David N. Dralle 1 and Sally E. Thompson 1 Department of Civil and Environmental Engineering, University of California, Berkeley, Berkeley, California, USA Abstract In seasonally dry climates, a distinct rainy season is followed by a pronounced dry season dur- ing 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 mathe- matically 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. Received 7 JUL 2015 Accepted 17 JAN 2016 Accepted article online 20 JAN 2016 1. Introduction Seasonally dry ecosystems (SDEs), which include Mediterranean, tropical monsoonal, and tropical savannah climates, cover approximately 30% of the Earth’s land area [Peel et al., 2007] and contain several biodiversity hot spots [Miles et al., 2006; Klausmeyer and Shaw, 2009]. Pronounced climatic variability is a common fea- ture of these regions [Fatichi et al., 2012] and is projected to intensify in future climate scenarios [Gao and Giorgi, 2008; Garc ia-Ruiz et al., 2011; Dominguez et al., 2012]. Consequently, a number of studies classify SDEs and their water resources as climatically vulnerable [Nohara et al., 2006; Parry, 2007; Gao and Giorgi, 2008; Klausmeyer and Shaw, 2009; Garc ia-Ruiz et al., 2011]. Projecting the variability of water availability and the risks of water shortfalls in these regions could therefore provide useful insights into vegetation and eco- system risk [Vico et al., 2015; M€ uller et al., 2014]. Process-based stochastic methods provide a minimal modeling framework to obtain the probability distri- butions of soil moisture and streamflow [Milly, 1993; Rodr iguez-Iturbe et al., 1999; Laio et al., 2002; Botter et al., 2007]. Since hydroclimatic variation strongly impacts plants through soil moisture [Taiz and Zeiger, 2010; Thompson and Katul, 2012], these models have also been used to predict ecological response and to assess the vulnerability of ecosystems [Porporato et al., 2004; Viola et al., 2008; Thompson et al., 2013 2014]. To date, the majority of methods have been developed under conditions where either the climatic forcing can be considered stationary in time [Rodr iguez-Iturbe et al., 1999; Porporato et al., 2004; Botter et al., 2007] or where transient dynamics between seasons are not considered [Miller et al., 2007; Kumagai et al., 2009]. Studies that considered the effects on soil moisture of seasonality in rainfall or evaporative demand, or tran- sient dynamics between seasons, have typically focused on the mean soil moisture dynamics [D’Odorico et al., 2000; Laio et al., 2001; Feng et al., 2012; Feng et al., 2015]. C 2016. American Geophysical Union. V All Rights Reserved. DRALLE AND THOMPSON Viola et al. [2008] first investigated the impacts of transient soil moisture dynamics on plant water stress dur- ing the growing season in Mediterranean ecosystems. In that study, the steady state PDF of soil moisture during the wet season represents the end of wet season conditions, after which the dry season proceeds following a step change in rainfall statistics and potential evapotranspiration. For a site with shallow soil or a small mean rainfall depth (relative to the total possible amount of soil water storage), this approach is appropriate because the variance of wet season conditions will be small. However, to accurately quantify SEASONAL SOIL MOISTURE PDFS

Spatially variable water table recharge and the hillslope hydrologic response: Analytical solutions to the linearized hillslope Boussinesq equation

© 2014. American Geophysical Union. All Rights Reserved. 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.

Stochastic modeling of interannual variation of hydrologic variables

Quantifying the inter-annual variability of hydrologic variables (such as annual flow volumes, solute or sediment loads) is a central challenge in hydrologic modeling. Annual or seasonal hydrologic variables are themselves the integral of instantaneous variations, and can be well-approximated as an aggregate sum of the daily variable. Process-based, probabilistic techniques are available to describe the stochastic structure of daily flow, yet estimating inter-annual variations in the corresponding aggregated variable requires consideration of the autocorrelation structure of the flow time series. Here, we present a method based on a probabilistic streamflow description to obtain the inter-annual variability of flow-derived variables. The results provide insight into the mechanistic genesis of inter-annual variability of hydrologic processes. Such clarification can assist in the characterization of ecosystem risk and uncertainty in water resources management. We demonstrate two applications, one quantifying seasonal flow variability and the other quantifying net suspended sediment export.