Infrastructure Engineering - Research Publications

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    Analytical methods for ecosystem resilience: A hydrological investigation
    Peterson, TJ ; Western, AW ; Argent, RM (AMERICAN GEOPHYSICAL UNION, 2012-10-16)
    In recent years a number of papers have quantitatively explored multiple steady states and resilience within a wide range of hydrological systems. Many have identified multiple steady states by conducting simulations from different initial state variables and a few have used the more advanced technique of equilibrium or limit cycle continuation analysis to quantify how the number of steady states may change with a single model parameter. However, like resilience investigations into other natural systems, these studies often omit explanation of these fundamental resilience science techniques; rely on complex numerical methods rather than analytical methods; and overlook use of more advanced techniques from nonlinear systems mathematics. In the interests of wider adoption of advanced resilience techniques within hydrology, and advancing resilience science more broadly, this paper details fundamental methods for quantitative resilience investigations. Using a simple model of a spatially lumped unconfined aquifer, one and two parameter continuation analysis was undertaken algebraically. The shape of each steady state attractor basin was then quantified using Lyapunov stability curves derived at a range of precipitation rates, but was found to be inconsistent with the resilience behavior demonstrated by stochastic simulations. Most notably, and contrary to standard resilience concepts, the switching between steady states from wet or dry periods (and vice versa) did not occur by crossing of the threshold between the steady states. It occurred by exceedance of the two steady-state domain, producing a counterclockwise hysteresis loop. Additionally, temporary steady states were identified that could not have been detected using equilibrium continuation with a constant forcing rate. By combining these findings with the Lyapunov stability curves, new measures of resilience were developed for endogenous disturbances to the model and for the recovery from disturbances exogenous to the model.
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    Seasonal and event dynamics of spatial soil moisture patterns at the small catchment scale
    Rosenbaum, U ; Bogena, HR ; Herbst, M ; Huisman, JA ; Peterson, TJ ; Weuthen, A ; Western, AW ; Vereecken, H (AMERICAN GEOPHYSICAL UNION, 2012-10-27)
    Our understanding of short- and long-term dynamics of spatial soil moisture patterns is limited due to measurement constraints. Using new highly detailed data, this research aims to examine seasonal and event-scale spatial soil moisture dynamics in the topsoil and subsoil of the small spruce-covered Ẅstebach catchment, Germany. To accomplish this, univariate and geo-statistical analyses were performed for a 1 year long 4-D data set obtained with the wireless sensor network SoilNet. We found large variations in spatial soil moisture patterns in the topsoil, mostly related to meteorological forcing. In the subsoil, temporal dynamics were diminished due to soil water redistribution processes and root water uptake. Topsoil range generally increased with decreasing soil moisture. The relationship between the spatial standard deviation of the topsoil soil moisture (SDθ) and mean water content (θ) showed a convex shape, as has often been found in humid temperate climate conditions. Observed scatter in topsoil SD θ(θ) was explained by seasonal and event-scale SD θ(θ) dynamics, possibly involving hysteresis at both time scales. Clockwise hysteretic SDθ(θ) dynamics at the event scale were generated under moderate soil moisture conditions only for intense precipitation that rapidly wetted the topsoil and increased soil moisture variability controlled by spruce throughfall patterns. This hysteretic effect increased with increasing precipitation, reduced root water uptake, and high groundwater level. Intense precipitation on dry topsoil abruptly increased SDθ but only marginally increased mean soil moisture. This was due to different soil rewetting behavior in drier upslope areas (hydrophobicity and preferential flow caused minor topsoil recharge) compared with the moderately wet valley bottom (topsoil water storage), which led to a more spatially organized pattern. This study showed that spatial soil moisture patterns monitored by a wireless sensor network varied with depth, soil moisture content, seasonally, and within single wetting and drying episodes. This was controlled by multiple factors including soil properties, topography, meteorological forcing, vegetation, and groundwater.
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    Multiple hydrological attractors under stochastic daily forcing: 1. Can multiple attractors exist?
    Peterson, TJ ; Western, AW (AMERICAN GEOPHYSICAL UNION, 2014-04-01)
    Including positive feedbacks in hydrological models has recently been shown to result in complex behavior with multiple steady states. When a large disturbance, say a major drought, is simulated within such models the hydrology changes. Once the disturbance ends the hydrology does not return to that prior to the disturbance, but rather, persists within an alternate state. These multiple steady states (henceforth attractors) exist for a single model parameterization and cause the system to have a finite resilience to such transient disturbances. A limitation of past hydrological resilience studies is that multiple attractors have been identified using mean annual or mean monthly forcing. Considering that most hydrological fluxes are subject to significant forcing stochasticity and do not operate at such large timescales, it remains an open question whether multiple hydrological attractors can exist when a catchment is subject to stochastic daily forcing. This question is the focus of this paper and it needs to be addressed prior to searching for multiple hydrological attractors in the field. To investigate this, a previously developed semidistributed hillslope ecohydrological model was adopted which exhibited multiple steady states under average monthly climate forcing. In this paper, the ecohydrological model was used to explore if feedbacks between the vegetation and a saline water table result in two attractors existing under daily stochastic forcing. The attractors and the threshold between them (henceforth repellor) were quantified using a new limit cycle continuation technique that upscaled climate forcing from daily to monthly (model and limit cycle code is freely available). The method was used to determine the values of saturated lateral hydraulic conductivity at which multiple attractors exist. These estimates were then assessed against time-integration estimates, which they agreed with. Overall, multiple attractors were found to exist under stochastic daily forcing. However, changing the climate forcing from monthly to daily did significantly reduce the parameter range over which two attractors existed. This suggests fewer catchments may have multiple attractors than previously considered.
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    Multiple hydrological attractors under stochastic daily forcing: 2. Can multiple attractors emerge?
    Peterson, TJ ; Western, AW ; Argent, RM (AMERICAN GEOPHYSICAL UNION, 2014-04-01)
    The companion paper showed that multiple steady state groundwater levels can exist within a hill-slope Boussinesq-vegetation model under daily stochastic forcing. Using a numerical limit-cycle continuation algorithm, the steady states (henceforth attractors) and the threshold between them (henceforth repellor) were quantified at a range of saturated lateral conductivity values, ksmax. This paper investigates if stochastic daily forcing can switch the catchment between both of the attractors. That is, an attractor may exist under average forcing conditions but can stochastic forcing switch the catchment into and out of each of the attractor basins-; i.e., making the attractor emerge. This was undertaken using the model of the companion paper and by completing daily time-integration simulations at six values of the saturated lateral hydraulic conductivity, ksmax; three having two attractors and three having only a deep water table attractor. By graphically analyzing the simulations, and comparing against simulations from a model modified to have only one attractor, multiple attractors were found to emerge under stochastic daily forcing. However, the emergence of attractors was significantly more subtle and complex than that suggested by the companion paper. That is, an attractor may exist but never emerge; both attractors may exist and both may emerge but identifying the switching between attractors was often ambiguous; and only one attractor may exist and but a second temporary attractor may exist and emerge during periods of high precipitation. This subtle and complex emergence of attractors was explained using continuation analysis of the climate forcing rate, and not a model parameter such as ksmax. It showed that the temporary attractor existed over a large range of ksmax values and this suggests that more catchments may have multiple attractors than suggested by the companion paper. By combining this continuation analysis with the time-integration simulations, hydrological signatures indicative of a switch of multiple attractors were proposed. These signatures may provide a means for identifying actual catchments that have switched between multiple attractors. Key Points Stochastic daily forcing can switch a catchment to both attractors Emergence of attractors differs significantly from the existence of attractors Switching between attractor basins can be subtle and difficult to identify
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    Nonlinear time-series modeling of unconfined groundwater head
    Peterson, TJ ; Western, AW (AMER GEOPHYSICAL UNION, 2014-10-01)
    This paper presents a nonlinear transfer function noise model for time-series modeling of unconfined groundwater hydrographs. The motivation for its development was that existing groundwater time-series models were unable to simulate large recharge events and multiyear droughts. This was because existing methods do not partition rainfall to runoff and do not account for nonlinear soil water drainage. To account for these nonlinear processes, a vertically integrated soil moisture module was added to an existing transfer function noise model. The soil moisture module has a highly flexible structure that allowed 84 different forms to be built. Application of the time-series model requires numerical calibration of parameters for the transfer functions, noise model and, for the nonlinear models, the soil moisture module. This was undertaken using the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) global calibration scheme. However, reproducible calibration to the global optima was challenging and a number of modifications were required to the transfer function noise model. In trialing the 84 nonlinear models and 2 linear models, each was applied to eleven observation bores within a paired catchment study area in Great Western, Victoria, Australia. In comparison with existing groundwater hydrograph time-series models, the proposed nonlinear time-series model performed significantly better at all observation bores during calibration and evaluation periods. Both the linear and nonlinear models were also used to quantify the impact of revegetation within the paired catchment; however, results were inconclusive, which is likely due to time-series data for the state of the revegetation being unavailable. By analyzing the application of 84 nonlinear models to each bore, an optimal structure for the soil moisture module was identified. It is unlikely, however, that this model structure would be appropriate for all climates and geologies. To encourage further investigations, open-source code for the highly flexible groundwater time-series modeling framework is available and we invite others to develop new models. Key Points Groundwater hydrograph models cannot simulate episodic recharge and droughts Nonlinear transformation of climate forcing overcame these weaknesses Robust calibration required reformulation of existing time-series equations
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    A synthetic study to evaluate the utility of hydrological signatures for calibrating a base flow separation filter
    Su, C-H ; Peterson, TJ ; Costelloe, JF ; Western, AW (AMER GEOPHYSICAL UNION, 2016-08-01)
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    Can we manage groundwater? A method to determine the quantitative testability of groundwater management plans
    White, EK ; Peterson, TJ ; Costelloe, J ; Western, AW ; Carrara, E (AMER GEOPHYSICAL UNION, 2016-06-01)
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    On the structural limitations of recursive digital filters for base flow estimation
    Su, C-H ; Costelloe, JF ; Peterson, TJ ; Western, AW (AMER GEOPHYSICAL UNION, 2016-06-01)
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    Equifinality and Flux Mapping: A New Approach to Model Evaluation and Process Representation Under Uncertainty
    Khatami, S ; Peel, MC ; Peterson, TJ ; Western, AW (AMER GEOPHYSICAL UNION, 2019-11-12)
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    Statistical Interpolation of Groundwater Hydrographs
    Peterson, TJ ; Western, AW (AMER GEOPHYSICAL UNION, 2018-07-01)