Infrastructure Engineering - Research Publications

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    Multiple stable states in hydrological models: An ecohydrological investigation
    Peterson, TJ ; Argent, RM ; Western, AW ; Chiew, FHS (American Geophysical Union, 2009-03-07)
    Many physical-based models of surface and groundwater hydrology are constructed without the possibility of multiple stable states for the same parameter set. For such a conceptualization, at the cessation of a transient hydrological disturbance of any magnitude the model will return to the same stable state and thus show an infinite resilience. To highlight and falsify this assumption, a numerical distributed ecohydrological model (coupled hillslope Boussinesq-vertically lumped vadose zone) is presented, in which qualitatively different steady state water table elevations exist for the same parameter set. The multiple steady states are shown to emerge from a positive feedback arising from a reduction in leaf area index (LAI) and thus transpiration, as a saline water table approaches the surface. Limit cycle continuation is also undertaken to quantify the state-space location of the threshold (repellor) between the steady states (attractors) and quantify the resilience. While the model is biophysically simple, it is sufficiently complex to challenge this potentially significant assumption within water resource planning.
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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)
    Abstract 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.
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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)
    Abstract Estimation of base flow from streamflow hydrographs has been a major challenge in hydrology for decades, leading to developments of base flow separation filters. When without tracer or groundwater data to calibrate the filters, the standard approach to apply these filters in practice involves some degrees of subjectivity in choosing the filter parameters. This paper investigates the use of signature‐based calibration in implementing base flow filtering by testing seven possible hydrological signatures of base flow against modeled daily base flow produced by Li et al. (2014) for a range of synthetic catchments simulated with HydroGeoSphere. Our evaluation demonstrates that such a calibration method with few selected signatures as objectives is capable of calibrating a filter–Eckhardt filter–to yield satisfactory base flow estimates at daily, monthly and long‐term time scales, outperforming the standard approach. The best performing signatures can be readily derived from streamflow time series. While their performance depends on the catchment characteristics, the catchments where the signature method performs can be distinguished using commonly‐used descriptors of flow dynamics.
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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)
    Abstract Groundwater is the world's largest freshwater resource and due to overextraction, levels have declined in many regions causing extensive social and environmental impacts. Groundwater management seeks to balance and mitigate the detrimental impacts of development, with plans commonly used to outline management pathways. Thus, plan efficiency is crucial, but seldom are plans systematically and quantitatively assessed for effectiveness. This study frames groundwater management as a system control problem in order to develop a novel testability assessment rubric to determine if plans meet the requirements of a control loop, and subsequently, whether they can be quantitatively tested. Seven components of a management plan equivalent to basic components of a control loop were determined, and requirements of each component necessary to enable testability were defined. Each component was weighted based upon proposed relative importance, then segmented into rated categories depending on the degree the requirements were met. Component importance varied but, a defined objective or acceptable impact was necessary for plans to be testable. The rubric was developed within the context of the Australian groundwater management industry, and while use of the rubric is not limited to Australia, it was applied to 15 Australian groundwater management plans and approximately 47% were found to be testable. Considering the importance of effective groundwater management, and the central role of plans, our lack of ability to test many plans is concerning.
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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)
    Abstract Recursive digital filters (RDFs) are widely used for estimating base flow from streamflow hydrographs, and various forms of RDFs have been developed based on different physical models. Numerical experiments have been used to objectively evaluate their performance, but they have not been sufficiently comprehensive to assess a wide range of RDFs. This paper extends these studies to understand the limitations of a generalized RDF method as a pathway for future field calibration. Two formalisms are presented to generalize most existing RDFs, allowing systematic tuning of their complexity. The RDFs with variable complexity are evaluated collectively in a synthetic setting, using modeled daily base flow produced by Li et al. (2014) from a range of synthetic catchments simulated with HydroGeoSphere. Our evaluation reveals that there are optimal RDF complexities in reproducing base flow simulations but shows that there is an inherent physical inconsistency within the RDF construction. Even under the idealized setting where true base flow data are available to calibrate the RDFs, there is persistent disagreement between true and estimated base flow over catchments with small base flow components, low saturated hydraulic conductivity of the soil and larger surface runoff. The simplest explanation is that low base flow “signal” in the streamflow data is hard to distinguish, although more complex RDFs can improve upon the simpler Eckhardt filter at these catchments.
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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)
    Abstract Uncertainty analysis is an integral part of any scientific modeling, particularly within the domain of hydrological sciences given the various types and sources of uncertainty. At the center of uncertainty rests the concept of equifinality, that is, reaching a given endpoint (finality) through different pathways. The operational definition of equifinality in hydrological modeling is that various model structures and/or parameter sets (i.e., equal pathways) are equally capable of reproducing a similar (not necessarily identical) hydrological outcome (i.e., finality). Here we argue that there is more to model equifinality than model structures/parameters, that is, other model components can give rise to model equifinality and/or could be used to explore equifinality within model space. We identified six facets of model equifinality, namely, model structure, parameters, performance metrics, initial and boundary conditions, inputs, and internal fluxes. Focusing on model internal fluxes, we developed a methodology called flux mapping that has fundamental implications in understanding and evaluating model process representation within the paradigm of multiple working hypotheses. To illustrate this, we examine the equifinality of runoff fluxes of a conceptual rainfall‐runoff model for a number of different Australian catchments. We demonstrate how flux maps can give new insights into the model behavior that cannot be captured by conventional model evaluation methods. We discuss the advantages of flux space, as a subspace of the model space not usually examined, over parameter space. We further discuss the utility of flux mapping in hypothesis generation and testing, extendable to any field of scientific modeling of open complex systems under uncertainty.