A software tool to assess uncertainty in transient-storage model parameters using Monte Carlo simulations

Ward, Adam S.; Kelleher, Christa; Mason, Seth J.K.; Wagener, Thorsten; McIntyre, Neil; McGlynn, B. L.; Runkel, Robert L.; Payn, R. A.

doi:10.1086/690444

Cited by 36 publications

(103 citation statements)

References 58 publications

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“…However, our results also demonstrate that with increased complexity comes increased uncertainty with respect to other model parameters. Studies utilizing 2SZ models, or any TSM for that matter, should ultimately evaluate the uncertainty associated with parameter estimates (echoing past recommendations; Kelleher et al, ; Wagener et al, ; Ward et al, ). This need for uncertainty evaluation is especially clear in our analysis, in that we demonstrate that while this uncertainty may be reduced for 2SZ as compared to 1SZ models for some scenarios and parameters, uncertainty can still increase for other scenarios and parameters.…”

Section: Discussionmentioning

confidence: 95%

“…Parameters that are not identifiable may provide a good inverse model fit without characterizing system processes and should not be overinterpreted (e.g., by comparing or interpreting values of insensitive or uncertain parameters). Thus, we echo calls for assessment of model parameter uncertainties, interactions, and identifiability as a requisite step prior to their interpretation (Kelleher et al, 2013;Wagener et al, 2002;Wagner & Harvey, 1997;Ward et al, 2017).…”

Section: Model Complexity and Conceptualization Simulations And Errorsmentioning

confidence: 94%

“…For each of the 27,000 runs, we calculated model fits in terms of a normalized root‐mean square error (nRMSE) for each BTC (Ura, Raz, and Rru) independently, according to

nRMSE = \frac{1}{C_{p}} {(\frac{\sum_{t = 1}^{n} {(O_{t} - S_{t})}^{2}}{n})}^{0.5}

where O t and S t correspond to observations and simulations at a given time step, n is the total number of observations, and C p is peak concentration for each tracer (employed to normalize RMSE values across tracers; g/m 3 ). RMSE (and close variants) remains one of the key objective functions used to assess BTC errors (Runkel, ; Ward et al, ). We also calculated a log‐transformed root‐mean square error (LRMSE; similar to a weighted RMSE), where the observed and simulated time series were log‐transformed prior to applying equation above.…”

Section: Transient Storage Modelingmentioning

confidence: 99%

“…When combined with field observations of tracers in the form of a BTC, estimates of model parameters representing the temporal (i.e., rate of exchange) and spatial scales (i.e., size) of reach‐averaged transient storage zone exchange can be obtained via inverse modeling (Runkel, ). This is done by employing one of many methods (e.g., Runkel, ; Wagener et al, ; Kelleher et al, ; Knapp & Cirpka, ) to search the parameter space for a parameter set that produces the simulation with lowest model error, assessed between a simulated and observed BTC for a given stream reach (Runkel, ; Ward et al, ). There are several recognized limitations to the time scales of transient storage zone exchange that may be assessed using TSM (e.g., Harvey et al, ) as well as accounting for spatial heterogeneity that exists at subreach scales (Harvey et al, ; Knapp et al, ).…”

Section: Introductionmentioning

confidence: 99%

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Exploring Tracer Information and Model Framework Trade‐Offs to Improve Estimation of Stream Transient Storage Processes

Kelleher

Ward

Knapp

et al. 2019

Water Resources Research

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Novel observation techniques (e.g., smart tracers) for characterizing coupled hydrological and biogeochemical processes are improving understanding of stream network transport and transformation dynamics. In turn, these observations are thought to enable increasingly sophisticated representations within transient storage models (TSMs). However, TSM parameter estimation is prone to issues with insensitivity and equifinality, which grow as parameters are added to model formulations. Currently, it is unclear whether (or not) observations from different tracers may lead to greater process inference and reduced parameter uncertainty in the context of TSM. Herein, we aim to unravel the role of in‐stream processes alongside metabolically active (MATS) and inactive storage zones (MITS) using variable TSM formulations. Models with one (1SZ) and two storage zones (2SZ) and with and without reactivity were applied to simulate conservative and smart tracer observations obtained experimentally for two reaches with differing morphologies. As we show, smart tracers are unsurprisingly superior to conservative tracers when it comes to partitioning MITS and MATS. However, when transient storage is lumped within a 1SZ formulation, little improvement in parameter uncertainty is gained by using a smart tracer, suggesting the addition of observations should scale with model complexity. Importantly, our work identifies several inconsistencies and open questions related to reconciling time scales of tracer observation with conceptual processes (parameters) estimated within TSM. Approaching TSM with multiple models and tracer observations may be key to gaining improved insight into transient storage simulation as well as advancing feedback loops between models and observations within hydrologic science.

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Section: Discussionmentioning

confidence: 95%

Section: Model Complexity and Conceptualization Simulations And Errorsmentioning

confidence: 94%

“…For each of the 27,000 runs, we calculated model fits in terms of a normalized root‐mean square error (nRMSE) for each BTC (Ura, Raz, and Rru) independently, according to

nRMSE = \frac{1}{C_{p}} {(\frac{\sum_{t = 1}^{n} {(O_{t} - S_{t})}^{2}}{n})}^{0.5}

Section: Transient Storage Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exploring Tracer Information and Model Framework Trade‐Offs to Improve Estimation of Stream Transient Storage Processes

Kelleher

Ward

Knapp

et al. 2019

Water Resources Research

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“…Despite the extensive literature exploring the implications of combined tracer injection experiments and transient storage model analysis (e.g., Gooseff et al, 2005;Kelleher et al, 2013;Kelleher et al, 2019;Wagener et al, 2002;Ward et al, 2017), there is a lack of consensus on methods for assessing fine particle dynamics. Despite the extensive literature exploring the implications of combined tracer injection experiments and transient storage model analysis (e.g., Gooseff et al, 2005;Kelleher et al, 2013;Kelleher et al, 2019;Wagener et al, 2002;Ward et al, 2017), there is a lack of consensus on methods for assessing fine particle dynamics.…”

Section: 1029/2019gl085849mentioning

confidence: 99%

Improving Predictions of Fine Particle Immobilization in Streams

Drummond

Schmadel

Kelleher

et al. 2019

Geophysical Research Letters

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Fine particles are critical to stream ecosystem functioning, influencing in-stream processes from pathogen transmission to carbon cycling, all of which depend on particle immobilization. However, our ability to predict particle immobilization is limited by (1) availability of combined solute and particle tracer data and (2) identifying parameters that appropriately represent fine particle immobilization, due to the myriad of objective functions and model formulations. We found that improved predictions of the full distribution of possible fine particle residence times requires using an objective function that assesses both the peak and tailing of breakthrough curves together with solute tracers to constrain in-stream transport processes. The representation of immobilization processes was significantly improved when solute tracer data were combined with a particle model, starkly contrasting the common assumption that fine particles transport as washload. We develop a clear strategy for improving fine particle transport predictions, reshaping the potential role of fine particles in water quality management.Plain Language Summary Fine particles, a general term that can be used to describe inorganic material like clays, particulate organic carbon, and harmful bacteria (i.e., pathogens), are important to stream functioning and water quality. The time it takes fine particles to move through a stream is difficult to predict primarily because there is no general guidance regarding the required data types and modeling approaches. Through comprehensive computational experiments and data analysis, we found that fine particles remain in streams much longer than commonly assumed, reshaping understanding of the role of fine particles in stream functioning and how waterborne pathogens are transmitted.

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Streambed restoration to remove fine sediment alters reach‐scale transient storage in a low‐gradient fifth‐order river, Indiana, USA

Ward

Morgan

White

et al. 2018

Hydrological Processes

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Hyporheic restoration is of increasing interest given the role of hyporheic zones in supporting ecosystem services and functions. Given the prevalence of sediment pollution to waterways, an emerging restoration technique involves the removal of sediment from the interstices of gravel‐bed streams. Here, we document streambed sediment removal following a large, accidental release of fine sediment into a gravel‐bed river. We use this as a natural experiment to assess the impact of fine sediment removal on reach‐scale measures of transient storage and to document the responses of reaches with contrasting morphology (restored vs. unrestored) to changing discharge one‐field season. We conducted a series of conservative solute tracer experiments in each reach, interpreting both summary statistics for the recovered in‐stream solute tracer time series. Additionally, we applied the transient storage model to interpret the results via model parameters, including a Monte Carlo analysis to measure parameter identifiability and sensitivity in each experiment. Despite the restoration effort resulting in an open matrix gravel bed in the restored reach, we did not find the significant differences in most time series metrics describing reach‐scale transport and transient storage. We hypothesize that this is due to enhanced vertical exchange with the gravel bed in the restored reach replacing lateral exchange with macrophyte beds in the unrestored reach, developing a conceptual model to explain our findings. Consequently, we found that the impact of reach‐scale removal of fine sediment is not measureable using reach‐scale solute tracer studies. We offer recommendations for future studies seeking to measure the impacts of stream restoration at the reach scale.

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A software tool to assess uncertainty in transient-storage model parameters using Monte Carlo simulations

Cited by 36 publications

References 58 publications

Exploring Tracer Information and Model Framework Trade‐Offs to Improve Estimation of Stream Transient Storage Processes

Exploring Tracer Information and Model Framework Trade‐Offs to Improve Estimation of Stream Transient Storage Processes

Improving Predictions of Fine Particle Immobilization in Streams

Streambed restoration to remove fine sediment alters reach‐scale transient storage in a low‐gradient fifth‐order river, Indiana, USA

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