Multi-objective Optimization of Catchment Reforestation Robust to Uncertainty in Bayesian-Calibrated Watershed Model Parameters

2021 ◽  
Author(s):  
Jared Smith ◽  
Laurence Lin ◽  
Julianne Quinn ◽  
Lawrence Band
Keyword(s):  
Computational Cost ◽  
Bayesian Framework ◽  
Hydrologic Model ◽  
Low Flow ◽  
Critical Parameters ◽  
Model Parameters ◽  
Calibration Data ◽  
Baltimore County ◽  
True Parameter ◽  
Multi Objective

<p>Urban land expansion is expected for our changing world, which unmitigated will result in increased flooding and nutrient exports that already wreak havoc on the wellbeing of coupled human-natural systems worldwide. Reforestation of urbanized catchments is one green infrastructure strategy to reduce stormwater volumes and nutrient exports. Reforestation designs must balance the benefits of flood flow reduction against the costs of implementation and the chance to exacerbate droughts via reduction in recharge that supplies low flows. Optimal locations and numbers of trees depend on the spatial distribution of runoff and streamflow in a catchment; however, calibration data are often only available at the catchment outlet. Equifinal model parameterizations for the outlet can result in uncertainty in the locations and magnitudes of streamflows across the catchment, which can lead to different optimal reforestation designs for different parameterizations.</p><p>Multi-objective robust optimization (MORO) has been proposed to discover reforestation designs that are robust to such parametric model uncertainty. However, it has not been shown that this actually results in better decisions than optimizing to a single, most likely parameter set, which would be less computationally expensive. In this work, the utility of MORO is assessed by comparing reforestation designs optimized using these two approaches with reforestation designs optimized to a synthetic true set of hydrologic model parameters. The spatially-distributed RHESSys ecohydrological model is employed for this study of a suburban-forested catchment in Baltimore County, Maryland, USA. Calibration of the model’s critical parameters is completed using a Bayesian framework to estimate the joint posterior distribution of the parameters. The Bayesian framework estimates the probability that different parameterizations generated the synthetic streamflow data, allowing the MORO process to evaluate reforestation portfolios across a probability-weighted sample of parameter sets in search of solutions that are robust to this uncertainty.</p><p>Reforestation portfolios are designed to minimize flooding, low flow intensity, and construction costs (number of trees). Comparing the Pareto front obtained from using MORO with the Pareto fronts obtained from optimizing to the estimated maximum a posteriori (MAP) parameter set and the synthetic true parameter set, we find that MORO solutions are closer to the synthetic solutions than are MAP solutions. This illustrates the value of considering parametric uncertainty in designing robust water systems despite the additional computational cost.</p>

scholarly journals Assessment of The Uncertainties of a Conceptual Hydrologic Model By Using Artificially Generated Flows

2012 ◽  
Vol 20 (4) ◽  
pp. 35-43 ◽  
Author(s):  
Peter Valent ◽  
Ján Szolgay ◽  
Carlo Riverso
Keyword(s):  
Calibration Method ◽  
Calibration Procedure ◽  
Hydrologic Model ◽  
Point Of View ◽  
Model Parameters ◽  
Calibration Data ◽  
Artificial Flow ◽  
Calibration Techniques ◽  
Hbv Model ◽  
Further Development

ABSTRACTMost of the studies that assess the performance of various calibration techniques have todeal with a certain amount of uncertainty in the calibration data. In this study we testedHBV model calibration procedures in hypothetically ideal conditions under the assumptionof no errors in the measured data. This was achieved by creating an artificial time seriesof the flows created by the HBV model using the parameters obtained from calibrating themeasured flows. The artificial flows were then used to replace the original flows in thecalibration data, which was then used for testing how calibration procedures can reproduceknown model parameters. The results showed that in performing one hundred independentcalibration runs of the HBV model, we did not manage to obtain parameters that werealmost identical to those used to create the artificial flow data without a certain degree ofuncertainty. Although the calibration procedure of the model works properly froma practical point of view, it can be regarded as a demonstration of the equifinality principle,since several parameter sets were obtained which led to equally acceptable or behaviouralrepresentations of the observed flows. The study demonstrated that this concept forassessing how uncertain hydrological predictions can be applied in the further developmentof a model or the choice of calibration method using artificially generated data.

scholarly journals Testing alternative uses of electromagnetic data to reduce the prediction error of groundwater models

2016 ◽  
Vol 20 (5) ◽  
pp. 1925-1946 ◽  
Author(s):  
Nikolaj Kruse Christensen ◽  
Steen Christensen ◽  
Ty Paul A. Ferre
Keyword(s):  
Electrical Resistivity ◽  
Hydraulic Conductivity ◽  
Prediction Error ◽  
Model Calibration ◽  
Hydrologic Model ◽  
Geophysical Data ◽  
Model Parameters ◽  
Calibration Data ◽  
Groundwater Model ◽  
And Inversion

Abstract. In spite of geophysics being used increasingly, it is often unclear how and when the integration of geophysical data and models can best improve the construction and predictive capability of groundwater models. This paper uses a newly developed HYdrogeophysical TEst-Bench (HYTEB) that is a collection of geological, groundwater and geophysical modeling and inversion software to demonstrate alternative uses of electromagnetic (EM) data for groundwater modeling in a hydrogeological environment consisting of various types of glacial deposits with typical hydraulic conductivities and electrical resistivities covering impermeable bedrock with low resistivity (clay). The synthetic 3-D reference system is designed so that there is a perfect relationship between hydraulic conductivity and electrical resistivity. For this system it is investigated to what extent groundwater model calibration and, often more importantly, model predictions can be improved by including in the calibration process electrical resistivity estimates obtained from TEM data. In all calibration cases, the hydraulic conductivity field is highly parameterized and the estimation is stabilized by (in most cases) geophysics-based regularization. For the studied system and inversion approaches it is found that resistivities estimated by sequential hydrogeophysical inversion (SHI) or joint hydrogeophysical inversion (JHI) should be used with caution as estimators of hydraulic conductivity or as regularization means for subsequent hydrological inversion. The limited groundwater model improvement obtained by using the geophysical data probably mainly arises from the way these data are used here: the alternative inversion approaches propagate geophysical estimation errors into the hydrologic model parameters. It was expected that JHI would compensate for this, but the hydrologic data were apparently insufficient to secure such compensation. With respect to reducing model prediction error, it depends on the type of prediction whether it has value to include geophysics in a joint or sequential hydrogeophysical model calibration. It is found that all calibrated models are good predictors of hydraulic head. When the stress situation is changed from that of the hydrologic calibration data, then all models make biased predictions of head change. All calibrated models turn out to be very poor predictors of the pumping well's recharge area and groundwater age. The reason for this is that distributed recharge is parameterized as depending on estimated hydraulic conductivity of the upper model layer, which tends to be underestimated. Another important insight from our analysis is thus that either recharge should be parameterized and estimated in a different way, or other types of data should be added to better constrain the recharge estimates.

scholarly journals A trading-space-for-time approach to probabilistic continuous streamflow predictions in a changing climate – accounting for changing watershed behavior

2011 ◽  
Vol 15 (11) ◽  
pp. 3591-3603 ◽  
Author(s):  
R. Singh ◽  
T. Wagener ◽  
K. van Werkhoven ◽  
M. E. Mann ◽  
R. Crane
Keyword(s):  
Spatial Relationship ◽  
Model Performance ◽  
Climate Scenario ◽  
Hydrologic Model ◽  
Climatic Conditions ◽  
Low Flow ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Watershed Model ◽  
The Impact

Abstract. Projecting how future climatic change might impact streamflow is an important challenge for hydrologic science. The common approach to solve this problem is by forcing a hydrologic model, calibrated on historical data or using a priori parameter estimates, with future scenarios of precipitation and temperature. However, several recent studies suggest that the climatic regime of the calibration period is reflected in the resulting parameter estimates and model performance can be negatively impacted if the climate for which projections are made is significantly different from that during calibration. So how can we calibrate a hydrologic model for historically unobserved climatic conditions? To address this issue, we propose a new trading-space-for-time framework that utilizes the similarity between the predictions under change (PUC) and predictions in ungauged basins (PUB) problems. In this new framework we first regionalize climate dependent streamflow characteristics using 394 US watersheds. We then assume that this spatial relationship between climate and streamflow characteristics is similar to the one we would observe between climate and streamflow over long time periods at a single location. This assumption is what we refer to as trading-space-for-time. Therefore, we change the limits for extrapolation to future climatic situations from the restricted locally observed historical variability to the variability observed across all watersheds used to derive the regression relationships. A typical watershed model is subsequently calibrated (conditioned) on the predicted signatures for any future climate scenario to account for the impact of climate on model parameters within a Bayesian framework. As a result, we can obtain ensemble predictions of continuous streamflow at both gauged and ungauged locations. The new method is tested in five US watersheds located in historically different climates using synthetic climate scenarios generated by increasing mean temperature by up to 8 °C and changing mean precipitation by −30% to +40% from their historical values. Depending on the aridity of the watershed, streamflow projections using adjusted parameters became significantly different from those using historically calibrated parameters if precipitation change exceeded −10% or +20%. In general, the trading-space-for-time approach resulted in a stronger watershed response to climate change for both high and low flow conditions.

scholarly journals Constraining subglacial processes from surface velocity observations using surrogate-based Bayesian inference

2021 ◽  
pp. 1-19
Author(s):  
Douglas Brinkerhoff ◽  
Andy Aschwanden ◽  
Mark Fahnestock
Keyword(s):  
Probability Distributions ◽  
Water Pressure ◽  
Model Development ◽  
Computational Cost ◽  
Hydrologic Model ◽  
Surface Velocity ◽  
Small Scale ◽  
Model Parameters ◽  
Stress Regime ◽  
Ice Dynamics

Abstract Basal motion is the primary mechanism for ice flux in Greenland, yet a widely applicable model for predicting it remains elusive. This is due to the difficulty in both observing small-scale bed properties and predicting a time-varying water pressure on which basal motion putatively depends. We take a Bayesian approach to these problems by coupling models of ice dynamics and subglacial hydrology and conditioning on observations of surface velocity in southwestern Greenland to infer the posterior probability distributions for eight spatially and temporally constant parameters governing the behavior of both the sliding law and hydrologic model. Because the model is computationally expensive, characterization of these distributions using classical Markov Chain Monte Carlo sampling is intractable. We skirt this issue by training a neural network as a surrogate that approximates the model at a sliver of the computational cost. We find that surface velocity observations establish strong constraints on model parameters relative to a prior distribution and also elucidate correlations, while the model explains 60% of observed variance. However, we also find that several distinct configurations of the hydrologic system and stress regime are consistent with observations, underscoring the need for continued data collection and model development.

scholarly journals A framework for testing the use of electric and electromagnetic data to reduce the prediction error of groundwater models

2015 ◽  
Vol 12 (9) ◽  
pp. 9599-9653 ◽  
Author(s):  
N. K. Christensen ◽  
S. Christensen ◽  
T. P. A. Ferre
Keyword(s):  
Hydraulic Conductivity ◽  
Tikhonov Regularization ◽  
Prediction Error ◽  
Model Calibration ◽  
Groundwater Modeling ◽  
Hydrologic Model ◽  
Geophysical Data ◽  
Model Parameters ◽  
Calibration Data ◽  
And Inversion

Abstract. Despite geophysics is being used increasingly, it is still unclear how and when the integration of geophysical data improves the construction and predictive capability of groundwater models. Therefore, this paper presents a newly developed HYdrogeophysical TEst-Bench (HYTEB) which is a collection of geological, groundwater and geophysical modeling and inversion software wrapped to make a platform for generation and consideration of multi-modal data for objective hydrologic analysis. It is intentionally flexible to allow for simple or sophisticated treatments of geophysical responses, hydrologic processes, parameterization, and inversion approaches. It can also be used to discover potential errors that can be introduced through petrophysical models and approaches to correlating geophysical and hydrologic parameters. With HYTEB we study alternative uses of electromagnetic (EM) data for groundwater modeling in a hydrogeological environment consisting of various types of glacial deposits with typical hydraulic conductivities and electrical resistivities covering impermeable bedrock with low resistivity. It is investigated to what extent groundwater model calibration and, often more importantly, model predictions can be improved by including in the calibration process electrical resistivity estimates obtained from TEM data. In all calibration cases, the hydraulic conductivity field is highly parameterized and the estimation is stabilized by regularization. For purely hydrologic inversion (HI, only using hydrologic data) we used Tikhonov regularization combined with singular value decomposition. For joint hydrogeophysical inversion (JHI) and sequential hydrogeophysical inversion (SHI) the resistivity estimates from TEM are used together with a petrophysical relationship to formulate the regularization term. In all cases, the regularization stabilizes the inversion, but neither the HI nor the JHI objective function could be minimized uniquely. SHI or JHI with regularization based on the use of TEM data produced estimated hydraulic conductivity fields that bear more resemblance to the reference fields than when using HI with Tikhonov regularization. However, for the studied system the resistivities estimated by SHI or JHI must be used with caution as estimators of hydraulic conductivity or as regularization means for subsequent hydrological inversion. Much of the lack of value of the geophysical data arises from a mistaken faith in the power of the petrophysical model in combination with geophysical data of low sensitivity, thereby propagating geophysical estimation errors into the hydrologic model parameters. With respect to reducing model prediction error, it depends on the type of prediction whether it has value to include geophysical data in the model calibration. It is found that all calibrated models are good predictors of hydraulic head. When the stress situation is changed from that of the hydrologic calibration data, then all models make biased predictions of head change. All calibrated models turn out to be a very poor predictor of the pumping well's recharge area and groundwater age. The reason for this is that distributed recharge is parameterized as depending on estimated hydraulic conductivity of the upper model layer which tends to be underestimated. Another important insight from the HYTEB analysis is thus that either recharge should be parameterized and estimated in a different way, or other types of data should be added to better constrain the recharge estimates.

scholarly journals Exploring hydrologically similar catchments in terms of the physical characteristics of upstream regions

2017 ◽  
Vol 49 (5) ◽  
pp. 1467-1483 ◽  
Author(s):  
Yi Jin ◽  
Jintao Liu ◽  
Lu Lin ◽  
Aihua Wang ◽  
Xi Chen
Keyword(s):  
Hydrologic Model ◽  
Physical Characteristics ◽  
High Flow ◽  
Low Flow ◽  
Model Parameters ◽  
Physical Factors ◽  
Ungauged Catchments ◽  
Response Factors ◽  
Average Annual Runoff ◽  
Huai River

Abstract Catchment classification strategies based on easily available physical characteristics are important for extrapolating hydrologic model parameters and improving hydrologic predictions in ungauged catchments. In this study, we conduct an experiment of catchment classification and explore the feasibility of characterizing hydrologically similar catchments using certain physical characteristics in upstream regions of the Huai River Basin. The similarity metrics of hydrologic response factors (high flow, low flow and average annual runoff) and physical factors (topography, shape, soil and vegetation) are fed into the K-means algorithm for catchment classification. All the catchments are classified into two classes regardless of the types of metrics used. By comparing the overlap coefficient (η) and Rand index (RI) between any two classification results, we found that the topography classification displays the highest concordance with the high flow classification (η = 79.2% and RI = 0.66) among all metrics. Including more metrics would not produce consistently better classification results. The optimal combination of metrics, with η = 87.5%, is the high flow metrics (Q10%, SFH and MAX90) with the topography metrics (AS and HI). The results indicate that the physical metrics adopted for hydrologic classification should be determined carefully in terms of specific hydrologic characteristics.

scholarly journals Calibrating a watershed simulation model involving human interference: an application of multi-objective genetic algorithms

2008 ◽  
Vol 10 (1) ◽  
pp. 97-111 ◽  
Author(s):  
Mohamad I. Hejazi ◽  
Ximing Cai ◽  
Deva K. Borah
Keyword(s):  
Error Term ◽  
Fitness Function ◽  
Calibration Procedure ◽  
Hydrologic Model ◽  
Storm Event ◽  
Model Parameters ◽  
Nsga Ii ◽  
Human Interference ◽  
Multi Objective ◽  
Reservoir Release

We calibrate a storm-event distributed hydrologic model to a watershed, in which runoff is significantly affected by reservoir storage and release, using a multi-objective genetic algorithm (NSGA-II). This paper addresses the following questions: What forms of the objective (fitness) function used in the optimization model will result in a better calibration? How does the error in reservoir release caused by neglected human interference or the imprecise storage–release function affect the calibration? Reservoir release is studied as a specific (and popular) form of human interference. Two procedures for handling reservoir releases are tested and compared: (1) treating reservoir releases to be solely determined by the hydraulic structure (predefined storage or stage-discharge relations) as if perfect, a procedure usually adopted in watershed model calibration; or (2) adding reservoir releases that are determined by the storage–discharge relation to an error term. The error term encompasses a time-variant human interference and a discharge function error, and is determined through an optimization-based calibration procedure. It is found that the calibration procedure with consideration of human interference not only results in a better match of modeled and observed hydrograph, but also more reasonable model parameters in terms of their spatial distribution and the robustness of the parameter values.

scholarly journals Considering rating curve uncertainty in water level predictions

2013 ◽  
Vol 17 (11) ◽  
pp. 4415-4427 ◽  
Author(s):  
A. E. Sikorska ◽  
A. Scheidegger ◽  
K. Banasik ◽  
J. Rieckermann
Keyword(s):  
Water Level ◽  
Bayesian Framework ◽  
Water Levels ◽  
Model Parameters ◽  
Calibration Data ◽  
Rainfall Runoff ◽  
Rating Curve ◽  
Rainfall Runoff Model ◽  
The Impact ◽  
Runoff Model

Abstract. Streamflow cannot be measured directly and is typically derived with a rating curve model. Unfortunately, this causes uncertainties in the streamflow data and also influences the calibration of rainfall-runoff models if they are conditioned on such data. However, it is currently unknown to what extent these uncertainties propagate to rainfall-runoff predictions. This study therefore presents a quantitative approach to rigorously consider the impact of the rating curve on the prediction uncertainty of water levels. The uncertainty analysis is performed within a formal Bayesian framework and the contributions of rating curve versus rainfall-runoff model parameters to the total predictive uncertainty are addressed. A major benefit of the approach is its independence from the applied rainfall-runoff model and rating curve. In addition, it only requires already existing hydrometric data. The approach was successfully demonstrated on a small catchment in Poland, where a dedicated monitoring campaign was performed in 2011. The results of our case study indicate that the uncertainty in calibration data derived by the rating curve method may be of the same relevance as rainfall-runoff model parameters themselves. A conceptual limitation of the approach presented is that it is limited to water level predictions. Nevertheless, regarding flood level predictions, the Bayesian framework seems very promising because it (i) enables the modeler to incorporate informal knowledge from easily accessible information and (ii) better assesses the individual error contributions. Especially the latter is important to improve the predictive capability of hydrological models.

Decoupling induced polarization effect from time domain electromagnetic data in a Bayesian framework

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. A59-A63 ◽  
Author(s):  
Hai Li ◽  
Guoqiang Xue ◽  
Yiming He
Keyword(s):  
Time Domain ◽  
Computational Cost ◽  
Bayesian Framework ◽  
Induced Polarization ◽  
Linear Perturbation ◽  
Model Parameters ◽  
Bayesian Sampling ◽  
3D Space ◽  
Time Domain Electromagnetic ◽  
Induced Polarization Effect

We have developed a scheme for decoupling the induced polarization (IP) effect from time-domain electromagnetic (TDEM) data. This scheme is achieved by simultaneously sampling the resistivity and pseudochargeability in a Bayesian framework. The TDEM and IP responses are simulated separately with the sampled model parameters and then are stacked to fit the IP-affected TDEM data. Thus, the influence of the IP phenomenon is eliminated in the process of recovering the resistivity. To reduce the computational cost brought by the Bayesian sampling, we use a 2D parametrization instead of sampling the full 3D space and we use a linear perturbation approximation for calculating the IP response. The linearized inversion results are used as the initial model, and a multiple proposed points algorithm is used to accelerate the sampling. We validate the proposed method with synthetic and field examples showing that it restores accurate estimates of electrical structures from the TDEM data that are significantly affected by the IP phenomenon. Our method could advance the application of the TDEM method to the scenario in which the IP may affect the TDEM data and mask the underlying geologic targets.

scholarly journals Relative impacts of climate change and land cover change on streamflow using SWAT in the Clackamas River Watershed, USA

2020 ◽  
Author(s):  
Junjie Chen ◽  
Heejun Chang
Keyword(s):  
Climate Change ◽  
Land Cover ◽  
Land Cover Change ◽  
Water Resource Management ◽  
Assessment Tool ◽  
Hydrologic Model ◽  
Low Flow ◽  
Model Parameters ◽  
River Watershed ◽  
Daily Streamflow

Abstract To understand the spatial–temporal pattern of climate and land cover (CLC) change effects on hydrology, we used three land cover change (LCC) coupled scenarios to estimate the changes in streamflow metrics in the Clackamas River Watershed in Oregon for the 2050s (2040–2069) and the 2080s (2070–2099). Coupled scenarios, which were split into individual and combined simulations such as climate change (CC), LCC, CLC change, and daily streamflow were simulated in the Soil and Water Assessment Tool. The interannual variability of streamflow was higher in the lower urbanized area than the upper forested region. The watershed runoff was projected to be more sensitive to CC than LCC. Under the CLC scenario, the top 10% peak flow and the 7-day low flow are expected to increase (2–19%) and decrease (+9 to −20 cm s), respectively, in both future periods. The center timing of runoff in the year is projected to shift 2–3 weeks earlier in response to warming temperature and more winter precipitation falling as rain. High streamflow variability in our findings suggests that uncertainties can stem from both climate models and hydrologic model parameters, calling for more adaptive water resource management in the watershed.

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