Inverse Modeling Approach Research Articles

Hydrochemical and isotopic characterization of groundwater in the southeastern part of the Plateaux Region, Togo

ABSTRACTHydrochemical, inverse geochemical modelling and isotopic approaches are used to assess the hydrogeochemical evolution of groundwater from the basement aquifers in the southeastern part of the Plateaux Region, Togo. Groundwater originates from present-day rainwater infiltration and is mostly fresh and slightly acidic to neutral. Hydrochemical facies are predominantly mixed cations-HCO3 associated with Ca/Mg-Cl, Na-HCO3 and Na-Cl water types in equilibrium with kaolinite and Ca/Mg-smectites. They are related to silicates hydrolysis, anthropogenic contamination, nitrification/denitrification, mixing along flowpaths and dissolution/precipitation of secondary minerals. The pattern of flow paths is in accordance with an increasing trend in total dissolved solids (TDS) toward the potentiometric depression located in the central and southern parts of the aquifer system. Inverse geochemical modelling using the NETPATH-WIN model showed the relative importance of biotite, plagioclase and amphibole weathering and dissolution of secondary carbonate minerals along the flowpath, suggesting that an abundance of minerals is not necessarily the main factor controlling the groundwater chemistry evolution.

Effect of clay content on permeability behavior of argillaceous porous media under stress dependence: A theoretical and experimental work

Prediction of permeability behavior of argillaceous porous media (APM) is a major challenge for science and engineering, despite considerable advances in using both theoretical and experimental means over the last few decades. Specifically, the effect of clay content on stress sensitivity of APM is still an open question. In this paper, laboratory tests are conducted to investigate the effect of clay content on behavior of permeability for artificial argillaceous sandstone samples under stress dependence. Then a corresponding theoretical model for stress dependent permeability of APM based on fractal theory is derived to interpret the experimental results. The predicted results from the developed theoretical model are consistent with those determined by experimental tests, which verifies the developed model. The proposed model can be invoked to effectively study the coupled flow-deformation behavior in APM. The results show that the normalized permeability increases with increasing the power law index, increasing elastic modulus, increasing rock initial porosity, and decreasing clay content at a given effective stress. This work provides a comprehensive experimental and theoretical study on stress-dependent permeability in APM, which is beneficial to study the effect of clay content on permeability behavior of APM under stress dependence. In addition, with this proposed model, we can conduct the estimation of specific parameters (e.g., the structure of pore surface, the fractal dimension of pore, the maximum pore radius, the minimum pore radius, clay content, initial irreducible water saturation, and rock elastic modulus) using inverse modeling approaches.

Real-time sea-level monitoring using Kalman filtering of GNSS-R data

Current GNSS-R (GNSS reflectometry) techniques for sea surface measurements require data collection over longer periods, limiting their usability for real-time applications. In this work, we present a new, alternative GNSS-R approach based on the unscented Kalman filter and the so-called inverse modeling approach. The new method makes use of a mathematical description that relates SNR (signal-to-noise ratio) variations to multipath effects and uses a B-spline formalism to obtain time series of reflector height. The presented algorithm can provide results in real time with a precision that is significantly better than spectral inversion methods and almost comparable to results from inverse modeling in post-processing mode. To verify the performance, the method has been tested at station GTGU at the Onsala Space Observatory, Sweden, and at the station SPBY in Spring Bay, Australia. The RMS (root mean square) error with respect to nearby tide gauge data was found to be 2.0 cm at GTGU and 4.8 cm at SPBY when evaluating the output corresponding to real-time analysis. The method can also be applied in post-processing, resulting in RMS errors of 1.5 cm and 3.3 cm for GTGU and SPBY, respectively. Finally, based on SNR data from GTGU, it is also shown that the Kalman filter approach is able to detect the presence of sea ice with a higher temporal resolution than the previous methods and traditional remote sensing techniques which monitor ice in coastal regions.

Quantifying the UK's carbon dioxide flux: an atmospheric inverse modelling approach using a regional measurement network

Abstract. We present a method to derive atmospheric-observation-based estimates of carbon dioxide (CO2) fluxes at the national scale, demonstrated using data from a network of surface tall-tower sites across the UK and Ireland over the period 2013–2014. The inversion is carried out using simulations from a Lagrangian chemical transport model and an innovative hierarchical Bayesian Markov chain Monte Carlo (MCMC) framework, which addresses some of the traditional problems faced by inverse modelling studies, such as subjectivity in the specification of model and prior uncertainties. Biospheric fluxes related to gross primary productivity and terrestrial ecosystem respiration are solved separately in the inversion and then combined a posteriori to determine net ecosystem exchange of CO2. Two different models, Data Assimilation Linked Ecosystem Carbon (DALEC) and Joint UK Land Environment Simulator (JULES), provide prior estimates for these fluxes. We carry out separate inversions to assess the impact of these different priors on the posterior flux estimates and evaluate the differences between the prior and posterior estimates in terms of missing model components. The Numerical Atmospheric dispersion Modelling Environment (NAME) is used to relate fluxes to the measurements taken across the regional network. Posterior CO2 estimates from the two inversions agree within estimated uncertainties, despite large differences in the prior fluxes from the different models. With our method, averaging results from 2013 and 2014, we find a total annual net biospheric flux for the UK of 8±79 Tg CO2 yr−1 (DALEC prior) and 64±85 Tg CO2 yr−1 (JULES prior), where negative values represent an uptake of CO2. These biospheric CO2 estimates show that annual UK biospheric sources and sinks are roughly in balance. These annual mean estimates consistently indicate a greater net release of CO2 than the prior estimates, which show much more pronounced uptake in summer months.

Demographic responses underlying eco-evolutionary dynamics as revealed with inverse modelling.

Changes in population dynamics due to interacting evolutionary and ecological processes are the direct result of responses in vital rates, that is stage‐specific growth, survival and fecundity. Quantifying through which vital rates population fitness is affected, instead of focusing on population trends only, can give a more mechanistic understanding of eco‐evolutionary dynamics.The aim of this study was to estimate the underlying demographic rates of aphid (Myzus persicae) populations. We analysed unpublished stage‐structure population dynamics data of a field experiment with caged and uncaged populations in which rapid evolutionary dynamics were observed, as well as unpublished results from an individual life table experiment performed in a glasshouse.Using data on changes in population abundance and stage distributions over time, we estimated transition matrices with inverse modelling techniques, in a Bayesian framework. The model used to fit across all experimental treatments included density as well as clone‐specific caging effects. We additionally used individual life table data to inform the model on survival, growth and reproduction.Results suggest that clones varied considerably in vital rates, and imply trade‐offs between reproduction and survival. Responses to densities also varied between clones. Negative density dependence was found in growth and reproduction, and the presence of predators and competitors further decreased these two vital rates, while survival estimates increased. Under uncaged conditions, population growth rates of the evolving populations were increased compared to the expectation based on the pure clones.Our inverse modelling approach revealed how much vital rates contributed to the eco‐evolutionary dynamics. The decomposition analysis showed that variation in population growth rates in the evolving populations was to a large extent shaped by plant size. Yet, it also revealed an impact of evolutionary changes in clonal composition. Finally, we discuss that inverse modelling is a complex problem, as multiple combinations of individual rates can result in the same dynamics. We discuss assumptions and limitations, as well as opportunities, of this approach.

Integrating physics-based models with sensor data: An inverse modeling approach

Physics-based building energy models (e.g., EnergyPlus) rely on some unknown input parameters (e.g., zone air infiltration) that are hard to measure, leading to uncertainty in simulation results especially for existing buildings with varying operating conditions. With the increasing deployment of smart thermostats, zone air temperature data are readily available, posing a new opportunity for building energy modeling if such data can be harnessed. This study presents a novel inverse modeling approach which inverses the zone air heat balance equation and uses the measured zone air temperature to analytically calculate the zone air infiltration rate and zone internal thermal mass (e.g., furniture, interior partitions), which are two important model parameters with great variability and difficult to measure. This paper introduces the technical concept and algorithms of the inverse models, their implementation in EnergyPlus, and verification using EnergyPlus simulated building performance data. The inverse modeling approach provides new opportunities for integrating data from massive IoT sensors and devices to enhance the accuracy of simulation results which are used to inform decision making on energy retrofits and efficiency improvements of existing buildings.

Sulphuric acid-mediated weathering on Taiwan buffers geological atmospheric carbon sinks

The chemical composition of the Gaoping River in Taiwan reflects the weathering of both silicate and carbonate rocks found in its metasedimentary catchment. Major dissolved ion chemistry and radiocarbon signatures of dissolved inorganic carbon (DIC) reveal the importance of pyrite-derived sulphuric acid weathering on silicates and carbonates. Two-thirds of the dissolved load of the Gaoping River derives from sulphuric acid-mediated weathering of rocks within its catchment. This is reflected in the lowest reported signatures DI14C for a small mountainous river (43 to 71 percent modern carbon), with rock-derived carbonate constituting a 14C-free DIC source. Using an inverse modelling approach integrating riverine major dissolved ion chemistry and DI14C, we provide quantitative constraints of mineral weathering pathways and calculate atmospheric CO2 fluxes resulting from the erosion of the Taiwan orogeny over geological timescales. The results reveal that weathering on Taiwan releases 0.31 ± 0.12 MtC/yr, which is offset by burial of terrestrial biospheric organic carbon in offshore sediments. The latter tips the balance with respect to the total CO2 budget of Taiwan such that the overall system acts as a net sink, with 0.24 ± 0.13 MtC/yr of atmospheric CO2 consumed over geological timescales.

Ex-situ priors: A Bayesian hierarchical framework for defining informative prior distributions in hydrogeology

Stochastic modeling is a common practice for modeling uncertainty in hydrogeology. In stochastic modeling, aquifer properties are characterized by their probability density functions (PDFs). The Bayesian approach for inverse modeling is often used to assimilate information from field measurements collected at a site into properties’ posterior PDFs. This necessitates the definition of a prior PDF, characterizing the knowledge of hydrological properties before undertaking any investigation at the site, and usually coming from previous studies at similar sites. In this paper, we introduce a Bayesian hierarchical algorithm capable of assimilating various information–like point measurements, bounds and moments–into a single, informative PDF that we call ex-situ prior. This informative PDF summarizes the ex-situ information available about a hydrogeological parameter at a site of interest, which can then be used as a prior PDF in future studies at the site. We demonstrate the behavior of the algorithm on several synthetic case studies, compare it to other methods described in the literature, and illustrate the approach by applying it to a public open-access hydrogeological dataset.

Atmospheric Origins of Variability in the South Atlantic Meridional Overturning Circulation

Abstract Insights from the RAPID–MOCHA observation network in the North Atlantic have motivated a recent focus on the South Atlantic, where water masses are exchanged with neighboring ocean basins. In this study, variability in the South Atlantic meridional overturning circulation (SAMOC) at 34°S is attributed to global atmospheric forcing using an inverse modeling approach. The sensitivity of the SAMOC to atmospheric state variables is computed with the adjoint of the Massachusetts Institute of Technology general circulation model, which is fit to 20 years of observational data in a dynamically consistent framework. The dynamical pathways highlighted by these sensitivity patterns show that the domain of influence for the SAMOC is broad, covering neighboring ocean basins even on short time scales. This result differs from what has previously been shown in the North Atlantic, where Atlantic meridional overturning circulation (AMOC) variability is largely governed by dynamics confined to that basin. The computed sensitivities are convolved with surface atmospheric state variability from ERA-Interim to attribute the influence of each external forcing variable (e.g., wind stress, precipitation) on the SAMOC from 1992 to 2011. Here, local wind stress perturbations are shown to dominate variability on seasonal time scales while buoyancy forcing plays a minor role, confirming results from past forward perturbation experiments. Interannual variability, however, is shown to have originated from remote locations across the globe, including a nontrivial component originating from the tropical Pacific. The influence of atmospheric forcing emphasizes the importance of continuous widespread observations of the global atmospheric state for attributing observed AMOC variability.

An Inverse Modeling Approach to Calibrate Parameters for a Drainage Model with Two Optimization Algorithms on Homogeneous/Heterogeneous Soil

Due to the time and spatial limitations of subsurface drainage pilots, simulation models have been extensively applied for evaluating these systems. Since the accuracy of simulation models depends enormously on the accuracy of model parameters, this study aims to develop an inverse modeling approach for estimating most influential soil hydraulic and solute transport parameters in a subsurface drainage system in an arid and semi-arid region. The SWAP model in conjunction with a genetic algorithm and PEST optimization tool was used to find optimum parameters by minimizing the differences between observed and simulated values of drainage discharge, watertable depth, and drainage salinity. Results revealed that the best simulation of drainage outputs was obtained by parameters which were estimated minimizing an objective function that included all three datasets via a genetic algorithm. Although assuming the soil as a homogeneous and heterogeneous medium had quite similar results from objective functions with one or two datasets, homogeneous assumption worked better in the objective function with three datasets. The inverse modelling approach with GA resulted in a better performance as compared to the PEST optimization tool, particularly in objective functions with two or three datasets.

Stochastic reconstruction of spatio-temporal rainfall patterns by inverse hydrologic modelling

Abstract. Knowledge of spatio-temporal rainfall patterns is required as input for distributed hydrologic models used for tasks such as flood runoff estimation and modelling. Normally, these patterns are generated from point observations on the ground using spatial interpolation methods. However, such methods fail in reproducing the true spatio-temporal rainfall pattern, especially in data-scarce regions with poorly gauged catchments, or for highly dynamic, small-scale rainstorms which are not well recorded by existing monitoring networks. Consequently, uncertainties arise in distributed rainfall–runoff modelling if poorly identified spatio-temporal rainfall patterns are used, since the amount of rainfall received by a catchment as well as the dynamics of the runoff generation of flood waves is underestimated. To address this problem we propose an inverse hydrologic modelling approach for stochastic reconstruction of spatio-temporal rainfall patterns. The methodology combines the stochastic random field simulator Random Mixing and a distributed rainfall–runoff model in a Monte Carlo framework. The simulated spatio-temporal rainfall patterns are conditioned on point rainfall data from ground-based monitoring networks and the observed hydrograph at the catchment outlet and aim to explain measured data at best. Since we infer a three-dimensional input variable from an integral catchment response, several candidates for spatio-temporal rainfall patterns are feasible and allow for an analysis of their uncertainty. The methodology is tested on a synthetic rainfall–runoff event on sub-daily time steps and spatial resolution of 1 km2 for a catchment partly covered by rainfall. A set of plausible spatio-temporal rainfall patterns can be obtained by applying this inverse approach. Furthermore, results of a real-world study for a flash flood event in a mountainous arid region are presented. They underline that knowledge about the spatio-temporal rainfall pattern is crucial for flash flood modelling even in small catchments and arid and semiarid environments.

Enhanced springback prediction for bending of high-strength spring steel using material data from an inverse modelling approach

Abstract Springs for electrical components made from strip materials and flat wires are produced using stamping and forming technologies. The process design of multi-stage stamping and bending processes is still based on expert knowledge and experimental tests. The complexity of the forming processes and the high-strength materials used for springs make the FE simulation of those processes a challenging task. For the springback prediction in FEM, however, an accurate description of the elasto-plastic material behaviour is mandatory. Under process conditions such as bending of spring steel, the locally occurring strains are many times higher than the ultimate elongation of approx. 2 % that can be determined in tensile test. For those materials, standard tests fail to receive enhanced material data such as the influence of plastic deformation on the Young’s modulus. The goal of this work is to determine the elasto-plastic material parameters of high-strength spring steel (X10CrNi18-8) using an inverse modelling approach by means of a 3-point bending test. The inverse approach is used for determining the Young’s modulus and hardening parameters of Ludwik-Hollomon’s law for bending of high-strength spring steel. Furthermore, this work focuses on the unloading at the end of the bending experiment and its effect on the elastic material parameters. The results demonstrate that the inversely determined material data show lower scattering compared to material data from tensile test. Furthermore, material data of high-strength spring steel from the inverse modelling approach significantly enhances the springback prediction under bending conditions compared to FE simulations using material data from tensile test.

Incorporating Dendrite Growth into Continuum Models of Electrolytes: Insights from NMR Measurements and Inverse Modeling

In this work we develop a combined experimental and inverse continuum modeling approach to the problem of determining properties of a lithium electrolyte from NMR measurements of ion concentration in a test cell. The experimental set-up consists of an enclosed, lithium-electrolyte-filled tube with lithium electrodes at either end. A constant current is passed between these electrodes and the resulting evolution of the spatial distribution of the lithium ions is monitored using NMR imaging techniques. Using the recently developed tools of inverse modeling, in combination with the concentration measurements acquired with NMR imaging, it is shown that the standard Planck-Nernst electrolyte model results in predictions of negative transference numbers. The observation of growing lithium dendrites on the cathode suggests the cause for these unphysical predictions and motivates the formulation of a generalized Planck-Nernst model that explicitly accounts for the presence of these growing lithium-metal dendrites. In this approach, lithium depletion in a dendritic region adjacent to the cathode is modelled by adding a suitably-chosen spatially distributed sink term. It is demonstrated that a model in which lithium is lost from the electrolyte uniformly throughout the dendritic region provides predictions of electrolyte data consistent with the literature and thereby remedies the shortcoming of the standard Planck-Nernst model. In addition, a state-of-the-art Bayesian technique is used to quantify the uncertainty of the inferred material properties.

Comparisons of inverse modelling approaches for predicting energy consumption, economic growth and CO<SUB align="right">2 emissions: a case study for low-income countries

This study examines the causal relationships between CO2 emissions, energy consumption and economic growth in low-income countries for the period 1995-2013. The artificial neural network (ANN) model is applied to predict three variables during 2014-2025. Our empirical results show that there is bidirectional causality between economic growth and CO2 emissions, as well as energy consumption and economic growth, and there is unidirectional causal relationship running from energy consumption to CO2 emissions. In order to reduce emissions and to avoid a negative effect on the economic growth, low-income countries should adopt the dual strategy of increasing investment in energy infrastructure and stepping up energy conservation policies to increase energy efficiency and reduce wastage of energy. Comparison with dynamic simultaneous-equation model shows that the ANN model performs better for predictions.

Sugarcane straw removal effects on soil water storage and drainage in southeastern Brazil

To enhance global bioenergy production, the Brazilian industry9s interest in using sugarcane (<i>Saccharum officinarum</i>) straw as a feedstock for electricity and cellulosic ethanol production has increased recently. However, indiscriminate straw removal may negatively affect key soil functions related to water infiltration, retention, and availability to plants. Therefore, a microlysimeter system with a 0.2 m soil column was built to evaluate the effects of straw removal rates on water drainage and water storage in a sandy clay loam soil from a commercial sugarcane field in southeastern Brazil. The experiment was conducted in an open area where the lysimeter system was subjected to rainfall. After assembly, the treatments consisting of four straw amounts of 0, 3, 6, and 12 Mg ha⁻¹ were applied, representing straw removal rates of 100% (bare soil), 75%, 50%, and 0%, respectively. The water drainage was quantified and collected for 17 months, and the soil water storage was measured over a two-month period. The soil water holding capacity was calibrated by an inverse modeling approach minimizing the differences between soil water storage measured in the field and simulated by a water balance model. Our results reveal that the amount of water drained from bare soil was 30% lower than no removal treatment. Bare soil had the lowest water storage for most of the days, indicating a greater susceptibility to losing water through evaporation and drying. The long-term simulation for early, mid, and late sugarcane harvest seasons suggests longer periods of water restriction to crop growth under higher straw removal rates (i.e., 100% and 75%), potentially impairing sugarcane growth and thus yield. Also, the findings suggest that partial residue maintenance, up to 6 Mg ha⁻¹ of straw (50% removal) on the soil surface, seems to be sufficient to prevent excessive water losses and daily variations of soil water content, sustaining soil water storage rates above the critical point for sugarcane growth.

Rapid increase in ozone-depleting chloroform emissions from China

Chloroform contributes to the depletion of the stratospheric ozone layer. However, due to its short lifetime and predominantly natural sources, it is not included in the Montreal Protocol that regulates the production and uses of ozone-depleting substances. Atmospheric chloroform mole fractions were relatively stable or slowly decreased during 1990–2010. Here we show that global chloroform mole fractions increased after 2010, based on in situ chloroform measurements at seven stations around the world. We estimate that the global chloroform emissions grew at the rate of 3.5% yr−1 between 2010 and 2015 based on atmospheric model simulations. We used two regional inverse modelling approaches, combined with observations from East Asia, to show that emissions from eastern China grew by 49 (41–59) Gg between 2010 and 2015, a change that could explain the entire increase in global emissions. We suggest that if chloroform emissions continuously grow at the current rate, the recovery of the stratospheric ozone layer above Antarctica could be delayed by several years. Atmospheric levels of chloroform increased after 2010, as a result of emissions in eastern China, according to analyses of measurements and inverse modelling.

Reply to: Discussion of “Eocene to mid-Pliocene landscape evolution in Scandinavia inferred from offshore sediment volumes and pre-glacial topography using inverse modeling” (Pedersen et al. 2018, Geomorphology, 303: 467–485)

Here we reply to the discussion paper by Rasmussen (2018). In his discussion, Rasmussen (2018) raises concern on the use of the offshore sediment record as a way of constraining sediment flux out of Scandinavia over time, in order to inform landscape evolution models. We acknowledge that this approach is associated with large uncertainties, particularly in relation to source areas outside of Scandinavia that may have contributed to the sediment volume, and potential sinks that lie outside of our study area. Based on the comments by Rasmussen (2018), we present now a new complimentary set of inversions that explores an alternative for the imposed sediment volume originating from Scandinavia. Specifically, we assume that a significantly smaller Eocene sediment volume originates from Scandinavia, and a larger uncertainty on sediment volumes from all the considered time periods. We find that a lower Eocene sediment flux from Scandinavia makes Cenozoic plateau uplift more compatible with the offshore sediment record. However, these new plateau scenarios result in large-scale topography that is even less compatible with our reconstructed mid-Pliocene landscape, compared to the previous peneplain scenarios presented in Pedersen et al. (2018). We still find the scenario with substantial initial topography best compatible with our mid-Pliocene landscape, although this scenario cannot match the offshore record to the same degree when a lower Eocene sediment flux is assumed.On a final note, we emphasize that our inverse modeling approach is designed to incorporate geological information directly into the modeling, which will reduce the gap between geological observations and modeling. We therefore welcome any additional information that can inform and improve our modeling approach. However, we are dependent on some level of quantification in order to incorporate geological observations and exploit the full potential of this approach.

Inverse modeling approach for parametric frequency domain analysis of an electrohydraulic system

Abstract This paper presents parametric frequency domain analys.isf an electrohydraulic system, in particular, with respect to the hydraulic supply pressure. The supply pressure is a design parameter of significance such that it affects control bandwidth, load capability and system durability. However, intensive analysis on this parameter has not been reported yet due to the nonlinear dynamic features of an electrohydraulic system. In this paper, the inverse generalized frequency response functions are derived and used to conduct multi-dimensional Fourier analysis of the control input and to investigate its relation to the supply pressure. In addition, the hydraulic energy consumption is analyzed with respect to the supply pressure. The analysis reveals that the supply pressure is a critical design parameter that determines the degree of nonlinearity and trade-off between the control bandwidth and energy consumption.

An inverse modeling approach for the thermal response modeling of green façades

Green façades or vertical greenery systems (VGSs) are continuously gaining attention among urbanists for improving the living comfort and energy efficiency in urban areas. However, modeling and simulating the thermal response of VGSs remains a research topic. This paper introduces a novel inverse modeling approach for modeling the thermal responseof VGSs on building envelopes. The modeling approach considers the VGSs as a homogeneous layer with apparent thermo-physical properties. The approach optimizes the apparent thermo-physical properties by calibrating the inverse model using data generated by a detailed thermal response model of VGS or experimental data. It is shown that the predicted temperature of VGS deviates by less than ±1.3 °C, while the heat flux on the inner side of the building envelope deviates by less than ±0.3 W/m2 compared to the measured values.

Temporal estimation of hydrodynamic parameter variability in stormwater constructed wetlands – The hysteresis effect during multi-rainfall events

Constructed wetland (CW) systems are increasingly implemented as appropriate water treatment facilities, the efficiency of which varies with time due to possible malfunctions such as clogging related to excessive loads of suspended solids or inadequate CW sizing. Numerical flow modeling was used to evaluate filtering performance and to improve the design of CWs. Such modeling usually involves the so-called van Genuchten-Mualem (vGM) soil hydrodynamic parameters which are difficult to measure. This paper focuses on the sensitivity of the model with respect to the vGM parameters revealing a predominant influence of the shape parameters and the saturated conductivity of the filter on the piezometric heads, during feeding and drainage. A simple, robust and low-cost inverse modeling approach, deterministic and stochastic, for the identification of the soil hydrodynamic properties from piezometric heads measured during successive storm events is also presented. The temporal variability of hydrodynamic parameters was assessed and analyzed with regards to modeling efficiency. Principal component analysis showed that the estimated hydrodynamic parameters from the feeding and drainage sub-periods were significantly different.