Inverse Modeling Approach Research Articles

Inverse modeling approach for determining soil hydraulic properties as affected by application of cattle manure

Numerical codes are extensively used in the modeling of water and solute transport in the vadose zone. The application of these codes depends on knowledge of soil hydraulic properties such as soil water retention curve and hydraulic conductivity. Application of cattle manure to the soil can increase soil organic matter (SOM) contents. Increases in SOM associated with changes in the structure and adsorption properties of soil and, thus, their hydraulic properties. In this study the effect of cattle manure on soil hydraulic properties was investigated using inverse method. Applied inverse method was based on Levenberg-Marquart optimization algorithm to estimate hydraulic properties of soil in transient condition using C++ programming language along with forward model (HydroGeoSphere) as a numerical code. Nine iron cylinders of 57 cm in inner diameter and about 40 cm in height were filled with Sandy clay loam soil of 30 cm in height. Cattle manure applied at 0, 30, and 60 Mg/ha at three replications in a completely random design. One year after cattle manure application, saturated hydraulic conductivity, porosity, and water retention curve parameters (van Genuchten function, α and β) were estimated using inverse method. Statistical analysis showed that the automatic calibration is sensitive to α more than the other parameters. The results showed that porosity, saturated hydraulic conductivity, residual water content, α and β increased significantly (P value is less than 0.05) with application 30 and 60 Mg/ha cattle manure. But there was no significant difference (P value is less than 0.05) in β between application of 30 and 60 Mg/ha cattle manure. The study also indicated that α was 25.0% and 50.0% higher and β was 9.6% and 12.6% lower than control treatment in 30 and 60 Mg/ha treatments. In addition, application cattle manure showed positive effect on hydraulic parameters of soil. Keywords: soil hydraulic property, parameter estimation, inverse method, HydroGeoSphere, unsaturated flow, cattle manure DOI: 10.3965/j.ijabe.20140702.004 Citation: Ali Rasoulzadeh, Ali Yaghoubi. Inverse modeling approach for determining soil hydraulic properties as affected by application of cattle manure. Int J Agric & Biol Eng, 2014; 7(2): 27－35.

A contaminant transport model for wetlands accounting for distinct residence time bimodality

• A 2-D depth-averaged model is presented accounting for vegetation resistance. • RTDs are analyzed for different vegetation densities in a channelized wetland . • Wetland channelization results in a bimodality of the RTDs. • A parameterization of the RTDs is proposed based on a 1-D 2-domain transport model. • The model parameters are related to specific geometry and vegetation parameters. Vegetation plays a major role in controlling the fate of contaminants in natural and constructed wetlands. Estimating the efficiency of contaminant removal of a wetland requires separate knowledge of the residence time statistics in the main flow channels, where the flow velocity is relatively higher, and in the more densely vegetated zones, where the velocity is smaller and most of the biochemical transformations occur. A conceptual wetland characterized by a main flow channel (MFC) and lateral vegetated zones (LVZs) is modeled here using a two-dimensional depth-averaged hydrodynamic and advection–dispersion model. The effect of vegetation is described as a flow resistance represented in the hydrodynamic model as a function of the stem density. Simulations are performed for a given flow discharge and for increasing values of the ratio between the vegetation density in the LVZs and in the MFC. Residence time distributions (RTDs) of a nonreactive tracer are derived from numerical simulations of the solute breakthrough curves (BTCs) resulting from a continuous concentration input. Results show that increasing vegetation densities produce an increasingly pronounced bimodality of the RTDs. At longer times, the RTDs decrease exponentially, with different timescales depending on the stem density ratio and other system parameters. The overall residence time distribution can be decomposed into a first component associated with the relatively fast transport in the MFC, and a second component associated with the slower transport in the LVZs. The weight of each temporal component is related to the exchange flux at the MFC-LVZ interface. A one-dimensional transport model is proposed that is capable to reproduce the RTDs predicted by the depth-averaged model, and the relationship between model and system parameters is investigated using a combination of direct and inverse modeling approaches.

Uncertainty-based analysis on water quality response to water diversions for Lake Chenghai: A multiple-pattern inverse modeling approach

Summary While water diversion and dilution are often proposed and implemented for lake eutrophication management, their effectiveness and efficiency in achieving water quality goals is often questionable. Although water quality modeling (WQM) has been applied to quantify lake responses to water diversion and dilution in practice, it is necessary to improve the existing analysis approaches with an uncertainty-based decision-support framework to address the situation of severe data limitation that exists in many real-world cases. This study implemented an enhanced multiple-pattern inverse water quality modeling (MPIWQM) approach in a water diversion study for a terminal plateau lake in southwestern China to address the difficulty of developing robust water-diversion decision support under data limitation and model uncertainty. A two-dimensional, longitudinal and vertical hydrodynamic and water quality model was developed to simulate water circulation and nutrient fate and transport in the lake. To overcome a severe limitation of data, this study employed a multiple-pattern load-parameter estimation (MPLE) method that couples the numerical model with a Genetic Algorithm (GA) and a cluster algorithm to construct an uncertainty-based decision support system. Execution of the MPLE approach resulted in 27 load-parameter patterns for the case study to represent all possible combinations of loading-parameter patterns conditioned on the available water quality data in the lake. The uncertainty-based decision-support framework was then applied to evaluate three realistic water diversion scenarios proposed by local management authorities, and the system was able to predict a range of possibilities given a specific water diversion condition. The scenario analysis results showed that (a) within the range of uncertainties represented by the 27 load-parameter patterns, the model consistently predict that the water diversions would unlikely cause significant water quality improvement in the lake; (b) the water quality response to water diversion demonstrates clear spatial variability, temporal variability, and the effect is in general cumulative over time; (c) different water quality constituents respond to the diversions differently, where the chemical oxygen demand (COD) demonstrates the strongest response, while the total phosphorus (TP) the weakest; and (d) none of the proposed water diversion scenarios is able to reverse, or significantly mitigate the water quality deterioration trend in the lake.

Forward and inverse modelling approaches for prediction of light stimulus from electrophysiological response in plants

In this paper, system identification approach has been adopted to develop a novel dynamical model for describing the relationship between light as an environmental stimulus and the electrical response as the measured output for a bay leaf (Laurus nobilis) plant. More specifically, the target is to predict the characteristics of the input light stimulus (in terms of on–off timing, duration and intensity) from the measured electrical response – leading to an inverse problem. We explored two major classes of system estimators to develop dynamical models – linear and nonlinear – and their several variants for establishing a forward and also an inverse relationship between the light stimulus and plant electrical response. The best class of models are given by the Nonlinear Hammerstein–Wiener (NLHW) estimator showing good data fitting results over other linear and nonlinear estimators in a statistical sense. Consequently, a few set of models using different functional variants of NLHW has been developed and their accuracy in detecting the on–off timing and intensity of the input light stimulus are compared for 19 independent plant datasets (including 2 additional species viz. Zamioculcas zamiifolia and Cucumis sativus) under similar experimental scenario.

Inverse estimation of snow accumulation along a radar transect on Nordenskiöldbreen, Svalbard

We present an inverse modeling approach to reconstruct annual accumulation patterns from ground‐penetrating radar (GPR) data. A coupled surface energy balance‐snow model simulates surface melt and the evolution of subsurface density, temperature, and water content. The inverse problem consists of iteratively calibrating accumulation, serving as input for the model, by finding a match between modeled and observed radar travel times. The inverse method is applied to a 16 km GPR transect on Nordenskiöldbreen, Svalbard, yielding annual accumulation patterns for 2007–2012. Accumulation patterns with a mean of 0.75 meter water equivalent (mwe) a−1contain substantial spatial variability, with a mean annual standard deviation of 0.17 mwe a−1, and show only partial consistency from year to year. In contrast to traditional methods, accounting for melt water percolation, refreezing, and runoff facilitates accurate accumulation reconstruction in areas with substantial melt. Additionally, accounting for horizontal density variability along the transect is shown to reduce spatial variability in reconstructed accumulation, whereas incorporating irreducible water storage lowers accumulation estimates. Correlating accumulation to terrain characteristics in the dominant wind direction indicates a strong preference of snow deposition on leeward slopes, whereas weaker correlations are found with terrain curvature. Sensitivity experiments reveal a nonlinear response of the mass balance to accumulation changes. The related negative impact of small‐scale accumulation variability on the mean net mass balance is quantified, yielding a negligible impact in the accumulation zone and a negative impact of −0.09 mwe a−1in the ablation area.

Inverse Procedural Modelling of Trees

AbstractProcedural tree models have been popular in computer graphics for their ability to generate a variety of output trees from a set of input parameters and to simulate plant interaction with the environment for a realistic placement of trees in virtual scenes. However, defining such models and their parameters is a difficult task. We propose an inverse modelling approach for stochastic trees that takes polygonal tree models as input and estimates the parameters of a procedural model so that it produces trees similar to the input. Our framework is based on a novel parametric model for tree generation and uses Monte Carlo Markov Chains to find the optimal set of parameters. We demonstrate our approach on a variety of input models obtained from different sources, such as interactive modelling systems, reconstructed scans of real trees and developmental models.

Modeling geochemical datasets for source apportionment: Comparison of least square regression and inversion approaches

Mathematical modeling of geochemical datasets finds frequent applications in Earth Sciences, particularly in areas of source apportionment and provenance studies. In this work, source apportionment modeling have been considered based on two commonly used methods, the Least Square Regression (LSR) and Inverse Modeling (IM), to determine the contributions of (i) solutes from different sources to global river water, and (ii) various rocks to a glacial till. The purpose of this exercise is to compare the results from the two mathematical methods, infer their merits and drawbacks and indicate approaches to enhance their reliability.The application of the LSR and IM approaches to determine the source contributions to global river water using the same a-priori end member compositions yielded divergent results; the LSR analysis giving impossibly negative values of Na contribution from one of the sources (evaporites), in contrast to the IM approach which yield reliable estimates of source contributions, and a set of a-posteriori source compositions and associated uncertainties. Interestingly, the use of the a-posteriori composition derived from the IM approach in the LSR analysis as an input for end-member composition gave source contributions that were consistent with those derived from IM. Calculations based on the IM show that 46±8% of Na in global river is derived from silicate weathering, consistent with some of the earlier reported estimates.In case of the glacial till, the source contributions based on both the approaches were similar, however even in this case better agreement between the two approaches is obtained when the a-posteriori composition data of end members derived from the IM is used as input in the LSR model. These comparisons demonstrate that the IM is better suited for source apportionment studies among the two models, as it requires only rough estimates of end member composition, unlike the LSR that needs source composition to be better constrained. In addition, the IM also provides uncertainties in the source contributions and best estimates of their composition.

North American terrestrial CO2 uptake largely offset by CH4 and N2O emissions: toward a full accounting of the greenhouse gas budget.

The terrestrial ecosystems of North America have been identified as a sink of atmospheric CO2 though there is no consensus on the magnitude. However, the emissions of non-CO2 greenhouse gases (CH4 and N2O) may offset or even overturn the climate cooling effect induced by the CO2 sink. Using a coupled biogeochemical model, in this study, we have estimated the combined global warming potentials (GWP) of CO2, CH4 and N2O fluxes in North American terrestrial ecosystems and quantified the relative contributions of environmental factors to the GWP changes during 1979–2010. The uncertainty range for contemporary global warming potential has been quantified by synthesizing the existing estimates from inventory, forward modeling, and inverse modeling approaches. Our “best estimate” of net GWP for CO2, CH4 and N2O fluxes was −0.50 ± 0.27 Pg CO2 eq/year (1 Pg = 1015 g) in North American terrestrial ecosystems during 2001–2010. The emissions of CH4 and N2O from terrestrial ecosystems had offset about two thirds (73 %±14 %) of the land CO2 sink in the North American continent, showing large differences across the three countries, with offset ratios of 57 % ± 8 % in US, 83 % ± 17 % in Canada and 329 % ± 119 % in Mexico. Climate change and elevated tropospheric ozone concentration have contributed the most to GWP increase, while elevated atmospheric CO2 concentration have contributed the most to GWP reduction. Extreme drought events over certain periods could result in a positive GWP. By integrating the existing estimates, we have found a wide range of uncertainty for the combined GWP. From both climate change science and policy perspectives, it is necessary to integrate ground and satellite observations with models for a more accurate accounting of these three greenhouse gases in North America.Electronic supplementary materialThe online version of this article (doi:10.1007/s10584-014-1072-9) contains supplementary material, which is available to authorized users.

Column-averaged CO2 concentrations in the subarctic from GOSAT retrievals and NIES transport model simulations

The distribution of atmospheric carbon dioxide (CO2) in the subarctic was investigated using the National Institute for Environmental Studies (NIES) three-dimensional transport model (TM) and retrievals from the Greenhouse gases Observing SATellite (GOSAT). Column-averaged dry air mole fractions of subarctic atmospheric CO2 (XCO2) from the NIES TM for four flux combinations were analyzed. Two flux datasets were optimized using only surface observations and two others were optimized using both surface and GOSAT Level 2 data. Two inverse modeling approaches using GOSAT data were compared. In the basic approach adopted in the GOSAT Level 4 product, the GOSAT observations are aggregated into monthly means over 5° × 5° grids. In the alternative method, the model–observation misfit is estimated for each observation separately. The XCO2 values simulated with optimized fluxes were validated against Total Carbon Column Observing Network (TCCON) ground-based high-resolution Fourier Transform Spectrometer (FTS) measurements. Optimized fluxes were applied to study XCO2 seasonal variability over the period 2009–2010 in the Arctic and subarctic regions. The impact on CO2 levels of emissions from enhancement of biospheric respiration induced by the high temperature and strong wildfires occurring in the summer of 2010 was analyzed. Use of GOSAT data has a substantial impact on estimates of the level of CO2 interanual variability.

The effect of snow: How to better model ground surface temperatures

We present an inverse modeling approach for reconstructing the effective thermal conductivity of snow on a daily basis using air temperature, ground temperature and snow depth measurements. The method is applied to four sites in Alaska. To validate the method we used measured snow densities and snow water equivalents. The modeled thermal conductivities of snow for the two interior Alaska sites have relatively low values and reach their maximum near the end of the snow season, while the conductivities at the two sites on the Alaskan North Slope are higher and reach their maximum earlier in the snow season. We show that the reconstructed daily thermal conductivities allow for more accurate modeling of ground surface temperatures when compared to applying a constant thermal conductivity for the snow layer.

A comparative approach of inverse modelling applied to an irradiative batch dryer employing several artificial neural networks

The present work has focused on a comparison between commonly employed artificial neural networks (ANNs) in engineering applications to identify the most efficient ANN for the inverse modelling of an irradiating furnace/dryer in terms of accuracy and computing time. To this end, several ANNs were designed, trained and employed to estimate the heat emitted during the irradiative batch drying process with the aid of NeuroSolution®.As part of the study, different ANNs were designed and trained to play the role of the inverse heat transfer model. The reasons for exploiting these ANNs were derived from various studies in the literature, in which ANNs were employed for engineering modelling purposes. The results showed that the multiple layer perceptron (MLP) with the Levenberg–Marquadt (LM) in the back propagation (BP) was the best ANN among the methods evaluated to solve the inverse heat estimation problems used in irradiative batch drying processes. An important advantage of the ANN method in comparison with the classical inverse heat transfer modelling approaches is that a detailed knowledge of geometrical and thermal properties of the system (such as wall conductivity, emissivity, etc.) is not required. Such properties are difficult to measure and may undergo significant changes during the temperature transient mode.In this study, genetic algorithms (GAs) have been employed to determine the key parameters of the employed ANNs. These parameters are normally found heuristically or by a trial and error brute force process. The results demonstrate that the aforementioned parameters may be estimated much more accurately and faster by the GA method. The performance of the networks has been improved as well and the number of required hidden layers has been discovered using a non trial–error method, which eliminates time-consuming repeating procedures and produces more accurate results.

An inverse-model approach to multivariable norm optimal iterative learning control with auxiliary optimisation

Motivated by the commonly encountered problem in which tracking is only required at selected intermediate points within the time interval, a general optimisation-based iterative learning control (ILC) algorithm is derived that ensures convergence of tracking errors to zero whilst simultaneously minimising a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. In practice, the proposed solutions enable a repeated tracking task to be accurately completed whilst simultaneously reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear. The theory is developed using the well-known norm optimal ILC (NOILC) framework, using general linear, functional operators between real Hilbert spaces. Solutions are derived using feedforward action, convergence is proved and robustness bounds are presented using both norm bounds and positivity conditions. Algorithms are specified for both continuous and discrete-time state-space representations, with the latter including application to multi-rate sampled systems. Experimental results using a robotic manipulator confirm the practical utility of the algorithms and the closeness with which observed results match theoretical predictions.

Kinetic modeling of laboratory CO2‐exposure experiments performed on whole rock reservoir samples

AbstractMineralogical and geochemical observations from laboratory CO2‐exposure experiments on reservoir rocks are compared with predictions from geochemical modeling that was performed using PHREEQC software. The Pitzer‐based Eq 3/6 thermodynamic database, provided by Quintessa Ltd., was applied. For kinetic modeling, a Lasaga‐type rate equation was implemented and different models were parameterized taking kinetic rate law parameters from literature. Based on previous modeling studies a modified inverse modeling approach is presented here. This comprises several different Fe‐proxies and improved statistical ranking preferences that were implemented in particular to better match modeled and measured concentrations of dissolved K+, Fe2+ and Al3+. Compared to the previous approach, the presented modeling results are in good (better) agreement with experimental data. Systematic discrepancies between modeling and observation still occur regarding K‐bearing mineral phases and corresponding K+ brine concentrations. Despite missing correlation between K+ and Cl− concentrations, potential reasons for these discrepancies may be increased K+ brine concentrations during the experiments due to dissolution of K‐rich salt(s), such as sylvite. Much better matches were generated for dissolved Fe2+ concentrations. Goethite mainly controls the chemical behavior of dissolved Fe2+ in kinetic simulations. Based on both the available equilibrium and kinetic modeling results, the ultimate fate of dissolved Al3+ and the analysis of Al‐bearing mineral phases potentially controlling dissolved Al3+ brine concentrations cannot be conclusively determined. The overall best ranked kinetic model comprises anhydrite, dolomite, goethite, K‐feldspar and kaolinite. Despite minor inconsistencies dissolved Fe2+, Al3+ and Si4+ were in particular much better reproduced by the best ranked kinetic models.

Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions

Abstract. Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include nonnegativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination of the relative merits of each. This paper investigates the applicability of several approaches to bounded inverse problems. A common method of data transformations is found to unrealistically skew estimates for the examined example application. The method of Lagrange multipliers and two Markov chain Monte Carlo (MCMC) methods yield more realistic and accurate results. In general, the examined MCMC approaches produce the most realistic result but can require substantial computational time. Lagrange multipliers offer an appealing option for large, computationally intensive problems when exact uncertainty bounds are less central to the analysis. A synthetic data inversion of US anthropogenic methane emissions illustrates the strengths and weaknesses of each approach.

Inverse modeling of dissolved O2 and δ18O-DO to estimate aquatic metabolism, reaeration and respiration isotopic fractionation: effects of variable light regimes and input uncertainties

A transient model, hereafter referred to as ROM-TM, was developed to quantify river ecosystem metabolic rates and reaeration rates from field observation of changes in dissolved O2 (DO) and the ratio of 18O to 16O in DO (δ18O-DO). ROM-TM applies an inverse modeling approach and is programmed using MATLAB. Parameters describing photosynthesis, ecosystem respiration, gas exchange, and isotopic fractionation, such as maximum photosynthetic rate (Pm), photosynthetic efficiency parameter (a), respiration rate at 20 °C (R20), gas exchange coefficient (K), respiration isotopic fractionation factor (aR), and photorespiration coefficient (βR), can be abstracted by minimizing the sum of square errors between the fitted data and the observed field data. Then DO and δ18O-DO time series can be reconstructed using estimated parameters and input variables. Besides being capable of teasing apart metabolic processes and gas exchange to provide daily average estimates of metabolic parameters at the ecosystem scale, ROM-TM can be used to address issues related to light including light saturation phenomena at the ecosystem level, the effect of cloud cover on the metabolic balance, and photorespiration. Error and uncertainty analysis demonstrates that ROM-TM is stable and robust for the random errors of DO time series. The photosynthetic parameters Pm and a are more sensitive than other parameters to lower-resolution time series data.

Inversion of Time-Lapse Electric Potential Data to Estimate Fracture Connectivity in Geothermal Reservoirs

An inverse modeling approach was developed to characterize fracture connectivity in geothermal reservoirs using an injection of a conductive fluid and time-lapse electric potential measurements. Discrete fracture networks with sparsely connected fractures were modeled and a flow simulator was used to solve electric fields as a conductive tracer flows through the fracture networks. The electric potential difference between well pairs drops progressively in time as the conductive fluid fills interconnected fractures along paths from the injector toward the producer. Therefore, the fractional connected area of reservoirs could be estimated using inverse modeling to match the response to other fracture networks by comparing time histories of the electric potential. This method was compared to estimating fractional connected area using tracer return curves alone and the study showed that locations of connected areas were estimated better using the electric potential approach. A sensitivity analysis was performed to study the effect of fractional connected area on time-lapse electric potential and tracer return data. The study verified the advantages of using electric potential measurements instead of only the tracer return curves.

An inverse modeling approach for tree-ring-based climate reconstructions under changing atmospheric CO2 concentrations

An inverse modeling approach for tree-ring-based climate reconstructions under changing atmospheric CO<SUB>2</SUB> concentrations

Pollutant source identification in a city district by means of a street network inverse model

This study presents the performances of an inverse modelling approach aiming to identify position and emission rate of a localised pollutant source placed within a city district. To that purpose we combine wind tunnel experiments and an urban dispersion model. Experiments are performed in an idealised urban canopy, made up of regularly spaced blocks, and provide the pollutant concentration field downwind from the source within the canopy. The urban dispersion model, named SIRANE, is an operational model that simulates the main mechanisms governing the pollutant transfer within a network of streets.

Movement rules for juvenile steelhead: dynamic linking of movement behaviour to habitat and density

AbstractWe incorporated explanatory factors including stream habitat type and fish density into individual‐based models with dynamic connections among adjacent habitat units to infer dispersal behaviour of juvenile steelheadOncorhynchus mykissin a Great Lakes watershed. We used mark–recapture data and an inverse modelling approach to estimate daily probability of steelhead moving out of a habitat unit, P(move),according to four competing models. The models used included (i) a null model where all fish had equal movement probability; (ii) a habitat‐dependent model where P(move) depended on the habitat type; (iii) a density‐dependent model of P(move); and (iv) a model where P(move) depended on both density and habitat type. The habitat‐dependent model provided the most parsimonious fit to the observed data according to Akaike's information criteria (AICc). In the null model, P(move) averaged 0.70, whereas P(move) averaged 0.75 in pools, 0.68 in riffles and 0.73 in runs in the habitat‐dependent model.

Using inverse modeling to estimate parameter values for three dimensional transport of contaminants in Lake Ontario

&lt;p&gt;The Great Lakes form an important freshwater drinking source for many urban areas surrounding the Lakes but also provide a sink for pollutants and runoff. Consequently introducing new drinking water intakes into any of these water bodies requires investigation into local pollutant sources and their transport in order to determine the most appropriate location and depth of any new intake. Two methods involving the calibration of a 3D wind driven transport model, to spill data collected over a 4 week period, are described. The methods include the traditional trial and error approach and the application of a nonlinear inverse model to optimize parameter estimates. Results show that calibration using the inverse modeling approach was an improvement over the traditional trial and error approach by providing a clear quantitative analysis of parameter sensitivity and importance, and ultimately yielding a better fit between observed and simulated data. The calibrated three-dimensional model was ultimately applied to assess the impacts of a potential local pollutant source to several proposed new drinking water intakes located along the north shore of Lake Ontario.&lt;/p&gt;