Inverse Modeling Approach Research Articles

An inverse modeling approach to obtain P–T conditions of metamorphic stages involving garnet growth and resorption

An inverse modeling approach to obtain <i>P–T</i> conditions of metamorphic stages involving garnet growth and resorption

Reliability of Genotype-Specific Parameter Estimation for Crop Models: Insights from a Markov Chain Monte-Carlo Estimation Approach

Abstract. Parameter estimation is a critical step in successful application of dynamic crop models to simulate crop growth and yield under various climatic and management scenarios. Although inverse modeling parameterization techniques significantly improve the predictive capabilities of models, whether these approaches can recover the true parameter values of a specific genotype or cultivar is seldom investigated. In this study, we applied a Markov Chain Monte-Carlo (MCMC) method to the DSSAT dry bean model to estimate (recover) the genotype-specific parameters (GSPs) of 150 synthetic recombinant inbred lines (RILs) of dry bean. The synthetic parents of the population were assigned contrasting GSP values obtained from a database, and each of these GSPs was associated with several quantitative trait loci. A standard inverse modeling approach that simultaneously estimated all GSPs generated a set of values that could reproduce the original synthetic observations, but many of the estimated GSP values significantly differed from the original values. However, when parameter estimation was carried out sequentially in a stepwise manner, according to the genetically controlled plant development process, most of the estimated parameters had values similar to the original values. Developmental parameters were more accurately estimated than those related to dry mass accumulation. This new approach appears to reduce the problem of equifinality in parameter estimation, and it is especially relevant if attempts are made to relate parameter values to individual genes. Keywords: Crop models, Equifinality, Genotype-specific parameters, Markov chain Monte-Carlo, Parameterization.

Vegetation of Eurasia from the last glacial maximum to present: Key biogeographic patterns

Continental-scale estimates of vegetation cover, including land-surface properties and biogeographic trends, reflect the response of plant species to climate change over the past millennia. These estimates can help assess the effectiveness of simulations of climate change using forward and inverse modelling approaches. With the advent of transient and contiguous time-slice palaeoclimate simulations, vegetation datasets with similar temporal qualities are desirable. We collated fossil pollen records for the period 21,000–0 cal yr BP (kyr cal BP; calibrated ages) for Europe and Asia north of 40°N, using extant databases and new data; we filtered records for adequate dating and sorted the nomenclature to conform to a consistent yet extensive taxon list. From this database we extracted pollen spectra representing 1000-year time-slices from 21 kyr cal BP to present and used the biomization approach to define the most likely vegetation biome represented. Biomes were mapped for the 22 time slices, and key plant functional types (PFTs, the constituents of the biomes) were tracked though time. An error matrix and index of topographic complexity clearly showed that the accuracy of pollen-based biome assignments (when compared with modern vegetation) was negatively correlated with topographic complexity, but modern vegetation was nevertheless effectively mapped by the pollen, despite moderate levels of misclassification for most biomes. The pattern at 21 ka is of herb-dominated biomes across the whole region. From the onset of deglaciation (17–18 kyr cal BP), some sites in Europe record forest biomes, particularly the south, and the proportion of forest biomes gradually increases with time through 14 kyr cal BP. During the same period, forest biomes and steppe or tundra biomes are intermixed across the central Asian mountains, and forest biomes occur in coastal Pacific areas. These forest biome occurrences, plus a record of dated plant macrofossils, indicate that some tree populations existed in southern and Eastern Europe and central and far-eastern Eurasia. PFT composition of the herbaceous biomes emphasises the significant contribution of diverse forbs to treeless vegetation, a feature often obscured in pollen records. An increase in moisture ca. 14 kyr cal BP is suggested by a shift to woody biomes and an increase in sites recording initialization and development of lakes and peat deposits, particularly in the European portion of the region. Deforestation of Western Europe, presumably related to agricultural expansion, is clearly visible in the most recent two millennia.

Quantification of the zygotic barrier between interbreeding taxa using gene flow data

Hybridization and introgression via interspecific gene flow are common processes in the plant kingdom. The effectiveness of these processes is governed by the strengths of multiple zygotic barriers. These barriers have often been quantified in artificial settings using laborious and time‐consuming hand‐pollination experiments, but their quantification is nonexistent in the landscape. In this study, we utilized gene flow data within a spatially explicit simulation to assess the strengths of zygotic barriers. Our model system consisted of Populus nigra and its hybrid, P. × canadensis, which interbreed under natural conditions. The study population was located in the floodplain of the Eder River in central Germany. Pollen‐mediated introgression rates from hybrid males into the seeds of individual female trees were used as the target pattern using an inverse modeling approach. Simulations that treated pollen from both taxa equally revealed a large discrepancy between the observed and modeled rates of introgression for both taxa. The discrepancy was reduced by introducing a zygotic barrier against the pollen from the hybrid males. The best model outcome values indicated comparably strong zygotic barriers acting against pollen‐mediated introgressive gene flow into the two parental taxa, P. nigra and P. × canadensis. The sensitivity of our model was tested by applying different dispersal functions. Four common probability density functions were used along with a pollen dispersal function that had previously been fitted to gene flow data from the same dataset. The best barrier value was almost independent of the dispersal functions used here. Moreover, it was within the range previously determined in hand‐pollination‐based investigations, validating our model. These data indicate that the inverse modeling approach is a powerful method for quantifying hidden processes, and we discuss its use as a valuable tool for generating new insights into plant mating systems that are relevant to evolutionary biology and risk analyses in conservation efforts.

Dimensionality reduction for efficient Bayesian estimation of groundwater flow in strongly heterogeneous aquifers

We focus on the Bayesian estimation of strongly heterogeneous transmissivity fields conditional on data sampled at a set of locations in an aquifer. Log-transmissivity, Y, is modeled as a stochastic Gaussian process, parameterized through a truncated Karhunen–Loeve (KL) expansion. We consider Y fields characterized by a short correlation scale as compared to the size of the observed domain. These systems are associated with a KL decomposition which still requires a high number of parameters, thus hampering the efficiency of the Bayesian estimation of the underlying stochastic field. The distinctive aim of this work is to present an efficient approach for the stochastic inverse modeling of fully saturated groundwater flow in these types of strongly heterogeneous domains. The methodology is grounded on the construction of an optimal sparse KL decomposition which is achieved by retaining only a limited set of modes in the expansion. Mode selection is driven by model selection criteria and is conditional on available data of hydraulic heads and (optionally) Y. Bayesian inversion of the optimal sparse KLE is then inferred using Markov Chain Monte Carlo (MCMC) samplers. As a test bed, we illustrate our approach by way of a suite of computational examples where noisy head and Y values are sampled from a given randomly generated system. Our findings suggest that the proposed methodology yields a globally satisfactory inversion of the stochastic head and Y fields. Comparison of reference values against the corresponding MCMC predictive distributions suggests that observed values are well reproduced in a probabilistic sense. In a few cases, reference values at some unsampled locations (typically far from measurements) are not captured by the posterior probability distributions. In these cases, the quality of the estimation could be improved, e.g., by increasing the number of measurements and/or the threshold for the selection of KL modes.

Vertical modeling of the nitrogen cycle in the eastern tropical South Pacific oxygen deficient zone using high‐resolution concentration and isotope measurements

AbstractMarine oxygen deficient zones (ODZs) have long been identified as sites of fixed nitrogen (N) loss. However, the mechanisms and rates of N loss have been debated, and traditional methods for measuring these rates are labor‐intensive and may miss hot spots in spatially and temporally variable environments. Here we estimate rates of heterotrophic nitrate reduction, heterotrophic nitrite reduction (denitrification), nitrite oxidation, and anaerobic ammonium oxidation (anammox) at a coastal site in the eastern tropical South Pacific (ETSP) ODZ based on high‐resolution concentration and natural abundance stable isotope measurements of nitrate (NO3−) and nitrite (NO2−). These measurements were used to estimate process rates using a two‐step inverse modeling approach. The modeled rates were sensitive to assumed isotope effects for NO3− reduction and NO2− oxidation. Nevertheless, we addressed two questions surrounding the fates of NO2− in the ODZ: (1) Is NO2− being primarily reduced to N2 or oxidized to NO3− in the ODZ? and (2) what are the contributions of anammox and denitrification to NO2− removal? Depth‐integrated rates from the model suggest that 72–88% of the NO2− produced in the ODZ was oxidized back to NO3−, while 12–28% of NO2− was reduced to N2. Furthermore, our model suggested that 36–74% of NO2− loss was due to anammox, with the remainder due to denitrification. These model results generally agreed with previously measured rates, though with a large range of uncertainty, and they provide a long‐term integrated view that compliments incubation experiments to obtain a broader picture of N cycling in ODZs.

A 3D regional crustal model of the NE Atlantic based on seismic and gravity data

Abstract We present a 3D regional crustal model for the North Atlantic, which is based on the integration of seismic constraints and gravity data. The model addresses the crustal thickness geometry, and includes information on sedimentary thickness, the presence of high-velocity zones in the lower crust, and information on the crustal density distribution in the continental and oceanic domains. Using an iterative forward- and inverse-modelling approach, we adhere to the seismic constraints within their uncertainty, but manage to enhance the crustal geometry in areas where seismic data are sparse or absent. A number of basins are resolved with more detail. Recently released seismic reflection data beneath the NE Greenland Shelf allowed for a major improvement of the crustal thickness estimates. Estimated Moho depths beneath the basins there vary between 15 and 25 km, which is compatible with the conjugate Norwegian margin. A major lower-crustal seismic velocity anomaly in the vicinity of the Greenland–Iceland–Faroe Ridge complex is supported by density modelling. We discuss the validity and uncertainties of our model assumptions and discuss the correlation with the main structural elements of the North Atlantic.

Impacts of (Nano)formulations on the Fate of an Insecticide in Soil and Consequences for Environmental Exposure Assessment.

The development of nanopesticides has recently received an increased level of attention. However, there are very few data about the environmental fate of these new products, and it is not known whether nanoformulations can be evaluated within the current pesticide regulatory framework. Sorption and degradation parameters of the insecticide bifenthrin were measured in two soils for (i) the pure active ingredient, (ii) three nanoformulations, and (iii) a commercially available formulation. In most cases, fate parameters derived for the nanopesticides were significantly different from those derived for the pure active ingredient (factors of up to 10 for sorption and 1.8 for degradation), but discrepancies were not easy to relate to the characteristics of the nanocarriers. In some cases, differences were also observed between the commercial formulation and the pure active ingredient (factors of up to 1.4 for sorption and 1.7 for degradation). In the regulatory context, the common assumption that formulations do not influence the environmental fate of pesticide active ingredients after application seems therefore not always adequate. In the absence of direct measurement, an inverse modeling approach was successfully applied to evaluate the durability of the formulations in soil (release half-life ranged between 11 and 74 days). Predicted groundwater concentrations very much depended on the modeling approach adopted but overall suggest that the nanoformulations studied could reduce losses to groundwater.

Decision making under uncertainty in environmental projects using mathematical simulation modeling

In decision-making processes, reliability and risk aversion play a decisive role. The aim of this study is to perform an uncertainty assessment of the effects of future scenarios of sustainable groundwater pumping strategies on the quantitative and chemical status of an aquifer. The good status of the aquifer is defined according to the terms established by the EU Water Framework Directive (WFD). A decision support systems (DSS) is presented, which makes use of a stochastic inverse model (GC method) and geostatistical approaches to calibrate equally likely realizations of hydraulic conductivity (K) fields for a particular case study. These K fields are conditional to available field data, including hard and soft information. Then, different future scenarios of groundwater pumping strategies are generated, based on historical information and WFD standards, and simulated for each one of the equally likely K fields. The future scenarios lead to different environmental impacts and levels of socioeconomic development of the region and, hence, to a different degree of acceptance among stakeholders. We have identified the different stakeholders implied in the decision-making process, the objectives pursued and the alternative actions that should be considered by stakeholders in a public participation project (PPP). The MonteCarlo simulation provides a highly effective way for uncertainty assessment and allows presenting the results in a simple and understandable way even for non-experts stakeholders. The methodology has been successfully applied to a real case study and lays the foundations to perform a PPP and stakeholders’ involvement in a decision-making process as required by the WFD. The results of the methodology can help the decision-making process to come up with the best policies and regulations for a groundwater system under uncertainty in groundwater parameters and management strategies and involving stakeholders with conflicting interests.

The application of inverse modeling in characterizing hydraulic conductivity beneath the city of Berlin, Germany

In geothermal reservoir characterization and basin modeling, often conclusions are drawn and decisions are made using uncertain or incomplete data sets. Particularly, there are limited hydrogeological data in the Berlin area in the North German Basin. The groundwater in this sedimentary basin is divided into a shallow freshwater aquifer (with about 500 m depth) and a brackish to saline groundwater aquifer within deeper sedimentary layers. Between these two different groundwater compartments, a natural hydrogeological boundary is provided by the presence of an impervious clay-enriched layer (Rupelian Clay), which is discontinuous, eroded or not deposited in some local areas. Thereby, the distribution of hydraulic conductivity of Rupelian Clay aquitard that represents a vertical and horizontal partitioning of the aquifers below Berlin is of main importance in groundwater management. We use an inverse modeling approach to estimate the spatial distribution of hydraulic conductivity of the Rupelian Clay aquitard, using available local data within the Berlin province. We use a commercial finite element fluid flow simulator that interfaces to a parameter estimation package. A Gauss–Levenberg–Marquardt algorithm is used to adjust the hydraulic conductivity of the aquitard such that the hydraulic head observations are reproduced. Subsequently, the updated hydraulic conductivity of the Rupelian Clay is used as input to the forward modeling, in order to estimate the pressure and temperature fields. The results of the inverse modeling suggest a more continuous distribution of the Rupelian Clay layer below the Berlin area in comparison with previous published studies. Hence, the convective heat and fluid flow are more restricted, and there is less interaction between shallow and deep aquifers. Change in the predicted temperature field is more pronounced for deeper strata.

Solving Multiobjective Optimization Problems in Unknown Dynamic Environments: An Inverse Modeling Approach.

Evolutionary multiobjective optimization in dynamic environments is a challenging task, as it requires the optimization algorithm converging to a time-variant Pareto optimal front. This paper proposes a dynamic multiobjective optimization algorithm which utilizes an inverse model set to guide the search toward promising decision regions. In order to reduce the number of fitness evalutions for change detection purpose, a two-stage change detection test is proposed which uses the inverse model set to check potential changes in the objective function landscape. Both static and dynamic multiobjective benchmark optimization problems have been considered to evaluate the performance of the proposed algorithm. Experimental results show that the improvement in optimization performance is achievable when the proposed inverse model set is adopted.

Partitioning N2O emissions within the U.S. Corn Belt using an inverse modeling approach

AbstractNitrous oxide (N2O) emissions within the US Corn Belt have been previously estimated to be 200–900% larger than predictions from emission inventories, implying that one or more source categories in bottom‐up approaches are underestimated. Here we interpret hourly N2O concentrations measured during 2010 and 2011 at a tall tower using a time‐inverted transport model and a scale factor Bayesian inverse method to simultaneously constrain direct and indirect agricultural emissions. The optimization revealed that both agricultural source categories were underestimated by the Intergovernmental Panel on Climate Change (IPCC) inventory approach. However, the magnitude of the discrepancies differed substantially, ranging from 42 to 58% and from 200 to 525% for direct and indirect components, respectively. Optimized agricultural N2O budgets for the Corn Belt were 319 ± 184 (total), 188 ± 66 (direct), and 131 ± 118 Gg N yr−1 (indirect) in 2010, versus 471 ± 326, 198 ± 80, and 273 ± 246 Gg N yr−1 in 2011. We attribute the interannual differences to varying moisture conditions, with increased precipitation in 2011 amplifying emissions. We found that indirect emissions represented 41–58% of the total agricultural budget, a considerably larger portion than the 25–30% predicted in bottom‐up inventories, further highlighting the need for improved constraints on this source category. These findings further support the hypothesis that indirect emissions are presently underestimated in bottom‐up inventories. Based on our results, we suggest an indirect emission factor for runoff and leaching ranging from 0.014 to 0.035 for the Corn Belt, which represents an upward adjustment of 1.9–4.6 times relative to the IPCC and is in agreement with recent bottom‐up field studies.

Inverse modelling approach in 3-point bending for elasto- plastic material parameter identification of thin spring steel

Under process conditions such as bending of flat wire made from high strength spring steel, the occurring strains are many times higher than the maximum strains determined from uniaxial tensile tests. To determine the elasto-plastic material behaviour of high strength spring steel (X10CrNi18-8), an inverse modelling approach using a simple testing method is presented. A 3-point bending test with the resulting force-displacement measurements is used for the inverse analysis. The inverse approach is used for determining the Young's modulus and hardening parameters of the Ludwik-Hollomon's law for bending of high strength spring steel. FE simulations with the optimised material data meet the experimentally measured punch forces during bending. The optimised material data considerably enhances the springback prediction.

Inverse approach to estimating larval dispersal reveals limited population connectivity along 700 km of wave-swept open coast.

Demographic connectivity is fundamental to the persistence and resilience of metapopulations, but our understanding of the link between reproduction and recruitment is notoriously poor in open-coast marine populations. We provide the first evidence of high local retention and limited connectivity among populations spanning 700 km along an open coast in an upwelling system. Using extensive field measurements of fecundity, population size and settlement in concert with a Bayesian inverse modelling approach, we estimated that, on average, Petrolisthes cinctipes larvae disperse only 6.9 km (±25.0 km s.d.) from natal populations, despite spending approximately six weeks in an open-coast system that was once assumed to be broadly dispersive. This estimate differed substantially from our prior dispersal estimate (153.9 km) based on currents and larval duration and behaviour, revealing the importance of employing demographic data in larval dispersal estimates. Based on this estimate, we predict that demographic connectivity occurs predominantly among neighbouring populations less than 30 km apart. Comprehensive studies of larval production, settlement and connectivity are needed to advance an understanding of the ecology and evolution of life in the sea as well as to conserve ecosystems. Our novel approach provides a tractable framework for addressing these questions for species occurring in discrete coastal populations.

Inverse Modelling Approach to the Determination of Concentration-Dependent Transport Properties in Electrolytes: The Effect of Ion Pairing

The goal of the present investigation was to extend the recently proposed inverse modelling approach for determining concentration-dependent transport properties (salt diffusivity and Li+ cation transference number) to concentrated lithium salt solutions in solvents with relatively low permittivity. We demonstrated in our previous studies that NMR concentration profiles can be used for estimating the concentration dependent transport properties of LiTFSI solution in propylene carbonate (PC) under minimal assumption, including that of negligible ion pairing (simplified transport model) [1], which is valid for solvents with relative high permittivity [2] (εr ≈ 65 for PC). Herein we consider the case where ion paring effects cannot be neglected, due to the low permittivity of the solvent, as is the case for concentrated solutions of Li salts in mixed organic carbonate solvents (εr≈ 26 for EC:DMC 1:1). The data for the present study was obtained in the form of NMR intensity images of the 19F nuclei in the PF6 - anions of LiPF6 dissolved in a binary mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC), recorded under galvanostatic conditions. The NMR images were then post-processed to obtain lithium concentration profiles. The formation of non-negligible amounts of ion pairs in the present work significantly affects the estimation of transport properties of the system. As a result, the simplified transport model produces thermodynamically inconsistent results, manifested as negative transference numbers obtained from the inverse modelling analysis (Fig. 1). To remedy this situation, we considered an extended transport model which assumes that oppositely charged ions combine to form neutral ion pairs and which tracks the concentration of neutral ion pairs in addition to the concentration of free ions. However, due to the presence of a reaction term describing the formation and disintegration of ion pairs, the resulting PDE system is extremely stiff. Using methods of asymptotic analysis, corresponding to the limit of fast reaction rates, we have reduced the modeling problem to a more simple system describing the evolution of the total lithium concentration, which is computationally tractable. As this reduced system may not satisfy all boundary conditions of the original extended system, an additional material property called boundary transference number was introduced and its optimal dependence on the total concentration was identified via inverse analysis. The unknown material properties are concentration dependent (except for the equilibrium constant K) and are reconstructed with minimal assumptions using methods of variational optimization, to minimize the least-square error between the experimentally determined and simulated concentration values. The optimization problem is solved using a gradient-based method with a careful treatment of uncertainties resulting from the presence of noise in the experimental data. A key element of our computational approach is identification of the sensitivity of the PDE system solutions to perturbations of the constitutive relations, which is achieved through a novel adjoint-based approach. As shown in Fig. 2, the reconstruction produces thermodynamically consistent results for the Li+transference number under conditions when ion pairing effects cannot be neglected.

Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data

Thin layer flow cells are used in electrochemical research as experimental devices which allow to perform investigations of electrocatalytic surface reactions under controlled conditions using reasonably small electrolyte volumes. The paper introduces a general approach to simulate the complete cell using accurate numerical simulation of the coupled flow, transport and reaction processes in a flow cell. The approach is based on a mass conservative coupling of a divergence-free finite element method for fluid flow and a stable finite volume method for mass transport. It allows to perform stable and efficient forward simulations that comply with important physical constraints, namely mass conservation and maximum principles for the involved species. In this context, several recent approaches to obtain divergence-free velocity approximations from finite element simulations are discussed. In order to perform parameter identification, the forward simulation method is coupled to standard optimization tools. After an assessment of the inverse modeling approach using hypothetical, but realistic data, first results of the identification of solubility and transport data for O2 dissolved in organic electrolytes are presented. A plausibility study for a more complex situation with surface reactions concludes the paper and shows possible extensions of the presented numerical tools.

Inverse transport modeling of volcanic sulfur dioxide emissions using large-scale simulations

Abstract. An inverse transport modeling approach based on the concepts of sequential importance resampling and parallel computing is presented to reconstruct altitude-resolved time series of volcanic emissions, which often cannot be obtained directly with current measurement techniques. A new inverse modeling and simulation system, which implements the inversion approach with the Lagrangian transport model Massive-Parallel Trajectory Calculations (MPTRAC) is developed to provide reliable transport simulations of volcanic sulfur dioxide (SO2). In the inverse modeling system MPTRAC is used to perform two types of simulations, i.e., unit simulations for the reconstruction of volcanic emissions and final forward simulations. Both types of transport simulations are based on wind fields of the ERA-Interim meteorological reanalysis of the European Centre for Medium Range Weather Forecasts. The reconstruction of altitude-dependent SO2 emission time series is also based on Atmospheric InfraRed Sounder (AIRS) satellite observations. A case study for the eruption of the Nabro volcano, Eritrea, in June 2011, with complex emission patterns, is considered for method validation. Meteosat Visible and InfraRed Imager (MVIRI) near-real-time imagery data are used to validate the temporal development of the reconstructed emissions. Furthermore, the altitude distributions of the emission time series are compared with top and bottom altitude measurements of aerosol layers obtained by the Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP) and the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite instruments. The final forward simulations provide detailed spatial and temporal information on the SO2 distributions of the Nabro eruption. By using the critical success index (CSI), the simulation results are evaluated with the AIRS observations. Compared to the results with an assumption of a constant flux of SO2 emissions, our inversion approach leads to an improvement of the mean CSI value from 8.1 to 21.4 % and the maximum CSI value from 32.3 to 52.4 %. The simulation results are also compared with those reported in other studies and good agreement is observed. Our new inverse modeling and simulation system is expected to become a useful tool to also study other volcanic eruption events.

Time-domain reflectometry probing systems for the monitoring of hydrological processes in the unsaturated zone

Precise measurements of the downward movement of precipitation through the unsaturated zone, as well as return flow of moisture to the atmosphere via evaporation, have always been challenging in regard to in-situ monitoring techniques. This study investigates the profile of volumetric water-content fluctuations within the unsaturated zone through a combination of field techniques, including in-situ measurements of the volumetric porewater content at different depths using specially designed time-domain reflectometry (TDR) probes. The probes are installed through direct-push vibro-coring methods, at significant depths within the unsaturated zone, providing continuous readings of the soil-moisture content throughout the unsaturated column. The measured waveform is analyzed by using the inverse modeling approach resulting in an apparent relative dielectric permittivity profile of the surrounding medium along the TDR probe length. The approach sufficiently analyzes the mechanisms of water fluxes through significant depths within the unsaturated zone, which in turn can be used to quantify groundwater recharge at areas where the unsaturated zone hydrology plays a key role in the recharge of the underlying aquifers (such as arid and hydrologically sensitive areas). The approach was applied at an experimental field site in the Upper Rhine Valley, Germany.

Multivariable control of a debutanizer column using equation based artificial neural network model inverse control strategies

The debutanizer column is an important unit operation in petroleum refining industries as it is the main column to produce liquefied petroleum gas as its top product and light naphtha as its bottom product. This system is difficult to handle from a control standpoint due to its nonlinear behavior, multivariable interaction and existence of numerous constraints on both its manipulated and state variable. Neural network techniques have been increasingly used for a wide variety of applications where statistical methods have been traditionally employed. In this work we propose to use an equation based MIMO (Multi Input Multi Output) neural network based multivariable control strategy to control the top and bottom temperatures of the column simultaneously, while manipulating the reflux and reboiler flow rates respectively. This equation based neural network model represented by a multivariable equation, instead of the normal black box structure, has the advantage of being robust in nature while being easier to interpret in terms of its input output variables. It is implemented for set point changes and disturbance changes and the results show that the neural network based model method in the direct inverse and internal model approach performs better than the conventional PID method in both cases.

Estimating Emissions and Environmental Fate of Di-(2-ethylhexyl) Phthalate in Yangtze River Delta, China: Application of Inverse Modeling.

A georeferenced multimedia model was developed for evaluating the emissions and environmental fate of di-2-ethylhexyl phthalate (DEHP) in the Yangtze River Delta (YRD), China. Due to the lack of emission inventories, the emission rates were estimated using the observed concentrations in soil as inputs for the multimedia model solved analytically in an inverse manner. The estimated emission rates were then used to evaluate the environmental fate of DEHP with the regular multimedia modeling approach. The predicted concentrations in air, surface water, and sediment were all consistent with the ranges and spatial variations of observed data. The total emission rate of DEHP in YRD was 13.9 thousand t/year (95% confidence interval: 9.4-23.6), of which urban and rural sources accounted for 47% and 53%, respectively. Soil in rural areas and sediment stored 79% and 13% of the total mass, respectively. The air received 61% of the total emissions of DEHP but was only associated with 0.2% of the total mass due to fast degradation and intensive deposition. We suggest the use of an inverse modeling approach under a tiered risk assessment framework to assist future development and refinement of DEHP emission inventories.