Improved atmospheric constraints on Southern Ocean CO2 exchange.

We present improved estimates of air-sea CO2 exchange over three latitude bands of the Southern Ocean using atmospheric CO2 measurements from global airborne campaigns and an atmospheric 4-box inverse model based on a mass-indexed isentropic coordinate (Mθe). These flux estimates show two features not clearly resolved in previous estimates based on inverting surface CO2 measurements: a weak winter-time outgassing in the polar region and a sharp phase transition of the seasonal flux cycles between polar/subpolar and subtropical regions. The estimates suggest much stronger summer-time uptake in the polar/subpolar regions than estimates derived through neural-network interpolation of pCO2 data obtained with profiling floats but somewhat weaker uptake than a recent study by Long et al. [Science 374, 1275-1280 (2021)], who used the same airborne data and multiple atmospheric transport models (ATMs) to constrain surface fluxes. Our study also uses moist static energy (MSE) budgets from reanalyses to show that most ATMs tend to have excessive diabatic mixing (transport across moist isentrope, θe, or Mθe surfaces) at high southern latitudes in the austral summer, which leads to biases in estimates of air-sea CO2 exchange. Furthermore, we show that the MSE-based constraint is consistent with an independent constraint on atmospheric mixing based on combining airborne and surface CO2 observations.

Inverting a model of neuromuscular control to estimate descending activation patterns that generate fast-reaching movements.

Reaching movements generally show smooth kinematic profiles that are invariant across varying movement speeds even as interaction torques and muscle properties vary nonlinearly with speed. How the brain brings about these invariant profiles is an open question. We developed an analytical inverse dynamics method to estimate descending activation patterns directly from observed joint angle trajectories based on a simple model of the stretch reflex, and of muscle and biomechanical dynamics. We estimated descending activation patterns for experimental data from eight different planar two-joint movements performed at two movement times (fast: 400 ms; slow: 800 ms). The temporal structure of descending activation differed qualitatively across speeds, consistent with the idea that the nervous system uses an internal model to generate anticipatory torques during fast movement. This temporal structure also depended on the cocontraction level of antagonistic muscle groups. Comparing estimated muscle activation and descending activation revealed the contribution of the stretch reflex to movement generation that was found to set in after about 20% of movement time.NEW & NOTEWORTHY By estimating descending activation patterns directly from observed movement kinematics based on a model of the dynamics of the stretch reflex, of muscle force generation, and of the biomechanics of the limb, we observed how brain signals must be temporally structured to enable fast movement.

From theory to practical fundamentals of electroencephalographic source imaging in localizing the epileptogenic zone.

With continued advancement in computational technologies, the analysis of electroencephalography (EEG) has shifted from pure visual analysis to a noninvasive computational technique called EEG source imaging (ESI), which involves mathematical modeling of dipolar and distributed sources of a given scalp EEG pattern. ESI is a noninvasive phase I test for presurgical localization of the seizure onset zone in focal epilepsy. It is a relatively inexpensive modality, as it leverages scalp EEG and magnetic resonance imaging (MRI) data already collected typically during presurgical evaluation. With an adequate number of electrodes and combined with patient-specific MRI-based head models, ESI has proven to be a valuable and accurate clinical diagnostic tool for localizing the epileptogenic zone. Despite its advantages, however, ESI is routinely used at only a minority of epilepsy centers. This paper reviews the current evidence and practical fundamentals for using ESI of interictal and ictal epileptic activity during the presurgical evaluation of drug-resistant patients. We identify common errors in processing and interpreting ESI studies, describe the differences in approach needed for localizing interictal and ictal EEG discharges through practical examples, and describe best practices for optimizing the diagnostic information available from these studies.

Vapor pressure deficit helps explain biogenic volatile organic compound fluxes from the forest floor and canopy of a temperate deciduous forest.

Biogenic volatile organic compounds (BVOCs) play critical roles in ecological and earth-system processes. Ecosystem BVOC models rarely include soil and litter fluxes and their accuracy is often challenged by BVOC dynamics during periods of rapid ecosystem change like spring leaf out. We measured BVOC concentrations within the air space of a mixed deciduous forest and used a hybrid Lagrangian/Eulerian canopy transport model to estimate BVOC flux from the forest floor, canopy, and whole ecosystem during spring. Canopy flux measurements were dominated by a large methanol source and small isoprene source during the leaf-out period, consistent with past measurements of leaf ontogeny and theory, and indicative of a BVOC flux situation rarely used in emissions model testing. The contribution of the forest floor to whole-ecosystem BVOC flux is conditional on the compound of interest and is often non-trivial. We created linear models of forest floor, canopy, and whole-ecosystem flux for each study compound and used information criteria-based model selection to find the simplest model with the best fit. Most published BVOC flux models do not include vapor pressure deficit (VPD), but it entered the best canopy, forest floor, and whole-ecosystem BVOC flux model more than any other study variable in the present study. Since VPD is predicted to increase in the future, future studies should investigate how it contributes to BVOC flux through biophysical mechanisms like evaporative demand, leaf temperature and stomatal function.

Tandem internal models execute motor learning in the cerebellum.

In performing skillful movement, humans use predictions from internal models formed by repetition learning. However, the computational organization of internal models in the brain remains unknown. Here, we demonstrate that a computational architecture employing a tandem configuration of forward and inverse internal models enables efficient motor learning in the cerebellum. The model predicted learning adaptations observed in hand-reaching experiments in humans wearing a prism lens and explained the kinetic components of these behavioral adaptations. The tandem system also predicted a form of subliminal motor learning that was experimentally validated after training intentional misses of hand targets. Patients with cerebellar degeneration disease showed behavioral impairments consistent with tandemly arranged internal models. These findings validate computational tandemization of internal models in motor control and its potential uses in more complex forms of learning and cognition.

Quantitative food web modeling unravels the importance of the microphytobenthos-meiofauna pathway for a high trophic transfer by meiofauna in soft-bottom intertidal food webs.

Meiofauna are known to have an important role on many ecological processes, although, their role in food web dynamics is often poorly understood, partially as they have been an overlooked and under sampled organism group. Here, we used quantitative food web modeling to evaluate the trophic relationship between meiofauna and their food sources and how meiofauna can mediate the carbon flow to higher trophic levels in five contrasting soft-bottom intertidal habitats (including seagrass beds, mudflats and sandflats). Carbon flow networks were constructed using the linear inverse model-Markov chain Monte Carlo technique, with increased resolution of the meiofauna compartments (i.e. biomass and feeding ecology of the different trophic groups of meiofauna) compared to most previous modeling studies. These models highlighted that the flows between the highly productive microphytobenthos and the meiofauna compartments play an important role in transferring carbon to the higher trophic levels, typically more efficiently so than macrofauna. The pathway from microphytobenthos to meiofauna represented the largest flow in all habitats and resulted in high production of meiofauna independent of habitat. All trophic groups of meiofauna, except for selective deposit feeders, had a very high dependency on microphytobenthos. Selective deposit feeders relied instead on a wider range of food sources, with varying contributions of bacteria, microphytobenthos and sediment organic matter. Ecological network analyses (e.g. cycling, throughput and ascendency) of the modeled systems highlighted the close positive relationship between the food web efficiency and the assimilation of high-quality food sources by primary consumers, e.g. meiofauna and macrofauna. Large proportions of these flows can be attributed to trophic groups of meiofauna. The sensitivity of the network properties to the representation of meiofauna in the models leads to recommending a greater attention in ecological data monitoring and integrating meiofauna into food web models.

Groundwater hydrogeochemical formation and evolution in a karst aquifer system affected by anthropogenic impacts.

Karst groundwater, an important water source, is often highly influenced by human impacts, causing environmental damage and threats to human health. However, studies on the anthropogenic influences on the hydrogeochemical evolution of karst groundwater are relatively rare. To assess hydrogeochemical formation and evolution, we focused on a typical karst groundwater system (Jinan, China) which is composed of cold groundwater (av. temperature 13-17 °C), springs and geothermal water (av. temperature > 30 °C) and is significantly affected by human activities. The study was performed by means of water samples collecting and analyzing and isotope analysis (2H, 18O and 14C). The statistical analysis and inverse models were also applied to further understand geochemical processes and anthropogenic influences. The 2H, 18O and 14C results indicate that the cold karst groundwater is easily influenced and contaminated by the local environment, while geothermal water is relatively old with a slow rate of recharge. The hydrochemical types of cold karst groundwater are mainly HCO3-Ca and HCO3·SO4-Ca, while geothermal water hydrochemical types are SO4-Ca·Na and SO4-Ca. Groundwater Ca2+, Mg2+, HCO3- and SO42- are mainly controlled by carbonate equilibrium, gypsum dissolution and dedolomitization. Groundwater Na+, K+ and Cl- are mainly derived from halite dissolution, and in geothermal water, they are also affected by incongruent dissolution of albite and K-feldspar. Anthropogenic nitrogen produces ammonium resulting in nitrification and reduction in CO2(g) consumption and HCO3- release from carbonate dissolution. Principal component analysis and inverse models also indicate that nitrification and denitrification have significantly affected water-rock interactions. Our study suggests that karst groundwater quality is dominated by water-rock interactions and elucidates the influence of anthropogenic nitrogen. We believe that this paper will be a good reference point to study anthropogenic influences on the groundwater environment and to protect karst groundwater globally.

The Cerebellar Thalamus.

The thalamus is a neural processor and integrator for the activities of the forebrain. Surprisingly, little is known about the roles of the "cerebellar" thalamus despite the anatomical observation that all the cortico-cerebello-cortical loops make relay in the main subnuclei of the thalamus. The thalamus displays a broad range of electrophysiological responses, such as neuronal spiking, bursting, or oscillatory rhythms, which contribute to precisely shape and to synchronize activities of cortical areas. We emphasize that the cerebellar thalamus deserves a renewal of interest to better understand its specific contributions to the cerebellar motor and associative functions, especially at a time where the anatomy between cerebellum and basal ganglia is being rewritten.

Investigation on the Dependency of Phase Retrieval Accuracy Versus Edge Enhancement to the Noise Ratio of X-ray Propagation-Based Phase-Contrast Imaging.

Phase retrieval is necessary for propagation-based phase-contrast imaging (PB-PCI). Arhatari established a model for predicting the impact of the sample-to-detector distance and the system noise on the phase retrieval performance. We have extended Arhatari's model to account for the parameters of excessive source size, finite detector resolution, and geometrical magnification for more practical cases. However, there exist interaction effects among these parameters resulting in difficulty of predicting the phase retrieval performance. In this study, we found that optimizing the trade-off among these parameters for phase retrieval is consistent with the improvement of edge enhancement to noise ratio (EE/N) in the "forward problem" of the PB-PCI. Hence, we engaged in establishing a relationship between EE/N and phase retrieval performance in terms of the "forward problem" and "inverse problem" of the PB-PCI, respectively. Our results showed that, at fixed detector resolution, phase retrieval from the phase-contrast projections at the same EE/N level resulted in the consistent phase retrieval performance. Therefore, the performance of phase retrieval can be predicted based on the EE/N level and be quantitatively optimized by increasing EE/N.

Introducing a general framework for pollution source identification in surface water resources (theory and application).

Studies on pollution source identification in water resources date back over three decades. These studies use inverse solution of the transport equation for recovering the release history and/or the location of the pollutant sources. Each of these studies has its own advantages and limitations in accordance with the methods employed and the complexity of the solutions. Moreover, conducted studies on pollution source identification in surface water resources (e.g. rivers) are fewer in number compared to those on groundwater resources. In nearly all previous related studies on rivers, researchers have often developed their own numerical forward models, but these models have never taken into account the complexity of the problem in real conditions, such as river topography, real flow conditions, etc. Therefore, compared to commercial models, these models have many drawbacks and limitations. Thus, it would be desirable to provide a framework that can be employed to solve the transport equation in the inverse model using available software packages. In this study, the inverse solution of the transport equation for recovering release histories of multiple pollutant sources in rivers is achieved by the help of ready software packages via a feasible framework. The proposed framework can be readily applied in one-, two-, and three-dimensional problems. The underlying concept of the proposed framework is the linearity of the governing equation, i.e. transport equation. Furthermore, the present study presents the conditions and rules for the arrangement (number and location) of the measurement points of the pollutant concentration under various conditions. The proper arrangement of the measurement points is significant, since it solves the non-uniqueness problem of the inverse model. The most important factor affecting the arrangement of the measurement points is the flow pattern. In this study, it is suggested that the complexity of the flow pattern may lead to practical arrangements for the control points. The proposed procedure was verified by the use of three series of data in one- and two-dimensional domains under real conditions of flow and topography by employing well-known existing software packages. In each test case, a proper and practical arrangement was proposed for the measurement points of the concentration-time curve. The suggested arrangement resulted in the correct operation of the inverse model. The proposed inverse model showed a good capability with a reasonable percentage of errors of the recovering release rate of pollutant sources. Accordingly, it can be conveniently used in cases where forward models are readily available.

Regional atmospheric CO2 inversion reveals seasonal and geographic differences in Amazon net biome exchange.

Understanding tropical rainforest carbon exchange and its response to heat and drought is critical for quantifying the effects of climate change on tropical ecosystems, including global climate-carbon feedbacks. Of particular importance for the global carbon budget is net biome exchange of CO2 with the atmosphere (NBE), which represents nonfire carbon fluxes into and out of biomass and soils. Subannual and sub-Basin Amazon NBE estimates have relied heavily on process-based biosphere models, despite lack of model agreement with plot-scale observations. We present a new analysis of airborne measurements that reveals monthly, regional-scale (~1-8 × 10(6)  km(2) ) NBE variations. We develop a regional atmospheric CO2 inversion that provides the first analysis of geographic and temporal variability in Amazon biosphere-atmosphere carbon exchange and that is minimally influenced by biosphere model-based first guesses of seasonal and annual mean fluxes. We find little evidence for a clear seasonal cycle in Amazon NBE but do find NBE sensitivity to aberrations from long-term mean climate. In particular, we observe increased NBE (more carbon emitted to the atmosphere) associated with heat and drought in 2010, and correlations between wet season NBE and precipitation (negative correlation) and temperature (positive correlation). In the eastern Amazon, pulses of increased NBE persisted through 2011, suggesting legacy effects of 2010 heat and drought. We also identify regional differences in postdrought NBE that appear related to long-term water availability. We examine satellite proxies and find evidence for higher gross primary productivity (GPP) during a pulse of increased carbon uptake in 2011, and lower GPP during a period of increased NBE in the 2010 dry season drought, but links between GPP and NBE changes are not conclusive. These results provide novel evidence of NBE sensitivity to short-term temperature and moisture extremes in the Amazon, where monthly and sub-Basin estimates have not been previously available.

Cerebellum as a forward but not inverse model in visuomotor adaptation task: a tDCS-based and modeling study.

Despite several pieces of evidence, which suggest that the human brain employs internal models for motor control and learning, the location of these models in the brain is not yet clear. In this study, we used transcranial direct current stimulation (tDCS) to manipulate right cerebellar function, while subjects adapt to a visuomotor task. We investigated the effect of this manipulation on the internal forward and inverse models by measuring two kinds of behavior: generalization of training in one direction to neighboring directions (as a proxy for inverse models) and localization of the hand position after movement without visual feedback (as a proxy for forward model). The experimental results showed no effect of cerebellar tDCS on generalization, but significant effect on localization. These observations support the idea that the cerebellum is a possible brain region for internal forward, but not inverse model formation. We also used a realistic human head model to calculate current density distribution in the brain. The result of this model confirmed the passage of current through the cerebellum. Moreover, to further explain some observed experimental results, we modeled the visuomotor adaptation process with the help of a biologically inspired method known as population coding. The effect of tDCS was also incorporated in the model. The results of this modeling study closely match our experimental data and provide further evidence in line with the idea that tDCS manipulates FM's function in the cerebellum.

Precise control of movement kinematics by optogenetic inhibition of Purkinje cell activity.

Purkinje cells (PCs) of the cerebellar cortex are necessary for controlling movement with precision, but a mechanistic explanation of how the activity of these inhibitory neurons regulates motor output is still lacking. We used an optogenetic approach in awake mice to show for the first time that transiently suppressing spontaneous activity in a population of PCs is sufficient to cause discrete movements that can be systematically modulated in size, speed, and timing depending on how much and how long PC firing is suppressed. We further demonstrate that this fine control of movement kinematics is mediated by a graded disinhibition of target neurons in the deep cerebellar nuclei. Our results prove a long-standing model of cerebellar function and provide the first demonstration that suppression of inhibitory signals can act as a powerful mechanism for the precise control of behavior.

A multi-objective multi-tasking evolutionary algorithm based inverse mapping and adaptive transformation strategy: IM-MFEA.

Multi-tasking optimization algorithm attracts much attention because the knowledge transfer between tasks enables the algorithm to process multiple related tasks simultaneously. However, negative knowledge transfer occasionally occurs, which may weaken the performance of the algorithm. To reduce the impact of negative knowledge transfer, a multi-objective multi-tasking optimization algorithm (IM-MFEA) based on inverse model mapping and an objective transformation strategy is proposed. First, correlation analysis is applied in an inverse mapping strategy to improve the accuracy of the inverse mapping model. Then, following the pattern of using the source domain solutions to assist the optimization of the target domain, the adaptive transformation strategy is used to improve the quality of the source domain solution in the objective space. These transformed solutions are reconstructed through the inverse mapping strategy. Finally, these reconstructed source domain solutions are mated with the target domain solutions to generate competitive offspring individuals for the target domain. To verify the effectiveness of the IM-MFEA, comprehensive experiments were conducted on nine multi-objective multi-factorial optimization (MFO) benchmark problems. Empirical results demonstrate that IM-MFEA is superior to other algorithms in 90% of test instances by inverted generational distance (IGD) and hypervolume (HV) value indicators.

Dynamic multi-objective evolutionary optimization algorithm based on two-stage prediction strategy.

Tracking pareto-optimal set or pareto-optimal front in limited time is an important problem of dynamic multi-objective optimization evolutionary algorithms (DMOEAs). However, the current DMOEAs suffer from some deficiencies. In the early optimization process, the algorithms may suffer from random search. In the late optimization process, the knowledge which can accelerate the convergence rate is not fully utilized. To address the above issue, a DMOEA based on the two-stage prediction strategy (TSPS) is proposed. TSPS divides the optimization progress into two stages. At the first stage, multi-region knee points are selected to capture the pareto-optimal front shape, which can accelerate the convergence and maintaining good diversity at the same time. At the second stage, improved inverse modeling is applied to search the representative individuals, which can improve the diversity of the population and is beneficial to predicting the moving location of the pareto-optimal front. Experimental results on dynamic multi-objective optimization test suites show that TSPS is superior to the other six DMOEAs. In addition, the experimental results also show that the proposed method has the ability to respond quickly to environmental changes.

Application of cavity ring-down spectroscopy and a novel near surface Gaussian plume estimation approach to inverse model landfill methane emissions.

Fugitive methane emissions from municipal solid waste landfills impact global climate change and reliable emissions quantification is of increasing importance. Ground-based cavity ring-down spectrometer (CRDS) measurements were used to determine methane concentrations and isotopic compositions of carbon in CH4. Then, CH4 oxidation through various cover materials was assessed using the Keeling plot method. A novel inverse modeling approach using Gaussian dispersion analysis, termed near-surface Gaussian plume estimation (NSGPE), was developed to predict whole-site landfill methane emissions. The concentration data obtained around the landfill perimeter with the mobile ground-based CRDS were used. Methane concentration data were integrated to parameterize discretized point source emissions from a Gaussian dispersion model. Post-processing algorithms were applied to refine modeling predictions to account for the influence of topographical and meteorological conditions on methane transport. Results indicate spatially resolved and consistent emissions estimates among multiple optimization simulations, with refinements increasing the resolution and spatial trends of emissions. Post-processing algorithms resolve consistent overestimation of emissions commonly observed using conventional Gaussian dispersion models.•Ground-based CRDS used to obtain methane concentration and oxidation data.•Novel inverse Gaussian dispersion modeling approach developed to predict methane emissions from landfills accounting for site-specific topography and meteorology.•Post-processing algorithms refine emissions estimates.

Broadband diffuse optical spectroscopy of two-layered scattering media containing oxyhemoglobin, deoxyhemoglobin, water, and lipids.

We investigated the relationship between chromophore concentrations in two-layered scattering media and the apparent chromophore concentrations measured with broadband optical spectroscopy in conjunction with commonly used homogeneous medium inverse models. We used diffusion theory togenerate optical data from a two-layered distribution of relevant tissue absorbers, namely, oxyhemoglobin, deoxyhemoglobin, water, and lipids, with a top-layer thickness in the range 1-15 mm. The generated data consisted of broadband continuous-wave (CW) diffuse reflectance in the wavelength range 650-1024 nm, and frequency-domain (FD) diffuse reflectance at 690 and 830 nm; two source-detector distances of 25 and 35 mm were used to simulate a dual-slope technique. The data were inverted using diffusion theory for a semi-infinite homogeneous medium to generate reduced scattering coefficients at 690 and 830 nm (from FD data) and effective absorption spectra in the range 650-1024 nm (from CW data). The absorption spectra were then converted into effective total concentration and oxygen saturation of hemoglobin, as well as water and lipid concentrations. For absolute values, it was found that the effective hemoglobin parameters are typically representative of the bottom layer, whereas water and lipid represent some average of the respective concentrations in the two layers. For concentration changes, lipid showed a significant cross-talk with other absorber concentrations, thus indicating that lipid dynamics obtained in these conditions may not be reliable. These systematic simulations of broadband spectroscopy of two-layered media provide guidance on how to interpret effective optical properties measured with similar instrumental setups under the assumption of medium homogeneity.

Quantification of the heterogeneous effect of static and dynamic perivascular structures on patient-specific local aortic wall mechanics using inverse finite element modeling and DENSE MRI.

Recent studies have highlighted the relevance of perivascular interactions on aortic wall mechanics. Most of the approaches assume static perivascular structures; however, the beating heart dynamically displaces the neighboring aorta. We develop a model to account for the effect of periaortic interactions due to static and dynamic structures by prescribing a moving elastic foundation boundary condition (EFBC) embedded into an inverse finite element algorithm using in vivo displacements from 2D displacement encoding with stimulated echoes (DENSE) MRI as target data. We applied this method at three different locations of interest, the distal aortic arch (DAA), descending thoracic aorta (DTA), and infrarenal abdominal aorta (IAA) for a total of 27 cases in healthy humans. The model reproduces the target diastole-to-systole deformation and bulk displacement of the aortic wall with median displacement errors below 0.5mm. The EFBC showed good agreement with the location of anatomical features and was consistent among individuals of similar characteristics. Results show that an energy source acting on the adventitia is required to reproduce the displacements measured at the vicinity of the heart, but not at the abdomen. The average adventitial load as a percentage of the luminal pulse-pressure was found to increase with age and to decrease along the descending aorta, from 61% at the DAA to 37% at the DTA, and 30% at the IAA. This approach offers a patient-specific method to estimate in vivo adventitial loads and aortic wall stiffness, which can bring a better understanding of normal and pathological in vivo aortic function.

A dual prediction strategy with inverse model for evolutionary dynamic multiobjective optimization.

In practical applications and daily life, dynamic multiobjective optimization problems (DMOPs) are ubiquitous. The purpose of dealing with DMOPs is to track moving Pareto Front (PF) and find a series of Pareto Set (PS) at different times. Prediction-based strategies improve the performance of multiobjective evolutionary algorithms in dynamic environments. However, how to ensure the accuracy of prediction models is always a challenge. In this study, a dual prediction strategy with inverse model (DPIM) is developed, to alleviate the negative impact of inaccurate prediction. When a change is confirmed, DPIM responses to it by predicting the individuals in the objective space. Furthermore, the inverse model is established to connect the decision space with the objective space, which can guide the search for promising decision areas. Specifically, the inverse model is also predicted to minimize the error in the process of mapping the population from the objective space back to the decision space. The effectiveness of the proposed DPIM is proved by comparison with four effective DMOEAs on 14 benchmark problems with various real-word scenarios. The experimental results show that DPIM can obtain high-quality populations with good convergence and distribution in dynamic environments.

Tracing riverine sulfate source in an agricultural watershed: Constraints from stable isotopes.

The sulfate pollution in water environment gains more and more concerns in recent years. The discharge of domestic, municipal, and industrial wastewaters increases the riverine sulfate concentrations, which may cause local health and ecological problems. To better understand the sources of sulfate, this study collected water samples in a typical agricultural watershed in East Thailand. The source apportionment of sulfide was conducted by using stable isotopes and receptor models. The δ34SSO4 value of river water varied from 1.2‰ to 16.4‰, with a median value of 8.9‰. The hydrochemical data indicated that the chemical compositions of Mun river water were affected by the anthropogenic inputs and natural processes such as halite dissolution, carbonate, and silicate weathering. The positive matrix factorization (PMF) model was not suitable to trace source of riverine sulfate, because the meaning of the extracted factors seems to be vague. Based on the elemental ratio and isotopic composition, the inverse model yielded the relative contribution of sulfide oxidation (approximately 46.5%), anthropogenic input (approximately 41.5%), and gypsum dissolution (approximately 12%) to sulfate in Mun river water. This study indicates that the selection of models for source apportionment should be careful. The large contribution of anthropogenic inputs calls an urgent concern of the Thai government to establish effective management strategies in the Mun River basin.