Parameter Uncertainty Propagation Research Articles

Statistical analysis of parameters and adsorption isotherm models.

The present work intends to discuss parameter estimation and statistical analysis in adsorption. The Langmuir and Tóth isotherm models are compared for a set of carbon dioxide adsorption data on 13X zeolite from literature at different temperatures: 303, 323, 373, and 423 K. Statistical analyses were performed under frequentist and Bayesian perspectives. Under the frequentist statistical view, parameters were estimated using Maximum Likelihood estimation (MLE). Statistical analyses of parameters were performed by confidence regions in terms of elliptical approximation and likelihood region, while the evaluation of models was performed by chi-square statistics. The results showed that, for these nonlinear models, the elliptical region offers a poor approximation of the parameter estimates' confidence region, especially for the most correlated parameter pairs. Additionally, the four-parameter Tóth's equation yields less correlated parameters than the three-parameter Langmuir model. From a Bayesian perspective, the Markov chain Monte Carlo (MCMC) technique facilitated the reconstruction of the probability density functions of parameters as well as enabled the propagation of parametric uncertainties in the model responses. Finally, the accurate assessment of experimental uncertainty significantly influences the evaluation of models and their respective parameters.

Predicting the Temperature-Driven Development of Stage-Structured Insect Populations with a Bayesian Hierarchical Model

AbstractThe management of forest pests relies on an accurate understanding of the species’ phenology. Thermal performance curves (TPCs) have traditionally been used to model insect phenology. Many such models have been proposed and fitted to data from both wild and laboratory-reared populations. Using Hamiltonian Monte Carlo for estimation, we implement and fit an individual-level, Bayesian hierarchical model of insect development to the observed larval stage durations of a population reared in a laboratory at constant temperatures. This hierarchical model handles interval censoring and temperature transfers between two constant temperatures during rearing. It also incorporates individual variation, quadratic variation in development rates across insects’ larval stages, and “flexibility” parameters that allow for deviations from a parametric TPC. Using a Bayesian method ensures a proper propagation of parameter uncertainty into predictions and provides insights into the model at hand. The model is applied to a population of eastern spruce budworm (Choristoneura fumiferana) reared at 7 constant temperatures. Resulting posterior distributions can be incorporated into a workflow that provides prediction intervals for the timing of life stages under different temperature regimes. We provide a basic example for the spruce budworm using a year of hourly temperature data from Timmins, Ontario, Canada. Supplementary materials accompanying this paper appear on-line.

Analysis of material parameter uncertainty propagation in preoperative flap suture simulation

Skin flap transplantation is the most commonly used method to repair tissue defect and cover the wound. In clinic, finite element method is often used to design the pre-operation scheme of flap suture. However, the material parameters of skin flap are uncertain due to experimental errors and differences in body parts. How to consider the influence of material parameter uncertainty on the mechanical response of flap suture in the finite element modeling is an urgent problem to be solved at present. Therefore, the influence of material parameter uncertainty propagation in skin flap suture simulation was studied, Firstly, the geometric model of clinical patient’s hand wound was constructed by using reverse modeling technology, the patient’s three-dimensional wound was unfolded into a flat surface by using curved surface expansion method, yielding a preliminary design contour for the patient’s transplant flap. Based on the acquired patient wound geometry model, the finite element model of flap suture with different fiber orientations and different sizes was constructed in Abaqus, and the uncertainty propagation analysis method based on Monte Carlo simulation combined with surrogate model technology was further used to analyze the stress response of flap suture considering the uncertainty of material parameters. Results showed that the overall stress value was relatively lower when the average fiber orientation was 45°. which could be used as the optimal direction for the flap excision. when the preliminary design contour of the flap was scaled down within 90%, the stress value after flap suturing remained within a safe range.

Stochastic response analysis of 3D vibro-acoustic system with acoustic impedance and modeling parameter uncertainties

A novel stochastic response analysis scheme for 3D vibro-acoustic systems is constructed based on the PUFEM/FEM and the direct probability integral method, and the effect of uncertain acoustic impedance and modeling parameters on the system response is investigated. The proposed scheme has the capability of capturing waveform within the element, the small system matrices and easy handling acoustic impedance, also can efficiently treat the propagation of parameter uncertainties through transforming the integration of the response probability density function into the summation of the response under each representative point by partitioning the input probability space and smoothing the Dirac δ function. Numerical examples show that the mean and standard deviation of the responses computed by the proposed scheme agree well with the MCS, but the agreement of the standard deviation is slightly lower at the frequency with large response dispersion. The effect of uncertain acoustic impedance on the system response is mainly at the low frequencies, where the location and amplitude of resonance peaks fluctuate significantly. Uncertain modeling parameters synthetically modify the stiffness and mass matrix, altering the intrinsic properties and response of the system, and the response at the higher frequency is more sensitive to the uncertain modeling parameters.

A Prediction Model for Skin Wound Suture Forces With Uncertain Material Parameters

To evaluate the forces required for the suture of skin wounds quickly and effectively, the nonlinear finite element method was used to calculate the suture forces for skin wounds with different sizes and material parameters. With the calculated results as samples, the prediction model for skin wound suture forces was constructed by means of the EBF neural network model. Given the uncertain skin material parameters influencing the reliability of numerical results, the Monte-Carlo method was used to analyze the uncertainty propagation of skin material parameters. Finally, the prediction analysis and measuring experiment of wound suture forces were carried out with pig skin specimens to verify the reliability of the method. The results showed that, the suture force increases first and then decreases according to the suture point sequence, and the peak force occurs before the center of the wound. For a 40 mm×10 mm wound, the peak suture force is about 1.7 N, and that for a 40 mm×14 mm wound is about 2.5 N. Influenced by the uncertainty of material parameters, the prediction results of suture forces fluctuate by as much as ±0.6 N. The proposed theoretical prediction model provides an effective solution to the problem of parameter uncertainty propagation for biological soft tissue materials such as skins, and makes an important mechanical reference for robotic surgical suture.

A Bayesian perspective on the information content of soil water measurements for the hydrological characterization of the vadose zone

Transient measurements from soil water monitoring installments are frequently coupled with Richards-based solvers to inversely estimate soil hydraulic parameters (SHPs) and numerically describe vadose zone water fluxes, such as groundwater recharge. To reduce model predictive uncertainty, the experimental setup should be designed to maximize the information content of observations. However, in practice, this is generally done by relying on the a priori expertise of the scientist/user, without exploiting the advantages of model-based experimental design. Thus, the main aim of this study is to demonstrate how model-based experimental design can be used to maximize the information content of observations in multiple synthetic scenarios encompassing different soil textural compositions and climatic conditions. The hydrological model HYDRUS is coupled with a Nested Sampling estimator to calculate the parameters’ posterior distributions and the Kullback-Leibler divergences. Results indicate that the combination of seepage flow, soil water content, and soil matric potential measurements generally leads to highly informative designs especially for fine textured soils, while results from coarse soils are generally affected by higher uncertainty. Additionally, the propagation of parameter uncertainties in a contrasting (dry) climate scenario strongly increased prediction uncertainties for sandy soil, not only in terms of the cumulative amount and magnitude of the peak, but also in the temporal variability of the seepage flow. A complementary real-world application with a sandy soil lysimeter identified a combination of seepage data and matric potential as the most informative design and confirmed findings of the synthetic scenarios, in which matric potential proved to be more informative than soil water content measurements.

Uncertainty Propagation Based MINLP Approach for Artificial Neural Network Structure Reduction

The performance of artificial neural networks (ANNs) is highly influenced by the selection of input variables and the architecture defined by hyper parameters such as the number of neurons in the hidden layer and connections between network variables. Although there are some black-box and trial and error based studies in the literature to deal with these issues, it is fair to state that a rigorous and systematic method providing global and unique solution is still missing. Accordingly, in this study, a mixed integer nonlinear programming (MINLP) formulation is proposed to detect the best features and connections among the neural network elements while propagating parameter and output uncertainties for regression problems. The objective of the formulation is to minimize the covariance of the estimated parameters while by (i) detecting the ideal number of neurons, (ii) synthesizing the connection configuration between those neurons, inputs and outputs, and (iii) selecting optimum input variables in a multi variable data set to design and ensure identifiable ANN architectures. As a result, suggested approach provides a robust and optimal ANN architecture with tighter prediction bounds obtained from propagation of parameter uncertainty, and higher prediction accuracy compared to the traditional fully connected approach and other benchmarks. Furthermore, such a performance is obtained after elimination of approximately 85% and 90% of the connections, for two case studies respectively, compared to traditional ANN in addition to significant reduction in the input subset.

Assessing uncertainty propagation in hybrid models for daily streamflow simulation based on arbitrary polynomial chaos expansion

Accurate streamflow prediction is of significant importance in watershed management and has been attracting a lot of research interest. Hybrid hydrological models that employ advantages of physically-based models (PBMs) and data-driven models (DDMs) emerge recently as reliable tools for analyzing hydrological processes. Both PBMs and DDMs have uncertain parameters that could affect the hybrid modeling results. Conventional computational algorithms that rely on repeated sampling, such as Monte Carlo Simulation (MCS), have been recognized as robust tools for assessing the propagation of parameter uncertainties. However, the efficiency of these computational algorithms can decrease exponentially as the number of parameters increases. Meanwhile, although parameter uncertainty of PBMs has been widely studied, that of DDMs in a hybrid modeling framework has not been well investigated. In this study, a hybrid model framework is proposed for streamflow prediction, and an effective arbitrary polynomial chaos expansion (aPCE) method is implemented to assess the propagation of DDM parameter uncertainty within the hybrid modeling framework. The hybrid hydrological model integrating fully-distributed MIKE SHE and four machine-learning techniques increases the coefficient of determination (R2) from 0.70 to 0.82 for two validation periods. The aPCE method generates highly similar probabilistic results as MCS and achieves a 90% efficiency enhancement in uncertainty assessment. The results prove that aPCE is an efficient alternative to MCS for assessing uncertainties of hyperparameters in hybrid models. This study helps improve the performance of the streamflow prediction and also provide an insight into the uncertainty propagation involved in the hybrid models.

Quantifying the propagation of parametric uncertainty on flux balance analysis

Flux balance analysis (FBA) and associated techniques operating on stoichiometric genome-scale metabolic models play a central role in quantifying metabolic flows and constraining feasible phenotypes. At the heart of these methods lie two important assumptions: (i) the biomass precursors and energy requirements neither change in response to growth conditions nor environmental/genetic perturbations, and (ii) metabolite production and consumption rates are equal at all times (i.e., steady-state). Despite the stringency of these two assumptions, FBA has been shown to be surprisingly robust at predicting cellular phenotypes. In this paper, we formally assess the impact of these two assumptions on FBA results by quantifying how uncertainty in biomass reaction coefficients, and departures from steady-state due to temporal fluctuations could propagate to FBA results. In the first case, conditional sampling of parameter space is required to re-weigh the biomass reaction so as the molecular weight remains equal to 1 g mmol−1, and in the second case, metabolite (and elemental) pool conservation must be imposed under temporally varying conditions. Results confirm the importance of enforcing the aforementioned constraints and explain the robustness of FBA biomass yield predictions.

Propagation of uncertainty of soil hydraulic parameterization in the prediction of water balance components: A stochastic analysis in kaolinitic clay soils

Hydrological models are powerful tools to understand soil–vegetation–atmosphere transport (SVAT) processes. These processes are partially controlled by soil water retention and hydraulic conductivity, in process-based models described by analytical functions (K-θ-h) that define the dependence between pressure head (h), soil water content (θ) and hydraulic conductivity (K). Given the nonlinearity of these process-based SVAT models, stochastic analysis is an interesting tool to get insight in the pattern of model outputs given the uncertainty in the K–θ–h functions. We developed a stochastic framework to evaluate outputs of the SWAP hydrological model according to the uncertainty in the van Genuchten-Mualem K–θ–h analytical functions (VGM). A multivariate Gaussian joint distribution analysis stochastically sampled VGM parameters using two statistical methods, one considering and one disregarding parameter correlations. We evaluated the relations of VGM parameters and simulation outputs (i) for an internal drainage scenario to predict pressure head at flux-based field capacity and (ii) for a cropped scenario to predict water balance components. We also assessed the relative importance of each parameter using linear regression and random forest methods. The hydrological stochastic simulations showed that the developed algorithm allowed to perform multiple SWAP model runs in a quick and unassisted manner on a common personal computer. Although the degree of VGM uncertainty of the studied soils did not affect the SWAP simulation results considerably, model output uncertainty increased when uncorrelated stochastic realizations of VGM parameters were used. The relative propagation of parameter uncertainty showed to be dependent on the simulated scenario (boundary conditions) and on the soil itself. For the correlated VGM stochastic realizations, both criteria used to analyze the parameter importance detected the VGM parameter l as one of the most relevant in determining water balance components variation. This is an interesting outcome, as this parameter is hardly ever determined, and commonly assumed to a predefined value.

Anomalous features in internal cylinder flow instabilities subject to uncertain rotational effects

We study the flow dynamics inside a high-speed rotating cylinder after introducing strong symmetry-breaking disturbance factors at cylinder wall motion. We propose and formulate a mathematically robust stochastic model for the rotational motion of the cylinder wall alongside the stochastic representation of incompressible Navier–Stokes equations. We employ a comprehensive stochastic computational fluid dynamics framework combining the spectral/hp element method and the probabilistic collocation method to obtain high-fidelity realizations of our mathematical model in order to quantify the propagation of parametric uncertainty for dynamics-representative quantities of interests. We observe that the modeled symmetry-breaking disturbances cause a flow instability arising from the wall. Utilizing global sensitivity analysis approaches, we identify the dominant source of uncertainty in our proposed model. We next perform a qualitative and quantitative statistical analysis on the fluctuating fields characterizing the fingerprints and measures of intense and rapidly evolving non-Gaussian behavior through space and time. We claim that such non-Gaussian statistics essentially emerge and evolve due to an intensified presence of coherent vortical motions initially triggered by the flow instability due to the symmetry-breaking rotation of the cylinder. We show that this mechanism causes memory effects in the flow dynamics in a way that noticeable anomaly in the time-scaling of enstrophy record is observed in the long run apart from the onset of instability. Our findings suggest an effective strategy to exploit controlled flow instabilities in order to enhance the turbulent mixing in engineering applications.

Regional Calibration With Isotope Tracers Using a Spatially Distributed Model: A Comparison of Methods

AbstractAccurate representation of flow sources in process‐based hydrologic models remains challenging for remote, data‐scarce regions. This study applies stable isotope tracers (18O and 2H) in water as auxiliary data for the calibration of the isoWATFLOOD™ model. The most efficient method of those evaluated for introducing isotope data into model calibration was the PA‐DDS multiobjective search algorithm. The compromise solutions incorporating isotope data performed slightly inferior in terms of streamflow simulation compared to the calibrated solution using streamflow data only. However, the former solution outperformed the latter one in terms of isotope simulation. Approximation of the model parameter uncertainty into internal flow path partitioning was explored. Inclusion of isotope error facilitated a broader examination of the total parameter space, resulting in significant differences in internal storage and flow paths, most significantly for soil storage and evapotranspiration loss. Isotope‐optimized calibration reduced evaporation rates and increased soil moisture content within the model, impacting soil water velocity but not streamflow celerity. Flow‐only calibration resulted in artificially narrow model prediction bounds, significantly underestimating the propagation of parameter uncertainty, while isotope‐informed calibrations yielded more reliable and robust bound on model predictions. Our findings demonstrate that the accuracy of a complex, spatially distributed, and process‐based model cannot be judged from one summative flow‐based model performance evaluation metric alone.

Propagation of parameter uncertainty in SWAT: A probabilistic forecasting method based on polynomial chaos expansion and machine learning

Soil and Water Assessment Tool (SWAT) is one of the most widely used semi-distributed hydrological models. Assessment of the uncertainties in SWAT outputs is a popular but challenging topic due to the significant number of parameters. The purpose of this study is to investigate the use of Polynomial Chaos Expansion (PCE) in assessing uncertainty propagation in SWAT under the impact of significant parameter sensitivity. Furthermore, for the first time, a machine learning technique (i.e., artificial neural network, ANN) is integrated with PCE to expand its capability in generating probabilistic forecasts of daily flow. The traditional PCE and the proposed PCE-ANN methods are applied to a case study in the Guadalupe watershed in Texas, USA to assess the uncertainty propagation in SWAT for flow prediction during the historical and forecasting periods. The results show that PCE provides similar results as the traditional Monte-Carlo (MC) method, with a coefficient of determination (R2) value of 0.99 for the mean flow, during the historical period; while the proposed PCE-ANN method reproduces MC output with a R2 value of 0.84 for mean flow during the forecasting period. It is also indicated that PCE and PCE-ANN are as reliable as but much more efficient than MC. PCE takes about 1% of the computational time required by MC; PCE-ANN only takes a few minutes to produce probabilistic forecasting, while MC requires running the model for dozens or hundreds, even thousands, of times. Notably, the development of the PCE-ANN framework is the first attempt to explore PCE’s probabilistic forecasting capability using machine learning. PCE-ANN is a promising uncertainty assessment and probabilistic forecasting technique, as it is more efficient in terms of computation time, and it does not cause loss of essential uncertainty information.

Sparse polynomial surrogates for non-intrusive, high-dimensional uncertainty quantification of aeroelastic computations

This paper is concerned with aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. More specifically, the influence of variable operational and structural parameters (random inputs) on the drag performance and deformation (outputs) of a flexible wing in transonic regime, is assessed. Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantification techniques are favored. Polynomial surrogate models based on homogeneous chaos expansions in the random inputs are commonly considered in this respect. The polynomial expansion coefficients are constructed using either structured sampling sets of the input parameters, as Gauss quadrature nodes, or unstructured sampling sets, as in Monte-Carlo methods. In complex systems such as the advanced aeroelastic test case studied here, the output quantities of interest generally depend only weakly on the multiple cross-interactions between the random inputs. Consequently, only low-order polynomials significantly contribute to their surrogates, which thus have a sparse structure in the underlying polynomial bases. This feature prompts to use compressed sensing, or compressive sampling theory for the construction of the polynomial surrogates. The proposed methodology is non-adapted and considers unstructured sampling sets orders of magnitude smaller than the ones required by the usual techniques with structured sampling sets. It is illustrated in the present work for a moderately to high dimensional parametric space.

Causality and Bayesian Network PDEs for multiscale representations of porous media

Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between processes on these two scales is essential to both the derivation of macroscopic models of, e.g., transport phenomena in natural porous media, and the design of novel materials, e.g., for energy storage. Microscopic properties exhibit complex statistical correlations and geometric constraints that present challenges for the estimation of macroscopic quantities of interest (QoIs), e.g., in the context of global sensitivity analysis (GSA) of macroscopic QoIs with respect to microscopic material properties. We present a systematic way of building correlations into stochastic multiscale models through Bayesian Networks. The proposed framework allows us to construct the joint probability density function (PDF) of model parameters through causal relationships that are informed by domain knowledge and emulate engineering processes, e.g., the design of hierarchical nanoporous materials. These PDFs also serve as input for the forward propagation of parametric uncertainty thereby yielding a Bayesian Network PDE. To assess the impact of causal relationships and microscale correlations on macroscopic material properties, we propose a moment-independent GSA and corresponding effect rankings for Bayesian Network PDEs, based on the differential Mutual Information, that leverage the structure of Bayesian Networks and account for both correlated inputs and complex non-Gaussian (skewed, multimodal) QoIs. Our findings from numerical experiments, which feature a non-intrusive uncertainty quantification workflow, indicate two practical outcomes. First, the inclusion of correlations through structured priors based on causal relationships informed by domain knowledge impacts predictions of QoIs and has important implications for engineering design. Second, structured priors with non-trivial correlations yield different effect rankings than independent priors; these rankings are more consistent with the anticipated physics.

Uncertainty quantification in three dimensional natural convection using polynomial chaos expansion and deep neural networks

This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation and global sensitivity analysis. In case A, stochastic variation is introduced in the two non-dimensional parameters (Rayleigh and Prandtl numbers) with an assumption that the boundary temperature is uniform. Being a two dimensional stochastic problem, the polynomial chaos expansion (PCE) method is used as a surrogate model. Case B deals with non-uniform stochasticity in the boundary temperature. Instead of the traditional Gaussian process model with the Karhunen-Loève expansion, a novel approach is successfully implemented to model uncertainty in the boundary condition. The boundary is divided into multiple domains and the temperature imposed on each domain is assumed to be an independent and identically distributed (i.i.d) random variable. Deep neural networks are trained with the boundary temperatures as inputs and Nusselt number, internal temperature or velocities as outputs. The number of domains which is essentially the stochastic dimension is 4, 8, 16 or 32. Rigorous training and testing process shows that the neural network is able to approximate the outputs to a reasonable accuracy. For a high stochastic dimension such as 32, it is computationally expensive to fit the PCE. This paper demonstrates a novel way of using the deep neural network as a surrogate modeling method for uncertainty quantification with the number of simulations much fewer than that required for fitting the PCE, thus, saving the computational cost.

Propagation of structural uncertainty in watershed hydrologic models

Structural, parametric and measurement uncertainties are inherent in watershed hydrology models. Among these, structural uncertainty results from simplified representation of reality in models and has proven to be particularly challenging to characterize. Often, flow measurements are available at the outlet or a few other locations within a watershed, and distributed model parameters are calibrated to replicate observed streamflow values. Subsequently, one can quantify uncertainty in streamflow estimation at the measured locations. The objective of this study is the quantification of structural and parametric uncertainty at unmeasured locations using a calibrated watershed hydrologic model. While propagation of parametric uncertainty to unmeasured locations is a relatively simple task in a Bayesian framework, this study is focused on the problem of structural uncertainty propagation. We propose to treat the hydrologic model as a stochastic function by treating the parameters of the model as random quantities, even in the limit of infinite information through data, thus enabling us to accommodate the uncertainty due to structural errors. A mathematical formulation of the method and applications over two different watersheds, using hourly and daily flow data, are presented. The structural uncertainty band at ungauged locations enveloped all the streamflow observations at daily-scale and missed most of the observations at hourly-scale. Structural uncertainty varies spatially at unmeasured locations within the watershed. Consequently, streamflows estimated at unmeasured locations may be accompanied by wide uncertainty bands implying the need for caution when using them.

A prediction–evaluation approach to the full-scale emplacement experiment (FE) in Mont Terri

AbstractA prediction–evaluation approach is developed to assess the propagation of parameter, conceptual and scenario uncertainties in the estimated near-field temperatures of the full-scale emplacement experiment at the Mont Terri rock laboratory. The uncertainty assessment is performed using a three-dimensional thermo-hydraulic numerical model of the full-scale emplacement experiment that represents the emplaced materials and surrounding Opalinus Clay and accounts for heat generation at the heaters. The propagation of parametric uncertainties is assessed using a first-order second-moment method supplemented by Monte Carlo simulations sampling the uncertain parameter space. The risk of uncertain parameters resulting in the failure of the maximum temperature criteria is evaluated with a first-order reliability method. Conceptual and scenario uncertainties are evaluated with deterministic simulation variants. After the conclusion of predictive modelling, a mid-term evaluation of the temperature predictions is performed through a comparison with measurements after 2.5 years of heating. The comparison indicates that the best estimates of temperature agree well with the measurements and that the 95% error bands assessed with parametric uncertainty envelope the measured values in almost all locations. Additional comparison with the measured degree of water saturation and the relative humidity is performed to assess the hydraulic behaviour and set the ground for the long-term evaluation, which will include predictions of the near-field pore pressures.

On the robustness of variational multiscale error estimators for the forward propagation of uncertainty

The numerical simulation of physical phenomena and engineering problems can be affected by numerical errors and various types of uncertainties. Characterizing the former in computational frameworks involving system parameter uncertainties becomes a key issue. In this work, we study the behavior of new variational multiscale (VMS) error estimators for the propagation of parametric uncertainties in a Convection–Diffusion–Reaction (CDR) problem. A sensitivity analysis is performed to assess the performance of the error estimator with respect to the mesh discretization and physical parameters (here, the viscosity value and advection velocity). Three different manufactured analytical solutions are considered as benchmarking tests. Next, the performance of the VMS error estimators is evaluated for the CDR problem with uncertain input parameters. For this purpose, two probabilistic models are constructed for the viscosity and advection direction, and the uncertainties are propagated using a polynomial chaos expansion approach. A convergence analysis is specifically carried out for different configurations, corresponding to regimes where the CDR operator is either smooth or non-smooth. An assessment of the proposed error estimator is finally conducted for the three tests, considering both the viscous- and convection-dominated regimes.

Improved allometric proxies for eelgrass conservation

Current anthropogenic influences threaten the permanence of eelgrass, a relevant macrophyte that brings about important ecological benefits including nursery for waterfowl and fish species, shoreline stabilization, nutrient recycling and carbon sequestration. Eelgrass restoration normally involves transplanted plots and monitoring success requires noninvasive assessments of standing stock and productivity. Allometric scaling of eelgrass leaf biomass and length can provide proxies for these assessments, but accuracy of allometric projections is mainly resultant of uncertainty propagation of parameters, so for the sake of suitability it is very important ensuring the most accurate estimates. The traditional approach for producing estimates of allometric parameters considers a linear regression model involving logarithms of the original response and explanatory variables along with a normally distributed additive error. The suitability of this method has been questioned on the ground of biased results raising nonlinear regression as a necessary amendment. Here we demonstrate that this controversy can be surpassed allowing for a logistic error structure and heteroscedasticity in the traditional method. The present arrangement delivered parameter estimates from raw data surpassing inconveniences of the traditional fitting procedure. Moreover, associated allometric proxies for average leaf biomass in shoots entailed similar reproducibilities than produced by using nonlinear regression and quality controlled data. In achieving suitable accuracy levels, the present approach required a sample of raw data of about 9% of involved in prior estimations based on quality controlled data. The improvements associated to the present approach grant highly consistent non-destructive assessments for the sake of eelgrass conservation.