Adjusting a process-based growth model for varying site conditions through parameter estimation

1993 ◽  
Vol 23 (9) ◽  
pp. 1837-1851 ◽  
Author(s):  
Risto Sievänen ◽  
Thomas E. Burk
Keyword(s):  
Growth Model ◽  
Present Model ◽  
Biological Significance ◽  
Site Quality ◽  
Model Parameters ◽  
Identifiability Analysis ◽  
Stand Growth ◽  
Estimated Parameters ◽  
Identifiability Problems ◽  
Logical Data

The problem of estimating the parameters of a process-based growth model using typical stand growth measurements (of tree dimensions) is studied. The data consist of measurements of diameter, height, number of trees, and live crown ratio obtained from plots representing different site qualities. An analysis of the identifiability of model parameters is made which shows (i) that the structure of the model makes certain parameter combinations unidentifiable and (ii) that the data at hand do not support all the parameters. It is not possible to reduce the number of parameters in the model without losing its biological significance. Therefore, as a remedy for identifiability problems, the model has been modified slightly on the basis of identifiability analysis and initial estimations and the set of parameters to be estimated has been restricted. A division of the parameters into two groups is sought: those estimated with all plots combined and those that are allowed to vary from plot to plot. The estimated parameters have biologically reasonable values, and the variation in accordance with plot site quality is logical. Data-based analysis shows that apart from some unidentifiable parameter combinations, the parameters of the present model are estimated rather consistently. Analysis of the loss function components indicates that measurements of diameter, height, density, and live crown ratio are needed for reliable fitting of the model.

scholarly journals A Dynamic Stand Growth Model System for Loblolly Pine Responding to Mid-Rotation Treatments

Forests ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 556
Author(s):  
Mauricio Zapata-Cuartas ◽  
Bronson P. Bullock ◽  
Cristian R. Montes ◽  
Michael B. Kane
Keyword(s):  
Growth Model ◽  
Loblolly Pine ◽  
Basal Area ◽  
Model System ◽  
Growth And Yield ◽  
Site Quality ◽  
Response To Treatment ◽  
Plantation Management ◽  
Vegetation Control ◽  
Dominant Height

Intensive loblolly pine (Pinus taeda L.) plantation management in the southeastern United States includes mid-rotation silvicultural practices (MRSP) like thinning, fertilization, competitive vegetation control, and their combinations. Consistent and well-designed long-term studies considering interactions of MRSP are required to produce accurate projections and evaluate management decisions. Here we use longitudinal data from the regional Mid-Rotation Treatment study established by the Plantation Management Research Cooperative (PMRC) at the University of Georgia across the southeast U.S. to fit and validate a new dynamic model system rooted in theoretical and biological principles. A Weibull pdf was used as a modifier function coupled with the basal area growth model. The growth model system and error projection functions were estimated simultaneously. The new formulation results in a compatible and consistent growth and yield system and provides temporal responses to treatment. The results indicated that the model projections reproduce the observed behavior of stand characteristics. The model has high predictive accuracy (the cross-validation variance explained was 96.2%, 99.7%, and 98.6%; and the prediction root mean square distance was 0.704 m, 19.1 trees ha−1, and 1.03 m2ha−1 for dominant height (DH), trees per hectare (N), and basal area (BA), respectively), and can be used to project the current stand attributes following combinations of MRSP and with different thinning intensities. Simulations across southern physiographic regions allow us to conclude that the most overall ranking of MRSP after thinning is fertilization + competitive vegetation control (Fert + CVC) > fertilization only (Fert) > competitive vegetation control only (CVC), and Fert + CVC show less than additive effect. Because of the model structure, the response to treatment changes with location, age of application, and dominant height growth as indicators of site quality. Therefore, the proposed model adequately represents regional growth conditions.

scholarly journals Growth of the tambaqui Colossoma macropomum (Cuvier) (Characiformes: Characidae): which is the best model?

2005 ◽  
Vol 65 (1) ◽  
pp. 129-139 ◽  
Author(s):  
M. A. H Penna ◽  
M. A Villacorta-Corrêa ◽  
T. Walter ◽  
M. Petrere-JR
Keyword(s):  
Growth Model ◽  
Negative Correlation ◽  
The Other ◽  
Data Sources ◽  
Von Bertalanffy ◽  
Data Set ◽  
Colossoma Macropomum ◽  
Von Bertalanffy Model ◽  
Estimated Parameters ◽  
Schnute Model

In order to decide which is the best growth model for the tambaqui Colossoma macropomum Cuvier, 1818, we utilized 249 and 256 length-at-age ring readings in otholiths and scales respectively, for the same sample of individuals. The Schnute model was utilized and it is concluded that the Von Bertalanffy model is the most adequate for these data, because it proved highly stable for the data set, and only slightly sensitive to the initial values of the estimated parameters. The phi' values estimated from five different data sources presented a CV = 4.78%. The numerical discrepancies between these values are of not much concern due to the high negative correlation between k and L<FONT FACE=Symbol>¥</FONT> viz, so that when one of them increases, the other decreases and the final result in phi' remains nearly unchanged.

scholarly journals A Novel Approach to Modelling Stand-Level Growth of an Even-Aged Forest Using a Volume Productivity Index with Application to New Zealand-Grown Coast Redwood

Forests ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1155 ◽  
Author(s):  
Mark O. Kimberley ◽  
Michael S. Watt
Keyword(s):  
New Zealand ◽  
Growth Model ◽  
Growth Models ◽  
Stand Density ◽  
Site Index ◽  
Growth And Yield ◽  
Productivity Index ◽  
Site Quality ◽  
Spatial And Temporal Variation ◽  
Coast Redwood

Empirical growth models are widely used to predict the growth and yield of plantation tree species, and the precise estimation of site quality is an important component of these models. The most commonly used proxy for site quality in growth models is Site Index (SI), which describes the mean height of dominant trees at a specified base age. Although SI is widely used, considerable research shows significant site-dependent variation in height for a given volume, with this latter variable more closely reflecting actual site productivity. Using a national dataset, this study develops and describes a stand-level growth and yield model for even-aged New Zealand-grown coast redwood (Sequoia sempervirens). We used a novel modelling approach that quantifies site quality using SI and a volume-based index termed the 300 Index, defined as the volume mean annual increment at age 30 years for a reference regime of 300 stems ha−1. The growth model includes a number of interrelated components. Mean top height is modelled from age and SI using a polymorphic Korf function. A modified anamorphic Korf function is used to describe tree quadratic mean diameter (Dq) as a function of age, stand density, SI and a diameter site index. As the Dq model includes stand density in its formulation, it can predict tree growth for different stand densities and thinning regimes. The mortality model is based on a simple attritional equation improved through incorporation of the Reineke stand density index to account for competition-induced mortality. Using these components, the model precisely estimates stand-level volume. The developed model will be of considerable value to growers for yield projection and regime evaluation. By more robustly describing the site effect, the growth model provides researchers with an improved framework for quantifying and understanding the causes of spatial and temporal variation in plantation productivity.

scholarly journals Uncertainty Quantification in Epidemiological Models for COVID-19 Pandemic

2020 ◽  
Author(s):  
Leila Taghizadeh ◽  
Ahmad Karimi ◽  
Clemens Heitzinger
Keyword(s):  
Inverse Modeling ◽  
Posteriori Probability ◽  
Model Parameters ◽  
Epidemiological Models ◽  
Unknown Parameters ◽  
Protective Measures ◽  
A Posteriori Probability ◽  
Estimated Parameters ◽  
Forward And Inverse Modeling ◽  
Inversion Techniques

AbstractThe main goal of this paper is to develop the forward and inverse modeling of the Coronavirus (COVID-19) pandemic using novel computational methodologies in order to accurately estimate and predict the pandemic. This leads to governmental decisions support in implementing effective protective measures and prevention of new outbreaks. To this end, we use the logistic equation and the SIR system of ordinary differential equations to model the spread of the COVID-19 pandemic. For the inverse modeling, we propose Bayesian inversion techniques, which are robust and reliable approaches, in order to estimate the unknown parameters of the epidemiological models. We use an adaptive Markov-chain Monte-Carlo (MCMC) algorithm for the estimation of a posteriori probability distribution and confidence intervals for the unknown model parameters as well as for the reproduction number. Furthermore, we present a fatality analysis for COVID-19 in Austria, which is also of importance for governmental protective decision making. We perform our analyses on the publicly available data for Austria to estimate the main epidemiological model parameters and to study the effectiveness of the protective measures by the Austrian government. The estimated parameters and the analysis of fatalities provide useful information for decision makers and makes it possible to perform more realistic forecasts of future outbreaks.

scholarly journals Parameter Estimation of DC Motor using Adaptive Transfer Function Based on Nelder-Mead Optimisation

2018 ◽  
Vol 9 (3) ◽  
pp. 696 ◽  
Author(s):  
Byamakesh Nayak ◽  
Sangeeta Sahu ◽  
Tanmoy Roy Choudhury
Keyword(s):  
Experimental Data ◽  
Transfer Function ◽  
Adaptive Method ◽  
Dc Motor ◽  
Model Parameters ◽  
Current Response ◽  
Adaptive Model ◽  
Unknown Parameters ◽  
Dc Motors ◽  
Estimated Parameters

<p>This paper explains an adaptive method for estimation of unknown parameters of transfer function model of any system for finding the parameters. The transfer function of the model with unknown model parameters is considered as the adaptive model whose values are adapted with the experimental data. The minimization of error between the experimental data and the output of the adaptive model have been realised by choosing objective function based on different error criterions. Nelder-Mead optimisation Method is used for adaption algorithm. To prove the method robustness and for students learning, the simple system of separately excited dc motor is considered in this paper. The experimental data of speed response and corresponding current response are taken and transfer function parameters of  dc motors are adapted based on Nelder-Mead optimisation to match with the experimental data. The effectiveness of estimated parameters with different objective functions are compared and validated with machine specification parameters.</p>

scholarly journals An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City

2021 ◽  
Author(s):  
Sheng Zhang ◽  
Joan Ponce ◽  
Zhen Zhang ◽  
Guang Lin ◽  
George Karniadakis
Keyword(s):  
New York ◽  
New York City ◽  
York City ◽  
Robustness Analysis ◽  
Data Driven ◽  
Model Parameters ◽  
Calibration Model ◽  
Epidemiological Models ◽  
Analysis Model ◽  
Identifiability Analysis

AbstractEpidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time when the pandemic lasts. However, often the available data are not sufficient to identify the model parameters and hence infer the unobserved dynamics. Here, we develop a general framework for building a trustworthy data-driven epidemiological model, consisting of a workflow that integrates data acquisition and event timeline, model development, identifiability analysis, sensitivity analysis, model calibration, model robustness analysis, and forecasting with uncertainties in different scenarios. In particular, we apply this framework to propose a modified susceptible–exposed–infectious–recovered (SEIR) model, including new compartments and model vaccination in order to forecast the transmission dynamics of COVID-19 in New York City (NYC). We find that we can uniquely estimate the model parameters and accurately predict the daily new infection cases, hospitalizations, and deaths, in agreement with the available data from NYC’s government’s website. In addition, we employ the calibrated data-driven model to study the effects of vaccination and timing of reopening indoor dining in NYC.

scholarly journals Kinetic Analysis of 2-[11C]Thymidine PET Imaging Studies of Malignant Brain Tumors: Compartmental Model Investigation and Mathematical Analysis

2002 ◽  
Vol 1 (3) ◽  
pp. 153535002002021
Author(s):  
Joanne M. Wells ◽  
David A. Mankoff ◽  
Mark Muzi ◽  
Finbarr O'Sullivan ◽  
Janet F. Eary ◽  
...  
Keyword(s):  
Brain Tumor ◽  
Brain Tumors ◽  
Cellular Proliferation ◽  
Compartment Model ◽  
Response To Therapy ◽  
Model Parameters ◽  
Normal Brain ◽  
Identifiability Analysis ◽  
Pet Tracer ◽  
Thymidine Transport

2-[11C]Thymidine (TdR), a PET tracer for cellular proliferation, may be advantageous for monitoring brain tumor progression and response to therapy. We previously described and validated a five-compartment model for thymidine incorporation into DNA in somatic tissues, but the effect of the blood–brain barrier on the transport of TdR and its metabolites necessitated further validation before it could be applied to brain tumors. Methods: We investigated the behavior of the model under conditions experienced in the normal brain and brain tumors, performed sensitivity and identifiability analysis to determine the ability of the model to estimate the model parameters, and conducted simulations to determine whether it can distinguish between thymidine transport and retention. Results: Sensitivity and identifiability analysis suggested that the non-CO2 metabolite parameters could be fixed without significantly affecting thymidine parameter estimation. Simulations showed that K1t and KTdR could be estimated accurately ( r = .97 and .98 for estimated vs. true parameters) with standard errors < 15%. The model was able to separate increased transport from increased retention associated with tumor proliferation. Conclusion: Our model adequately describes normal brain and brain tumor kinetics for thymidine and its metabolites, and it can provide an estimate of the rate of cellular proliferation in brain tumors.

scholarly journals Selection of catchment descriptors for the physical similarity approach. Part II: Application

2013 ◽  
Vol 8 (No. 4) ◽  
pp. 186-194
Author(s):  
M. Heřmanovský ◽  
P. Pech
Keyword(s):  
Land Cover ◽  
A Priori ◽  
Model Parameters ◽  
Physical Similarity ◽  
Model Parameter ◽  
Soil Moisture Accounting ◽  
Estimated Parameters ◽  
Selection Of

This paper demonstrates an application of the previously published method for selection of optimal catchment descriptors, according to which similar catchments can be identified for the purpose of estimation of the Sacramento &ndash; Soil Moisture Accounting (SAC-SMA) model parameters for a set of tested catchments, based on the physical similarity approach. For the purpose of the analysis, the following data from the Model Parameter Estimation Experiment (MOPEX) project were taken: a priori model parameter sets used as reference values for comparison with the newly estimated parameters, and catchment descriptors of four categories (climatic descriptors, soil properties, land cover and catchment morphology). The inverse clustering method, with Andrews&rsquo; curves for a homogeneity check, was used for the catchment grouping process. The optimal catchment descriptors were selected on the basis of two criteria, one comparing different subsets of catchment descriptors of the same size (MIN), the other one evaluating the improvement after addition of another catchment descriptor (MAX). The results suggest that the proposed method and the two criteria used may lead to the selection of a subset of conditionally optimal catchment descriptors from a broader set of them. As expected, the quality of the resulting subset of optimal catchment descriptors is mainly dependent on the number and type of the descriptors in the broader set. In the presented case study, six to seven catchment descriptors (two climatic, two soil and at least two land-cover descriptors) were identified as optimal for regionalisation of the SAC-SMA model parameters for a set of MOPEX catchments.

ANALYSIS OF A LIMPET FISHERY USING A METAPHYSIOLOGICAL STAND-GROWTH MODEL

1994 ◽  
Vol 8 (2) ◽  
pp. 139-161 ◽  
Author(s):  
Rodrigo H. Bustamante ◽  
Wayne M. Getz ◽  
George M. Branch
Keyword(s):  
Growth Model ◽  
Stand Growth
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