Parameter estimation for functional–structural plant models when data are scarce: using multiple patterns for rejecting unsuitable parameter sets

Abstract Background and Aims Functional–structural plant (FSP) models provide insights into the complex interactions between plant architecture and underlying developmental mechanisms. However, parameter estimation of FSP models remains challenging. We therefore used pattern-oriented modelling (POM) to test whether parameterization of FSP models can be made more efficient, systematic and powerful. With POM, a set of weak patterns is used to determine uncertain parameter values, instead of measuring them in experiments or observations, which often is infeasible. Methods We used an existing FSP model of avocado (Persea americana ‘Hass’) and tested whether POM parameterization would converge to an existing manual parameterization. The model was run for 10 000 parameter sets and model outputs were compared with verification patterns. Each verification pattern served as a filter for rejecting unrealistic parameter sets. The model was then validated by running it with the surviving parameter sets that passed all filters and then comparing their pooled model outputs with additional validation patterns that were not used for parameterization. Key Results POM calibration led to 22 surviving parameter sets. Within these sets, most individual parameters varied over a large range. One of the resulting sets was similar to the manually parameterized set. Using the entire suite of surviving parameter sets, the model successfully predicted all validation patterns. However, two of the surviving parameter sets could not make the model predict all validation patterns. Conclusions Our findings suggest strong interactions among model parameters and their corresponding processes, respectively. Using all surviving parameter sets takes these interactions into account fully, thereby improving model performance regarding validation and model output uncertainty. We conclude that POM calibration allows FSP models to be developed in a timely manner without having to rely on field or laboratory experiments, or on cumbersome manual parameterization. POM also increases the predictive power of FSP models.

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Parameter variations in prediction skill optimization at ECMWF

Nonlinear Processes in Geophysics ◽

10.5194/npg-20-1001-2013 ◽

2013 ◽

Vol 20 (6) ◽

pp. 1001-1010 ◽

Cited By ~ 10

Author(s):

P. Ollinaho ◽

P. Bechtold ◽

M. Leutbecher ◽

M. Laine ◽

A. Solonen ◽

...

Keyword(s):

Parameter Estimation ◽

Weather Prediction ◽

Prediction Skill ◽

Convective Precipitation ◽

Ensemble Prediction ◽

Model Parameters ◽

Ongoing Research ◽

Medium Range ◽

Parameter Values ◽

Very High

Abstract. Algorithmic numerical weather prediction (NWP) skill optimization has been tested using the Integrated Forecasting System (IFS) of the European Centre for Medium-Range Weather Forecasts (ECMWF). We report the results of initial experimentation using importance sampling based on model parameter estimation methodology targeted for ensemble prediction systems, called the ensemble prediction and parameter estimation system (EPPES). The same methodology was earlier proven to be a viable concept in low-order ordinary differential equation systems, and in large-scale atmospheric general circulation models (ECHAM5). Here we show that prediction skill optimization is possible even in the context of a system that is (i) of very high dimensionality, and (ii) carefully tuned to very high skill. We concentrate on four closure parameters related to the parameterizations of sub-grid scale physical processes of convection and formation of convective precipitation. We launch standard ensembles of medium-range predictions such that each member uses different values of the four parameters, and make sequential statistical inferences about the parameter values. Our target criterion is the squared forecast error of the 500 hPa geopotential height at day three and day ten. The EPPES methodology is able to converge towards closure parameter values that optimize the target criterion. Therefore, we conclude that estimation and cost function-based tuning of low-dimensional static model parameters is possible despite the very high dimensional state space, as well as the presence of stochastic noise due to initial state and physical tendency perturbations. The remaining question before EPPES can be considered as a generally applicable tool in model development is the correct formulation of the target criterion. The one used here is, in our view, very selective. Considering the multi-faceted question of improving forecast model performance, a more general target criterion should be developed. This is a topic of ongoing research.

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Parameter sensitivity and uncertainty analysis for a storm surge and wave model

Natural Hazards and Earth System Science ◽

10.5194/nhess-16-2195-2016 ◽

2016 ◽

Vol 16 (10) ◽

pp. 2195-2210 ◽

Cited By ~ 12

Author(s):

Luis A. Bastidas ◽

James Knighton ◽

Shaun W. Kline

Keyword(s):

Numerical Models ◽

Model Performance ◽

Wave Model ◽

Parameter Sensitivity ◽

Sensitivity Threshold ◽

Model Parameters ◽

Hurricane Wind ◽

Output Uncertainty ◽

Model Response ◽

Wave Models

Abstract. Development and simulation of synthetic hurricane tracks is a common methodology used to estimate hurricane hazards in the absence of empirical coastal surge and wave observations. Such methods typically rely on numerical models to translate stochastically generated hurricane wind and pressure forcing into coastal surge and wave estimates. The model output uncertainty associated with selection of appropriate model parameters must therefore be addressed. The computational overburden of probabilistic surge hazard estimates is exacerbated by the high dimensionality of numerical surge and wave models. We present a model parameter sensitivity analysis of the Delft3D model for the simulation of hazards posed by Hurricane Bob (1991) utilizing three theoretical wind distributions (NWS23, modified Rankine, and Holland). The sensitive model parameters (of 11 total considered) include wind drag, the depth-induced breaking γB, and the bottom roughness. Several parameters show no sensitivity (threshold depth, eddy viscosity, wave triad parameters, and depth-induced breaking αB) and can therefore be excluded to reduce the computational overburden of probabilistic surge hazard estimates. The sensitive model parameters also demonstrate a large number of interactions between parameters and a nonlinear model response. While model outputs showed sensitivity to several parameters, the ability of these parameters to act as tuning parameters for calibration is somewhat limited as proper model calibration is strongly reliant on accurate wind and pressure forcing data. A comparison of the model performance with forcings from the different wind models is also presented.

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Data Assimilation for a Coupled Ocean–Atmosphere Model. Part II: Parameter Estimation

Monthly Weather Review ◽

10.1175/2008mwr2544.1 ◽

2008 ◽

Vol 136 (12) ◽

pp. 5062-5076 ◽

Cited By ~ 42

Author(s):

Dmitri Kondrashov ◽

Chaojiao Sun ◽

Michael Ghil

Keyword(s):

Parameter Estimation ◽

State Estimation ◽

Tropical Pacific ◽

The State ◽

Vector Model ◽

Model Parameters ◽

Ocean Atmosphere ◽

Augmented State ◽

Parameter Values ◽

The Tropical Pacific

Abstract The parameter estimation problem for the coupled ocean–atmosphere system in the tropical Pacific Ocean is investigated using an advanced sequential estimator [i.e., the extended Kalman filter (EKF)]. The intermediate coupled model (ICM) used in this paper consists of a prognostic upper-ocean model and a diagnostic atmospheric model. Model errors arise from the uncertainty in atmospheric wind stress. First, the state and parameters are estimated in an identical-twin framework, based on incomplete and inaccurate observations of the model state. Two parameters are estimated by including them into an augmented state vector. Model-generated oceanic datasets are assimilated to produce a time-continuous, dynamically consistent description of the model’s El Niño–Southern Oscillation (ENSO). State estimation without correcting erroneous parameter values still permits recovering the true state to a certain extent, depending on the quality and accuracy of the observations and the size of the discrepancy in the parameters. Estimating both state and parameter values simultaneously, though, produces much better results. Next, real sea surface temperatures observations from the tropical Pacific are assimilated for a 30-yr period (1975–2004). Estimating both the state and parameters by the EKF method helps to track the observations better, even when the ICM is not capable of simulating all the details of the observed state. Furthermore, unobserved ocean variables, such as zonal currents, are improved when model parameters are estimated. A key advantage of using this augmented-state approach is that the incremental cost of applying the EKF to joint state and parameter estimation is small relative to the cost of state estimation alone. A similar approach generalizes various reduced-state approximations of the EKF and could improve simulations and forecasts using large, realistic models.

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Hydrological Modelling in Data Sparse Environment: Inverse Modelling of a Historical Flood Event

Water ◽

10.3390/w12113242 ◽

2020 ◽

Vol 12 (11) ◽

pp. 3242

Author(s):

András Bárdossy ◽

Faizan Anwar ◽

Jochen Seidel

Keyword(s):

Model Performance ◽

Flood Event ◽

Historical Event ◽

Model Parameters ◽

Parameter Uncertainties ◽

Difficult Situation ◽

Output Uncertainty ◽

Time Period ◽

Extreme Flood ◽

Historical Observation

We dealt with a rather frequent and difficult situation while modelling extreme floods, namely, model output uncertainty in data sparse regions. A historical extreme flood event was chosen to illustrate the challenges involved. Our aim was to understand what the causes might have been and specifically to show how input and model parameter uncertainties affect the output. For this purpose, a conceptual model was calibrated and validated with recent data rich time period. Resulting model parameters were used to model the historical event which subsequently resulted in a rather poor hydrograph. Due to the bad model performance, a spatial simulation technique was used to invert the model for precipitation. Constraints, such as taking the precipitation values at historical observation locations in to account, with correct spatial structures and following the observed regional distributions were used to generate realistic precipitation fields. Results showed that the inverted precipitation improved the performance significantly even when using many different model parameters. We conclude that while modelling in data sparse conditions both model input and parameter uncertainties have to be dealt with simultaneously to obtain meaningful results.

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Parameter sensitivity and uncertainty analysis for a storm surge and wave model

Natural Hazards and Earth System Sciences Discussions ◽

10.5194/nhessd-3-6491-2015 ◽

2015 ◽

Vol 3 (10) ◽

pp. 6491-6534 ◽

Cited By ~ 1

Author(s):

L. A. Bastidas ◽

J. Knighton ◽

S. W. Kline

Keyword(s):

Numerical Models ◽

Model Performance ◽

Wave Model ◽

Parameter Sensitivity ◽

Sensitivity Threshold ◽

Model Parameters ◽

Hurricane Wind ◽

Output Uncertainty ◽

Model Response ◽

Wave Models

Abstract. Development and simulation of synthetic hurricane tracks is a common methodology used to estimate hurricane hazards in the absence of empirical coastal surge and wave observations. Such methods typically rely on numerical models to translate stochastically generated hurricane wind and pressure forcing into coastal surge and wave estimates. The model output uncertainty associated with selection of appropriate model parameters must therefore be addressed. The computational overburden of probabilistic surge hazard estimates is exacerbated by the high dimensionality of numerical surge and wave models. We present a model parameter sensitivity analysis of the Delft3D model for the simulation of hazards posed by Hurricane Bob (1991) utilizing three theoretical wind distributions (NWS23, modified Rankine, and Holland). The sensitive model parameters (of eleven total considered) include wind drag, the depth-induced breaking γB, and the bottom roughness. Several parameters show no sensitivity (threshold depth, eddy viscosity, wave triad parameters and depth-induced breaking αB) and can therefore be excluded to reduce the computational overburden of probabilistic surge hazard estimates. The sensitive model parameters also demonstrate a large amount of interactions between parameters and a non-linear model response. While model outputs showed sensitivity to several parameters, the ability of these parameters to act as tuning parameters for calibration is somewhat limited as proper model calibration is strongly reliant on accurate wind and pressure forcing data. A comparison of the model performance with forcings from the different wind models is also presented.

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Sensitivity and identifiability of hydraulic and geophysical parameters from streaming potential signals in unsaturated porous media

10.5194/hess-2017-730 ◽

2018 ◽

Author(s):

Anis Younes ◽

Jabran Zaouali ◽

Francois Lehmann ◽

Marwan Fahs

Keyword(s):

Parameter Estimation ◽

Order Approximation ◽

Streaming Potential ◽

Strong Interactions ◽

Residual Water ◽

Data Set ◽

Sparse Polynomial ◽

Marquardt Algorithm ◽

Highly Nonlinear ◽

Parameter Values

Abstract. Fluid flow in a charged porous medium generates electric potentials called Streaming potential (SP). The SP signal is related to both hydraulic and electrical properties of the soil. In this work, Global Sensitivity Analysis (GSA) and parameter estimation procedures are performed to assess the influence of hydraulic and geophysical parameters on the SP signals and to investigate the identifiability of these parameters from SP measurements. Both procedures are applied to a synthetic column experiment involving a falling head infiltration phase followed by a drainage phase. GSA is used through variance-based sensitivity indices, calculated using sparse Polynomial Chaos Expansion (PCE). To allow high PCE orders, we use an efficient sparse PCE algorithm which selects the best sparse PCE from a given data set using the Kashyap Information Criterion (KIC). Parameter identifiability is performed using two approaches: the Bayesian approach based on the Markov Chain Monte Carlo (MCMC) method and the First-Order Approximation (FOA) approach based on the Levenberg Marquardt algorithm. GSA results show that at short times, the saturated hydraulic conductivity (KS) and the voltage coupling coefficient at saturation (Csat) are the most influential parameters, whereas, at long times, the residual water content (σr), the Mualem-van Genuchten parameter (n) and the Archies’s saturation exponent (na) become influential with strong interactions between them. The Mualem-van Genuchten parameter (α) has a very weak influence on the SP signals during the whole experiment. Results of parameter estimation show that, although the studied problem is highly nonlinear, when several SP data collected at different altitudes inside the column are used to calibrate the model, all hydraulic (KS, σr, and n) and geophysical (na and Csat) parameters can be reasonably estimated from the SP measurements. Further, in this case, the FOA approach provides accurate estimations of both mean parameter values and uncertainty regions. Conversely, when the number of SP measurements used for the calibration is strongly reduced, the FOA approach yields accurate mean parameter values (in agreement with MCMC results) but inaccurate and even unphysical confidence intervals for parameters with large uncertainty regions.

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Constraining Land Surface and Atmospheric Parameters of a Locally Coupled Model Using Observational Data

Journal of Hydrometeorology ◽

10.1175/jhm407.1 ◽

2005 ◽

Vol 6 (2) ◽

pp. 156-172 ◽

Cited By ~ 41

Author(s):

Yuqiong Liu ◽

Hoshin V. Gupta ◽

Soroosh Sorooshian ◽

Luis A. Bastidas ◽

William J. Shuttleworth

Keyword(s):

Parameter Estimation ◽

Observational Data ◽

Land Surface ◽

Climate Model ◽

Model Performance ◽

Computational Time ◽

Parameter Estimates ◽

Model Parameters ◽

Atmospheric Parameters ◽

Estimation Process

Abstract In coupled land surface–atmosphere modeling, the possibility and benefits of constraining model parameters using observational data bear investigation. Using the locally coupled NCAR Single-column Community Climate Model (NCAR SCCM), this study demonstrates some feasible, effective approaches to constrain parameter estimates for coupled land–atmosphere models and explores the effects of including both land surface and atmospheric parameters and fluxes/variables in the parameter estimation process, as well as the value of conducting the process in a stepwise manner. The results indicate that the use of both land surface and atmospheric flux variables to construct error criteria can lead to better-constrained parameter sets. The model with “optimal” parameters generally performs better than when a priori parameters are used, especially when some atmospheric parameters are included in the parameter estimation process. The overall conclusion is that, to achieve balanced, reasonable model performance on all variables, it is desirable to optimize both land surface and atmospheric parameters and use both land surface and atmospheric fluxes/variables for error criteria in the optimization process. The results also show that, for a coupled land–atmosphere model, there are potential advantages to using a stepwise procedure in which the land surface parameters are first identified in offline mode, after which the atmospheric parameters are determined in coupled mode. This stepwise scheme appears to provide comparable solutions to a fully coupled approach, but with considerably reduced computational time. The trade-off in the ability of a model to satisfactorily simulate different processes simultaneously, as observed in most multicriteria studies, is most evident for sensible heat and precipitation in this study for the NCAR SCCM.

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Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

Biogeosciences ◽

10.5194/bg-14-1647-2017 ◽

2017 ◽

Vol 14 (6) ◽

pp. 1647-1701 ◽

Cited By ~ 17

Author(s):

Markus Schartau ◽

Philip Wallhead ◽

John Hemmings ◽

Ulrike Löptien ◽

Iris Kriest ◽

...

Keyword(s):

Parameter Estimation ◽

Data Assimilation ◽

Parameter Identification ◽

Estimation Methods ◽

Model Parameters ◽

Ecosystem Modelling ◽

Ecosystem Models ◽

Element Cycling ◽

Biogeochemical Models ◽

Parameter Values

Abstract. To describe the underlying processes involved in oceanic plankton dynamics is crucial for the determination of energy and mass flux through an ecosystem and for the estimation of biogeochemical element cycling. Many planktonic ecosystem models were developed to resolve major processes so that flux estimates can be derived from numerical simulations. These results depend on the type and number of parameterizations incorporated as model equations. Furthermore, the values assigned to respective parameters specify a model's solution. Representative model results are those that can explain data; therefore, data assimilation methods are utilized to yield optimal estimates of parameter values while fitting model results to match data. Central difficulties are (1) planktonic ecosystem models are imperfect and (2) data are often too sparse to constrain all model parameters. In this review we explore how problems in parameter identification are approached in marine planktonic ecosystem modelling. We provide background information about model uncertainties and estimation methods, and how these are considered for assessing misfits between observations and model results. We explain differences in evaluating uncertainties in parameter estimation, thereby also discussing issues of parameter identifiability. Aspects of model complexity are addressed and we describe how results from cross-validation studies provide much insight in this respect. Moreover, approaches are discussed that consider time- and space-dependent parameter values. We further discuss the use of dynamical/statistical emulator approaches, and we elucidate issues of parameter identification in global biogeochemical models. Our review discloses many facets of parameter identification, as we found many commonalities between the objectives of different approaches, but scientific insight differed between studies. To learn more from results of planktonic ecosystem models we recommend finding a good balance in the level of sophistication between mechanistic modelling and statistical data assimilation treatment for parameter estimation.

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Sequential Parameter Estimation for Mammalian Cell Model Based on In Silico Design of Experiments

Processes ◽

10.3390/pr6080100 ◽

2018 ◽

Vol 6 (8) ◽

pp. 100 ◽

Cited By ~ 4

Author(s):

Zhenyu Wang ◽

Hana Sheikh ◽

Kyongbum Lee ◽

Christos Georgakis

Keyword(s):

Parameter Estimation ◽

Mammalian Cells ◽

Cell Model ◽

Cell Metabolism ◽

Model Performance ◽

Sequential Estimation ◽

Parameter Estimates ◽

Model Parameters ◽

Algebraic Equations ◽

Estimation Of Parameters

Due to the complicated metabolism of mammalian cells, the corresponding dynamic mathematical models usually consist of large sets of differential and algebraic equations with a large number of parameters to be estimated. On the other hand, the measured data for estimating the model parameters are limited. Consequently, the parameter estimates may converge to a local minimum far from the optimal ones, especially when the initial guesses of the parameter values are poor. The methodology presented in this paper provides a systematic way for estimating parameters sequentially that generates better initial guesses for parameter estimation and improves the accuracy of the obtained metabolic model. The model parameters are first classified into four subsets of decreasing importance, based on the sensitivity of the model’s predictions on the parameters’ assumed values. The parameters in the most sensitive subset, typically a small fraction of the total, are estimated first. When estimating the remaining parameters with next most sensitive subset, the subsets of parameters with higher sensitivities are estimated again using their previously obtained optimal values as the initial guesses. The power of this sequential estimation approach is illustrated through a case study on the estimation of parameters in a dynamic model of CHO cell metabolism in fed-batch culture. We show that the sequential parameter estimation approach improves model accuracy and that using limited data to estimate low-sensitivity parameters can worsen model performance.

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Global estimation of rainfall-runoff model parameters: an empirical experiment

10.5194/egusphere-egu21-13224 ◽

2021 ◽

Author(s):

Léonard Santos ◽

Jafet C. M. Andersson ◽

Berit Arheimer

Keyword(s):

Land Use ◽

Parameter Estimation ◽

World Wide ◽

Global Scale ◽

Second Step ◽

Model Parameters ◽

Earth System ◽

Climate Classification ◽

Soil Map ◽

Parameter Values

When setting up global scale hydrological models, parameter estimation is a crucial step. Some modellers assign pre-defined parameter values to physical characteristics (such as soil, land cover, etc.) while others estimate parameter values based on observed hydrological data. In both cases, the regionalisation of parameters is a major challenge since both literature values and observed data are often lacking and assumptions are needed. This work aims at identifying suitable parameter regions to perform a regional calibration of the global model World-Wide HYPE (Arheimer et al., 2020) through empirical tests. The work is organised in two steps. First we compare different ways of taking soil into account when creating hydrological response units. The soil is either considered uniform, indexed to land use or to a simplified soil map. The best soil representation is selected based on the model performance at a global scale. Based on this best representation, the second step aims at evaluating different ways to regionalise the soil parameters of the hydrological model. &#160;Previous classifications of hydrological uniform regions are tested for regionalisation of model parameters: hydrobelts (Meybeck et al., 2013), K&#246;ppen climate regions (Kottek et al., 2006), soil capacity index (Wang-Erlandsson et al., 2016) and hydroclimatic regions (Knoben et al., 2018). For the first step, the results show that the best solution is to represent soil by land use. This counterintuitive result is due to the fact that adding information based on a soil map add another calibration step. To avoid increased equifinality, such an effort increases the need for data, which is often lacking at the global scale. &#160;For the second step, the creation of parameter regions contributed with minor improvement in terms of model performances, probably because the choice of regions was not suitable for the model approach. Also, the improvement has shown to be higher when available discharge data for calibration were better distributed over the different regions. This work shows that, when calibrating a model at very large scale, a balance should be found between available data and parameter regions resolution.&#160; References Arheimer, B., Pimentel, R., Isberg, K., Crochemore, L., Andersson, J. C. M., Hasan, A., and Pineda, L.: Global catchment modelling using World-Wide HYPE (WWH), open data and stepwise parameter estimation, Hydrol. Earth Syst. Sci. 24, 535&#8211;559, 2020. Knoben, W. J., Woods, R. A., and Freer, J. E.: A Quantitative Hydrological Climate Classification Evaluated With Independent Streamflow Data. Water Resources Research, 54(7), 5088-5109, 2018. Kottek, M., Grieser, J., Beck, C., Rudolf, B., and Rubel, F.: World map of the K&#246;ppen-Geiger climate classification updated. Meteorologische Zeitschrift, 15, 259-263, 2006. Meybeck, M., Kummu, M., and D&#252;rr, H. H.: Global hydrobelts and hydroregions: improved reporting scale for waterrelated issues? Hydrology and Earth System Sciences, 17(3), 1093-1111, 2013. Wang-Erlandsson, L., Bastiaanssen, W. G. M., Gao, H., J&#228;germeyr, J., Senay, G. B., van Dijk, A. I. J. M., Guerschman, J. P., Keys, P. W., Gordon, L. J., and Savenije, H. H. G.: Global root zone storage capacity from satellite-based evaporation, Hydrology Earth System Sciences, 20, 1459-1481, 2016.

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