Bayesian calibration of firn densification models

Abstract. Firn densification modelling is key to understanding ice sheet mass balance, ice sheet surface elevation change, and the age difference between ice and the air in enclosed air bubbles. This has resulted in the development of many firn models, all relying to a certain degree on parameter calibration against observed data. We present a novel Bayesian calibration method for these parameters and apply it to three existing firn models. Using an extensive dataset of firn cores from Greenland and Antarctica, we reach optimal parameter estimates applicable to both ice sheets. We then use these to simulate firn density and evaluate against independent observations. Our simulations show a significant decrease (24 % and 56 %) in observation–model discrepancy for two models and a smaller increase (15 %) for the third. As opposed to current methods, the Bayesian framework allows for robust uncertainty analysis related to parameter values. Based on our results, we review some inherent model assumptions and demonstrate how firn model choice and uncertainties in parameter values cause spread in key model outputs.

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Bayesian calibration of firn densification models

10.5194/tc-2019-274 ◽

2020 ◽

Author(s):

Vincent Verjans ◽

Amber Alexandra Leeson ◽

Christopher Nemeth ◽

C. Max Stevens ◽

Peter Kuipers Munneke ◽

...

Keyword(s):

Mass Balance ◽

Optimal Parameter ◽

Ice Sheet ◽

Calibration Method ◽

Parameter Estimates ◽

Age Difference ◽

Bayesian Calibration ◽

Independent Observations ◽

Ice Sheet Mass Balance ◽

Parameter Values

Abstract. Firn densification modelling is key to understanding ice sheet mass balance, ice sheet surface elevation change, and the age difference between ice and the air in enclosed air bubbles. This has resulted in the development of many firn models, all relying to a certain degree on parameter calibration against observed data. We present a novel Bayesian calibration method for these parameters, and apply it to three existing firn models. Using an extensive dataset of firn cores from Greenland and Antarctica, we reach optimal parameter estimates applicable to both ice sheets. We then use these to simulate firn density and evaluate against independent observations. Our simulations show a significant decrease (25 and 55 %) in observation-model discrepancy for two models and a small increase (11 %) for the third. As opposed to current methods, the Bayesian framework allows for robust uncertainty analysis related to parameter values. Based on our results, we review some inherent model assumptions and demonstrate how model- and parameter-related uncertainties potentially affect ice sheet mass balance assessments.

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Bayesian parameter estimation and interpretation for an intermediate model of tree-ring width

Climate of the Past Discussions ◽

10.5194/cpd-9-615-2013 ◽

2013 ◽

Vol 9 (1) ◽

pp. 615-645 ◽

Cited By ~ 5

Author(s):

S. E. Tolwinski-Ward ◽

K. J. Anchukaitis ◽

M. N. Evans

Keyword(s):

Tree Ring ◽

Optimal Parameter ◽

Ring Width ◽

Physical Space ◽

The United States ◽

Parameter Estimates ◽

Tree Ring Width ◽

Multidimensional Parameter ◽

Parameter Values ◽

Insight Into

Abstract. We present a Bayesian model for estimating the parameters of the VS-Lite forward model of tree-ring width. The scheme also provides information about the uncertainty of the parameter estimates, as well as the uncertainty of VS-Lite itself. By inferring VS-Lite's parameters for synthetically-generated ring-width series at several hundred sites across the United States, we show that the Bayesian algorithm is skillful and robust to climatic nonstationarity over the interval tested. We also infer optimal parameter values for modeling observed ring-width data at the same network of sites. The estimated parameter values cluster in physical space, and their locations in multidimensional parameter space provide insight into the dominant climatic controls on modeled tree-ring growth at each site.

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Bayesian parameter estimation and interpretation for an intermediate model of tree-ring width

Climate of the Past ◽

10.5194/cp-9-1481-2013 ◽

2013 ◽

Vol 9 (4) ◽

pp. 1481-1493 ◽

Cited By ~ 47

Author(s):

S. E. Tolwinski-Ward ◽

K. J. Anchukaitis ◽

M. N. Evans

Keyword(s):

Tree Ring ◽

Optimal Parameter ◽

Full Range ◽

Ring Width ◽

Physical Space ◽

Estimation Procedure ◽

The United States ◽

Parameter Estimates ◽

Tree Ring Width ◽

Parameter Values

Abstract. We present a Bayesian model for estimating the parameters of the VS-Lite forward model of tree-ring width for a particular chronology and its local climatology. The scheme also provides information about the uncertainty of the parameter estimates, as well as the model error in representing the observed proxy time series. By inferring VS-Lite's parameters independently for synthetically generated ring-width series at several hundred sites across the United States, we show that the algorithm is skillful. We also infer optimal parameter values for modeling observed ring-width data at the same network of sites. The estimated parameter values covary in physical space, and their locations in multidimensional parameter space provide insight into the dominant climatic controls on modeled tree-ring growth at each site as well as the stability of those controls. The estimation procedure is useful for forward and inverse modeling studies using VS-Lite to quantify the full range of model uncertainty stemming from its parameterization.

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Least Bumpiness Calibration With Extrapolative Bias Correction

Volume 2A: 44th Design Automation Conference ◽

10.1115/detc2018-86163 ◽

2018 ◽

Author(s):

Chanyoung Park ◽

Nam H. Kim ◽

Raphael T. Haftka

Keyword(s):

Parameter Estimation ◽

Potential Risk ◽

Bias Correction ◽

Model Calibration ◽

Latin Hypercube Sampling ◽

Calibration Method ◽

Large Error ◽

Parameter Estimates ◽

Bayesian Calibration ◽

Calibration Parameter

Bias correction is important for model calibration to obtain unbiased calibration parameter estimates and make accurate prediction. However, calibration often relies on insufficient samples, and so bias correction often mostly depends on extrapolation. For example, bias correction with twelve samples in nine-dimensional box generated by Latin Hypercube Sampling (LHS) has less than 0.1% interpolation domain in the box. Since bias correction is coupled with calibration parameter estimation, calibration with extrapolative bias correction can lead a large error in the calibrated parameters. This paper proposes an idea of calibration with minimum bumpiness correction. The bumpiness of bias correction is a good measure of assessing the potential risk of a large error in the correction. By minimizing bumpiness, the risk of extrapolation can be reduced while the accuracy of parameter estimates can be achieved. It was found that this calibration method gave more accurate results than Bayesian calibration for an analytical example. It was also found that there are common denominators between the proposed method and the Bayesian calibration with bias correction.

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A Comparison of Parameter Estimation for Distributed Hydrological Modelling Using Automatic and Manual Methods

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.356-360.2372 ◽

2011 ◽

Vol 356-360 ◽

pp. 2372-2375 ◽

Cited By ~ 2

Author(s):

Xiang Hu Li ◽

Qi Zhang ◽

Min Shao ◽

Yun Liang Li

Keyword(s):

Model Simulation ◽

Optimal Parameter ◽

Model Fitting ◽

Main Tool ◽

Calibration Method ◽

Distributed Hydrological Model ◽

Fitting Procedure ◽

The Difference ◽

Distributed Hydrological Models ◽

Parameter Values

Distributed hydrological models have become the main tool to study the hydrology natural law and solve the hydrology practice question. However, the definition of model parameter values limits their application. Manual calibration is time consuming and often tedious, and the automatic calibration method could be an innovative way of improving the traditional model fitting procedure. PEST is designed for easy linkage with other models and has been applied to many distributed hydrological model. Therefore, the PEST model is selected in this paper to link with the WATLAC model and calibrate the parameters, and compare the calibration results with manual results. The results show that the difference of two group parameter values is obvious. The PEST model can easily drive the WATLAC model and gain the optimal parameter values efficiently. The WATLAC model produces an overall good fit, the Ens values, except in 2001, are more than 0.83 and with an average of 0.93. But the relative runoff depth errors are larger slightly than manual results. The simulated stream flow hydrographs with PEST demonstrated a closer agreement with the observed hydrographs, while, the model simulation using manual calibration method behaved not very well and there was a tendency for the model to enlarge the peak flows.

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GNSS Profile from the Greenland Korth Expeditions in the Context of Satellite Data

Applied Sciences ◽

10.3390/app11031115 ◽

2021 ◽

Vol 11 (3) ◽

pp. 1115

Author(s):

Aleš Bezděk ◽

Jakub Kostelecký ◽

Josef Sebera ◽

Thomas Hitziger

Keyword(s):

Ice Sheet ◽

Satellite Observations ◽

Elevation Change ◽

Gradual Decline ◽

Satellite Gravimetry ◽

Surface Elevation Change ◽

Satellite Radar ◽

Gnss Measurements ◽

Gnss Data ◽

Satellite Radar Altimetry

Over the last two decades, a small group of researchers repeatedly crossed the Greenland interior skiing along a 700-km long route from east to west, acquiring precise GNSS measurements at exactly the same locations. Four such elevation profiles of the ice sheet measured in 2002, 2006, 2010 and 2015 were differenced and used to analyze the surface elevation change. Our goal is to compare such locally measured GNSS data with independent satellite observations. First, we show an agreement in the rate of elevation change between the GNSS data and satellite radar altimetry (ERS, Envisat, CryoSat-2). Both datasets agree well (2002–2015), and both correctly display local features such as an elevation increase in the central part of the ice sheet and a sharp gradual decline in the surface heights above Jakobshavn Glacier. Second, we processed satellite gravimetry data (GRACE) in order for them to be comparable with local GNSS measurements. The agreement is demonstrated by a time series at one of the measurement sites. Finally, we provide our own satellite gravimetry (GRACE, GRACE-FO, Swarm) estimate of the Greenland mass balance: first a mild decrease (2002–2007: −210 ± 29 Gt/yr), then an accelerated mass loss (2007–2012: −335 ± 29 Gt/yr), which was noticeably reduced afterwards (2012–2017: −178 ± 72 Gt/yr), and nowadays it seems to increase again (2018–2019: −278 ± 67 Gt/yr).

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Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

Applied Sciences ◽

10.3390/app11156955 ◽

2021 ◽

Vol 11 (15) ◽

pp. 6955

Author(s):

Andrzej Rysak ◽

Magdalena Gregorczyk

Keyword(s):

Optimal Parameter ◽

Differential Transform Method ◽

Bifurcation Diagrams ◽

Transform Method ◽

Rossler System ◽

Differential Transform ◽

Rössler System ◽

Fractional System ◽

Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

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Selecting single cell clustering parameter values using subsampling-based robustness metrics

BMC Bioinformatics ◽

10.1186/s12859-021-03957-4 ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Ryan B. Patterson-Cross ◽

Ariel J. Levine ◽

Vilas Menon

Keyword(s):

Single Cell ◽

Optimal Parameter ◽

Clustering Algorithms ◽

Cell Types ◽

Parameter Selection ◽

Data Set ◽

Biologically Relevant ◽

Cell Clustering ◽

Parameter Values ◽

Robustness Metrics

Abstract Background Generating and analysing single-cell data has become a widespread approach to examine tissue heterogeneity, and numerous algorithms exist for clustering these datasets to identify putative cell types with shared transcriptomic signatures. However, many of these clustering workflows rely on user-tuned parameter values, tailored to each dataset, to identify a set of biologically relevant clusters. Whereas users often develop their own intuition as to the optimal range of parameters for clustering on each data set, the lack of systematic approaches to identify this range can be daunting to new users of any given workflow. In addition, an optimal parameter set does not guarantee that all clusters are equally well-resolved, given the heterogeneity in transcriptomic signatures in most biological systems. Results Here, we illustrate a subsampling-based approach (chooseR) that simultaneously guides parameter selection and characterizes cluster robustness. Through bootstrapped iterative clustering across a range of parameters, chooseR was used to select parameter values for two distinct clustering workflows (Seurat and scVI). In each case, chooseR identified parameters that produced biologically relevant clusters from both well-characterized (human PBMC) and complex (mouse spinal cord) datasets. Moreover, it provided a simple “robustness score” for each of these clusters, facilitating the assessment of cluster quality. Conclusion chooseR is a simple, conceptually understandable tool that can be used flexibly across clustering algorithms, workflows, and datasets to guide clustering parameter selection and characterize cluster robustness.

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Greenland ice sheet mass balance: a review

Reports on Progress in Physics ◽

10.1088/0034-4885/78/4/046801 ◽

2015 ◽

Vol 78 (4) ◽

pp. 046801 ◽

Cited By ~ 85

Author(s):

Shfaqat A Khan ◽

Andy Aschwanden ◽

Anders A Bjørk ◽

John Wahr ◽

Kristian K Kjeldsen ◽

...

Keyword(s):

Mass Balance ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Ice Sheet Mass Balance

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Monitoring southwest Greenland’s ice sheet melt with ambient seismic noise

Science Advances ◽

10.1126/sciadv.1501538 ◽

2016 ◽

Vol 2 (5) ◽

pp. e1501538 ◽

Cited By ~ 39

Author(s):

Aurélien Mordret ◽

T. Dylan Mikesell ◽

Christopher Harig ◽

Bradley P. Lipovsky ◽

Germán A. Prieto

Keyword(s):

Mass Loss ◽

Mass Balance ◽

Sea Level ◽

Seismic Noise ◽

Seismic Velocity ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Sea Level Changes ◽

Ice Sheet Mass Balance ◽

Velocity Changes

The Greenland ice sheet presently accounts for ~70% of global ice sheet mass loss. Because this mass loss is associated with sea-level rise at a rate of 0.7 mm/year, the development of improved monitoring techniques to observe ongoing changes in ice sheet mass balance is of paramount concern. Spaceborne mass balance techniques are commonly used; however, they are inadequate for many purposes because of their low spatial and/or temporal resolution. We demonstrate that small variations in seismic wave speed in Earth’s crust, as measured with the correlation of seismic noise, may be used to infer seasonal ice sheet mass balance. Seasonal loading and unloading of glacial mass induces strain in the crust, and these strains then result in seismic velocity changes due to poroelastic processes. Our method provides a new and independent way of monitoring (in near real time) ice sheet mass balance, yielding new constraints on ice sheet evolution and its contribution to global sea-level changes. An increased number of seismic stations in the vicinity of ice sheets will enhance our ability to create detailed space-time records of ice mass variations.

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