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The calibration of complex computer codes using uncertainty quantification (UQ) methods is a rich area of statistical methodological development. When applying these techniques to simulators with spatial output, it is now standard to use principal component decomposition to reduce the dimensions of the outputs in order to allow Gaussian process emulators to predict the output for calibration. We introduce the \"terminal case,\" in which the model cannot reproduce observations to within model discrepancy, and for which standard calibration methods in UQ fail to give sensible results. We show that even when there is no such issue with the model, the standard decomposition on the outputs can and usually does lead to a terminal case analysis. We present a simple test to allow a practitioner to establish whether their experiment will result in a terminal case analysis, and a methodology for defining calibration-optimal bases that avoid this whenever it is not inevitable. We present the optimal rotation algorithm for doing this, and demonstrate its efficacy for an idealized example for which the usual principal component methods fail. We apply these ideas to the CanAM4 model to demonstrate the terminal case issue arising for climate models. We discuss climate model tuning and the estimation of model discrepancy within this context, and show how the optimal rotation algorithm can be used in developing practical climate model tuning tools. Supplementary materials for this article are available online.

​​​​​​​Consideration of uncertainty in volcanic ash cloud forecasts is increasingly of interest, with an industry goal to provide probabilistic forecasts alongside deterministic forecasts. Simulations of volcanic clouds via dispersion modelling are subject to a number of uncertainties relating to the eruption itself (mass of ash emitted and when), parameterisations of physical processes, and the meteorological conditions. To fully explore these uncertainties through atmospheric dispersion model simulations alone may be expensive, and instead, an emulator can be used to increase understanding of uncertainties in the model inputs and outputs, going beyond combinations of source, physical, and meteorological inputs that were simulated by the dispersion model. We emulate the NAME (Numerical Atmospheric-dispersion Modelling Environment) dispersion model for simulations of the Raikoke 2019 eruption and use these emulators to compare simulated ash clouds to observations derived from satellites, constraining NAME source and internal parameters via history matching. We demonstrate that the effect of varying both meteorological scenarios and model parameters can be captured in this way with accurate emulation and using only a small number of runs per meteorological scenario. We show that accounting for meteorological uncertainty simultaneously with other uncertainties may lead to the identification of different sensitive model parameters and may lead to less constrained source and internal NAME parameters; however, through idealised experiments, we argue that this is a reasonable result and is properly accounting for all sources of uncertainty in the model inputs.

(1) Generate accurate estimates of the relationship between decimal age (i.e., chronological and relative) with swimming performance based on longitudinal data. (2) Determine whether corrective adjustment procedures can remove Relative Age Effects (RAEs) from junior/youth swimming. Longitudinal and repeated years of cross-sectional performance data were examined. (1) Participants were 553 male 100m Freestyle swimmers (10–18 years) who participated in ≥five annual events between 1999–2017. Growth curve modelling quantified the relationship between age and swimming performance, permitting corrective adjustment calculations. (2) Participants were N=2141 male 100m Freestyle swimmers (13–16 years) who swam at state/national events in 2015–2017. Relative age distributions for ‘All’, ‘Top 50%’, ‘25%’ and ‘10%’ of swimming times were examined based on raw and correctively adjusted swim times. Chi-square, Cramer’s V and Odds Ratios (OR) determined whether relative age (quartile) inequalities existed according to age-groups, selection level and correctively adjusted swim times. Based on raw swim times, for ‘All’ swimmers RAEs was evident at 13 and 14 years-old and dissipated thereafter. But, RAE effect sizes substantially increased with selection level, with large-medium effects between 13–15 years-old (e.g., 15 years — Top 50% Q1v Q4 OR=2.28; Top 10%=6.02). However, when correctively adjusted swim times were examined, RAEs were predominantly absent across age-group and selection levels. With accurate longitudinal reference data, corrective adjustment procedures effectively removed RAEs from 100m Freestyle swimming performance, suggesting the potential to improve swimming participation experience and performance evaluation.

Inter-individual differences in maturation-associated development can lead to variations in physical performance, resulting in performance (dis)advantages and maturation selection bias within youth sport systems. To address such bias and account for maturational differences, Maturation-based Corrective Adjustment Procedures (Mat-CAPs) could be beneficial. The present study aimed to: (1) determine maturity timing distributions in youth female swimming; (2) quantify the relationship between maturation status and 100-m front-crawl (FC) performance; (3) implement Mat-CAPs to remove maturational influences upon swimming performance. For Aim 1 and 2, participants were 663 female (10–15 years) swimmers who participated in 100-m FC events at Australian regional, state, and national-level competitions between 2016–2020 and underwent anthropometric assessment (mass, height and sitting height) to estimate maturity timing and offset. For Aim 3, participants aged 10–13 years were categorised into maturity timing categories. Maturity timing distributions for Raw (‘All’, ‘Top 50%’ and ‘Top 25%’) and Correctively Adjusted swim times were examined. Chi-square, Cramer’s V and Odds Ratios determined the presence of maturation biases, while Mat-CAPs identified whether such biases were removed in targeted age and selection-groups. Results identified that between 10–13 years, a significantly higher frequency of ‘early’ maturers was apparent, although tapered toward higher frequencies of ‘Late-normative’ maturers by 14–15 years. A curvilinear relationship between maturity-offset and swim performance was identified ( R 2 = 0.51, p<0.001) and utilised for Mat-CAPs. Following Mat-CAPs application, maturity timing biases evident in affected age-groups (10–13 years), and which were magnified at higher selection levels (‘Top 50%’ & ‘25%’ of swim performances) were predominantly removed. Findings highlight how maturation advantages in females occurred until approximately 13 years old, warranting restricted Mat-CAPs application. Mat-CAPS has the potential to improve female swimmer participation experiences and evaluation.

To determine the prevalence, magnitude and transient patterning of Relative Age Effects (RAEs) according to sex and stroke event across all age-groups at the Australian National age swimming Championships. Repeated years of cross-sectional participation data were examined. Participants were 6014 unique male (3185) and female (2829) swimmers (aged 12–18 years) who participated in Freestyle (50, 400m) and/or Breaststroke (100, 200m) at the National age swimming Championships between 2000–2014 (inclusive). RAE prevalence, magnitude and transience were determined using Chi-square tests and Cramer’s V estimates for effect size. Odds Ratios (OR) and 95% Confidence Intervals (CI) examined relative age quartile discrepancies. These steps were applied across age-groups and according to sex and each stroke event. Consistent RAEs with large-medium effect sizes were evident for males at 12–15 years of age respectively, and with large-medium effects for females at 12–14 respectively across all four swimming strokes. RAE magnitude then consistently reduced with age across strokes (e.g., Q1 vs. Q4 OR range 16year old males=0.94–1.20; females=0.68–1.41). With few exceptions, by 15–16 years RAEs had typically dissipated; and by 17–18 years, descriptive and significant inverse RAEs emerged, reflecting overrepresentation of relatively younger swimmers. Performance advantages associated with relative age (and thereby likely growth and maturation) are transient. Greater consideration of transient performance and participation in athlete development systems is necessary. This may include revising the emphasis of sport programmes according to developmental stages and delaying forms of athlete selection to improve validity.

With the growing complexity of land surface models used to represent the terrestrial part of wider Earth system models, the need for sophisticated and robust parameter optimisation techniques is paramount. Quantifying parameter uncertainty is essential for both model development and more accurate projections. In this study, we assess the power of history matching by comparing results to the variational data assimilation approach commonly used in land surface models for parameter estimation. Although both approaches have different setups and goals, we can extract posterior parameter distributions from both methods and test the model–data fit of ensembles sampled from these distributions. Using a twin experiment, we test whether we can recover known parameter values. Through variational data assimilation, we closely match the observations. However, the known parameter values are not always contained in the posterior parameter distribution, highlighting the equifinality of the parameter space. In contrast, while more conservative, history matching still gives a reasonably good fit and provides more information about the model structure by allowing for non-Gaussian parameter distributions. Furthermore, the true parameters are contained in the posterior distributions. We then consider history matching's ability to ingest different metrics targeting different physical parts of the model, thus helping to reduce the parameter space further and improve the model–data fit. We find the best results when history matching is used with multiple metrics; not only is the model–data fit improved, but we also gain a deeper understanding of the model and how the different parameters constrain different parts of the seasonal cycle. We conclude by discussing the potential of history matching in future studies.

The development of parameterizations is a major task in the development of weather and climate models. Model improvement has been slow in the past decades, due to the difficulty of encompassing key physical processes into parameterizations, but also of calibrating or “tuning” the many free parameters involved in their formulation. Machine learning techniques have been recently used for speeding up the development process. While some studies propose to replace parameterizations by data‐driven neural networks, we rather advocate that keeping physical parameterizations is key for the reliability of climate projections. In this paper we propose to harness machine learning to improve physical parameterizations. In particular, we use Gaussian process‐based methods from uncertainty quantification to calibrate the model free parameters at a process level. To achieve this, we focus on the comparison of single‐column simulations and reference large‐eddy simulations over multiple boundary‐layer cases. Our method returns all values of the free parameters consistent with the references and any structural uncertainties, allowing a reduced domain of acceptable values to be considered when tuning the three‐dimensional (3D) global model. This tool allows to disentangle deficiencies due to poor parameter calibration from intrinsic limits rooted in the parameterization formulations. This paper describes the tool and the philosophy of tuning in single‐column mode. Part 2 shows how the results from our process‐based tuning can help in the 3D global model tuning. Key Points We apply uncertainty quantification to single‐column model/large‐eddy simulation comparison to calibrate free parameters We revisit model development strategy with an emphasis on processes for model calibration The proposed tuning tool allows to formalize the complementary use of multicases with various metrics

Global assessments of air quality and health require comprehensive estimates of the exposures to air pollution that are experienced by populations in every country. However, there are many countries in which measurements from ground-based monitoring are sparse or non-existent, with quality-control and representativeness providing additional challenges. While ground-based monitoring provides a far from complete picture of global air quality, there are other sources of information that provide comprehensive coverage across the globe. The World Health Organization developed the Data Integration Model for Air Quality (DIMAQ) to combine information from ground measurements with that from other sources, such as atmospheric chemical transport models and estimates from remote sensing satellites in order to produce the information that is required for health burden assessment and the calculation of air pollution-related Sustainable Development Goals indicators. Here, we show an example of the use of DIMAQ with the Copernicus Atmosphere Monitoring Service Re-Analysis (CAMSRA) of atmospheric composition, which represents the best practices in meteorology and climate monitoring that were developed under the World Meteorological Organization’s Global Atmosphere Watch programme. Estimates of PM2.5 from CAMSRA are integrated within the DIMAQ framework in order to produce high-resolution estimates of air pollution exposure that can be aggregated in a coherent fashion to produce country-level assessments of exposures.

We describe the method of history matching, a method currently used to help quantify parametric uncertainty in climate models, and argue for its use in identifying and removing structural biases in climate models at the model development stage. We illustrate the method using an investigation of the potential to improve upon known ocean circulation biases in a coupled non-flux-adjusted climate model (the third Hadley Centre Climate Model; HadCM3). In particular, we use history matching to investigate whether or not the behaviour of the Antarctic Circumpolar Current (ACC), which is known to be too strong in HadCM3, represents a structural bias that could be corrected using the model parameters. We find that it is possible to improve the ACC strength using the parameters and observe that doing this leads to more realistic representations of the sub-polar and sub-tropical gyres, sea surface salinities (both globally and in the North Atlantic), sea surface temperatures in the sinking regions in the North Atlantic and in the Southern Ocean, North Atlantic Deep Water flows, global precipitation, wind fields and sea level pressure. We then use history matching to locate a region of parameter space predicted not to contain structural biases for ACC and SSTs that is around 1 % of the original parameter space. We explore qualitative features of this space and show that certain key ocean and atmosphere parameters must be tuned carefully together in order to locate climates that satisfy our chosen metrics. Our study shows that attempts to tune climate model parameters that vary only a handful of parameters relevant to a given process at a time will not be as successful or as efficient as history matching.