Abstract
Maritime engineering relies on model forecasts for many different processes, including meteorological and oceanographic forcings, structural responses, and energy demands. Understanding the ...performance and evaluation of such forecasting models is crucial in instilling reliability in maritime operations. Evaluation metrics that assess the point accuracy of the forecast (such as root-mean-squared error) are commonplace, but with the increased uptake of probabilistic forecasting methods such evaluation metrics may not consider the full forecasting distribution. The statistical theory of proper scoring rules provides a framework in which to score and compare competing probabilistic forecasts, but it is seldom appealed to in applications. This translational paper presents the underlying theory and principles of proper scoring rules, develops a simple panel of rules that may be used to robustly evaluate the performance of competing probabilistic forecasts, and demonstrates this with an application to forecasting surface winds at an asset on Australia’s North–West Shelf. Where appropriate, we relate the statistical theory to common requirements by maritime engineering industry. The case study is from a body of work that was undertaken to quantify the value resulting from an operational forecasting product and is a clear demonstration of the downstream impacts that statistical and data science methods can have in maritime engineering operations.
We present the AdaptSPEC-X method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to ...incorporate multiple time series, with mixture components parameterized by a time-varying mean and log spectrum. The mixture components are based on AdaptSPEC, a nonparametric model which adaptively divides the time series into an unknown number of segments and estimates the local log spectra by smoothing splines. AdaptSPEC-X extends AdaptSPEC in three ways. First, through the infinite mixture, it applies to multiple time series linked by covariates. Second, it can handle missing values, a common feature of time series which can cause difficulties for nonparametric spectral methods. Third, it allows for a time-varying mean. Through these extensions, AdaptSPEC-X can estimate time-varying means and spectra at observed and unobserved covariate values, allowing for predictive inference. Estimation is performed by Markov chain Monte Carlo (MCMC) methods, combining data augmentation, reversible jump, and Riemann manifold Hamiltonian Monte Carlo techniques. We evaluate the methodology using simulated data, and describe applications to Australian rainfall data and measles incidence in the United States. Software implementing the method proposed in this article is available in the R package BayesSpec. Supplementary files for this article are available online.
From Many to One: Consensus Inference in a MIP Cressie, Noel; Bertolacci, Michael; Zammit‐Mangion, Andrew
Geophysical research letters,
28 July 2022, Volume:
49, Issue:
14
Journal Article
Peer reviewed
Open access
A Model Intercomparison Project (MIP) consists of teams who estimate the same underlying quantity (e.g., temperature projections to the year 2070). A simple average of the ensemble of the teams' ...outputs gives a consensus estimate, but it does not recognize that some outputs are more variable than others. Statistical analysis of variance (ANOVA) models offer a way to obtain a weighted frequentist consensus estimate of outputs with a variance that is the smallest possible. Modulo dependence between MIP outputs, the ANOVA approach weights a team's output inversely proportional to its variance, from which optimally weighted estimates follow. ANOVA weights can also provide a prior distribution for Bayesian Model Averaging of the MIP outputs when external evaluation data are available. We use a MIP of carbon‐dioxide‐flux inversions to illustrate the ANOVA‐based weighting and subsequent frequentist consensus inferences.
Plain Language Summary
There can be disagreement between different teams of scientists on the best way to model and hence estimate complex geophysical phenomena. Model Intercomparison Projects (MIPs) address this in a scientific manner, where a common protocol about data and certain basic geophysical features is agreed upon by the teams. The collection of the different teams' outputs is analyzed, often using the ensemble mean and a measure of the ensemble variability. However, the results may indicate that it is inappropriate to treat all teams' outputs equally, which can happen when some teams have superior models or better numerical approximations. It may also happen that some teams share code or their models have common features beyond those specified in the protocol. We adapt a statistical technique called the analysis of variance (ANOVA) to this complex setting, obtain optimal weights on the outputs, and then estimate those weights. This results in a statistically optimal (i.e., most precise) consensus summary of the MIP; other weights give less‐precise inferences. We call this inference framework for MIPs, Statistically Unbiased Prediction and Estimation‐ANOVA, and we apply it to a MIP designed to estimate the sources and sinks of carbon dioxide.
Key Points
Consensus inference is provided for Multiple Intercomparison Project (MIP) outputs when little or no evaluation data are available
The statistical analysis of variance method quantifies the MIP outputs' variabilities to obtain optimally weighted frequentist consensus inference
Variance parameters for optimal weighting of outputs and consensus inference are estimated using likelihood‐based methodology
Earth’s CO2 battle: a view from space Cressie, Noel; Zammit-Mangion, Andrew; Jacobson, Josh ...
Significance (Oxford, England),
02/2023, Volume:
20, Issue:
1
Journal Article
Abstract
Our environment is undergoing rapid change as greenhouse gases warm the planet. Noel Cressie, Andrew Zammit-Mangion, Josh Jacobson, and Michael Bertolacci use WOMBAT, a Bayesian hierarchical ...statistical framework, to infer the spatio-temporal distribution of CO2 surface fluxes
WOMBAT (the WOllongong Methodology for Bayesian Assimilation of Trace-gases) is a fully Bayesian hierarchical statistical framework for flux inversion of trace gases from flask, in situ, and remotely ...sensed data. WOMBAT extends the conventional Bayesian synthesis framework through the consideration of a correlated error term, the capacity for online bias correction, and the provision of uncertainty quantification on all unknowns that appear in the Bayesian statistical model. We show, in an observing system simulation experiment (OSSE), that these extensions are crucial when the data are indeed biased and have errors that are spatio-temporally correlated. Using the GEOS-Chem atmospheric transport model, we show that WOMBAT is able to obtain posterior means and variances on non-fossil-fuel CO2 fluxes from Orbiting Carbon Observatory-2 (OCO-2) data that are comparable to those from the Model Intercomparison Project (MIP) reported in Crowell et al. (2019). We also find that WOMBAT's predictions of out-of-sample retrievals obtained from the Total Column Carbon Observing Network (TCCON) are, for the most part, more accurate than those made by the MIP participants.
Abstract Tropical lands play an important role in the global carbon cycle yet their contribution remains uncertain owing to sparse observations. Satellite observations of atmospheric carbon dioxide ...(CO 2 ) have greatly increased spatial coverage over tropical regions, providing the potential for improved estimates of terrestrial fluxes. Despite this advancement, the spread among satellite‐based and in‐situ atmospheric CO 2 flux inversions over northern tropical Africa (NTA), spanning 0–24°N, remains large. Satellite‐based estimates of an annual source of 0.8–1.45 PgC yr −1 challenge our understanding of tropical and global carbon cycling. Here, we compare posterior mole fractions from the suite of inversions participating in the Orbiting Carbon Observatory 2 (OCO‐2) Version 10 Model Intercomparison Project (v10 MIP) with independent in‐situ airborne observations made over the tropical Atlantic Ocean by the National Aeronautics and Space Administration (NASA) Atmospheric Tomography (ATom) mission during four seasons. We develop emergent constraints on tropical African CO 2 fluxes using flux‐concentration relationships defined by the model suite. We find an annual flux of 0.14 ± 0.39 PgC yr −1 (mean and standard deviation) for NTA, 2016–2018. The satellite‐based flux bias suggests a potential positive concentration bias in OCO‐2 B10 and earlier version retrievals over land in NTA during the dry season. Nevertheless, the OCO‐2 observations provide improved flux estimates relative to the in situ observing network at other times of year, indicating stronger uptake in NTA during the wet season than the in‐situ inversion estimates.
Plain Language Summary Satellite carbon dioxide (CO 2 ) observations over land imply a major revision to our understanding of the global carbon cycle linked to large emissions from northern tropical Africa (NTA) during the dry season, from October to May. We use aircraft observations made over the Atlantic Ocean in four seasons to evaluate flux models driven by a range of ground and satellite observations. Our results show that models using satellite observations over land overestimate annual emissions from NTA by approximately 1 PgC yr −1 , concentrated in the dry season. At other times of year, satellite CO 2 observations provide improved estimates of NTA exchange, with a stronger CO 2 uptake during the wet season.
Key Points Emergent constraints derived from aircraft carbon dioxide (CO2) measurements and inversions estimate a near neutral northern tropical African CO2 budget Inversions using satellite observations overestimate annual emissions from northern tropical Africa (NTA) by approximately 1 PgC yr−1 Satellite CO2 observations imply a strong sink during the wet season over NTA
Tropical lands play an important role in the global carbon cycle yet their contribution remains uncertain owing to sparse observations. Satellite observations of atmospheric carbon dioxide (CO2) have ...greatly increased spatial coverage over tropical regions, providing the potential for improved estimates of terrestrial fluxes. Despite this advancement, the spread among satellite‐based and in‐situ atmospheric CO2 flux inversions over northern tropical Africa (NTA), spanning 0–24°N, remains large. Satellite‐based estimates of an annual source of 0.8–1.45 PgC yr−1 challenge our understanding of tropical and global carbon cycling. Here, we compare posterior mole fractions from the suite of inversions participating in the Orbiting Carbon Observatory 2 (OCO‐2) Version 10 Model Intercomparison Project (v10 MIP) with independent in‐situ airborne observations made over the tropical Atlantic Ocean by the National Aeronautics and Space Administration (NASA) Atmospheric Tomography (ATom) mission during four seasons. We develop emergent constraints on tropical African CO2 fluxes using flux‐concentration relationships defined by the model suite. We find an annual flux of 0.14 ± 0.39 PgC yr−1 (mean and standard deviation) for NTA, 2016–2018. The satellite‐based flux bias suggests a potential positive concentration bias in OCO‐2 B10 and earlier version retrievals over land in NTA during the dry season. Nevertheless, the OCO‐2 observations provide improved flux estimates relative to the in situ observing network at other times of year, indicating stronger uptake in NTA during the wet season than the in‐situ inversion estimates.
Plain Language Summary
Satellite carbon dioxide (CO2) observations over land imply a major revision to our understanding of the global carbon cycle linked to large emissions from northern tropical Africa (NTA) during the dry season, from October to May. We use aircraft observations made over the Atlantic Ocean in four seasons to evaluate flux models driven by a range of ground and satellite observations. Our results show that models using satellite observations over land overestimate annual emissions from NTA by approximately 1 PgC yr−1, concentrated in the dry season. At other times of year, satellite CO2 observations provide improved estimates of NTA exchange, with a stronger CO2 uptake during the wet season.
Key Points
Emergent constraints derived from aircraft carbon dioxide (CO2) measurements and inversions estimate a near neutral northern tropical African CO2 budget
Inversions using satellite observations overestimate annual emissions from northern tropical Africa (NTA) by approximately 1 PgC yr−1
Satellite CO2 observations imply a strong sink during the wet season over NTA
Daily precipitation has an enormous impact on human activity, and the study of how it varies over time and space, and what global indicators influence it, is of paramount importance to Australian ...agriculture. We analyze over 294 million daily rainfall measurements since 1876, spanning 17,606 sites across continental Australia. The data are not only large but also complex, and the topic would benefit from a common and publicly available statistical framework. We propose a Bayesian hierarchical mixture model that accommodates mixed discrete-continuous data. The observational level describes site-specific temporal and climatic variation via a mixture-of-experts model. At the next level of the hierarchy, spatial variability of the mixture weights’ parameters is modeled by a spatial Gaussian process prior. A parallel and distributed Markov chain Monte Carlo sampler is developed which scales the model to large data sets. We present examples of posterior inference on the mixture weights, monthly intensity levels, daily temporal dependence, offsite prediction of the effects of climate drivers and long-term rainfall trends across the entire continent. Computer code implementing the methods proposed in this paper is available as an R package.
Abstract
The magnitude and distribution of China's terrestrial carbon sink remain uncertain due to insufficient observational constraints; satellite column‐average dry‐air mole fraction carbon ...dioxide (XCO
2
) retrievals may fill some of this gap. Here, we estimate China's carbon sink using atmospheric inversions of the Orbiting Carbon Observatory 2 (OCO‐2) XCO
2
retrievals within different platforms, including the Global Carbon Assimilation System (GCAS) v2, the Copernicus Atmosphere Monitoring Service, and the OCO‐2 Model Inter‐comparison Project (MIP). We find that they consistently place the largest net biome production (NBP) in the south on an annual basis compared to the northeast and other main agricultural areas during peak growing season, coinciding well with the distribution of forests and crops, respectively. Moreover, the mean seasonal cycle amplitude of NBP in OCO‐2 inversions is obviously larger than that of biosphere model simulations and slightly greater than surface CO
2
inversions. More importantly, the mean seasonal cycle of the OCO‐2 inversions is well constrained in the temperate, tropical, and subtropical monsoon climate zones, with better inter‐model consistency at a sub‐regional scale compared to in situ inversions and biosphere model simulations. In addition, the OCO‐2 inversions estimate the mean annual NBP in China for 2015–2019 to be between 0.34 (GCASv2) and 0.47 ± 0.16 PgC/yr (median ± std; OCO‐2 v10 MIP), and indicate the impacts of climate extremes (e.g., the 2019 drought) on the interannual variations of NBP. Our results suggest that assimilating OCO‐2 XCO
2
retrievals is crucial for improving our understanding of China's terrestrial carbon sink regime.
Plain Language Summary
The magnitude and distribution of China's terrestrial carbon sink remain underconstrained; satellite column‐average dry‐air mole fraction carbon dioxide (XCO
2
) retrievals from NASA's Carbon Observatory 2 (OCO‐2) could help reduce this uncertainty. This study revisited China's terrestrial carbon sink estimates based on state‐of‐the‐art OCO‐2 XCO
2
inversions, including the Global Carbon Assimilation System OCO‐2 inversion, the Copernicus Atmosphere Monitoring Service OCO‐2 inversion, and those in the OCO‐2 Model Inter‐comparison Project. We found that the assimilation of OCO‐2 XCO
2
retrievals offers effective constraints on the spatiotemporal patterns of the terrestrial carbon sink of China. This result suggests that the OCO‐2 XCO
2
inversions allow an improved understanding of China's land carbon sink over in situ CO
2
inversions and bottom‐up biosphere model simulations, including better representations in spatial distributions and seasonal cycles and more plausible interannual variations. These improvements suggest that the assimilation of OCO‐2 XCO
2
retrievals offers effective constraints on the spatiotemporal patterns of the terrestrial carbon sink of China.
Key Points
Orbiting Carbon Observatory 2 (OCO‐2) inversions reveal the largest carbon sink in China is in the south on an annual basis, while in the northeast during peak growing season
The seasonal cycle appears to be well constrained in the monsoon climate zones
OCO‐2 inversions are able to capture the impacts of climate extremes on China's carbon sink interannual variability
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