arXiv subjects

Siem Jan Koopman

Publications and source records attributed to Siem Jan Koopman.

8 recordsLinked to original sources

arXiv2026

Auditing the Global Carbon Budget: Exploring the 2024--2025 Vintage Shift

The Global Carbon Budget (GCB), the community reference dataset for the carbon cycle, is reissued annually. The 2025 release introduces several adjustments to the published series that we compare with prior releases starting in 2017. On a common 1959-2016 sample, the mean of the GCB budget imbalance jumps from within +/-0.17 GtC/yr of zero for every vintage 2017-2024 to 0.61 GtC/yr in 2025, the only vintage whose 95% confidence interval for the imbalance mean excludes zero. The size of the imbalance changes much less: its mean absolute value rises from 0.61 to 0.76 GtC/yr. It is the mean, the quantity the budget identity constrains, that moves. We document and explore this shift in two ways. First, we conduct a model-free analysis, where we attribute the shift to a new adjustment that places the published land sink 0.40 GtC/yr below its ensemble mean (the average of the underlying models), a smaller adjustment in the ocean sink in the opposite direction, and a change in the composition of the bookkeeping ensemble. Second, we consider a dynamic statistical GCB model augmented with climate covariates. Its parameters are estimated for every GCB vintage 2017-2025. The coefficients of atmospheric concentrations in the sink equations shift in opposite directions on the 2025 issue, mirroring the model-free findings. A constant in the budget equation, statistically unnecessary in every vintage from 2017-2024, is required in 2025 and is estimated at -0.59 (0.09) GtC/yr. There is a persistent drifting imbalance across the entire sample in the budget equation. Each of the three adjustments is documented in the 2025 release and rests on evidence about the component it corrects. Their joint effect is a budget that closes over the last ten years and carries a mean imbalance of 0.61 GtC/yr over the full record. We argue that this cost to the full sample outweighs the gain on the last ten years.

stat.AP↗

arXiv2026

Neural networks for nonlinear regression with serially correlated disturbances: Evidence from cloud cover

We propose a new treatment of nonlinear regression with serially correlated disturbances that incorporates autoregressive moving average structures into feedforward neural networks. The resulting model provides an alternative to modeling temporal dependence using lagged variables. In simulations, the proposed method accurately recovers regression functions of varying complexity and the underlying error dynamics across a range of time-series lengths and signal-to-noise ratios. Finite-sample properties and out-of-sample predictive performances are shown to be robust to model misspecification induced by omitted lagged variables and incorrect specification of the error dynamics. Cloud cover is an important factor in climate projections. In an empirical study of cloud cover prediction for a grid of locations within and around the Mediterranean Sea, our proposed model yields more accurate predictions than existing methods, including long short-term memory networks. Serially correlated disturbances in place of lagged variables improve predictive accuracy across a range of land and ocean environments. Improvements over linear models with serially correlated disturbances are particularly pronounced in mountain areas, consistent with the presence of stronger nonlinear effects in cloud formation in such regions.

econ.EM↗

arXiv2026

Continuous-time state-space methods for d18O and d13C in the Cenozoic Era

Time series analysis of d18O and d13C from benthic foraminifera for paleoclimatology poses significant challenges. The data span tens of millions of years, with sparse early records, dense later ones, uneven time stamps, and occasional multiples. These time series are largely non-stationary, exhibiting temporary, varying trends. We propose a continuous-time state space framework that handles these irregularities effectively. Univariate signal-plus-noise models are specified for d18O and d13C, with parameters estimated via maximum likelihood using Kalman filter recursions for signal extraction and likelihood evaluation. The framework interprets state space models as time-domain Butterworth filters. Measurement-error variances are differentiated by deep-sea drill site, including site-specific level offsets, and the record is partitioned into sub-periods reflecting the distinct climate states that drive the transition variance. Two extensions of the univariate model are explored: (i) modifying the signal specification for the Kalman filter to approximate a Butterworth filter of any order, and (ii) specifying a bivariate signal-plus-noise model for joint analysis. Results reveal substantial signal changes during the ``icehouse'' period (3.3 to 0.0006 Ma); the correlation between d18O and d13C signals is generally positive but turns negative during this period.

stat.AP↗

arXiv2026

Continuous-time state space analysis of d18O, d13C, and CO2 in the Cenozoic Era

We develop a continuous-time state-space framework for the joint reconstruction of three Cenozoic climate proxies, benthic foraminiferal d18O and d13C and atmospheric CO2, from irregularly and unevenly sampled multi-site, multi-method data spanning the last 67 million years. The latent signals follow a trivariate random walk in continuous time; the measurement equation differentiates the error variance by drill site for the isotopes and by proxy group for CO2, with bias intercepts placing all sources on a common scale, and the transition equation lets the innovation covariance and a deterministic La2004 Milankovitch forcing depend on the prevailing climate state. All parameters are estimated by maximum likelihood through the Kalman filter with diffuse initialization. The estimated cross-proxy correlations reverse sign between the early Cenozoic greenhouse and the icehouse, the orbital sensitivity of the isotopes strengthens as continental ice sheets grow, and the reconstructed CO2 path, reported with calibrated confidence bands, places the atmospheric CO$_2$ thresholds of the major Cenozoic glaciations in relation to present-day concentrations.

stat.AP↗

arXiv2024

Estimating breakpoints between climate states in the Cenozoic Era

This study presents a statistical time-domain approach for identifying transitions between climate states, referred to as breakpoints, using well-established econometric tools. We analyze a 67.1 million year record of the oxygen isotope ratio delta-O-18 derived from benthic foraminifera. The dataset is presented in Westerhold et al. (2020), where the authors use recurrence analysis to identify six climate states. Fixing the number of breakpoints to five, our procedure results in breakpoint estimates that closely align with those identified by Westerhold et al. (2020). By treating the number of breakpoints as a parameter to be estimated, we provide the statistical justification for more than five breakpoints in the time series. Further, our approach offers the advantage of constructing confidence intervals for the breakpoints, and it allows for testing the number of breakpoints present in the time series.

stat.AP↗

arXiv2024

A Regression-Based Approach to the CO2 Airborne Fraction: Enhancing Statistical Precision and Tackling Zero Emissions

The global fraction of anthropogenically emitted carbon dioxide (CO$_2$) that stays in the atmosphere, the CO$_2$ airborne fraction, has been fluctuating around a constant value over the period 1959 to 2022. The consensus estimate of the airborne fraction is around $44\%$; the remaining $56\%$ is absorbed by the oceanic and terrestrials biospheres. In this study, we show that the conventional estimator of the airborne fraction, based on a ratio of changes in atmospheric CO$_2$ concentrations and CO$_2$ emissions, suffers from a number of statistical deficiencies, such as non-existence of moments and a non-Gaussian limiting distribution. We propose an alternative regression-based estimator of the airborne fraction that does not suffer from these deficiencies. We show that the regression-based estimator has a Gaussian limiting distribution and reduces estimation uncertainty substantially. Our empirical analysis leads to an estimate of the airborne fraction over 1959--2022 of $47.0\%$ ($\pm 1.1\%$; $1 σ$), implying a higher, and better constrained, estimate than the current consensus. Using climate model output, we show that a regression-based approach provides sensible estimates of the airborne fraction, also in future scenarios where emissions are at or near zero.

stat.AP↗

arXiv2024

A Statistical Reduced Complexity Climate Model for Probabilistic Analyses and Projections

We propose a new statistical reduced complexity climate model. The centerpiece of the model consists of a set of physical equations for the global climate system which we show how to cast in non-linear state space form. The parameters in the model are estimated using the method of maximum likelihood with the likelihood function being evaluated by the extended Kalman filter. Our statistical framework is based on well-established methodology and is computationally feasible. In an empirical analysis, we estimate the parameters for a data set comprising the period 1959-2022. A likelihood ratio test sheds light on the most appropriate equation for converting the level of atmospheric concentration of carbon dioxide into radiative forcing. Using the estimated model, and different future paths of greenhouse gas emissions, we project global mean surface temperature until the year 2100. Our results illustrate the potential of combining statistical modelling with physical insights to arrive at rigorous statistical analyses of the climate system.

stat.AP↗

arXiv2023

Is there evidence of a trend in the CO2 airborne fraction?

In a paper recently published in this journal, van Marle et al. (van Marle et al., 2022) introduce an interesting new data set for land use and land cover change CO2 emissions (LULCC) that they use to study whether a trend is present in the airborne fraction (AF), defined as the fraction of CO2 emissions remaining in the atmosphere. Testing the hypothesis of a trend in the AF has attracted much attention, with the overall consensus that no statistical evidence is found for a trend in the data (Knorr, 2009; Gloor et al., 2010; Raupach et al., 2014; Bennedsen et al., 2019). In their paper, van Marle et al. analyze the AF as implied by three different LULCC emissions time series (GCP, H&N, and their new data series). In a Monte Carlo simulation study based on their new LULCC emissions data, van Marle et al. find evidence of a declining trend in the AF. In this note, we argue that the statistical analysis presented in van Marle et al. can be improved in several respects. Specifically, the Monte Carlo study presented in van Marle et al. is not conducive to determine whether there is a trend in the AF. Further, we re-examine the evidence for a trend in the AF by using a variety of different statistical tests. The statistical evidence for an uninterrupted (positive or negative) trend in the airborne fraction remains mixed at best. When allowing for a break in the trend, there is some evidence for upward trends in both subsamples.

stat.AP↗