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Solar-induced chlorophyll fluorescence, or SIF, is a part of the natural process of photosynthesis. SIF can be measured from space by instruments such as the Orbiting Carbon Observatory-2 (OCO-2), making it a useful proxy for monitoring gross primary production (GPP), which is a critical component of Earth’s carbon cycle. The complex physical relationship between SIF and GPP is frequently studied using OCO-2 observations of SIF since they offer the finest spatial resolution available. However, measurement error (noise) and large gaps in spatial coverage limit the use of OCO-2 SIF to highly aggregated scales. To study the relationship between SIF and GPP across varying spatial scales, de-noised and gap-filled (i.e., Level 3) SIF data products are needed. Using a geostatistical methodology called cokriging, which includes kriging as a special case, we develop coSIF: a Level 3 SIF data product at a 0.05-degree resolution. As a natural secondary variable for cokriging, OCO-2 observes column-averaged atmospheric carbon dioxide concentrations (XCO2) simultaneously with SIF. There is a suggested lagged spatio-temporal dependence between SIF and XCO2, which we characterize through spatial covariance and cross-covariance functions. Our approach is highly parallelizable and accounts for non-stationary measurement errors in the observations. Importantly, each datum in the resulting coSIF data product is accompanied by a measure of uncertainty. Extant approaches do not provide formal uncertainty quantification, nor do they leverage the cross-dependence with XCO2.

Arctic sea ice extent (SIE) has drawn increasing attention from scientists in recent years because of its fast decline in the Boreal summer and early fall. The measurement of SIE is derived from remote sensing data and is both a lagged and leading indicator of climate change. To characterize at a local level the decline in SIE, we use remote-sensing data at 25 km resolution to fit a spatio-temporal logistic autoregressive model of the sea-ice evolution in the Arctic region. The model incorporates last year’s ice/water binary observations at nearby grid cells in an autoregressive manner with autoregressive coefficients that vary both in space and time. Using the model-based estimates of ice/water probabilities in the Arctic region, we propose several graphical summaries to visualize the spatio-temporal changes in Arctic sea ice beyond what can be visualized with the single time series of SIE. In ever-higher latitude bands, we observe a consistently declining temporal trend of sea ice in the early fall. We also observe a clear decline in and contraction of the sea ice’s distribution between 70∘N–75∘N, and of most concern is that this may reflect the future behavior of sea ice at ever-higher latitudes under climate change.

FRK is an R software package for spatial/spatio-temporal modeling and prediction with large datasets. It facilitates optimal spatial prediction (kriging) on the most commonly used manifolds (in Euclidean space and on the surface of the sphere), for both spatial and spatio-temporal fields. It differs from many of the packages for spatial modeling and prediction by avoiding stationary and isotropic covariance and variogram models, instead constructing a spatial random effects (SRE) model on a fine-resolution discretized spatial domain. The discrete element is known as a basic areal unit (BAU), whose introduction in the software leads to several practical advantages. The software can be used to (i) integrate multiple observations with different supports with relative ease; (ii) obtain exact predictions at millions of prediction locations (without conditional simulation); and (iii) distinguish between measurement error and fine-scale variation at the resolution of the BAU, thereby allowing for reliable uncertainty quantification. The temporal component is included by adding another dimension. A key component of the SRE model is the specification of spatial or spatio-temporal basis functions; in the package, they can be generated automatically or by the user. The package also offers automatic BAU construction, an expectation-maximization (EM) algorithm for parameter estimation, and functionality for prediction over any user-specified polygons or BAUs. Use of the package is illustrated on several spatial and spatio-temporal datasets, and its predictions and the model it implements are extensively compared to others commonly used for spatial prediction and modeling.

Carbon-climate feedbacks, which amplifies or attenuates atmospheric CO _2 from fossil fuel emissions, are one of the largest sources of uncertainty in climate projections. However, these feedbacks depend both on temperature and its coupling to water and energy cycles, especially in the tropics. We show that atmospheric aridity—quantified as vapor pressure deficit (VPD)—is a good proxy for this coupling. Tropical VPD is strongly correlated to the global CO _2 growth rate (CGR) with observed present-day sensitivities of −2.5 ± 0.4 GtC mb ^−1 yr ^−1 . The sensitivity of CGR to tropical VPD interannual variability has increased by a factor of 1.7 ± 0.3 in the 21st century. A combination of causality and statistical analysis point to mechanistic moisture drivers of the VPD–CGR sensitivities, independent of temperature. Observational records provide evidence that tropical atmospheric aridity is linked to both water deficit and spatially correlated with evaporative fraction suggesting that CGR variability is indirectly driven by land—atmosphere coupling (compound soil and atmospheric drought). This coupling is manifest as a kind of carbon-climate feedback in CMIP6 Earth System Models where long–term increases in tropical VPD reduce tropical carbon storage but with a substantial inter-model range [−1.4 to −59.4 GtC mb ^−1 ]. However, by employing a hierarchical emergent constraint, the best estimate of atmospheric aridity—carbon cycle feedback ( φ _TL ) is $-19\ \pm$ 10 GtC mb ^−1 , which is 28% lower than model estimates with an uncertainty reduction of 50%. Our results bridge the role of moisture and land–atmosphere coupling on net carbon variability to the vulnerability of carbon storage in a changing climate.

The SAR model is widely used in spatial econometrics to model Gaussian processes on a discrete spatial lattice, but for large datasets, fitting it becomes computationally prohibitive, and hence, its usefulness can be limited. A computationally-efficient spatial model is the spatial random effects (SRE) model, and in this article, we calibrate it to the SAR model of interest using a generalisation of the Moran operator that allows for heteroskedasticity and an asymmetric SAR spatial dependence matrix. In general, spatial data have a measurement-error component, which we model, and we use restricted maximum likelihood to estimate the SRE model covariance parameters; its required computational time is only the order of the size of the dataset. Our implementation is demonstrated using mean usual weekly income data from the 2011 Australian Census.

Satellite remote sensing of trace gases such as carbon dioxide (CO2) has increased our ability to observe and understand Earth’s climate. However, these remote sensing data, specifically Level 2 retrievals, tend to be irregular in space and time, and hence, spatio-temporal prediction is required to infer values at any location and time point. Such inferences are not only required to answer important questions about our climate, but they are also needed for validating the satellite instrument, since Level 2 retrievals are generally not co-located with ground-based remote sensing instruments. Here, we discuss statistical approaches to construct Level 3 products from Level 2 retrievals, placing particular emphasis on the strengths and potential pitfalls when using statistical prediction in this context. Following this discussion, we use a spatio-temporal statistical modelling framework known as fixed rank kriging (FRK) to obtain global predictions and prediction standard errors of column-averaged carbon dioxide based on Version 7r and Version 8r retrievals from the Orbiting Carbon Observatory-2 (OCO-2) satellite. The FRK predictions allow us to validate statistically the Level 2 retrievals globally even though the data are at locations and at time points that do not coincide with validation data. Importantly, the validation takes into account the prediction uncertainty, which is dependent both on the temporally-varying density of observations around the ground-based measurement sites and on the spatio-temporal high-frequency components of the trace gas field that are not explicitly modelled. Here, for validation of remotely-sensed CO2 data, we use observations from the Total Carbon Column Observing Network. We demonstrate that the resulting FRK product based on Version 8r compares better with TCCON data than that based on Version 7r, in terms of both prediction accuracy and uncertainty quantification.

Global maps of total-column carbon dioxide (CO2) mole fraction (in units of parts per million) are important tools for climate research since they provide insights into the spatial distribution of carbon intake and emissions as well as their seasonal and annual evolutions. Currently, two main remote sensing instruments for total-column CO2 are the Orbiting Carbon Observatory-2 (OCO-2) and the Greenhouse gases Observing SATellite (GOSAT), both of which produce estimates of CO2 concentration, called profiles, at 20 different pressure levels. Operationally, each profile estimate is then convolved into a single estimate of column-averaged CO2 using a linear pressure weighting function. This total-column CO2 is then used for subsequent analyses such as Level 3 map generation and colocation for validation. In principle, total-column CO2 in these applications may be more efficiently estimated by making optimal estimates of the vector-valued CO2 profiles and applying the pressure weighting function afterwards. These estimates will be more efficient if there is multivariate dependence between CO2 values in the profile. In this article, we describe a methodology that uses a modified Spatial Random Effects model to account for the multivariate nature of the data fusion of OCO-2 and GOSAT. We show that multivariate fusion of the profiles has improved mean squared error relative to scalar fusion of the column-averaged CO2 values from OCO-2 and GOSAT. The computations scale linearly with the number of data points, making it suitable for the typically massive remote sensing datasets. Furthermore, the methodology properly accounts for differences in instrument footprint, measurement-error characteristics, and data coverages.