Search

The constellation of Earth-observing satellites has now produced atmospheric greenhouse gas concentration estimates covering a period of several years. Their global coverage is providing additional information on the global carbon cycle. These products can be combined with complex inversion systems to infer the magnitude of carbon sources and sinks around the globe. Multiple factors, including the atmospheric transport model and satellite product aggregation method, can impact such flux estimates. Analysis of variance (ANOVA) is a well-established statistical framework for estimating common signals while partitioning variability across factors in the analysis of experiments. Functional ANOVA extends this approach with a statistical model that incorporates spatiotemporal correlation for each ANOVA component. The approach is illustrated on inversion experiments with different satellite retrieval aggregation methods and identifies consistent significant patterns in flux increments that span large spatial scales. Functional ANOVA identifies these patterns while accounting for the uncertainty at small spatial scales that is attributed to differences in the aggregation method. Functional ANOVA is also applied to a recent flux model intercomparison project (MIP), and the relative magnitudes of inversion system effects and data source (satellite versus in situ) are similar but exhibit slightly different importance for fluxes over different continents. In all examples, the unexplained residual variability is locally sizable in magnitude but with limited spatial and temporal correlation. These common behaviors across flux inversion experiments demonstrate the diagnostic capability for functional ANOVA to simultaneously distinguish the spatiotemporal coherence of carbon cycle processes and algorithmic factors. [ABSTRACT FROM AUTHOR]

The constellation of Earth-observing satellites now produces atmospheric greenhouse gas concentration estimates across multiple years. Their global coverage is providing additional information on the global carbon cycle. These products are combined with complex inversion systems to infer the magnitude of carbon sources and sinks around the globe. Multiple factors, including the atmospheric transport model and satellite product aggregation method, can impact flux estimates. Functional analysis of variance (ANOVA) invokes a spatio-temporal statistical model to efficiently estimate common flux signals across multiple inversions, and partitions variability across the discrete factors considered. The approach is illustrated on inversion experiments with different satellite retrieval aggregation methods and identifies significant flux anomalies in the presence of mode differences across aggregation methods. Functional ANOVA is also applied to a recent flux model intercomparison project (MIP), and the relative magnitudes of transport model effects and data source (satellite versus in situ) are similar but exhibit slightly different importance for inversions over different continents. [ABSTRACT FROM AUTHOR]

Remote Visible/Shortwave Infrared (VSWIR) imaging spectroscopy is a powerful tool for measuring the composition of Earth's surface over wide areas. This compositional information is captured by the spectral surface reflectance, where distinct shapes and absorption features indicate the chemical, bio- and geophysical properties of the materials in the scene. Estimating this surface reflectance requires removing the influence of atmospheric distortions caused by water vapor and particles. Traditionally reflectance is estimated by considering one location at a time, disentangling atmospheric and surface effects independently at all locations in a scene. However, this approach does not take advantage of spatial correlations between contiguous pixels. We propose an extension to a common Bayesian approach, Optimal Estimation, by introducing atmospheric correlations into the multivariate Gaussian prior. We show how this approach can be implemented as a small change to the traditional estimation procedure, thus limiting the additional computational burden. We demonstrate a simple version of the technique using simulations and multiple airborne radiance data sets. Our results show that the predicted atmospheric fields are smoother and more realistic than independent inversions given the assumption of spatial correlation and may reduce bias in the surface reflectance retrievals compared to post-process smoothing. [ABSTRACT FROM AUTHOR]

Soil moisture is spatially variable due to complex interactions between geologic, topographic, vegetation, and atmospheric variables. Correct representation of subgrid soil moisture variability is crucial in improving land surface modeling schemes and remote sensing retrievals. In addition to the mean structure, the variance and correlation of soil moisture are affected by the underlying land surface heterogeneity. This often violates the underlying assumption of stationarity/isotropy made by classical geostatistical models. The present study proposes a geostatistical framework to predict and upscale soil moisture in a nonstationary setting using a flexible spatial model whose variance/correlation structure varies with changing land surface characteristics. The proposed framework is applied to model soil moisture distribution using in situ data in the Red River watershed in Southern Manitoba, Canada. It is seen that both the variance and correlation structure exhibits spatial nonstationarity for the given surface heterogeneity driven primarily by vegetation and soil texture. At the beginning of the crop season, soil texture plays a critical role in the drying cycle by decreasing variance and increasing correlation as the soil becomes drier. Once the crops begin to mature, vegetation becomes the dominant driver, promoting spatial correlation and reducing SM variance. We upscale our point scale soil moisture predictions to the airborne extent (∼1.5 km) and find that the upscaled soil moisture agrees well with the observed airborne data with root‐mean‐square error values ranging from 0.04 to 0.08 (v/v). The proposed framework can be used to predict and upscale soil moisture in heterogeneous environments. Plain Language Summary: Soil moisture (SM) is a critical variable governing the global water and energy cycles. Understanding how SM varies in space is therefore critical. This spatial variation of SM can be typically defined by three statistical quantities: mean (average value), variance (how far the individual SM values are from the average value), and correlation (how individual SM values are related to each other). Variance/correlation of SM are typically assumed to be constant in traditional geostatistics methods. This is a major shortcoming because it has been well established that land surface characteristics such as soil, vegetation, and topography affects the spatial variability of SM. In this study, we propose a framework that accounts for the effect of these characteristics on the variance/correlation of SM. We apply our framework to a watershed in Manitoba, Canada, and find that our framework performs significantly better than the traditional method. We find that soil texture and vegetation affect SM distribution at different stages of crop growth. We aggregate our point scale SM predictions to 1.5‐km (airborne) scale and find that our predictions mimic observed SM data at this scale. We conclude that our framework can be used to predict and aggregate SM using surface data. Key Points: Proposed a framework to assess spatial nonstationarity of soil moistureOptimal prediction and upscaling of soil moisture under nonstationarityQuantified the effects of soil texture and vegetation on the spatial variance/correlation of soil moisture [ABSTRACT FROM AUTHOR]

The use of satellite measurements in climate studies promises many new scientific insights if those data can be efficiently exploited. Due to sparseness of daily data sets, there is a need to fill spatial gaps and to borrow strength from adjacent days. Nonetheless, these satellites are typically capable of conducting on the order of 100,000 retrievals per day, which makes it impossible to apply traditional spatio-temporal statistical methods, even in supercomputing environments. To overcome these challenges, we make use of a spatio-temporal mixed-effects model. For each massive daily data set, dimension reduction is achieved by essentially modelling the underlying process as a linear combination of spatial basis functions on the globe. The application of a dynamical autoregressive model in time, over the reduced space, allows rapid sequential computation of optimal smoothing predictions via the Kalman smoother; this is known as Fixed Rank Smoothing (FRS). The dimension-reduced mixed-effects model contains a number of unknown parameters, including covariance and propagator matrices, which describe the spatial and temporal dependence structure in the reduced-dimensional process. We take an empirical-Bayes approach to inference, which involves estimating the parameters and substituting them into the optimal predictors. Method-of-moments (MM) parameter estimation (currently used in FRS) is typically inefficient compared to maximum likelihood (ML) estimation and can result in large sampling variability. Here, we develop ML estimation via an expectation-maximization (EM) algorithm, which offers stable computation of valid estimators and makes efficient use of spatial and temporal dependence in the data. The two parameter-estimation approaches, MM and ML, are compared in a simulation study. We also apply our methodology to global satellite CO measurements: We optimally smooth the sparse daily CO maps obtained by the Atmospheric InfraRed Sounder (AIRS) instrument on the Aqua satellite; then, using FRS with EM-estimated parameters, a complete sequence of the daily global CO fields can be obtained, together with their associated prediction uncertainties. [ABSTRACT FROM AUTHOR]