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Instrumental global temperature records are derived from the network of in situ measurements of land and sea surface temperatures. This observational evidence is seen as being fundamental to climate science. Therefore, the accuracy of these measurements is of prime importance for the analysis of temperature variability. There are spatial gaps in the distribution of instrumental temperature measurements across the globe. This lack of spatial coverage introduces coverage error. An approximate Bayesian computation based multi-resolution lattice kriging is developed and used to quantify the coverage errors through the variance of the spatial process at multiple spatial scales. It critically accounts for the uncertainties in the parameters of this advanced spatial statistics model itself, thereby providing, for the first time, a full description of both the spatial coverage uncertainties along with the uncertainties in the modeling of these spatial gaps. These coverage errors are combined with the existing estimates of uncertainties due to observational issues at each station location. It results in an ensemble of 100 000 monthly temperatures fields over the entire globe that samples the combination of coverage, parametric and observational uncertainties from 1850 to 2018 over a 5∘×5∘ grid.

Total column ozone variations estimated using ground-based stations provide important independent source of information in addition to satellite-based estimates. This estimation has been vigorously challenged by data inhomogeneity in time and by the irregularity of the spatial distribution of stations, as well as by interruptions in observation records. Furthermore, some stations have calibration issues and thus observations may drift. In this paper we compare the spatial interpolation of ozone levels using the novel stochastic partial differential equation (SPDE) approach with the covariance-based kriging. We show how these new spatial predictions are more accurate, less uncertain and more robust. We construct long-term zonal means to investigate the robustness against the absence of measurements at some stations as well as instruments drifts. We conclude that time series analyzes can benefit from the SPDE approach compared to the covariance-based kriging when stations are missing, but the positive impact of the technique is less pronounced in the case of drifts.

Downscaling is a technique that is used to extract high-resolution information from regional scale variables produced by coarse resolution models such as Chemical Transport Models (CTMs). Statistical downscaling methods in geophysics often rely on Empirical Orthogonal Functions (EOFs). EOFs are spatial Principal Components (PCs) that display space-time modes of variability of a quantity over a region. Here we present a novel statistical downscaling method that employs Fitted Empirical Orthogonal Functions (F-EOFs) to provide local forecasts. F-EOFs differ from EOFs in that they represent space-time variations associated with a particular location through the use of inverse regression. We illustrate our downscaling method, for ozone levels over the US, with the Regional chEmical trAnsport Model (REAM) whose outputs are over 70 by 70 km grid cells. We use ground level ozone observations from monitoring stations within the south-eastern US region to downscale REAM. We select the first leading F-EOFs and regress our observations on the corresponding F-EOF loadings. We also compare our results to linear regression and PC regression. The regression on F-EOFs shows the best predictive ability. To examine the consistency of our results we repeat the analysis for different fitting and validation periods. Furthermore, in our application, PFC regression also outperforms PC regression as a dimension reduction technique.

The Regional Air Quality forecAST (RAQAST) model is a regional chemical transport modeling system for ozone and its precursors over the United States. Since the grid size is 70 by 70 km, forecasts cannot be made for a specific surface site. We use EPA monitoring stations from the Atlanta area to downscale and improve local forecasts using RAQAST outputs. We use the Model Diagnostic and Correction (MDC) approach. First, we regress the observations on the model outputs with an autoregressive noise component. Second, we regress the residuals of this first regression on variables associated with wind speed, precipitation amounts and the diurnal cycle. Deficiencies of 3-D model results are identified and corrected. Evaluation using measurements for a different period confirms that the statistically adjusted outputs reduce forecast errors by up to 25%.

In this paper, we introduce a statistical method for examining and adjusting chemical-transport models. We illustrate the findings with total column ozone predictions, based on the University of Illinois at Urbana-Champaign 2-D (UIUC 2-D) chemical-transport model of the global atmosphere. We propose a general diagnostic procedure for the model outputs in total ozone over the latitudes ranging from 60° South to 60° North to see if the model captures some typical patterns in the data. The method proceeds in two steps to avoid possible collinearity issues. First, we regress the measurements given by a cohesive data set from the SBUV(/2) satellite system on the model outputs with an autoregressive noise component. Second, we regress the residuals of this first regression on the solar flux, the annual cycle, the Antarctic or Arctic Oscillation, and the Quasi Biennial Oscillation. If the coefficients from this second regression are statistically significant, then they mean that the model did not simulate properly the pattern associated with these factors. Systematic anomalies of the model are identified using data from 1979 to 1995, and statistically corrected afterwards. The 1996–2003 validation sample confirms that the combined approach yields better predictions than the direct UIUC 2-D outputs.

This paper is devoted to the modeling of altitude-dependent patterns of ozone variations over time. Umkehr ozone profiles (quarter of Umkehr layer) from 1978 to 2011 are investigated at two locations: Boulder (USA) and Arosa (Switzerland). The study consists of two statistical stages. First we approximate ozone profiles employing an appropriate basis. To capture primary modes of ozone variations without losing essential information, a functional principal component analysis is performed. It penalizes roughness of the function and smooths excessive variations in the shape of the ozone profiles. As a result, data-driven basis functions (empirical basis functions) are obtained. The coefficients (principal component scores) corresponding to the empirical basis functions represent dominant temporal evolution in the shape of ozone profiles. We use those time series coefficients in the second statistical step to reveal the important sources of the patterns and variations in the profiles. We estimate the effects of covariates – month, year (trend), quasi-biennial oscillation, the solar cycle, the Arctic oscillation, the El Niño/Southern Oscillation cycle and the Eliassen–Palm flux – on the principal component scores of ozone profiles using additive mixed effects models. The effects are represented as smooth functions and the smooth functions are estimated by penalized regression splines. We also impose a heteroscedastic error structure that reflects the observed seasonality in the errors. The more complex error structure enables us to provide more accurate estimates of influences and trends, together with enhanced uncertainty quantification. Also, we are able to capture fine variations in the time evolution of the profiles, such as the semi-annual oscillation. We conclude by showing the trends by altitude over Boulder and Arosa, as well as for total column ozone. There are great variations in the trends across altitudes, which highlights the benefits of modeling ozone profiles.

[1] One major question that arises with the implementation of the Montreal Protocol and its subsequent conventions is our ability to determine that an ozone “recovery” is in process. Toward this we have utilized a statistical model suggested by Reinsel et al. (2002) that utilizes the idea of a trend and a trend change at a specific time and applied it to 12 ozonesonde stations in the midlatitudes of the Northern Hemisphere. The lower stratosphere, in particular, is of significance as this is where the ozone concentration is a maximum and also where heterogeneous ozone losses have been noted. This statistical methodology suffers, however, from the ambiguities of having to select a specific time for the ozone trend to change and the fact that the Mt Pinatubo volcanic aerosols impacted the ozone amount. Within this paper, we analyze the ozonesonde station data utilizing the above model but examine the statistical stability of the computed results by allowing the point of inflection to change from 1995 through 2000 and also exclude varying amounts of data from the post-Pinatubo period. The results indicate that while the impacts of deleting data and changing the inflection point are nontrivial, the overall results are consistent in that there has been a major change in the ozone trend in the time frame of 1996 and that a reasonable scenario is to utilize a change point in 1996 and exclude 2 years of data after the 1991 Mt. Pinatubo eruption. In addition, we include a term for the Arctic oscillation within the statistical model and demonstrate that it is statistically significant.

[1] Since the implementation of the international controls on ozone-depleting chemicals, an important focus in studies of stratospheric ozone has been on the detection of a turnaround in the downward trend. The usual statistical assumption of a piecewise linear representation of the trend does not account for the chemistry involved. Because the actual change is not expected to be piecewise linear, we model the trend using results from a University of Illinois at Urbana-Champaign two-dimensional (UIUC 2-D) chemical transport model of the global atmosphere. As part of the analysis, ozone observations are considered in the spectral domain using a cohesive data set from the SBUV-SBUV/2 satellite system at northern midlatitudes. In this study we find that the new model is better at capturing the long-range correlation of the data than assuming a linear trend. We also compare several statistical trend models, based either on a regression on a linear trend or on the Effective Equivalent Stratospheric Chlorine (EESC). Including a constant halocarbon emissions run of the UIUC 2-D model in the regression, the controlled EESC approach shows the best fit. The smallest future data length necessary to detect a recovery with a certain probability is obtained in this latter case.