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\"A comprehensive introduction to the most commonly used statistical methods relevant in atmospheric, oceanic and climate sciences. Each method is described step-by-step using plain language, and illustrated with concrete examples, with relevant statistical and scientific concepts explained as needed. Particular attention is paid to nuances and pitfalls, with sufficient detail to enable the reader to write relevant code. Topics covered include hypothesis testing, time series analysis, linear regression, data assimilation, extreme value analysis, Principal Component Analysis, Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. The specific statistical challenges that arise in climate applications are also discussed, including model selection problems associated with Canonical Correlation Analysis, Predictable Component Analysis, and Covariance Discriminant Analysis. Requiring no previous background in statistics, this is a highly accessible textbook and reference for students and early-career researchers in the climate sciences\"-- Provided by publisher.

Statistical Methods in the Atmospheric Sciences, Third Edition, explains the latest statistical methods used to describe, analyze, test, and forecast atmospheric data.This revised and expanded text is intended to help students understand and communicate what their data sets have to say, or to make sense of the scientific literature in.

Aerosol optical depth (AOD) has become a crucial metric for assessing global climate change. Although global and regional AOD trends have been studied extensively, it remains unclear what factors are driving the inter-decadal variations in regional AOD and how to quantify the relative contribution of each dominant factor. This study used a long-term (1980–2016) aerosol dataset from the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2) reanalysis, along with two satellite-based AOD datasets (MODIS/Terra and MISR) from 2001 to 2016, to investigate the long-term trends in global and regional aerosol loading. Statistical models based on emission factors and meteorological parameters were developed to identify the main factors driving the inter-decadal changes of regional AOD and to quantify their contribution. Evaluation of the MERRA-2 AOD with the ground-based measurements of AERONET indicated significant spatial agreement on the global scale (r= 0.85, root-mean-square error = 0.12, mean fractional error = 38.7 %, fractional gross error = 9.86 % and index of agreement = 0.94). However, when AOD observations from the China Aerosol Remote Sensing Network (CARSNET) were employed for independent verification, the results showed that MERRA-2 AODs generally underestimated CARSNET AODs in China (relative mean bias = 0.72 and fractional gross error =−34.3 %). In general, MERRA-2 was able to quantitatively reproduce the annual and seasonal AOD trends on both regional and global scales, as observed by MODIS/Terra, although some differences were found when compared to MISR. Over the 37-year period in this study, significant decreasing trends were observed over Europe and the eastern United States. In contrast, eastern China and southern Asia showed AOD increases, but the increasing trend of the former reversed sharply in the most recent decade. The statistical analyses suggested that the meteorological parameters explained a larger proportion of the AOD variability (20.4 %–72.8 %) over almost all regions of interest (ROIs) during 1980–2014 when compared with emission factors (0 %–56 %). Further analysis also showed that SO2 was the dominant emission factor, explaining 12.7 %–32.6 % of the variation in AOD over anthropogenic-aerosol-dominant regions, while black carbon or organic carbon was the leading factor over the biomass-burning-dominant (BBD) regions, contributing 24.0 %–27.7 % of the variation. Additionally, wind speed was found to be the leading meteorological parameter, explaining 11.8 %–30.3 % of the variance over the mineral-dust-dominant regions, while ambient humidity (including soil moisture and relative humidity) was the top meteorological parameter over the BBD regions, accounting for 11.7 %–35.5 % of the variation. The results of this study indicate that the variation in meteorological parameters is a key factor in determining the inter-decadal change in regional AOD.

Statistical downscaling of Global Climate Models (GCMs) allows researchers to study local climate change effects decades into the future. A wide range of statistical models have been applied to downscaling GCMs but recent advances in machine learning have not been explored compared to traditional approaches. In this paper, we compare five Perfect Prognosis (PP) approaches, Ordinary Least Squares, Elastic-Net, and Support Vector Machine along with two machine learning methods Multi-task Sparse Structure Learning (MSSL) and Autoencoder Neural Networks. In addition, we introduce a hybrid Model Output Statistics and PP approach by modeling the residuals of Bias Correction Spatial Disaggregation (BCSD) with MSSL. Metrics to evaluate each method’s ability to capture daily anomalies, large-scale climate shifts, and extremes are analyzed. Generally, we find inconsistent performance between PP methods in their ability to predict daily anomalies and extremes as well as monthly and annual precipitation. However, results suggest that L1 sparsity constraints aid in reducing error through internal feature selection. The MSSL+BCSD coupling, when compared with BCSD, improved daily, monthly, and annual predictability but decreased performance at the extremes. Hence, these results suggest that the direct application of state-of-the-art machine learning methods to statistical downscaling does not provide direct improvements over simpler, longstanding approaches.

Aerosol particles are a complex component of the atmospheric system which influence climate directly by interacting with solar radiation, and indirectly by contributing to cloud formation. The variety of their sources, as well as the multiple transformations they may undergo during their transport (including wet and dry deposition), result in significant spatial and temporal variability of their properties. Documenting this variability is essential to provide a proper representation of aerosols and cloud condensation nuclei (CCN) in climate models. Using measurements conducted in 2016 or 2017 at 62 ground-based stations around the world, this study provides the most up-to-date picture of the spatial distribution of particle number concentration (Ntot) and number size distribution (PNSD, from 39 sites). A sensitivity study was first performed to assess the impact of data availability on Ntot's annual and seasonal statistics, as well as on the analysis of its diel cycle. Thresholds of 50 % and 60 % were set at the seasonal and annual scale, respectively, for the study of the corresponding statistics, and a slightly higher coverage (75 %) was required to document the diel cycle. Although some observations are common to a majority of sites, the variety of environments characterizing these stations made it possible to highlight contrasting findings, which, among other factors, seem to be significantly related to the level of anthropogenic influence. The concentrations measured at polar sites are the lowest (∼ 102 cm−3) and show a clear seasonality, which is also visible in the shape of the PNSD, while diel cycles are in general less evident, due notably to the absence of a regular day–night cycle in some seasons. In contrast, the concentrations characteristic of urban environments are the highest (∼ 103–104 cm−3) and do not show pronounced seasonal variations, whereas diel cycles tend to be very regular over the year at these stations. The remaining sites, including mountain and non-urban continental and coastal stations, do not exhibit as obvious common behaviour as polar and urban sites and display, on average, intermediate Ntot (∼ 102–103 cm−3). Particle concentrations measured at mountain sites, however, are generally lower compared to nearby lowland sites, and tend to exhibit somewhat more pronounced seasonal variations as a likely result of the strong impact of the atmospheric boundary layer (ABL) influence in connection with the topography of the sites. ABL dynamics also likely contribute to the diel cycle of Ntot observed at these stations. Based on available PNSD measurements, CCN-sized particles (considered here as either >50 nm or >100 nm) can represent from a few percent to almost all of Ntot, corresponding to seasonal medians on the order of ∼ 10 to 1000 cm−3, with seasonal patterns and a hierarchy of the site types broadly similar to those observed for Ntot. Overall, this work illustrates the importance of in situ measurements, in particular for the study of aerosol physical properties, and thus strongly supports the development of a broad global network of near surface observatories to increase and homogenize the spatial coverage of the measurements, and guarantee as well data availability and quality. The results of this study also provide a valuable, freely available and easy to use support for model comparison and validation, with the ultimate goal of contributing to improvement of the representation of aerosol–cloud interactions in models, and, therefore, of the evaluation of the impact of aerosol particles on climate.

This study investigates the presence of trends in annual maximum daily precipitation time series obtained from a global dataset of 8326 high-quality land-based observing stations with more than 30 years of record over the period from 1900 to 2009. Two complementary statistical techniques were adopted to evaluate the possible nonstationary behavior of these precipitation data. The first was a Mann–Kendall nonparametric trend test, and it was used to evaluate the existence of monotonic trends. The second was a nonstationary generalized extreme value analysis, and it was used to determine the strength of association between the precipitation extremes and globally averaged near-surface temperature. The outcomes are that statistically significant increasing trends can be detected at the global scale, with close to two-thirds of stations showing increases. Furthermore, there is a statistically significant association with globally averaged near-surface temperature, with the median intensity of extreme precipitation changing in proportion with changes in global mean temperature at a rate of between 5.9% and 7.7% K−1, depending on the method of analysis. This ratio was robust irrespective of record length or time period considered and was not strongly biased by the uneven global coverage of precipitation data. Finally, there is a distinct meridional variation, with the greatest sensitivity occurring in the tropics and higher latitudes and the minima around 13°S and 11°N. The greatest uncertainty was near the equator because of the limited number of sufficiently long precipitation records, and there remains an urgent need to improve data collection in this region to better constrain future changes in tropical precipitation.

Epidemiological studies have consistently linked exposure to PM2.5 with adverse health effects. The oxidative potential (OP) of aerosol particles has been widely suggested as a measure of their potential toxicity. Several acellular chemical assays are now readily employed to measure OP; however, uncertainty remains regarding the atmospheric conditions and specific chemical components of PM2.5 that drive OP. A limited number of studies have simultaneously utilised multiple OP assays with a wide range of concurrent measurements and investigated the seasonality of PM2.5 OP. In this work, filter samples were collected in winter 2016 and summer 2017 during the atmospheric pollution and human health in a Chinese megacity campaign (APHH-Beijing), and PM2.5 OP was analysed using four acellular methods: ascorbic acid (AA), dithiothreitol (DTT), 2,7-dichlorofluorescin/hydrogen peroxidase (DCFH) and electron paramagnetic resonance spectroscopy (EPR). Each assay reflects different oxidising properties of PM2.5, including particle-bound reactive oxygen species (DCFH), superoxide radical production (EPR) and catalytic redox chemistry (DTT/AA), and a combination of these four assays provided a detailed overall picture of the oxidising properties of PM2.5 at a central site in Beijing. Positive correlations of OP (normalised per volume of air) of all four assays with overall PM2.5 mass were observed, with stronger correlations in winter compared to summer. In contrast, when OP assay values were normalised for particle mass, days with higher PM2.5 mass concentrations (µgm-3) were found to have lower mass-normalised OP values as measured by AA and DTT. This finding supports that total PM2.5 mass concentrations alone may not always be the best indicator for particle toxicity. Univariate analysis of OP values and an extensive range of additional measurements, 107 in total, including PM2.5 composition, gas-phase composition and meteorological data, provided detailed insight into the chemical components and atmospheric processes that determine PM2.5 OP variability. Multivariate statistical analyses highlighted associations of OP assay responses with varying chemical components in PM2.5 for both mass- and volume-normalised data. AA and DTT assays were well predicted by a small set of measurements in multiple linear regression (MLR) models and indicated fossil fuel combustion, vehicle emissions and biogenic secondary organic aerosol (SOA) as influential particle sources in the assay response. Mass MLR models of OP associated with compositional source profiles predicted OP almost as well as volume MLR models, illustrating the influence of mass composition on both particle-level OP and total volume OP. Univariate and multivariate analysis showed that different assays cover different chemical spaces, and through comparison of mass- and volume-normalised data we demonstrate that mass-normalised OP provides a more nuanced picture of compositional drivers and sources of OP compared to volume-normalised analysis. This study constitutes one of the most extensive and comprehensive composition datasets currently available and provides a unique opportunity to explore chemical variations in PM2.5 and how they affect both PM2.5 OP and the concentrations of particle-bound reactive oxygen species.

Precipitation has a strong and constant impact on different economic sectors, environment and social activities all over the world. An increasing interest for monitoring and estimating the precipitation characteristics can be claimed in the last decades. However, in some areas, the ground-based network is still sparse and the spatial data coverage insufficiently addresses the needs. In the last decades, different interpolation methods provide an efficient response for describing the spatial distribution of precipitation. In this study, we compare the performance of seven interpolation methods used for retrieving the mean annual precipitation over the mainland Portugal, as follows: local polynomial interpolation (LPI), global polynomial interpolation (GPI), radial basis function (RBF), inverse distance weighted (IDW), ordinary cokriging (OCK), universal cokriging (UCK) and empirical Bayesian kriging regression (EBKR). We generate the mean annual precipitation distribution using data from 128 rain gauge stations covering the period 1991 to 2000. The interpolation results were evaluated using cross-validation techniques and the performance of each method was evaluated using mean error (ME), mean absolute error (MAE), root mean square error (RMSE), Pearson’s correlation coefficient (R) and Taylor diagram. The results indicate that EBKR performs the best spatial distribution. In order to determine the accuracy of spatial distribution generated by the spatial interpolation methods, we calculate the prediction standard error (PSE). The PSE result of EBKR prediction over mainland Portugal increases from south to north.

Southern Africa produces almost a third of the Earth’s biomass burning (BB) aerosol particles, yet the fate of these particles and their influence on regional and global climate is poorly understood. ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) is a 5-year NASA EVS-2 (Earth Venture Suborbital-2) investigation with three intensive observation periods designed to study key atmospheric processes that determine the climate impacts of these aerosols. During the Southern Hemisphere winter and spring (June–October), aerosol particles reaching 3–5 km in altitude are transported westward over the southeast Atlantic, where they interact with one of the largest subtropical stratocumulus (Sc) cloud decks in the world. The representation of these interactions in climate models remains highly uncertain in part due to a scarcity of observational constraints on aerosol and cloud properties, as well as due to the parameterized treatment of physical processes. Three ORACLES deployments by the NASA P-3 aircraft in September 2016, August 2017, and October 2018 (totaling ~ 350 science flight hours), augmented by the deployment of the NASA ER-2 aircraft for remote sensing in September 2016 (totaling ~ 100 science flight hours), were intended to help fill this observational gap. ORACLES focuses on three fundamental science themes centered on the climate effects of African BB aerosols: (a) direct aerosol radiative effects, (b) effects of aerosol absorption on atmospheric circulation and clouds, and (c) aerosol–cloud microphysical interactions. This paper summarizes the ORACLES science objectives, describes the project implementation, provides an overview of the flights and measurements in each deployment, and highlights the integrative modeling efforts from cloud to global scales to address science objectives. Significant new findings on the vertical structure of BB aerosol physical and chemical properties, chemical aging, cloud condensation nuclei, rain and precipitation statistics, and aerosol indirect effects are emphasized, but their detailed descriptions are the subject of separate publications. The main purpose of this paper is to familiarize the broader scientific community with the ORACLES project and the dataset it produced.

Teleconnections are sources of predictability for regional weather and climate, but the relative contributions of different teleconnections to regional anomalies are usually not understood. While physical knowledge about the involved mechanisms is often available, how to quantify a particular causal pathway from data are usually unclear. Here, we argue for adopting a causal inference-based framework in the statistical analysis of teleconnections to overcome this challenge. A causal approach requires explicitly including expert knowledge in the statistical analysis, which allows one to draw quantitative conclusions. We illustrate some of the key concepts of this theory with concrete examples of well-known atmospheric teleconnections. We further discuss the particular challenges and advantages these imply for climate science and argue that a systematic causal approach to statistical inference should become standard practice in the study of teleconnections.