Abstract
Abstract. Detecting a tropospheric ozone trend from sparsely sampled ozonesonde profiles (typically once per week) is challenging due to the short-lived anomalies in the time series resulting from ozone's high temporal variability. To enhance trend detection, we have developed a sophisticated statistical approach that utilizes a geoadditive model to assess ozone variability across a time series of vertical profiles. Treating the profile time series as a set of individual time series on discrete pressure surfaces, a class of smoothing spline ANOVA (analysis of variance) models is used for the purpose of jointly modeling multiple correlated time series (on separate pressure surfaces) by their associated seasonal and interannual variabilities. This integrated fit method filters out the unstructured variation through a statistical regularization (i.e., a roughness penalty) by taking advantage of the additional correlated data points available on the pressure surfaces above and below the surface of interest. We have applied this technique to the trend analysis of the vertically correlated time series of tropospheric ozone observations from (1) IAGOS (In-service Aircraft for a Global Observing System) commercial aircraft profiles above Europe and China throughout 1994–2017 and (2) NOAA GML's (Global Monitoring Laboratory) ozonesonde records at Hilo, Hawaii, (1982–2018) and Trinidad Head, California (1998–2018). We illustrate the ability of this technique to detect a consistent trend estimate and its effectiveness in reducing the associated uncertainty in the profile data due to the low sampling frequency. We also conducted a sensitivity analysis of frequent IAGOS profiles above Europe (approximately 120 profiles per month) to determine how many profiles in a month are required for reliable long-term trend detection. When ignoring the vertical correlation, we found that a typical sampling strategy (i.e. four profiles per month) might result in 7 % of sampled trends falling outside the 2σ uncertainty interval derived from the full dataset with an associated 10 % of mean absolute percentage error. Based on a series of sensitivity studies, we determined optimal sampling frequencies for (1) basic trend detection and (2) accurate quantification of the trend. When applying the integrated fit method, we find that a typical sampling frequency of four profiles per month is adequate for basic trend detection; however, accurate quantification of the trend requires 14 profiles per month. Accurate trend quantification can be achieved with only 10 profiles per month if a regular sampling frequency is applied. In contrast, the standard separated fit method, which ignores the vertical correlation between pressure surfaces, requires 8 profiles per month for basic trend detection and 18 profiles per month for accurate trend quantification. While our method improves trend detection from sparse datasets, the key to substantially reducing the uncertainty is to increase the sampling frequency.
Highlights
The vertical profile is a type of time series data that reports the composition or thermodynamic properties of the atmosphere from the surface to an altitude that can range from a few tens of meters to more than 30 km
The analysis of trends based on vertical profile data is conducted on particular altitude bins or pressure levels which are treated as independent time series (e.g., Miller et al, 2006; Harris et al, 2015; Lossow et al, 2019; Petropavlovskikh et al, 2019), but due to the low sampling frequency of vertical profiles, the vertically distributed trend estimates may be inconsistent from one layer to the
Several studies have demonstrated that IAGOS data above western Europe are consistent with ozonesonde records in the upper troposphere–lower stratosphere (UTLS) (Staufer et al, 2013, 2014), and the data have compared well to regional surface and free tropospheric ozonesonde records (Thouret et al, 1998; Logan et al, 2012; Petetin et al, 2018)
Summary
The vertical profile is a type of time series data that reports the composition (e.g., ozone, water vapor, carbon monoxide) or thermodynamic properties (e.g., temperature, relative humidity, wind speed) of the atmosphere from the surface to an altitude that can range from a few tens of meters (e.g., tethered weather balloons) to more than 30 km (e.g., ozonesondes). In terms of producing an area average based on multiple stations dispersed across a given region, a typical procedure is to create a surface gridded product, which usually aggregates all available monitoring stations within the grid cell without considering spatial sampling and irregularities (Simmons et al, 2010) Another example is the trend analysis of ozonesonde profiles based on units of partial pressure with observations integrated into a limited number of layers for the simplification of the analysis and calculation of column sum (Tiao et al, 1986; Miller et al, 2006). The dimension reduction technique, e.g., principal component analysis, known as the empirical orthogonal function, is commonly used to reduce correlated multivariate data into uncorrelated vectors that maximize the explained variance with as few vectors as possible This approach is used to calculate certain climate indices, such as Atlantic and Antarctic oscillations (https://psl.noaa.gov/data/climateindices/list/, last access: 19 August 2020). This technique is a purely numerical algorithm that is not based on physical principles; a meaningful interpretation of the outcome can be subjective or prohibitive
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