The mole fraction and meteorological datasets were combined by aligning them to the InTEM baseline flag time period.

Initial exploration of the datasets showed a significant imbalance between the baseline and non-baseline classes, with seven of the nine sites seeing baseline points being less than one-third of the dataset. The effect of class balance on model performance was explored by varying the percentage of baseline points in the training set (by randomly under-sampling the non-baseline class), and by implementing a sample weight system that assigns more importance to the baseline observations, accounting for the natural class imbalance without needing to remove any training data points. The optimal baseline proportion and sample weighting was found to be both model- and site- specific, although the proportion of baselines was always within 20 %–40 % and the sample weight did not exceed 3. The exact values can be found in the Supplement (Sect. S4.2).

The meteorological parameters included as inputs or features to the ML model were the eastward and northward wind components (ms-1) at 10 ma.g.l. and at two pressure levels, 850 and 500 hPa, surface pressure (Pa), and boundary layer height (m). These data were interpolated to a 17-point grid system around each site, based on two 3×3 grids covering ±5 and ±10° latitude and longitude. To provide the algorithm with further information on changes in atmospheric conditions, all meteorological variables were also provided at time intervals prior to the measurement point. The number and spacing of these intervals were treated as hyperparameters and optimised individually for each model type and site, with intervals up to 72 h prior to the measurement time tested, to allow the model to capture the recent meteorological history for each location. It was found that, in most cases, adding features at 6, 12, 18, and 24 h prior to the measurement time yielded the best performance. Additionally, two temporal variables were added into the dataset to represent the time of day and the day of year. These two variables were integers ranging from 0 to 23 and 1 to 366, respectively. A list of all input variables can be found in the Supplement (Sect. S2).

Normalisation of the meteorological inputs was explored to account for the range of physical quantities with different units and dynamic ranges. Features were scaled separately for each variable category across the 17-point grid (e.g. all eastward wind components at a given height) by their mean and standard deviation. This normalisation was also treated as a hyperparameter, allowing testing with all model types.

A multilayer perceptron (MLP) was trained to predict baseline classifications for each of the nine AGAGE sites. The method was also tested using two tree-based methods, a random forest and a gradient boosting algorithm, the results of which can be found in the Supplement (Sects. S7 and S8). The three discussed methods were chosen as they outperformed alternatives in early testing, but it is likely that several other suitable architectures also exist.

Overall model performance for correctly classifying baseline vs. non-baseline air masses was analysed by considering confusion matrices for each site. These matrices compare the predicted and “true” classifications of the testing set. Figure  shows the MLP confusion matrices for the nine AGAGE sites considered in this work. The outcomes of the confusion matrices have been normalised by testing set size and plotted as points on a precision/recall “bullseye” diagram. The inner circles are the MLP model predictions of baseline values. The left half of each diagram represents true baseline points, and the right-hand side are true non-baseline points. Therefore, the correctly identified baselines (true positives) lie in the left-hand segment of the inner circles (white). False positives, or points incorrectly identified as baseline, are in the yellow segment to the right of the inner circle. Points in the blue segment (left-hand side of outer circle) represent missed baselines, or false negatives, whereas the purple area (right-hand side of the outer circle) are true negatives; points identified as non-baseline that are indeed non-baseline. A perfect model would only have points in the white area and the purple area. The fraction of points in the left half of the inner circle (white) compared to the total number in the inner circle (white and yellow) is the precision. The recall is the ratio of points in the inner left circle (white) to the total number of points on the left (white and blue).

The distribution of points in Fig.  reflects optimisation of F1 score in the MLP training, in which a high precision and recall is rewarded jointly; in most cases, the majority of predicted baseline points are true positives (precision) and many of the available baseline points have been correctly identified (recall). These statistics are also summarised in Table . As seen in the table, there is some variation between sites, with highest overall scores being obtained at Kennaook/Cape Grim, Australia, and poorer performance at Monte Cimone, Italy, which sees particularly low recall (0.355). These differences are likely a product of both the complexity of the meteorology at the site and the complexity of surrounding fluxes; Kennaook/Cape Grim is a coastal site, whose meteorology is dominated by strongly prevailing westerly flows, whereas Monte Cimone is a mountain site in a region of complex topography. Kennaook/Cape Grim, therefore, sees more baseline meteorological events and so has a higher proportion of baseline data points. Sites with lower baseline proportions (such as Monte Cimone), are more challenging. Our features, which are a subset of meteorological variables on a relatively low-density grid around each site, may not capture well the flows in regions of more inhomogeneous topography and meteorology. Furthermore, in some cases, the outer grid (±10°) may not be enhancing model performance, but may instead add noise, if it is frequently in a different meteorological regime to the measurement site (e.g. in a different meteorological hemisphere, as may sometimes be the case at Ragged Point, Barbados, and Cape Matatula, American Samoa). Restricting the domain to the inner grid (±5°) and/or replacing the outer grid with a smaller, higher-resolution one, may improve model performance at some sites.

Our feature importance analysis (Sect. ) reveals that wind components are typically the most critical for model performance, with PBLH and surface pressure generally being of lower importance (see Sect. S6 in the Supplement). However, it should be noted that these variables will be strongly correlated with one-another, so it is not possible to fully isolate the influence of each variable individually. Additionally, in most cases, the analysis showed that the models were not learning much from the two temporal features (time of day and day of year), and so these can likely be removed without negatively impacting model performance. This feature importance pattern aligns with that seen in ML-based LPDM footprint emulation studies .

Whilst the above analysis demonstrates the model's ability to categorise air masses into baseline or non-baseline points, perhaps the most important test of the algorithm is in its ability to reproduce quantities that are used in real-world applications. Here, we focus on the simulation of baseline mole fractions and evaluate the model's ability to calculate robust baseline monthly means, which are commonly used to track changes in greenhouse gases and ozone depleting substances e.g..

The model was applied to a subset of 10 atmospheric trace species measured by the AGAGE network . These 10 compounds were chosen to span a range of sources, atmospheric lifetimes, and atmospheric histories (e.g. those that are growing in the atmosphere, such as HFCs, vs. those that are declining, such as CFCs).

Examples of the baseline flags applied to HFC-134a measurements at Mace Head and Gosan are shown in Fig. . The figure reflects the accuracy of the categorisation shown in Fig. ; the majority of the InTEM baseline points are identified correctly. The influence of false positives is seen as a number of apparently above-baseline points that are categorised as baseline (noting that a small number of these elevated points are incorrectly flagged as baseline in InTEM, which is why their full algorithm includes a subsequent statistical filtering step). At Gosan, similar to InTEM, the MLP algorithm identifies baseline values in the summer period, which sees Southern Hemispheric air intrusions. The rapid variation between Northern and Southern Hemispheric baselines would be very difficult to detect with statistical filters, which rely on baselines being smoothly varying. Similar plots for all other sites and the chosen sample species (those defined in Table ) are shown in the Supplement (Sect. S9).

When calculating the monthly averages from the baseline-labelled observations, the influence of false positives and false negatives is strongly muted. This is demonstrated in Fig. , which shows that for almost all months, the error in the MLP model-calculated HFC-134a monthly mean at Mace Head and Gosan is substantially smaller than the baseline variability (1σ standard deviation in the baseline) within a month. Where outliers occur, these tend to be during months where there were relatively few data points, meaning that any mischaracterisation of the baseline can have a disproportionate influence.

The overall performance of the algorithm applied to each species is summarised in Fig. , which shows the percentage error in the MLP-based monthly mean when compared to the InTEM-based equivalent, which is treated as the absolute truth here.

The CV metric demonstrates that variability in the true baselines is an indicator of model performance, as quantified by MAPE. As shown in the Supplement (Sect. S5), MAPE is generally higher for gases with high variability in their “true” baselines, compared to those with smaller CV. The smallest values of CV are associated with compounds that have relatively small gradients in the background atmosphere (e.g. CFC-12, N2O). Shorter-lived compounds such as dichloromethane, which tend to exhibit substantial seasonal variability and zonal gradients, tend to show the highest variability in their true baselines. This pattern is observed across all sites. We therefore recommend caution when applying the method to species with a high CV relative to other species at the same site.

The computational cost of our baseline classification model is negligible compared to the calculation of LPDM footprints; on a standard desktop computer, the models consistently took less than a minute of wall time to train (3 years of data). Prediction of 1 year of baseline flags for ∼ hourly data, for the most part, takes less than 10 s. This should be compared to the calculation of LPDM footprints, which takes approximately 10 core minutes for each data point (the calculation of a year of baseline flags by combining the LPDM footprints and a tracer flux field is on the order of seconds to minutes of core time). The proposed ML surrogate is therefore approximately five orders of magnitude faster than the full-physics approach.

For very long time series, such as those presented in Figs. and , the main cost associated with our model is the retrieval of subsets of meteorological analyses, which can take a substantial time due to network and storage latency from some archival services (although, of course, substantially larger data volumes are required to run the LPDM).

The envisaged use-cases for the ML algorithm are partly related to its small computational cost, and partly related to its ability to categorise baselines without the need for LPDM simulations. For example, we envisage that this algorithm can be built into data visualisation and quality assurance software, so that mole fraction baseline trends can be examined by data owners with low latency. This is compared to the current situation, in which LPDM runs need to be performed and integrated into the software, often by different research teams to those making the observation data, and often delayed by the availability of appropriate archived meteorology. These lags in the system can delay the analysis by weeks to months. Furthermore, our algorithm allows us to calculate baseline trends further back in time than is currently possible; at present, footprints have been calculated with NAME from 1989 onwards, and it would require a major resourcing effort (both in terms of staff time and computation) to extend these model runs to the beginning of the AGAGE record (1978). Datasets such as ERA5 cover this period and earlier, and can be used in the model prediction step. Finally, we envisage that this algorithm can be used to extend tracer-based methods beyond the period during which measurements were made. Consider, for example, a campaign in which 222Rn was used to derive baseline flags for one year at some location. Our algorithm can use these measurement-based flags in place of the NAME runs, and then be used to provide consistent flagging indefinitely beyond the study period.

These expected benefits must be weighed against the limitations of the model. Whilst we anticipate that improvements in the model architecture or training will be possible, it will always be an approximation of the training data, which is itself, in this case, model-based. Therefore, categorisation errors occur in the form of false positives (points labelled as baseline that are not), or false negatives (baselines that are missed), and so the algorithm should not be used if a precise categorisation is needed of a small number of samples. However, if aggregating over multiple measurements, for example, when calculating a monthly mean of ∼ hourly data, we have shown that the model has high skill in the majority of cases.