dataesr/scientific-paragraphs-categorization huggingface dataset:
Instead, r 2 implicitly includes evaluation of both the noise generated by measurement uncertainty and the scatter due to variability in the sources and emission ratios of each species through the ~5 years of measurements. For most species, this range of variability is much larger than the measurement uncertainty, so that it is negligible by comparison. This is not the case with CO 2 ff, which has an uncertainty of approximately 1 ppm, so this uncertainty will always contribute to an r 2 of less than unity. Thus, r 2 gives a simple metric to examine the types of relationships that occur in a real urban environment. We consider (a) the full flask dataset for each species, and (b) a pared dataset where the observations with the highest and lowest 5% of values for the non-CO 2 ff species are removed.
This "pared" dataset removes outlier points that can strongly influence the overall correlation, and we give some examples of reasons these outliers might occur and why it may be useful to exclude them later in this section. The full and pared r 2 values for all species measured in the INFLUX flask network are summarized in Figure  1  and correlation plots for all species are given in the Supplementary material. Figure  2  demonstrates the three general tracer-to-tracer relationships observed in the INFLUX flask observational dataset: linear, not strictly linear, and no obvious relationship. The regression of CO xs versus CO 2 ff xs shows that linear relationships can be found for some trace gases. Because CO and CO 2 ff originate from the same combustion processes and there are no other significant CO sources in the urban area (United States Environmental Protection Agency, 2006), the ratio remains fairly similar for the full dataset.
However, the combustion ratio itself is known to vary between car engines, furnaces, and the power plant, and therefore may vary across space and time. Further, even in the absence of any atmospheric variability in the ratio, the uncertainty of each CO 2 ff of ~1 ppm would induce a maximum r 2 of 0. 8 in our dataset. Nonetheless, in this dataset, the CO:CO 2 ff relationship appears consistent across multiple towers, seasons, and years  (Turnbull et al. , 2015a). Figure  2  also shows the example of the HFC-134a xs versus CO 2 ff xs relationship, that is not strictly linear. Because HFC-134a corresponds to leaks in mobile air conditioning systems, the emissions of HFC-134a do not scale with CO 2 ff emissions in a direct sense. CO 2 ff xs and HFC-134a xs do generally scale together, but there are some significant outliers that we speculate may be due to large HFC-134a leak events (such as air conditioner maintenance).
For example, CO 2 ff emissions from large electrical facilities are emitted from the top of the smoke stack, which may be several hundred meters above ground level, whereas SF 6 leakage from electrical boxes at the same facility will be at or near ground level and possibly hundreds of meters away from the smoke stack. In the case of some other species, it may simply be that there is no relationship with CO 2 ff (e. g. CH 2 Br 2 , which is produced from oceanic biological and chemical processes  (Fuhlbrügge et al. , 2016) ). These three plots in Figure  2 , then, illustrate three distinct possible linear regression scenarios: an obvious linear relationship, a relationship that may exist but may in the Supplemental material show the raw-data scatter plots for all species against CO 2 ff for the interested reader.
The calculated r 2 values from linear regressions of the raw data against CO 2 ff are included as a column in Figure  1  and indicate that, in this dataset, very few species have an appreciable correlation-only 4 of the 34 species even have an r 2 value above 0. 2. These are much lower than those found in previous studies such as  Turnbull et al. (2011)  and  Miller et al. (2012). We believe that this is a consequence of the relatively short distance between emission and detection in the INFLUX urban sample network. This leaves very little time for signals from multiple source sectors with different (or zero) emission ratios to become well-mixed before detection. Conversely, the low r 2 values imply that different sources are observed on different days, and consequently suggests that indeed it might be possible to separate these sources using observations.
Miller et al. (  2012 ) also found that, by separating out the seasonality of their signal, the winter measurements yield stronger correlation coefficients. For the Indianapolis dataset, separating out the winter signal (defined as measurements in December through February) yielded only marginal improvements in the correlation coefficients, with now 6 species having an r 2 value above 0. 2, where Benzene (C 6 H 6 ) is the only species besides CO (0. 58) with a value above 0. 3 at 0. 31. The relative changes in r 2 values from the INFLUX winter signal compared to the full dataset are small enough as to not warrant further investigation for the purposes of this manuscript.
Sector signatures and measures of success Using the framework described in the Methodology section above, we want to identify multi-species signatures for each CO 2 ff source sector and evaluate the SOM's capabilities for sector attribution of any pseudodatasets. Because every row of enhancement values in a pseudodataset will be assigned to a class (neuron) of the SOM, we evaluate a CO 2 ff source sector's signature by finding the class assigned to the mean of all pseudodata rows associated with that sector's contributions and comparing it against the emission matrix which was used to define that pseudodataset. We describe hereafter how we determine quantitatively whether the assigned class matches the original pseudodata. Figure  5  is used for demonstrative purposes. The SOM's classification result for the Industrial sector is chosen for this example, because it exhibits many of the potential difficulties which will be discussed in detail, especially around the idea of properly defining if an assigned class has been "successful" in its tracer assignments; it is not meant to be necessarily viewed as a representative case.
As Figure  5  demonstrates, the question of a successful classification is wrought with nuance. The classification result in the bar chart on the right is the result of a 1000class SOM classification for a pseudodataset based on the emission matrix on the left. For this source sector (here the Industrial sector), the emission matrix defines Tracer C and Tracer I emitting linearly with CO 2 ff emissions. The scale factor (α in Equation  3 ) is set to 1, so Tracer C and Tracer I should have the same enhancement values as CO 2 ff. No other tracer emits in this source sector, and 10 noise species are added to evaluate the impact of irrelevant flask data that may have been mistakenly included if this were a real-data multi-species analysis. The bar chart in Figure  5  shows that four of the random noise species are found to have higher average enhancement values than any of the known tracers and CO 2 ff.
Recall that the noise species are defined to fluctuate around the same order of magnitude as CO 2 ff (and that any real-data analysis will be expected to similarly put each species' measurements in the dataset through some normalization process before analysis to avoid biasing the clustering), so this represents an analysis scenario where 10 species in a dataset are unknowingly being emitted unpredictably and indiscriminately within the domain of interest. Although the we can test for apparent relationships before analysis, these noise species account for cases of misjudgment. Tracer C and Tracer I are correctly classified by the SOM to have enhancement magnitudes equal to CO 2 ff, however these magnitudes are only the fifth through the seventh largest among measured species for this source sector, respectively.
In the Here "Scaled" means that the tracers should have enhancements with magnitudes linearly scaled with CO 2 ff (in this case, the scale factor = 1, so they should have identical values). In this example, four of the noise species in the dataset have higher mean enhancements than the known emitting tracers, which may be problematic in a real-world case where it was not known ahead of time which tracers are expected to be emitting. DOI: https://doi. org/10. 1525/elementa. 131. f5 apportionment of the Indianapolis fossil fuel CO 2 signal Art. 21, page 13 of 22 example of Figure  5 , the Success Rate would be 2 5 7 1 + =. The Success Rate metric does not concern itself with the magnitude of the enhancement. The Top Rank metric evaluates specifically among the subset of known tracers from the emission matrix which are supposed to be emitting, meaning all of those nonnoise, non-CO 2 ff species from the emission matrix which are not set as zero when building the pseudodataset.
This thus also assumes that any random noise species will be able to be identified and ignored prior to analysis of any real dataset. All of the known possible tracers are sorted based on their enhancement values. The Top Rank asks the question of if the tracers that were supposed to be emitting in a given sector (based on the corresponding emission matrix) are the same tracers found to have the highest mean enhancement values among all potential tracers in that sector: _ , cor top emit N Top Rank N = (8) where N emit is the number of tracers which are supposed to be emitting (number of emitters), and N cor_top are the number of emitters which correctly occupy the top N emit spots of the N tracer values that have been sorted by enhancement value. In the example of Figure  5 , we can determine the Top Rank as follows.
We know that there are always 7 potential non-noise, non-CO 2 ff tracers in the emission matrix corresponding to the 7 CO 2 ff source sectors. Of these 7, the emission matrix on the left of Figure  5  shows that 2 tracers were assigned to be emitting when the pseudodataset was built: Tracer C and Tracer I. This means that N emit = 2. If we then sort the enhancement values for all tracers of the emission matrix (that is, ignoring the noise species), then how many of the top 2 spots (largest enhancement values) are occupied by either Tracer C or Tracer I? By looking at the sorted enhancement values plotted in the right of Figure  5 , we see that the answer is that both of them occupy the top 2 spots, so N cor_top = 2. Thus, the Top Rank would be 2 2 1 =. While the Top Rank metric has the advantage of accounting for the magnitude of the enhancements, it also introduces the assumption that the tracers which are emitting will have the largest mean enhancements.
One of the issues with this assumption is that the accuracy of this metric becomes highly dependent on the assumption that any noise species have been accurately identified and removed from the dataset prior to analysis. To address this secondary assumption, the Harsh Top Rank metric is defined as follows: is the number of expected emitters (from the corresponding emission matrix) correctly occupying the top N emit positions of the sorted N tot dataset. In the example of Figure  5 , the Harsh Top Rank is thus determined as follows. The total number of species in this pseudodataset is 18: 7 tracers from the emission matrix, 10 noise species, and CO 2 ff. Of these, we know that two tracers are expected to be emitting based on the emission matrix in the left of Figure  5 : Tracer C and Tracer I.
This means that N emit = 2, exactly as with Top Rank. After having sorted the species by enhancement value, as shown on the right of Figure  5 , we ask how many of the top 2 spots among all 18 species are occupied by Tracer C and Tracer I. The top 2 spots among all species in the dataset are clearly occupied by Rand 6 and Rand 10, however, so N cor_top = 0. The Harsh Top Rank value for this classification, then, would be 0 2 0 =. This is considered to be a more realistic metric, as noise species can negatively influence the success value. Control experiments: Proof of concept A total of 495 self-organizing map classifications are performed, consisting of 165 pseudodatasets from 33 emission matrices with 5 different amounts of noise species, all run with 3 different amounts of classes (nodes): 100, 200, and 1000.
The runs with different amounts of classes are performed since the optimal number will depend on the geometry of the dataset and is not known prior to classification. The ideal number of classes has enough to capture all of the similar groupings of datapoints (clusters) without having multiple classes assigned to the same grouping. Since this analysis is being done to address whether proper CO 2 ff source sector attribution is possible under ideal circumstances, these 495 trials represent the most ideal case for the INFLUX flask dataset. In these original 165 pseudodatasets, it is already known ahead of time which tracers are emitting from which sector, and the exact spatial bounds of the economic sectors are known (from Hestia). We also assume that the number of noise species not tied to a source sector is known.
This initial evaluation will provide our initial control experiments from which to evaluate the loss of information on the sector attribution. Figure  6  shows the mean results of the OSSE SOM classifications across all success metrics for each of the source sectors. The Airport and Electricity Production sectors have low and sporadic successes across all metrics, presumably because these sectors have small spatial signatures-only a few scattered pixels in the domain-which are not able to be well captured in the model. In all of the other sectors, though, the self-organizing map performs well across all success metrics. For these sectors, the Success Rate and Top Rank metrics are around the 90-100% range. The Harsh Top Rank is closer to the 70% range, though, showing the dramatic negative impact that is brought by the inclusion of extraneous species measurements in a dataset.
Additionally, Figure  7  is focused on the 200class SOM case, which seemed to perform the best of the three cases  (100-class, 200-class, and 1000-class) , and it shows only the results from the Top Rank success metric, for which the classification had the highest success values. These choices of 200-classes and the Top Rank metric will maintain consistent through the rest of the analysis as adjustments are made. For Figure  7 , each shaded region moving across the x-axis represents one of the incremental group-of-six emission matrices explained in the Methodology section (cf. subheading "Building the Pseudodatasets"). A brief description of how the tracers are defined in each scenario is included underneath the scatter plot. Emission matrices 1-6 (shaded gray) represent the emission matrices where the "Expected Tracers" (i.
e. related to the sectors) down the diagonal of the emission matrices were all set by applying a multiplicative factor (set to 1 here) to the original CO 2 ff emissions (thus referred to as "Scaled"). The off-diagonal "Unexpected Tracers" are also emitting "Scaled" and are incrementing "Across Sectors", moving down a column of the emission matrix. (For example, emission matrix 1 is set "Scaled" along the diagonal, but also has Tracer C emitting "Scaled" in the OnRoad sector. Emission matrix 2 is identical but also includes Tracer C emitting "Scaled" emissions from the Airport sector. ) Because each emission matrix has 5 pseudodatasets associated with it, corresponding to the inclusion of 5 amounts of noise tracers, the success values for all 5 pseudodatasets are plotted in Figure  7  for each emission matrix.
When results remain independent of the number of noise tracers, dots overlap. According to this Top Rank metric, the success values for tracer assignment are consistently high across our different cases. Figure  7  shows that the metrics tend to perform better in scenarios with fewer noise species in the dataset. The real-world implication of this is that species whose sources are not well-constrained should be removed from a dataset before beginning analysis. For the INFLUX flask data, this would at least mean removing all species with gray boxes in Figure  1  unless one is able to create or obtain emission maps for them. This point is accentuated if compared against the Harsh Top Rank metric, shown in Figure  S12  in the Supplemental material. Additionally, in scenarios where the tracers were scaled with CO 2 ff emissions, proper identification was lowest among all emission matrix scenario groups.
This is believed to be a result of the real CO 2 ff emission data, after being divided into sector contributions, having values close enough to 0 on the ppm scale that the SOM's nodes for one sector may be influenced by contributions in another, despite being defined as independent in the emission matrix from which the dataset was constructed. These influences lead to misclassifications, and, being near-zero, these misclassifications are proportionally greater in magnitude, which.
Introducing the domain-filling problem Considering that, in the control case, the identification of most sectors with the self-organizing map is successful, we evaluate whether these successes maintain their performance after introducing the domain-filling problem identified earlier and illustrated in Figure  4. For the control experiment, the pseudodatasets were constructed as a series of pseudo-flask measurements whereby the exact contributions from each source sector were known (defined by the corresponding emission matrix) and were explicitly stated in their own rows. The domain-filling case uses the same pseudo-flask measurements as a starting point, mimicking the real-world case, and projects them back into the domain using only the tower footprints. The new domain-filled sector values, then, are derived with the following formula: where ∆ y is the pseudo-flask enhancement for species y, n j is the number of pixels where the footprint overlaps Hestia sector j, and n tot is the total number of pixels contained in the footprint.
An approach like formula 10 is necessary to properly account for there not being any a priori information about any species' spatial emissions distribution within any given footprint, as is true for nearly every species in the real flask data case. The formula here in equation 10 is chosen instead of maintaining the form of equation 3, because direct reliance on the influence function would heavily favor identifying sources as being nearby the tower. Using this methodology, all 165 pseudodatasets are reconstructed, and the 495 self-organizing map trials are rerun. Figure  8  shows the new results for each noise scenario across all the emission matrices. In keeping with the control analysis, the 200-class case and the Top Rank success metric are used. The results of Figure  8  show success values around 40%, incrementally increasing to near 70%.
through an expanded dataset The two pseudodata scenarios (with and without the domain-filling problem) are rerun with an expanded dataset. Rather than only creating a pseudodata measurement from each tower with a real simultaneous flask measurement (on average ~2 towers per measurement time), a pseudodata measurement is simultaneously created for all functional towers in the domain every time any real flask measurement was recorded. In this way, we evaluate the impact of data availability on the domain-filling problem, assuming that there were not enough data points previously to allow the self-organizing map to compensate for the information lost through domain-filling. These tests are referred to as the "all towers" cases. First, the control results are rerun under the "all towers" conditions.
A high-resolution meteorological model was applied to each flask measurement to find the footprints within which emissions could have occurred. The overlaps of these footprints with predefined CO 2 ff emission source sectors from the Hestia inventory were scrutinized to identify any measured atmospheric species that could constrain atmospheric CO 2 ff measurements to their appropriate source sectors. The direct-attribution attempts with real data did not yield useful results, because of the large effects of several real-world sources of uncertainty. One such source of uncertainty in this analysis concerns which measured species are specifically known a priori to be related to which (if any) CO 2 ff source sectors, as defined in the Hestia dataproduct. Further, a consistent and prominent source of uncertainty comes from the lack of a priori knowlege for the expected spatial distribution of emissions for any non-CO 2 ff measured species within any projected footprint.
We showed here that the self-organizing map approach is unable to overcome this "domain-filling" problem to correctly attribute trace gases to specific sectors, even in a case with a greatly expanded dataset. The inability to overcome this limitation suggests that the real-world source apportionment problem may be irreconcilable without additional a priori information related to the processes emitting all observed gases of interest. It is additionally shown in the OSSE analysis that the inclusion of extraneous species in the dataset significantly hinders the ability to associate tracer emissions to their source sector. Only atmospheric species that are specifically relevant to the source attribution problem should be included in further analyses. Future investigations will aim at pre-identifying individual species-of-interest and at gathering first-guess spatial inventory estimates to address both the domain-filling problem and the issue of including unnecessary species.
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