Sources of black carbon at residential and traffic environments obtained by two source apportionment methods

This study investigated the sources of black carbon (BC) at two contrasting urban environments in Helsinki, Finland: residential area and street canyon. The measurement campaign in the residential area was conducted in winter–spring 2019, whereas in the street canyon the measurements were carried out in autumn 2015. The sources of BC were explored by using positive matrix factorization (PMF) for the organic and refractory black carbon (rBC) mass spectra collected with a soot particle aerosol mass spectrometer (SP-AMS). Based on the PMF analysis, two sites had different local BC sources; the largest fraction of BC originated from biomass burning at the residential site (38 %) and from the vehicular emissions in the street canyon (57 %). Also, the mass size distribution of BC diverged at the sites as BC from traffic was found at the particle size of ∼100–150 nm whereas BC from biomass combustion was detected at ∼300 nm. At both sites, a large fraction of BC was associated with urban background or long-range-transported BC indicated by the high oxidation state of organics related to those PMF factors. The results from the PMF analysis were compared with the source apportionment from the Aethalometer model calculated with two pairs of absorption Ångström values. It was found that several PMF factors can be attributed to wood combustion and fossil fuel fraction of BC provided by the Aethalometer model. In general, the Aethalometer model showed less variation between the sources within a day than PMF, indicating that it was less responsive to the fast changes in the BC sources at the site, or it could not distinguish between as many sources as PMF due to the similar optical properties of the BC sources. The results of this study increase understanding of the limitations and validity of the BC source apportionment methods in different environments. Moreover, this study advances the current knowledge of BC sources and especially the contribution of residential combustion in urban areas.

Picking Sequences and Monotonicity in Weighted Fair Division

We study the problem of fairly allocating indivisible items to agents with different entitlements, which captures, for example, the distribution of ministries among political parties in a coalition government. Our focus is on picking sequences derived from common apportionment methods, including five traditional divisor methods and the quota method. We paint a complete picture of these methods in relation to known envy-freeness and proportionality relaxations for indivisible items as well as monotonicity properties with respect to the resource, population, and weights. In addition, we provide characterizations of picking sequences satisfying each of the fairness notions, and show that the well-studied maximum Nash welfare solution fails resource- and population-monotonicity even in the unweighted setting. Our results serve as an argument in favor of using picking sequences in weighted fair division problems.

An evaluation of source apportionment of fine OC and PM2.5 by multiple methods: APHH-Beijing campaigns as a case study

This paper reports an evaluation of multiple source apportionment methods for OC and PM2.5.

A Mathematical Analysis of an Election System Proposed by Gottlob Frege

In 1998 a long-lost proposal for an election law by Gottlob Frege (1848–1925) was rediscovered in the Thüringer Universitäts- und Landesbibliothek in Jena, Germany. The method that Frege proposed for the election of representatives of a constituency features a remarkable concern for the representation of minorities. Its core idea is that votes cast for unelected candidates are carried over to the next election, while elected candidates incur a cost of winning. We prove that this sensitivity to past elections guarantees a proportional representation of political opinions in the long run. We find that through a slight modification of Frege’s original method even stronger proportionality guarantees can be achieved. This modified version of Frege’s method also provides a novel solution to the apportionment problem, which is distinct from all of the best-known apportionment methods, while still possessing noteworthy proportionality properties.

Are contributions of emissions to ozone a matter of scale? – a study using MECO(n) (MESSy v2.50)

Anthropogenic and natural emissions influence the tropospheric ozone budget, thereby affecting air quality and climate. To study the influence of different emission sources on the ozone budget, often source apportionment studies with a tagged tracer approach are performed. Studies investigating air quality issues usually rely on regional models with a fine spatial resolution, while studies focusing on climate-related questions often use coarsely resolved global models. It is well known that simulated ozone mixing ratios depend on the resolution of the model and the resolution of the emission inventory. Whether the contributions simulated using source apportionment approaches also depend on the model resolution, however, is still unclear. Therefore, this study attempts for the first time to analyse the impact of the model, the model resolution, and the emission inventory resolution on simulated ozone contributions using a diagnostic tagging method. The differences in the ozone contributions caused by these factors are compared with differences that arise from the usage of different emission inventories. To do so, we apply the MECO(n) (MESSy-fied ECHAM and COSMO models nested n times) model system which couples online a global chemistry-climate model with a regional chemistry-climate model equipped with a tagging scheme for source apportionment. The results of the global model (at 300 km horizontal resolution) are compared with the results of the regional model at 50 km (Europe) and 12 km (Germany) resolutions. Besides model-specific differences and biases that are discussed in detail, our results have important implications for other modelling studies and modellers applying source apportionment methods. First, contributions from anthropogenic emissions averaged over the continental scale are quite robust with respect to the model, model resolution, and emission inventory resolution. Second, differences on the regional scale caused by different models and model resolutions can be quite large, and regional models are indispensable for source apportionment studies on the subcontinental scale. Third, contributions from stratospheric ozone transported to the surface differ strongly between the models, mainly caused by differences in the efficiency of the vertical mixing. As stratospheric ozone plays an important role for ground level ozone, but the models show large differences in the amount of downward transported ozone, source apportionment methods should account for this source explicitly to better understand inter-model differences.

Multiwinner approval rules as apportionment methods

We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that some, but not all, of them induce apportionment methods that are well-established in the literature and in the actual practice of representation, be it proportional or non-proportional. For instance, we show that proportional approval voting induces the D’Hondt method and that Monroe’s rule induces the largest remainder method. Our approach also yields apportionment methods implementing degressive proportionality. Furthermore, we consider properties of apportionment methods and exhibit multiwinner rules that induce apportionment methods satisfying these properties.