Aerosol effects are one of the major uncertainties in assessing global climate change, ecosystem processes and human health. This is because they critically change the balance between the radiation entering and leaving the atmosphere, as well as influencing cloud formation and having direct effects on biological systems e.g. through the respiratory system. It is the direct radiative effects of aerosol that are the focus of this work. The Aerosol Optical Depth (AOD) is a measure of the extinction of radiation by aerosol throughout the depth of the atmosphere. It is wavelength dependent and is traditionally measured at a number of visible wavelengths, but there is little AOD data available at UV wavelengths especially in the UVB. The Brewer spectrophotometer makes direct sun measurements in the UV spectral range, which can in principle be used to calculate AOD at those wavelengths using a form of Beer's law. This work explores the capabilities of the Brewer for UV AOD measurements and applies the results to data from the Tropics and temperate mid-latitudes. Instrument specific weighting functions were tested for their ability to improve the AOD retrieval, but while they changed the partitioning of absorption between ozone and SO2, they had negligible effect on the resulting AOD. After correcting the existing Brewer software for AOD retrieval, data from Manchester UK were compared with independent measurements of AOD, and measurements from the Manchester instrument were also evaluated against a standard Brewer on location in Spain. The inter Brewer comparisons were consistent with differences of the order 6-10%, while comparison with independent methods was qualitatively consistent, but absolute differences were of the order 10-30%. This might partially be attributed to wavelength mismatches between the different methods, and assumptions in the various methods of calculating the AOD.Following the validation exercise the AOD was retrieved from Brewer instruments, using standard weighting functions, in Manchester from 2000- 2008 and Reading from 2003-2008. Based on this work in the UK, the method was then applied to data from Malaysia (1998-2007), where the climate is totally different to that of the UK. The AOD data obtained from the UK and from the Tropics have been compared. Kuala Lumpur, Malaysia gave the highest average AOD values probably due to it being a developing city with high pollution levels indicating a human impact on climate change. Brewer AOD measurements obtained at a narrow range of wavelengths were then used to calculate Angstrom parameters by applying Volz Method. The results, often generating a negative alpha, were deemed unreliable at the UK sites. This was largely attributed to the high solar zenith angle and low signal to noise of the direct sun measurement, exacerbated by a limited number of clear sky measurements available for the work. However, calculation of Angstrom parameters was more successful in Malaysia due to a low solar zenith angle, high intensity, and greater frequency of truly could free sky. Results indicated that aerosol particles in the capital Kuala Lumpur show a clear domination by fine mode. This domination is probably caused by urban pollution, mainly from road traffic, industrial and anthropogenic activities, which is consistent with a large capital city undergoing rapid development.Thus the capabilities and limitations of the Brewer spectrophotometer to provide both AOD data at UV wavelengths, and from those further aerosol properties, has been tested and demonstrated in two contrasting climatic regions. Air mass, limiting the UV signal, and stray-light within the instrument are two of the factors that limit the success of the Brewer for these measurements, which proved more reliable when the sun was high in the sky as in the Tropics.

This is a study concerning the use of starphotometry to retrieve night-time aerosol optical depths (AODs). In the summer of 2007 a SPSTAR03 starphotometer was installed at a rural site at Egbert, Ontario for the purpose of the nighttime AOD measurements. Two series of daytime / nighttime AODs were acquired using the CIMEL CE 318 sunphotometer and the SPSTAR03 from Aug. 31 to Sept. 19 2007 and from June 30 to July 5, 2008. The measurements were complemented by vertical backscatter coefficient profiles acquired using a pulsed lidar. We found that starphotometer AOD estimates, based on the application of a two star method (TSM) to low and high elevation stars, are susceptible to atmospheric inhomogeneity effects. Starphotometer AOD estimates based on the one star method (OSM) reduce this sensitivity, but require absolute calibration values. A level of continuity was obtained between the daytime sunphotometry and nighttime starphotometry data. A continuity parameter (defined as the average difference between the measured nighttime and interpolated daytime values) was calculated over four distinct periods. It yielded the differences of 0.160, 0.053, 0.139 (total, fine and coarse mode optical depths) for the low star and 0.195, 0.070, 0.149 for the high star. We argue that cloud screening would have reduced the continuity parameter differences for the coarse and total optical depths. For 5 out of , 8 nights of lidar operation, a combination of the Angstrom and Spectral Deconvolution Algorithm (SDA) analysis provided an indication of the nature of the atmospheric features seen in the lidar data. Fine and coarse-mode events were detected during the measurement periods using the SDA. Lidar data was used to better understand complex atmospheric phenomena and was found especially effective for cloud detection and general signal increase/decrease analysis.

This paper describes approaches to retrieve important aerosol results from the strong lidar return signals that are received by the space-borne CALIPSO lidar system after reflecting off-ocean surfaces. Relations, from which the theoretically expected values of area under ocean surface returns can be computed, are presented. A detailed description of the lidar system response to the ocean surface returns and the processes of sampling and averaging of lidar return signals are provided. An effective technique that reconstructs the lidar response to surface returnsstarting from down-linked samplesand calculates the area under it, has been developed and described. The calculated area values are validated after comparing them to their theoretically predicted counterpart values. Methods to retrieve aerosol optical depths (AODs) from these calculated areas are described and retrieval results are presented, including retrieval comparison with independent AOD measurements made by an airborne High Spectral Resolution Lidar (HSRL) that yielded quite good agreement. Techniques and results are also presented on using the spectral ratios of the surface response areas to determine spectral ratios of aerosol round-trip transmission and AOD spectral difference, without need of a specific/accurate ocean-surface reflectance model.

Indiana University-Purdue University Indianapolis (IUPUI) / This study looked at the time period of June through mid-October, 2013, based on the results of earlier studies that the strongest correlation between the PM2.5 and AOD data sets occurs during the summer and fall. Terra satellite data was used in this study due to availability of images for the geographic area of the state of Indiana during the time period of the study. PM2.5 measurements from 12 IDEM continuous monitoring sites, which were collected at noon local time, were compared with MODIS AOD data. Despite the limitations of useful data and smaller data sets, this study shows encouraging results, and illustrates that there is a relationship between remotely sensed MODIS AOD data and fine particulate matter (PM2.5) data collected from ground sensors within the geographic region of the state of Indiana. It is believed that this topic should be studied further and expanded upon.

Approved for public release, distribution is unlimited / This thesis assesses the performance of the Naval Postgraduate School Aerosol Optical Depth (NPS AOD) model utilizing very high spatial resolution QuickBird (QB) satellite data. QuickBird derived AOD results are compared to other satellite and ground based AOD results, specifically, AErosol RObotic NETwork (AERONET), MODerate resolution Imaging Spectroradiometer (MODIS), Multi-angle Imaging SpectroRadiometer (MISR), and Advanced Very High Resolution Radiometer (AVHRR). Data is collected around Sir Bu Nuair Island, United Arab Emirates in September 2004 as part of the UAE2 Campaign. Satellite measured radiances are calibrated and due to spatial resolution differences between sensors, modal radiances are calculated for areas matching the highest resolution sensor. The AOD model is based on AVHRR wavelengths; hence, the modal satellite measured radiances are linearly extrapolated to the effective wavelengths of AVHRR. Results show application of the NPS AOD model to QuickBird data yields findings that are consistent with other satellite and ground based retrievals. In general, the NPS AOD model works well for nadir and near-nadir view angles, but not for high zenith angles. / Lieutenant Commander, United States Navy

O objetivo desse trabalho foi estudar a relação entre profundidade óptica de aerossóis (AOD), obtida por sensoriamento remoto, e a concentração de material particulado (MP10 e MP2,5) medida próximo à superfície sobre a Região Metropolitana de São Paulo (RMSP). A profundidade óptica foi derivada a partir de medidas de radiâncias fornecidas pelos sensores MODIS. Estes sensores estão posicionados a bordo dos satélites EOS-TERRA e EOS-AQUA, operados pela NASA. As concentrações de MP10 e MP2,5 foram obtidas nas estações da rede operacional da CETESB. Foram feitos alguns estudos de caso considerando diferentes situações atmosféricas, aos quais se aplicou a metodologia proposta por Castanho (2005) que busca reduzir as incertezas na determinação da profundidade óptica derivada do MODIS e identificar qual o modelo de aerossol é mais adequado para aplicação em estudos de qualidade do ar. Os valores de AOD calculados para as diferentes situações foram comparados com aqueles obtidos pela AERONET e com as concentrações anteriormente citadas, buscando uma validação dos mesmos. Valores médios de AOD foram calculados para áreas de 10 km x 10 km ao redor das estações de monitoramento do MP. Testes foram realizados para verificar os efeitos de sazonalidade, da quantidade de água na coluna atmosférica, da resposta da AOD por faixas de concentração de MP10, da geometria do sensor, da presença de nuvens e da presença de aerossol acima da Camada de Mistura (CM). Os resultados foram apresentados por estações com o objetivo de se visualizar diferentes condições sobre a região estudada. Alguns dos fatores relevantes observados durante a comparação entre a concentração de MP10 e a AOD foram: a influência do período do ano e da quantidade de água na coluna atmosférica. A geometria do sensor foi fator determinante para melhora das correlações, quando limitado o ângulo de espalhamento em 140°. Situações em que há ausência de nuvens, identificadas através de imagens do MODIS no visível, também apresentaram melhores resultados. Outro fator de extrema importância foi a estrutura vertical da CM. Através de medidas obtidas de um LIDAR foi verificado que a presença de aerossóis acima da CM, a qual é determinada principalmente pelas condições atmosféricas, é determinante para as correlações entre AOD e o MP. / The main purpose of this work was to study the relationship between the Aerosol Optical Depth (AOD), obtained by remote sensing, and the particulate material concentration (PM10 and PM2.5), near to the surface over the Metropolitan Area of Sao Paulo (MASP). The Aerosol Optical Depth was retrieved based on reflectance measurements provided by MODIS sensors. These sensors are carried aboard EOS-TERRA and EOS-AQUA satellites, which are operated by NASA. The PM10 and PM2.5 concentrations were obtained in the CETESB operational network. Case studies were performed, considering several atmospheric conditions, applying the methodology proposed by CASTANHO (2005), designed both to reduce the uncertainty in the determination of the MODIS derived Optical Depth and to identify which aerosol model is more appropriated for air quality studies. Some derived results were compared with AERONET data and with the previously mentioned concentrations as a cross-check test. Mean AOD values were calculated using 10 km x 10 km area ground around PM monitoring stations. Tests were performed to estimate the effects of seasonality, atmospheric column water content, AOD response to PM10 concentration, sensor geometry, clouds and aerosol concentration above the Mixing Layer (ML). To stress the different conditions of the studied region, the results were presented considering each station. Some of the relevant observed factors in the PM10 concentration and AOD comparison were the year period influence and the atmospheric column water content. The sensor geometry was an important factor to the improvement of the obtained correlations when the scattering angle was bounded to 140°. Cloudless situations, identified by MODIS true color images, also improved the results. Another important factor was the Mixing Layer vertical structure. Using LIDAR measurements it was verified that the presence of aerosols above the ML, which is determined mainly by atmospheric conditions, is crucial for the correlations between AOD and PM.

Spatial distribution of diurnal variations of aerosol properties in South Korea, both long term and short term, is studied by using 9 AERONET sites from 1999 to 2017 for long-term averages and from an additional 10 sites during the KORUS-AQ field campaign. The extent to which WRF-Chem model and the GOCI satellite retrieval can describe these variations is also analyzed. In daily average, Aerosol Optical Depth (AOD) at 550 nm is 0.386 and shows a diurnal variation of +20 to -30% in inland sites, respectively larger than the counterparts of 0.308 and ± 20% in coastal sites. Both the inland and coastal sites have their diurnal variation peaks in the early morning and in the evening with noontime and early afternoon valleys. In contrast, Angstrom exponent values in all sites are between 1.2 and 1.4 with the exception of the inland rural sites having smaller values near 1.0 during the early morning hours. All inland sites experience a pronounced increase of Angström Exponent from morning to evening, reflecting overall decrease of particle size in daytime. To statistically obtain the climatology of diurnal variation of AOD, a minimum of requirement of ~2 years of observation is needed in coastal rural sites, twice more than the urban sites, which suggests that diurnal variation of AOD in urban setting is distinct and persistent. AERONET, GOCI, WRF-Chem, and observed PM2.5 data consistently show dual peaks for both AOD and PM2.5, one at ~ 10 KST and another ~14 KST. While Korean GOCI satellite is able to consistently capture the diurnal variation of AOD, WRF-Chem clearly has the deficiency to describe the relatively change of peaks and variations between the morning and afternoon, suggesting further studies for the diurnal profile of emissions. Overall, the relative small diurnal variation of PM2.5 is in high contrast with large AOD diurnal variation, which suggests the need to use AOD from geostationary satellites for constrain either modeling or analysis of surface PM2.5 for air quality application.

Σύμφωνα με την πρόσφατη έκθεση της Διακυβερνητικής Επιτροπής για την Κλιματική Αλλαγή (Intergovernmental Panel on Climate Change, IPCC), η επίδραση των αιωρούμενων σωματιδίων στο ενεργειακό ισοζύγιο της ατμόσφαιρας κρίνεται ως ιδιαίτερα σημαντική. Αυτό οφείλεται στα φαινόμενα σκέδασης και απορρόφησης που προκαλούν στην ηλιακή ακτινοβολία κατά τη διάδοσή της στην ατμόσφαιρα και στην επίδρασή τους στις ιδιότητες των νεφών. Στην παρούσα διπλωματική εργασία έγινε μια προσπάθεια ανάλυσης των δεδομένων που έχουμε στη διάθεσή μας από το διεθνές δίκτυο επίγειων σταθμών AERONET που λειτουργεί υπό την αιγίδα της NASA και από το δορυφορικό όργανο MODIS (Moderate Resolution Imaging Spectoradiometer) που βρίσκεται στους δορυφόρους πολικής τροχιάς Terra και Aqua με σκοπό την εξαγωγή συμπερασμάτων σχετικά με τη χωρική και εποχική διακύμανση των οπτικών ιδιοτήτων των αιωρούμενων σωματιδίων και σχετικά με την αντιπροσωπευτικότητα των επιγείων σταθμών σε σύγκριση με το MODIS των δορυφόρων Terra και Aqua. Η μελέτη έγινε για τρεις αστικές περιοχές της Ελλάδας, την Αθήνα, το Ηράκλειο και τη Θεσσαλονίκη, όπου υπάρχουν επίγειοι σταθμοί και δορυφορικά δεδομένα από τη γύρω περιοχή με χωρική ανάλυση 10x10 km2. Η δομή της εργασίας έχει ως εξής: Στο πρώτο κεφάλαιο, δίνεται ο ορισμός των αιωρούμενων σωματιδίων, αναλύεται η χημική τους σύσταση, οι μορφές στις οποίες απαντώνται στην ατμόσφαιρα, οι πηγές προέλευσής τους, η κατανομή τους σε διάφορες κατηγορίες με διαφορετικά κριτήρια όπως επίσης και οι μηχανισμοί απομάκρυνσής τους από την ατμόσφαιρα. Στο δεύτερο κεφάλαιο, αναλύονται οι φυσικές ιδιότητες των αιωρούμενων σωματιδίων και οι μηχανισμοί επίδρασής τους στην ακτινοβολία. Ιδιαίτερη σημασία δίνεται στον εκθέτη Angstrom και στο οπτικό βάθος των αιρούμενων σωματιδίων καθώς είναι το αντικείμενο της μελέτης μας. Στη συνέχεια, στο τρίτο κεφάλαιο, γίνεται μια αναφορά στις επιδράσεις των αιωρούμενων σωματιδίων όσον αφορά στο κλίμα και στο ενεργειακό ισοζύγιο καθώς επίσης στην υγεία και στην ορατότητα. Στο τέταρτο κεφάλαιο, γίνεται αρχικά μια αναφορά στο διεθνές δίκτυο επιγείων σταθμών AERONET και στο φασματο-ραδιόμετρο MODIS από όπου έχουμε τις μετρήσεις μας. Έπειτα, περιγράφεται το πρώτο στάδιο της επεξεργασίας των μετρήσεών μας, το οποίο περιλαμβάνει τη σχηματική σύγκριση των μετρήσεων που έχουμε από τους επιγείους σταθμούς και τους δορυφόρους. Περνώντας στο πέμπτο κεφάλαιο της εργασίας, αναλύεται η μέθοδος με την οποία γίνεται η χωρική ομαδοποίηση των μετρήσεων από τους δορυφόρους και στη συνέχεια ακολουθεί το δεύτερο στάδιο της επεξεργασίας των μετρήσεων κατά το οποίο αναπαρίστανται τα σχήματα ομαδοποίησης των δορυφορικών μετρήσεων με διάφορα κριτήρια. Τέλος, στο έκτο κεφάλαιο, σχολιάζονται τα τελικά αποτελέσματα και εξάγονται τα αντίστοιχα συμπεράσματα για την εποχική και χωρική διακύμανση των αιωρούμενων σωματιδίων, αλλά και την αντιπροσωπευτικότητα των επιγείων σταθμών σε σχέση με τους δορυφόρους. / According to a recent report by the Intergovernmental Panel on Climate Change (IPCC), the effect of suspended particles in the energy balance of the atmosphere is considered as very important. This is due to scattering and absorption phenomena caused by solar radiation during propagation in the atmosphere and their effect on the properties of clouds. This thesis was an attempt to analyze the available data by the international network of ground aerosol stations AERONET and the satellite instrument MODIS (Moderate Resolution Imaging Spectoradiometer) on-board the Terra and Aqua satellites and investigate the spatial and temporal variation of the optical properties of aerosols and the representativeness of the earth stations compared to the MODIS satellites Terra and Aqua. The study was conducted in three urban areas of Greece, Athens, Heraklion and Thessaloniki, where there are data from ground-based stations and satellite estimations from the surrounding area with a spatial resolution of 10x10 km2. The structure of this thesis is as follows: The first chapter begins with a definition of aerosols, the analysis of their chemical composition, the forms with which aerosols occur in the atmosphere, the sources of their origin, their distribution in categories with different criteria as well as the mechanisms for their removal from the atmosphere. The second chapter analyzes the physical properties of aerosols and mechanisms of their influence on radiation. Particular attention is given to the Angstrom exponent and the optical depth of aerosols, parameters that lie within the object of our study. In the third chapter, there is a description of the aerosol effects on climate and the energy balance as well as health and visibility. In the fourth chapter, there is firstly a description of the international AERONET network of ground stations and the MODIS spectral radiometer. Then, we describe the first stage of our measurement analysis, which includes the schematic comparison of measurements derived from ground stations and satellites. In the fifth chapter, we analyze the method for the spatial clustering of measurements from satellites and the clustering shapes of satellite measurements using different criteria. Finally, in the sixth chapter, we discuss the results and conclusions corresponding to the seasonal and spatial variability of aerosols, and the representativeness of the ground measurements in comparison with the satellite estimations.

O objetivo desse trabalho foi estudar a relação entre profundidade óptica de aerossóis (AOD), obtida por sensoriamento remoto, e a concentração de material particulado (MP10 e MP2,5) medida próximo à superfície sobre a Região Metropolitana de São Paulo (RMSP). A profundidade óptica foi derivada a partir de medidas de radiâncias fornecidas pelos sensores MODIS. Estes sensores estão posicionados a bordo dos satélites EOS-TERRA e EOS-AQUA, operados pela NASA. As concentrações de MP10 e MP2,5 foram obtidas nas estações da rede operacional da CETESB. Foram feitos alguns estudos de caso considerando diferentes situações atmosféricas, aos quais se aplicou a metodologia proposta por Castanho (2005) que busca reduzir as incertezas na determinação da profundidade óptica derivada do MODIS e identificar qual o modelo de aerossol é mais adequado para aplicação em estudos de qualidade do ar. Os valores de AOD calculados para as diferentes situações foram comparados com aqueles obtidos pela AERONET e com as concentrações anteriormente citadas, buscando uma validação dos mesmos. Valores médios de AOD foram calculados para áreas de 10 km x 10 km ao redor das estações de monitoramento do MP. Testes foram realizados para verificar os efeitos de sazonalidade, da quantidade de água na coluna atmosférica, da resposta da AOD por faixas de concentração de MP10, da geometria do sensor, da presença de nuvens e da presença de aerossol acima da Camada de Mistura (CM). Os resultados foram apresentados por estações com o objetivo de se visualizar diferentes condições sobre a região estudada. Alguns dos fatores relevantes observados durante a comparação entre a concentração de MP10 e a AOD foram: a influência do período do ano e da quantidade de água na coluna atmosférica. A geometria do sensor foi fator determinante para melhora das correlações, quando limitado o ângulo de espalhamento em 140°. Situações em que há ausência de nuvens, identificadas através de imagens do MODIS no visível, também apresentaram melhores resultados. Outro fator de extrema importância foi a estrutura vertical da CM. Através de medidas obtidas de um LIDAR foi verificado que a presença de aerossóis acima da CM, a qual é determinada principalmente pelas condições atmosféricas, é determinante para as correlações entre AOD e o MP. / The main purpose of this work was to study the relationship between the Aerosol Optical Depth (AOD), obtained by remote sensing, and the particulate material concentration (PM10 and PM2.5), near to the surface over the Metropolitan Area of Sao Paulo (MASP). The Aerosol Optical Depth was retrieved based on reflectance measurements provided by MODIS sensors. These sensors are carried aboard EOS-TERRA and EOS-AQUA satellites, which are operated by NASA. The PM10 and PM2.5 concentrations were obtained in the CETESB operational network. Case studies were performed, considering several atmospheric conditions, applying the methodology proposed by CASTANHO (2005), designed both to reduce the uncertainty in the determination of the MODIS derived Optical Depth and to identify which aerosol model is more appropriated for air quality studies. Some derived results were compared with AERONET data and with the previously mentioned concentrations as a cross-check test. Mean AOD values were calculated using 10 km x 10 km area ground around PM monitoring stations. Tests were performed to estimate the effects of seasonality, atmospheric column water content, AOD response to PM10 concentration, sensor geometry, clouds and aerosol concentration above the Mixing Layer (ML). To stress the different conditions of the studied region, the results were presented considering each station. Some of the relevant observed factors in the PM10 concentration and AOD comparison were the year period influence and the atmospheric column water content. The sensor geometry was an important factor to the improvement of the obtained correlations when the scattering angle was bounded to 140°. Cloudless situations, identified by MODIS true color images, also improved the results. Another important factor was the Mixing Layer vertical structure. Using LIDAR measurements it was verified that the presence of aerosols above the ML, which is determined mainly by atmospheric conditions, is crucial for the correlations between AOD and PM.

Abstract : This is a study concerning comparisons between the Dubovik Aerosol optical depth (AOD) retrievals from AEROCAN (ARONET) stations and AOD estimates from simulations provided by a chemical transport model (GEOS-Chem : Goddard Earth Observing System Chemistry). The AOD products associated with the Dubovik product are divided into total, fine and coarse mode components. The retrieval period is from January 2009 to January 2013 for 5 Arctic stations (Barrow, Alaska; Resolute Bay, Nunavut; 0PAL and PEARL (Eureka), Nunavut; and Thule, Greenland). We also employed AOD retrievals from 10 other mid-latitude Canadian stations for comparisons with the Arctic stations. The results of our investigation were submitted to Atmosphere-Ocean. To briefly summarize those results, the model generally but not always tended to underestimate the (monthly) averaged AOD and its components. We found that the subdivision into fine and coarse mode components could provide unique signatures of particular events (Asian dust) and that the means of characterizing the statistics (log-normal frequency distributions versus normal distributions) was an attribute that was common to both the retrievals and the model. / Résumé : Cette étude compare des épaisseurs optiques d’aérosols (AOD) à 5 stations arctiques d’AEROCAN (AERONET), obtenues d’une part à l’aide de l’algorithme d'inversion de Dubovik appliqué à des mesures in situ, et d’autre part du modèle de transport chimique (GEOS-Chem : Goddard Earth Observing Système Chemistry). Les produits d’AOD associés à l’algorithme d’inversion sont divisés en composantes totales, fines et grossières. Pour chacune des 5 stations (Barrow, Alaska, Resolute Bay, au Nunavut, 0PAL et PEARL (Eureka), Nunavut, et Thulé, au Groenland), la période de récupération est de janvier 2009 à janvier 2013. Nous avons également utilisé les mesureurs d’AOD de dix autres stations canadiennes de latitudes moyennes, à des fins de comparaison. Les résultats de l’étude ont été soumis à la revue Atmosphere-Ocean. Pour résumer brièvement ces résultats, le modèle a généralement, mais pas toujours, eu tendance à sous-estimer l'AOD moyenne et de ses composantes. Nous avons constaté que la subdivision en composantes fine et grossière pourrait fournir des signatures uniques d'événements particuliers (poussière asiatique) et que les moyens de caractériser des statistiques (les distributions de fréquence log-normale versus les distributions normales) était un attribut qui était commun aux deux les mesureurs et le modèle.