Dependence of Eemian Greenland temperature reconstructions on the ice sheet topography

The influence of a reduced Greenland Ice Sheet (GrIS) on Greenland's surface climate during the Eemian interglacial is studied using a set of simulations with different GrIS realizations performed with a comprehensive climate model. We find a distinct impact of changes in the GrIS topography on Greenland's surface air temperatures (SAT) even when correcting for changes in surface elevation, which influences SAT through the lapse rate effect. The resulting lapse-rate-corrected SAT anomalies are thermodynamically driven by changes in the local surface energy balance rather than dynamically caused through anomalous advection of warm/cold air masses. The large-scale circulation is indeed very stable among all sensitivity experiments and the Northern Hemisphere (NH) flow pattern does not depend on Greenland's topography in the Eemian. In contrast, Greenland's surface energy balance is clearly influenced by changes in the GrIS topography and this impact is seasonally diverse. In winter, the variable reacting strongest to changes in the topography is the sensible heat flux (SHF). The reason is its dependence on surface winds, which themselves are controlled to a large extent by the shape of the GrIS. Hence, regions where a receding GrIS causes higher surface wind velocities also experience anomalous warming through SHF. Vice-versa, regions that become flat and ice-free are characterized by low wind speeds, low SHF, and anomalous low winter temperatures. In summer, we find surface warming induced by a decrease in surface albedo in deglaciated areas and regions which experience surface melting. The Eemian temperature records derived from Greenland proxies, thus, likely include a temperature signal arising from changes in the GrIS topography. For the Eemian ice found in the NEEM core, our model suggests that up to 3.1 °C of the annual mean Eemian warming can be attributed to these topography-related processes and hence is not necessarily linked to large-scale climate variations.

Applications of random set theory in econometrics

In recent years, the econometrics literature has shown a growing interest in the study of partially identified models, in which the object of economic and statistical interest is a set rather than a point. The characterization of this set and the development of consistent estimators and inference procedures for it with desirable properties are the main goals of partial identification analysis. This review introduces the fundamental tools of the theory of random sets, which brings together elements of topology, convex geometry, and probability theory to develop a coherent mathematical framework to analyze random elements whose realizations are sets. It then elucidates how these tools have been fruitfully applied in econometrics to reach the goals of partial identification analysis.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

First thoughts on surface tonal patterns in Amawaka, a Panoan language of Peru and Brazil

Amawaka ([ɑmɨ̃ˈwɐkɑ]) is a highly endangered and underdocumented tonal language of the Headwaters (Fleck 2011) subgroup of the Panoan family in the Southwest Amazon Basin, spoken by approximately 200 people. Undocumented phonetic and phonological phenomena of Amawaka include its tonal structure, both in terms of surface realizations and the patterns underlying these realizations. Original audiovisual data from the author’s fieldwork in various Amawaka communities at the Peru-Brazil border will illuminate the as-yet obscure tonal systematicity of the language. Unlike other elements, monosyllabic bimoraic phonological nominal words with long vowels display variation in their surface realization. All the words with the open back unrounded /ɑ/, like /ˈkɑ̀:/ (patarashca, a traditional Amazonian dish), /ˈnɑ̀:/ “mestizo” etc. [with the exception of /ˈtɑ:/ “reed”, which surfaces with either a H or L tone] bear a low tone in isolation. This realization contrasts with all the encountered nominal monosyllables with vowels from the close and close-mid front and central spectrum /i, ɘ, ɨ, ɨ̃/, which clearly surface as high tone words in isolation, for example /ˈmɨ̃́:/ (a clay-lick for animals), /ˈwí:/ “Anopheles, spp. mosquito”. Monosyllables with close-mid back rounded /o/ have a less restrictive pitch that varies among speakers from low to high realizations, and sometimes even across the speech tokens from an individual speaker, e.g. /wó:/ or /wō:/ “hair”, /ɧō:/ or /ɧò:/ (a type of tarantula). Phrasal tonal phonology is more complex, when these three kinds of monosyllables appear in larger noun phrases. Some retain the same surface tones as their isolation form, while others seem to vary freely in their surface realization, e.g. /ˈtɘ́:.nɑ̀:/ or /ˈtɘ́:.nɑ́:/ ‘one mestizo’. Yet other monosyllables, e.g. /mɑ̀:/, exhibit a falling tone when preceded by a H syllable, suggesting probably latent tone sandhi phenomena, e.g /ˈtɘ́:.mɑ̂:/ (one clay-lick for parrots). In disyllabic, trisyllabic and quadrisyllabic nouns, tonal and stress patterns generally seem to be more consistent and tend to be retained both in isolation and in larger intonational phrases. Disyllabic nouns, for instance, surface as L-H or L-L when a glottal stop is in coda position. The association of L with a glottal stop is a feature that occurs in other Panoan languages as well, like Capanahua (Loos 1969), and more generally it is an areal feature, found in other parts of Amazonia (Hyman 2010). So, tone has significant interactions with the glottal stop and glottalization, which generally co-occurs with L. The data above suggest that the underlying tonal system of Amawaka is much more complex than the privative one-tone analysis (/H/ vs. Ø, i.e. lack of tone) that was proposed by Russell and Russell (1959). Evidence from field data suggests either an equipollent (Hyman 2010) two-tone opposition between /H/ and /L/, or a hybrid system, with both equipollent and privative features; that is, /H/ vs. /L/ vs. either Ø or /M/. This first systematic description of Amawaka tone, in conjunction with ongoing research, is poised to address broader questions concerning interrelationships between surface/underlying tone and other suprasegmental features, such as nasality, metrical stress, and intonation. References Fleck, David W. 2011. Panoan languages and linguistics. In Javier Ruedas and David W. Fleck (Eds.), Panoan Histories and Interethnic Identities, To appear. Hyman, Larry. 2010. Amazonia and the typology of tone systems. Presented at the conference Amazonicas III: The structure of the Amazonian languages. Bogotá. Loos, Eugene E. 1969. The phonology of Capanahua and its grammatical basis. Norman: SIL and U. Oklahoma. Russell, Robert & Dolores. 1959. Syntactotonemics in Amahuaca (Pano). Série Lingüistica Especial, 128-167. Publicaçoes do Museu Nacional, Rio de Janeiro, Brasil.

Towards an analysis of tonal patterns in Amawaka, a Panoan language of Peru and Brazil

Amawaka ([ɑmɨ̃ˈwɐkɑ]) is a highly endangered and underdocumented tonal language of the Headwaters (Fleck 2011) subgroup of the Panoan family in the Southwest Amazon Basin, spoken by approximately 200 people. Undocumented phonetic and phonological phenomena of Amawaka include its tonal structure, both in terms of surface realizations and the patterns underlying these realizations. Original audiovisual data from the author’s fieldwork in various Amawaka communities at the Peru-Brazil border will illuminate the as-yet obscure tonal systematicity of the language. Unlike other elements, monosyllabic bimoraic phonological nominal words with long vowels display variation in their surface realization. All the words with the open back unrounded /ɑ/, like /ˈkɑ̀:/ (a traditional Amazonian dish), /ˈnɑ̀:/ “mestizo” etc. [with the exception of /ˈtɑ:/ “reed”, which surfaces with either a H or L tone] bear a low tone in isolation. This realization contrasts with all the encountered nominal monosyllables with vowels from the close and close-mid front and central spectrum /i, ɘ, ɨ, ɨ̃/, which clearly surface as high tone words in isolation, for example /ˈmɨ̃́:/ (a clay-lick for animals), /ˈwí:/ “Anopheles, spp. mosquito”. Monosyllables with close-mid back rounded /o/ have a less restrictive pitch that varies among speakers from low to high realizations, and sometimes even across the speech tokens from an individual speaker, e.g. /wó:/ or /wō:/ “hair”, /ɧō:/ or /ɧò:/ (a type of tarantula). Phrasal tonal phonology is more complex, when these three kinds of monosyllables appear in larger noun phrases. Some retain the same surface tones as their isolation form, while others seem to vary freely in their surface realization, e.g. /ˈtɘ́:.nɑ̀:/ or /ˈtɘ́:.nɑ́:/ ‘one mestizo’. Yet other monosyllables, e.g. /mɑ̀:/, exhibit a falling tone when preceded by a H syllable, suggesting probably latent tone sandhi phenomena, e.g /ˈtɘ́:.mɑ̂:/ (one clay-lick for parrots). In disyllabic, trisyllabic and quadrisyllabic nouns, tonal and stress patterns generally seem to be more consistent and tend to be retained both in isolation and in larger intonational phrases. Disyllabic nouns, for instance, surface as L-H or L-L when a glottal stop is in coda position. The association of L with a glottal stop is a feature that occurs in other Panoan languages as well, like Capanahua (Loos 1969), and more generally it is an areal feature, found in other parts of Amazonia (Hyman 2010). So, tone has significant interactions with the glottal stop and glottalization, which generally co-occurs with L. The data above suggest that the underlying tonal system of Amawaka is much more complex than the privative one-tone analysis (/H/ vs. Ø, i.e. lack of tone) that was proposed by Russell and Russell (1959). Evidence from field data suggests either an equipollent (Hyman 2010) two-tone opposition between /H/ and /L/, or a hybrid system, with both equipollent and privative features; that is, /H/ vs. /L/ vs. either Ø or /M/. This first systematic description of Amawaka tone, in conjunction with ongoing research, is poised to address broader questions concerning interrelationships between surface/underlying tone and other suprasegmental features, such as nasality, metrical stress, and intonation. References Fleck, David W. 2011. Panoan languages and linguistics. In Javier Ruedas and David W. Fleck (Eds.), Panoan Histories and Interethnic Identities, To appear. Hyman, Larry. 2010. Amazonia and the typology of tone systems. Presented at the conference Amazonicas III: The structure of the Amazonian languages. Bogotá. Loos, Eugene E. 1969. The phonology of Capanahua and its grammatical basis. Norman: SIL and U. Oklahoma. Russell, Robert & Dolores. 1959. Syntactotonemics in Amahuaca (Pano). Série Lingüistica Especial, 128-167. Publicaçoes do Museu Nacional, Rio de Janeiro, Brasil.

Differentiating the Multipoint Expected Improvement for Optimal Batch Design

This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.