Adaptive observer for state variables of a time-varying nonlinear system with unknown constant parameters and delayed measurements

Unknown constant parameters estimation problem for a nonlinear time-varying system with delayed measurements is considered. The objective of this work is to design an adaptive observer for a nonlinear time-varying system. The observer must provide asymptotic convergence of the unknown constant parameters estimates to their true values. The main idea behind the method is to perform the parametrization of initial dynamical system based on GPEBO (Generalized Parameter Estimation Based Observer) technology and to build a linear regression model. The identification of linear regression model unknown parameters is performed using least square method with forgetting factor. This work develops the previously published approach for the case of nonlinear time-varying systems with delayed measurements. New parameters estimation algorithm can be applied for technical tasks, such as technical condition control and automatic control systems design

Climatic variability in the era of MIS-11 (370-440 ka BP) according to isotope composition (delta D, delta O-18, delta O-17) of ice from the Vostok station cores

The results of detailed isotopic studies of ice core samples from the Vostok station (East Antarctica) related to the MIS-11  era (the 11th sea isotope stage, i.e. 370–440 thousand years ago) are presented. Reconstruction of paleoclimatic conditions in this period of time was performed using the method of interpretation of the results of isotopic studies of ice, developed by the authors of the article, which is based on the joint analysis of three independent parameters: δD, d-excess, 17O-excess. The isotopic composition (δD) and the deuterium  excess depend on the following  three meteorological  parameters – the condensation temperature near the Vostok station, relative humidity,  and the sea surface temperature at the source of moisture, whereas 17O-excess depends only on the first two parameters. Accordingly,  the proposed method of interpretation allows reconstructing the paleoclimatic conditions (the condensation temperature and surface air temperature at the Vostok station; sea surface temperature and relative humidity  above the ocean) in two different regions in past epochs. For the first time, data on minor fluctuations in the relative humidity of the air in themoisture source throughout the MIS-11  era were obtained. The data resulted from the interpretation demonstrated that the relative humidity fluctuated within the measurement error of ±5%. Reconstructed climatic conditions in the era of MIS-11  were compared with published data for stations Vostok and Concordia, aswell as with the marine core data from 94-607 DSDP and ODP 177-1090. The results obtained on the basis of isotopic analysis of ice cores from stations Vostok and Concordia indicated that in the optimum MIS-11the air temperature was4 °C higher, and in the Termination V –8 °C lower than the present-day values. Thesimilarity of data between the marine columns DSDP  94-607 (North Atlantic), ODP 177-1090 (South Ocean)and our results points to the global nature of changes in the sea surface temperature during the MIS-11  era. The coordination  of the above results proves the high quality of the methods developed by the authors for measuring and interpreting the isotope composition of ice

Evolution of climate, glaciation and subglacial environments of Antarctica from the deep ice core and Lake Vostok water sample studies (Key results of implementation of the Russian Science Foundation project, 2014–2016)

Work on the project focused on the following five areas: 1)  field works in Antarctica at Vostok and Concordia stations; 2)  experimental and theoretical studies in the field of ice core and paleoclimate research; 3) experimental and theoretical works related to the exploration of subglacial Lake Vostok; 4) development of technology and drilling equipment for deep ice coring and exploration of subglacial lakes; 5) upgrading the analytical instrumentation in the Climate and Environmental Research Laboratory (CERL) of the Arctic and Antarctic Research Institute. The main achievements in the field of ice core and paleoclimate research include 1) further elaboration of a new method of ice core dating, which is based on the link between air content of ice and local insolation, 2) investigation of the possible applications of the 17O-excess measurements in ice core to the paleoclimate research, 3)  a better understanding of the mechanisms of the formation of relief-related variations in the isotopic content of an ice core drilled in the area of Antarctic megadunes, and 4) obtaining the first reliable data set on the variations of the 17O-excess in the Vostok core corresponding to marine isotope stage 11. As part of our studies of subglacial Lake Vostok, we have obtained a large body of new experimental data from the new ice core recovered from the 5G-3 borehole to the surface of the subglacial lake. Stacked profiles of isotopic composition, gas content and the size and orientation of the ice crystals in the lake ice have been composed from the data of three replicate cores from boreholes 5G-1, 5G-2 and 5G-3. The study reveals that the concentration of gases in the lake water beneath Vostok is unexpectedly low. A clear signature of the melt water in the surface layer of the lake, which is subject to refreezing on the icy ceiling of Lake Vostok, has been discerned in the three different properties of the accreted ice (the ice texture, the isotopic and gas content of the ice). These sets of data indicate in concert that poor mixing of the melt (and hydrothermal) water with the resident lake water and pronounced spatial and/or temporal variability of local hydrological conditions are likely to be the characteristics of the southern end of the lake. A considerable part of the funding allocated by the RSF to this project was used for upgrading the analytical instrumentation for ice core studies in the CERL of AARI. Using this grant, we purchased and started working with the Picarro L-2140i, a new-generation laser mass analyzer, and set the upgraded mass spectrometer Delta V Plus into operation. The new equipment was used to carry out research planned as part of the project, including the setting up and carrying out of new measurements of 17О in ice cores

Holocene hydrological variability of Lake Ladoga, northwest Russia, as inferred from diatom oxygen isotopes

This article presents a new comprehensive assessment of the Holocene hydrological variability of Lake Ladoga, northwest Russia. The reconstruction is based on oxygen isotopes of lacustrine diatom silica (δ18Odiatom) preserved in sediment core Co 1309, and is complemented by a diatom assemblage analysis and a survey of modern isotope hydrology. The data indicate that Lake Ladoga has existed as a freshwater reservoir since at least 10.8 cal. ka BP. The δ18Odiatom values range from +29.8 to +35.0‰, and relatively higher δ18Odiatom values around +34.7‰ between c. 7.1 and 5.7 cal. ka BP are considered to reflect the Holocene Thermal Maximum. A continuous depletion in δ18Odiatom since c. 6.1 cal. ka BP accelerates after c. 4 cal. ka BP, indicating Middle to Late Holocene cooling that culminates during the interval 0.8–0.2 cal. ka BP, corresponding to the Little Ice Age. Lake‐level rises result in lower δ18Odiatom values, whereas lower lake levels cause higher δ18Odiatom values. The diatom isotope record gives an indication for a rather early opening of the Neva River outflow at c. 4.4–4.0 cal. ka BP. Generally, overall high δ18Odiatom values around +33.5‰ characterize a persistent evaporative lake system throughout the Holocene. As the Lake Ladoga δ18Odiatom record is roughly in line with the 60°N summer insolation, a linkage to broader‐scale climate change is likely

Изотопный состав ледяных кернов, полученных на Западном плато Эльбруса

The results of the isotopic investigations of several ice cores obtained at the Western Plateau of Mt. Elbrus (the Caucasus) are presented. There is a distinct seasonal cycle in the isotopic composition record in these cores. Mean annual and seasonal values of the isotopic composition and accumulation rate were reconstructed for 89 years (1924–2012). These values were compared with the available regional meteorological data and the atmospheric circulation characteristics. It was shown that in the summer season the isotopic composition reflects the local temperature while in winter it depends on the atmospheric circulation.Представлены результаты изотопных исследований нескольких ледяных кернов, полученных на Западном плато Эльбруса (Кавказ). В изотопном составе кернов прослеживается чёткий сезонный сигнал. Рассчитаны среднегодовые и среднесезонные значения изотопного состава и скорости снегонакопления за 89 лет (с 1924 по 2012 г.). Эти значения сопоставлены с данными метеонаблюдений в регионе и с характеристиками циркуляции атмосферы. Показано, что в тёплый период года изотопный состав зависит от температуры воздуха в регионе, а в холодный – от особенностей циркуляции атмосферы

О возможности реконструкции климатического сигнала в нарушенной записи изотопного состава древнего льда (0,4–1,2 млн лет назад) в керне станции Восток (Центральная Антарктида)

In this work we have presented new detailed (with the resolution of 10 cm) stable water isotope (δD and δ18O) profile measured in the central Antarctic Vostok ice core section that contains old ice with the age from 0.4 to 1.2 million years. To interpret these data we have developed a model of molecular diffusion in ice and determined the value of so-called «diffusion length». We have demonstrated that the climatic signal in this ice interval is disturbed by a combination of two processes, ice layer folding (that is accompanied by layer overturning and mixing) and molecular diffusion. The whole old ice interval can be divided in 5  zones that differ in terms of character and intensity of these two processes. In three of these zones the climatic signal is partly preserved and could be restored to some extent. However, in the most interesting and old zone  5 (0.75–1.2  Ma) the climatic signal is nearly completely erased and could hardly be reconstructed. At the same time, the isotopic records obtained from the Vostok old ice have preserved the information on the mean level of the isotopic content of ice in glacial and interglacial stages. This gives an opportunity to reveal and study long-term climatic trends with typical duration longer than main climatic cycles (40–100 ka).Представлены новые детальные данные (с разрешением 10  см) об изотопном составе (δD и δ18O) керна со станции Восток в интервале 3318–3537  м, содержащего древний лёд возрастом 0,4–1,2  млн лет. Показано, что климатический сигнал в этом интервале льда сильно искажён совместным действием стратиграфических нарушений в залегании ледяных слоёв и молекулярной диффузии. Сделана попытка частично восстановить климатический сигнал в отдельных интервалах древнего льда

Изотопные характеристики атмосферных осадков в Приэльбрусье

The aim of the work was to study the isotopic characteristics of precipitation to establish the dependence of δ18O values on temperature at the time of precipitation and to get closer to understanding the processes that form the isotopic signature of the Elbrus snow cover and glacial ice. The sampling of precipitation was organized at Azau station, located at the foot of Elbrus at an altitude of 2300 m for the period from May 01.2019 to September 27.2021. The sampling was carried out once a day at 9:00 Moscow time. The air temperature was recorded at the meteorological station in the Terskol village (Roshydromet station No. 4334250). To study the main features of long-range air transport and possible sources of moisture, 5-day back trajectories were reconstructed using the NOAA HYSPLIT_4 trajectory model. The results showed that precipitation in the Elbrus region in winter was associated with the prevailing transfer from the Atlantic, in summer – with the predominance of transfer from the regions of Central Europe, the Mediterranean and Black Seas. The Mediterranean Sea in all seasons was the area from which the air and moisture were transferred to Elbrus. The values of δ18О and δ2 Н of precipitation varied from 0.52 to −28.22‰ and from 16.3 to −224.1‰, respectively, revealing regular seasonality with high values of δ18О and δ2 Н in summer and low in winter. The deuterium excess varied over a wide range from 24.8 to −14.6‰. All obtained values of δ18О and δ2 Н were approximated by the equation δ2 Н = 8δ18О + 7.06 (R2 = 0.98), which was close to the global meteoric water line. In general, for 2 years of observations, the relationship between the δ18О values of precipitation and the temperature of the surface air layer was expressed as 0.85‰/°С. Total mean absolute error in the reconstruction of air temperatures from the δ18О value of precipitation was 3.2°С due to objective reasons and also differences in meteorological conditions of two years of observations.Приведены результаты изучения изотопных характеристик осадков, выпадающих у подножия южного склона Эльбруса, Кавказ. Отбор осадков организован на станции Азау (абс. высота 2300 м) на ежедневной основе. Установлены основные источники осадков для Приэльбрусья с применением метода обратных траекторий движения воздушных масс. Значения δ18О осадков содержат выраженную связь с температурой приземного слоя воздуха: Δδ18О/ΔT = 0.85‰/°С

КЛИМАТИЧЕСКАЯ ИЗМЕНЧИВОСТЬ В ЭПОХУ МИС‑11 (370–440 ТЫС. ЛЕТ НАЗАД) ПО ДАННЫМ ИЗОТОПНОГО СОСТАВА (δD, δ18O, δ17O) ЛЕДЯНОГО КЕРНА СТАНЦИИ ВОСТОК

The results of detailed isotopic studies of ice core samples from the Vostok station (East Antarctica) related to the MIS-11  era (the 11th sea isotope stage, i.e. 370–440 thousand years ago) are presented. Reconstruction of paleoclimatic conditions in this period of time was performed using the method of interpretation of the results of isotopic studies of ice, developed by the authors of the article, which is based on the joint analysis of three independent parameters: δD, d-excess, 17O-excess. The isotopic composition (δD) and the deuterium  excess depend on the following  three meteorological  parameters – the condensation temperature near the Vostok station, relative humidity,  and the sea surface temperature at the source of moisture, whereas 17O-excess depends only on the first two parameters. Accordingly,  the proposed method of interpretation allows reconstructing the paleoclimatic conditions (the condensation temperature and surface air temperature at the Vostok station; sea surface temperature and relative humidity  above the ocean) in two different regions in past epochs. For the first time, data on minor fluctuations in the relative humidity of the air in themoisture source throughout the MIS-11  era were obtained. The data resulted from the interpretation demonstrated that the relative humidity fluctuated within the measurement error of ±5%. Reconstructed climatic conditions in the era of MIS-11  were compared with published data for stations Vostok and Concordia, aswell as with the marine core data from 94-607 DSDP and ODP 177-1090. The results obtained on the basis of isotopic analysis of ice cores from stations Vostok and Concordia indicated that in the optimum MIS-11the air temperature was4 °C higher, and in the Termination V –8 °C lower than the present-day values. Thesimilarity of data between the marine columns DSDP  94-607 (North Atlantic), ODP 177-1090 (South Ocean)and our results points to the global nature of changes in the sea surface temperature during the MIS-11  era. The coordination  of the above results proves the high quality of the methods developed by the authors for measuring and interpreting the isotope composition of ice.Представлены результаты детальных изотопных исследований  2 тыс. образцов  ледяного керна со станции Восток, относящихся к эпохе МИС-11 (370–440 тыс. л.н.). Обсуждаются методики измерения 17O-эксцесс на лазерном  анализаторе,  а также интерпретации  изотопного состава, основанные  на совместном  анализе  трёх независимых  параметров:  δD, d-excess и 17O-excess. Реконструированы климатические  условия в окрестностях станции Восток и в месте испарения  влаги (над океаном). Полученные результаты сравниваются с опубликованными результатами по станциям Восток и Конкордия, а также с данными по морским колонкам DSDP 94-607 и ODP 177-1090

Изотопный состав снега и льда на ледниках Новой Земли

In 2015–2016 during the research expeditions of Institute of Oceanology, Russian Academy of Sciences the study of stable water isotopes (18O and D) was conducted on glaciers of Novaya Zemlya. As a result, first data on isotopic composition of seasonal snow cover and glacial ice of different ages were obtained and its connection to recent climate change has been shown. The first studies of the isotopic composition of snow cover and glacial ice at Novaya Zemlya allowed determine the average values and the range of variability of δ18O and δD. It shown that for the Northern ice cap glacial ice δ18O vary within −13.91 ÷ −15.83 ‰ with an average value of −14.93 ‰ and −103,95 ÷ −116.75 ‰ for δD at −109.88 ‰ mean value. The maximum variations were recorded for summer snow samples (−8.35 ‰ for δ18O and −55.79 ‰ for δD), as well as for the horizon of superimposed ice (−20.67 ‰ for δ18O and −151.48 ‰ for δD) where isotopic composition has been inherited from winter precipitation. Insignificant differences in the coefficients of the meteoric water regression equation for precipitation on GNIP stations and glacial ice at Novaya Zemlya indicate similar conditions of air masses and precipitation formation both at GNIP station and on glaciers. Deuterium excess showed no seasonal fluctuations, and its values did not exceed 15 ‰, which shows that the proportion of continental precipitation of moisture is very low. Analysis of isotopic profiles obtained on the glaciers of Novaya Zemlya indicated the presence of significant melting. This applies not only to the modern shallow horizons, but also to the part of the glacial strata that formed in the highest part of the archipelago close to ice divide and came to the surface at the Serp i Molot Glacier tongue. Therefore, in terms of ice core palaeogeographic reconstructions the most interesting site is the highest part of the Northern ice cap where it is possible to assume the existence of colder horizons formed during the Little Ice Age and where the seasonal geochemical signal may be preserved.В 2015–2016 гг. проводились исследования стабильных изотопов 18О и D на ледниках Новой Земли. Установлены средние значения и диапазон изменчивости δ18O и δD. Показано, что для Северного ледникового купола величины δ18O в ледниковом льду варьируют в пределах −13,91 ÷ −15,83 ‰ при среднем значении −14,93 ‰. В изменениях эксцесса дейтерия не выявлено никаких сезонных колебаний, а его значения не превышают 15 ‰, что показывает крайне незначительную долю континентальной влаги в выпадающих осадках. Анализ изотопных профилей, полученных на ледниках Новой Земли, свидетельствует о значительном таянии

Связь изотопного состава разных типов осадков в Центральной Антарктиде с температурой воздуха

Water isotopes are key proxies to reconstruct past climatic conditions on our planet based on Antarctic ice core data. The accuracy of climate reconstructions depends on understanding the whole range of the processes involved in the formation of precipitation isotopic composition. The isotopic composition of precipitation in Central Antarctica has been studied in a number of works, but the difference between the isotopic composition of different types of precipitation has not yet been fully described.There are three main type of precipitation in Central Antarctica: snow, ice needles and hoar. The aim of this work is to establish the dependence of isotopic composition of different precipitation types on temperature. Precipitation samples were collected at Vostok station in Central Antarctica from 1998 to 2020 and further analyzed for δ18O and δD. For each precipitation event we have meteorological data, averaged over the time of precipitation fallout. Mean values of δD for each precipitation type were defined as follows: –444±6.5 ‰ for diamond dust, –480± 6 ‰ for hoar and –95±11 ‰ for snow. The seasonal variability of the temperature dependence of the isotopic composition was studied using the example of ice needles. According to our data, the dependence is insignificant in winter, but this needs to be confirmed by an extended dataset. The largest slope of the isotope-temperature dependence regression line is observed for the summer period and is equal to 5.34±3.11 ‰·°С–1, the autumn season has a slope of 2.1±1.3 ‰·°С–1, while for the spring period we do not have enough data for analysis. There is an insignificant difference in the slopes of the isotope-temperature dependence for different types of precipitation: 2.93±0.51 ‰·°С–1 for ice needles, 2.32±1.34 ‰·°С–1 for snow and 2.52±0.35 ‰·°С–1 for hoar. We studied the effect of blizzards on the isotopic composition of samples and concluded that one should avoid using data collected during a blizzard to study the differences in the formation of the isotopic signal for different types of precipitation.This work brings us closer to understanding how isotopic composition is formed in each type of precipitation and what information it provides. This will contribute to a more accurate interpretation of the isotope signal from ice cores.Изучение изотопного состава ледяных кернов дает нам ценную информацию о климате прошлого. Для правильной интерпретации данных, полученных из ледяных кернов, необходимо понимать процесс формирования изотопного сигнала в атмосферных осадках. В этой работе исследована зависимость изотопного состава трех основных для Центральной Антарктиды типов осадков — ледяных игл, изморози и снега — от приземной температуры воздуха. Использованы образцы, отобранные в районе российской внутриконтинентальной станции Восток в период с 1998 по 2020 г. Коэффициенты линейной регрессии между концентрацией дейтерия (dD) и температурой различаются статистически незначимо для всех типов осадков в пределах годового цикла: 2,93±0,51 ‰·°С–1 для ледяных игл, 2,32±1,34 ‰·°С–1 для снега и 2,52±0,35 ‰ °С–1 для изморози. Сделан анализ сезонной изменчивости изотопно-температурной зависимости для ледяных игл. Для зимнего периода связь между изотопным составом и температурой воздуха не обнаружена. Летом наблюдается наибольший наклон изотопно-температурной зависимости, равный 5,34±3,11 ‰·°С–1, наклон для осеннего периода равен 2,1±1,3 ‰·°С–1, тогда как для весеннего периода мы не располагаем достаточным количеством данных для анализа. В исследовании не использовались осадки, отобранные во время метелей, поскольку было установлено, что метель привносит снег с другим изотопным составом в образец