A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations

We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.

Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature. II. Different reconstructions of the total solar irradiance variation and dependence on response time scale

We have previously placed the solar contribution to recent global warming in context using observations and without recourse to climate models. It was shown that all solar forcings of climate have declined since 1987. The present paper extends that analysis to include the effects of the various time constants with which the Earth’s climate system might react to solar forcing. The solar input waveform over the past 100 years is defined using observed and inferred galactic cosmic ray fluxes, valid for either a direct effect of cosmic rays on climate or an effect via their known correlation with total solar irradiance (TSI), or for a combination of the two. The implications, and the relative merits, of the various TSI composite data series are discussed and independent tests reveal that the PMOD composite used in our previous paper is the most realistic. Use of the ACRIM composite, which shows a rise in TSI over recent decades, is shown to be inconsistent with most published evidence for solar influences on pre-industrial climate. The conclusions of our previous paper, that solar forcing has declined over the past 20 years while surface air temperatures have continued to rise, are shown to apply for the full range of potential time constants for the climate response to the variations in the solar forcings.

Climate variability-observations, reconstructions, and model simulations for the Atlantic-European and Alpine region from 1500-2100 AD

A detailed analysis is undertaken of the Atlantic-European climate using data from 500-year-long proxy-based climate reconstructions, a long climate simulation with perpetual 1990 forcing, as well as two global and one regional climate change scenarios. The observed and simulated interannual variability and teleconnectivity are compared and interpreted in order to improve the understanding of natural climate variability on interannual to decadal time scales for the late Holocene. The focus is set on the Atlantic-European and Alpine regions during the winter and summer seasons, using temperature, precipitation, and 500 hPa geopotential height fields. The climate reconstruction shows pronounced interdecadal variations that appear to “lock” the atmospheric circulation in quasi-steady long-term patterns over multi-decadal periods controlling at least part of the temperature and precipitation variability. Different circulation patterns are persistent over several decades for the period 1500 to 1900. The 500-year-long simulation with perpetual 1990 forcing shows some substantial differences, with a more unsteady teleconnectivity behaviour. Two global scenario simulations indicate a transition towards more stable teleconnectivity for the next 100 years. Time series of reconstructed and simulated temperature and precipitation over the Alpine region show comparatively small changes in interannual variability within the time frame considered, with the exception of the summer season, where a substantial increase in interannual variability is simulated by regional climate models.

Ecohydrological feedbacks confound peat-based climate reconstructions

Water-table reconstructions from Holocene peatlands are increasingly being used as indicators of terrestrial palaeoclimate in many regions of the world. However, the links between peatland water tables, climate, and long-term peatland development are poorly understood. Here we use a combination of high-resolution proxy climate data and a model of long-term peatland development to examine the relationship between rapid hydrological fluctuations in peatlands and climatic forcing. We show that changes in water-table depth can occur independently of climate forcing. Ecohydrological feedbacks inherent in peatland development can lead to a degree of homeostasis that partially disconnects peatland water-table behaviour from external climatic influences. We conclude by suggesting that further work needs to be done before peat-based climate reconstructions can be used to test climate models.

A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

Pollen-based continental climate reconstructions at 6 and 21 ka: a global synthesis

Subfossil pollen and plant macrofossil data derived from 14C-dated sediment profiles can provide quantitative information on glacial and interglacial climates. The data allow climate variables related to growing season warmth, winter cold, and plant-available moisture to be reconstructed. Continental-scale reconstructions have been made for the mid-Holocene (MH, around 6 ka) and Last Glacial Maximum (LGM, around 21 ka), allowing comparison with palaeoclimate simulations currently being carried out as part of the fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change. The synthesis of the available MH and LGM climate reconstructions and their uncertainties, obtained using modern analogue, regression and model-inversion techniques, is presented for four temperature variables and two moisture variables. Reconstructions of the same variables based on surface-pollen assemblages are shown to be accurate and unbiased. Reconstructed LGM and MH climate anomaly patterns are coherent, consistent between variables, and robust with respect to the choice of technique. They support a conceptual model of the controls of Late Quaternary climate change whereby the first-order effects of orbital variations and greenhouse forcing on the seasonal cycle of temperature are predictably modified by responses of the atmospheric circulation and surface energy balance.

Differentiation of neotropical ecosystems by modern soil phytolith assemblages and its implications for palaeoenvironmental and archaeological reconstructions

The interpretation of Neotropical fossil phytolith assemblages for palaeoenvironmental and archaeological reconstructions relies on the development of appropriate modern analogues. We analyzed modern phytolith assemblages from the soils of ten distinctive tropical vegetation communities in eastern lowland Bolivia, ranging from terra firme humid evergreen forest to seasonally-inundated savannah. Results show that broad ecosystems – evergreen tropical forest, semi-deciduous dry tropical forest, and savannah – can be clearly differentiated by examination of their phytolith spectra and the application of Principal Component Analysis (PCA). Differences in phytolith assemblages between particular vegetation communities within each of these ecosystems are more subtle, but can still be identified. Comparison of phytolith assemblages with pollen rain data and stable carbon isotope analyses from the same vegetation plots show that these proxies are not only complementary, but significantly improve taxonomic and ecosystem resolution, and therefore our ability to interpret palaeoenvironmental and archaeological records. Our data underline the utility of phytolith analyses for reconstructing Amazon Holocene vegetation histories and pre-Columbian land use, particularly the high spatial resolution possible with terrestrial soil-based phytolith studies.

Pollen-based biome reconstructions for Latin America at 0, 6000 and 18000 radiocarbon years

The biomisation method is used to reconstruct Latin American vegetation at 6000±500 and 18 000±1000 radiocarbon years before present (14C yr BP) from pollen data. Tests using modern pollen data from 381 samples derived from 287 locations broadly reproduce potential natural vegetation. The strong temperature gradient associated with the Andes is recorded by a transition from high altitude cool grass/shrubland and cool mixed forest to mid-altitude cool temperate rain forest, to tropical dry, seasonal and rain forest at low altitudes. Reconstructed biomes from a number of sites do not match the potential vegetation due to local factors such as human impact, methodological artefacts and mechanisms of pollen representivity of the parent vegetation.

3D cloud reconstructions: evaluation of scanning radar scan strategy with a view to surface shortwave radiation closure

The ability of six scanning cloud radar scan strategies to reconstruct cumulus cloud fields for radiation study is assessed. Utilizing snapshots of clean and polluted cloud fields from large eddy simulations, an analysis is undertaken of error in both the liquid water path and monochromatic downwelling surface irradiance at 870 nm of the reconstructed cloud fields. Error introduced by radar sensitivity, choice of radar scan strategy, retrieval of liquid water content (LWC), and reconstruction scheme is explored. Given an in␣nitely sensitive radar and perfect LWC retrieval, domain average surface irradiance biases are typically less than 3 W m␣2 ␣m␣1, corresponding to 5–10% of the cloud radiative effect (CRE). However, when using a realistic radar sensitivity of ␣37.5 dBZ at 1 km, optically thin areas and edges of clouds are dif␣cult to detect due to their low radar re-ectivity; in clean conditions, overestimates are of order 10 W m␣2 ␣m␣1 (~20% of the CRE), but in polluted conditions, where the droplets are smaller, this increases to 10–26 W m␣2 ␣m␣1 (~40–100% of the CRE). Drizzle drops are also problematic; if treated as cloud droplets, reconstructions are poor, leading to large underestimates of 20–46 W m␣2 ␣m␣1 in domain average surface irradiance (~40–80% of the CRE). Nevertheless, a synergistic retrieval approach combining the detailed cloud structure obtained from scanning radar with the droplet-size information and location of cloud base gained from other instruments would potentially make accurate solar radiative transfer calculations in broken cloud possible for the first time.

The atmospheric impact of uncertainties in recent Arctic Sea ice reconstructions

There are significant discrepancies between observational datasets of Arctic sea ice concentrations covering the last three decades, which result in differences of over 20% in Arctic summer sea ice extent/area and 5%–10% in winter. Previous modeling studies have shown that idealized sea ice anomalies have the potential for making a substantial impact on climate. In this paper, this theory is further developed by performing a set of simulations using the third Hadley Centre Coupled Atmospheric Model (HadAM3). The model was driven with monthly climatologies of sea ice fractions derived from three of these records to investigate potential implications of sea ice inaccuracies for climate simulations. The standard sea ice climatology from the Met Office provided a control. This study focuses on the effects of actual inaccuracies of concentration retrievals, which vary spatially and are larger in summer than winter. The smaller sea ice discrepancies in winter have a much larger influence on climate than the much greater summer sea ice differences. High sensitivity to sea ice prescription was observed, even though no SST feedbacks were included. Significant effects on surface fields were observed in the Arctic, North Atlantic, and North Pacific. Arctic average surface air temperature anomalies in winter vary by 2.5°C, and locally exceed 12°C. Arctic mean sea level pressure varies by up to 5 mb locally. Anomalies extend to 45°N over North America and Eurasia but not to lower latitudes, and with limited changes in circulation above the boundary layer. No statistically significant impact on climate variability was simulated, in terms of the North Atlantic Oscillation. Results suggest that the uncertainty in summer sea ice prescription is not critical but that winter values require greater accuracy, with the caveats that the influences of ocean–sea ice feedbacks were not included in this study.

Palaeovegetation in China during the late Quaternary: Biome reconstructions based on a global scheme of plant functional types

Two previous reconstructions of palaeovegetation across the whole of China were performed using a simple classification of plant functional types (PFTs). Now a more explicit, global PFT classification scheme has been developed, and a substantial number of additional pollen records have become available. Here we apply the global scheme of PFTs to a comprehensive set of pollen records available from China to test the applicability of the global scheme of PFTs in China, and to obtain a well-founded reconstruction of changing palaeovegetation patterns. A total of 806 pollen surface samples, 188 mid-Holocene (MH, 6000 14C yr BP) and 50 last glacial maximum (LGM, 18,000 14C yr BP) pollen records were used to reconstruct vegetation patterns in China, based on a new global classification system of PFTs and a standard numerical technique for biome assignment (biomization). The biome reconstruction based on pollen surface samples showed convincing agreement with present potential natural vegetation. Coherent patterns of change in biome distribution between MH, LGM and present are observed. In the MH, cold and cool-temperate evergreen needleleaf forests and mixed forests, temperate deciduous broadleaf forest, and warm-temperate evergreen broadleaf and mixed forest in eastern China were shifted northward by 200–500 km. Cold-deciduous forest in northeastern China was replaced by cold evergreen needleleaf forest while in central northern China, cold-deciduous forest was present at some sites now occupied by temperate grassland and desert. The forest–grassland boundary was 200–300 km west of its present position. Temperate xerophytic shrubland, temperate grassland and desert covered a large area on the Tibetan Plateau, but the area of tundra was reduced. Treeline was 300–500 m higher than present in Tibet. These changes imply generally warmer winters, longer growing seasons and more precipitation during the MH. Westward shifts of the forest–shrubland–grassland and grassland–desert boundaries imply greater moisture availability in the MH, consistent with a stronger summer monsoon. During the LGM, in contrast, cold-deciduous forest, cool-temperate evergreen needleleaf forest, cool mixed forests, warm-temperate evergreen broadleaf and mixed forest in eastern China were displaced to the south by 300–1000 km, while temperate deciduous broadleaf forest, pure warm-temperate evergreen forest, tropical semi-evergreen and evergreen broadleaf forests were restricted or absent from the mainland of southern China, implying colder winters than present. Strong shifts of temperate xerophytic shrubland, temperate grassland and desert to the south and east in northern and western China and on the Tibetan Plateau imply drier conditions than present.

Pollen-based reconstructions of biome distributions for Australia, Southeast Asia and the Pacific (SEAPAC region) at 0,6000 and 18,000 14C yr B.P.

Aim  This paper documents reconstructions of the vegetation patterns in Australia, Southeast Asia and the Pacific (SEAPAC region) in the mid-Holocene and at the last glacial maximum (LGM). Methods  Vegetation patterns were reconstructed from pollen data using an objective biomization scheme based on plant functional types. The biomization scheme was first tested using 535 modern pollen samples from 377 sites, and then applied unchanged to fossil pollen samples dating to 6000 ± 500 or 18,000 ± 1000 14C yr bp. Results  1. Tests using surface pollen sample sites showed that the biomization scheme is capable of reproducing the modern broad-scale patterns of vegetation distribution. The north–south gradient in temperature, reflected in transitions from cool evergreen needleleaf forest in the extreme south through temperate rain forest or wet sclerophyll forest (WSFW) and into tropical forests, is well reconstructed. The transitions from xerophytic through sclerophyll woodlands and open forests to closed-canopy forests, which reflect the gradient in plant available moisture from the continental interior towards the coast, are reconstructed with less geographical precision but nevertheless the broad-scale pattern emerges. 2. Differences between the modern and mid-Holocene vegetation patterns in mainland Australia are comparatively small and reflect changes in moisture availability rather than temperature. In south-eastern Australia some sites show a shift towards more moisture-stressed vegetation in the mid-Holocene with xerophytic woods/scrub and temperate sclerophyll woodland and shrubland at sites characterized today by WSFW or warm-temperate rain forest (WTRF). However, sites in the Snowy Mountains, on the Southern Tablelands and east of the Great Dividing Range have more moisture-demanding vegetation in the mid-Holocene than today. South-western Australia was slightly drier than today. The single site in north-western Australia also shows conditions drier than today in the mid-Holocene. Changes in the tropics are also comparatively small, but the presence of WTRF and tropical deciduous broadleaf forest and woodland in the mid-Holocene, in sites occupied today by cool-temperate rain forest, indicate warmer conditions. 3. Expansion of xerophytic vegetation in the south and tropical deciduous broadleaf forest and woodland in the north indicate drier conditions across mainland Australia at the LGM. None of these changes are informative about the degree of cooling. However the evidence from the tropics, showing lowering of the treeline and forest belts, indicates that conditions were between 1 and 9 °C (depending on elevation) colder. The encroachment of tropical deciduous broadleaf forest and woodland into lowland evergreen broadleaf forest implies greater aridity. Main conclusions  This study provides the first continental-scale reconstruction of mid-Holocene and LGM vegetation patterns from Australia, Southeast Asia and the Pacific (SEAPAC region) using an objective biomization scheme. These data will provide a benchmark for evaluation of palaeoclimate simulations within the framework of the Palaeoclimate Modelling Intercomparison Project.

Pollen-based reconstructions of Japanese biomes at 0, 6000 and 18,000 14C yr bp

A biomization method, which objectively assigns individual pollen assemblages to biomes ( Prentice et al., 1996 ), was tested using modern pollen data from Japan and applied to fossil pollen data to reconstruct palaeovegetation patterns 6000 and 18,000 14C yr bp Biomization started with the assignment of 135 pollen taxa to plant functional types (PFTs), and nine possible biomes were defined by specific combinations of PFTs. Biomes were correctly assigned to 54% of the 94 modern sites. Incorrect assignments occur near the altitudinal limits of individual biomes, where pollen transport from lower altitudes blurs the local pollen signals or continuous changes in species composition characterizes the range limits of biomes. As a result, the reconstructed changes in the altitudinal limits of biomes at 6000 and 18,000 14C yr bp are likely to be conservative estimates of the actual changes. The biome distribution at 6000 14C yr bp was rather similar to today, suggesting that changes in the bioclimate of Japan have been small since the mid-Holocene. At 18,000 14C yr bp the Japanese lowlands were covered by taiga and cool mixed forests. The southward expansion of these forests and the absence of broadleaved evergreen/warm mixed forests reflect a pronounced year-round cooling.