Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to overcome the difficulties arising in two such methods: (i) the criterium that the sum of residues of an elliptic solution should be zero, (ii) the construction of a first order differential equation admitting the given equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic

Varied Response of Western Pacific Hydrology to Climate Forcings over the Last Glacial Period

Atmospheric deep convection in the west Pacific plays a key role in the global heat and moisture budgets, yet its response to orbital and abrupt climate change events is poorly resolved. Here, we present four absolutely dated, overlapping stalagmite oxygen isotopic records from northern Borneo that span most of the last glacial cycle. The records suggest that northern Borneo’s hydroclimate shifted in phase with precessional forcing but was only weakly affected by glacial-interglacial changes in global climate boundary conditions. Regional convection likely decreased during Heinrich events, but other Northern Hemisphere abrupt climate change events are notably absent. The new records suggest that the deep tropical Pacific hydroclimate variability may have played an important role in shaping the global response to the largest abrupt climate change events

Extended Cave Drip Water Time Series Captures the 2015–2016 El Niño in Northern Borneo

Time series of cave drip water oxygen isotopes (δ18O) provide site‐specific assessments of the contributions of climate and karst processes to stalagmite δ18O records employed for hydroclimate reconstructions. We present ~12‐year‐long time series of biweekly cave drip water δ18O variations from three sites as well as a daily resolved local rainfall δ18O record from Gunung Mulu National Park in northern Borneo. Drip water δ18O variations closely match rainfall δ18O variations averaged over the preceding 3–18 months. We observe coherent interannual drip water δ18O variability of ~3‰ to 5‰ related to the El Niño–Southern Oscillation (ENSO), with sustained positive rainfall and drip water δ18O anomalies observed during the 2015/2016 El Niño. Evidence of nonlinear behavior at one of three drip water monitoring sites implies a time‐varying contribution from a longer‐term reservoir. Our results suggest that well‐replicated, high‐resolution stalagmite δ18O reconstructions from Mulu could characterize past ENSO‐related variability in regional hydroclimate.Plain Language SummaryCave stalagmites allow for the reconstruction of past regional rainfall variability over the last hundreds of thousands of years with robust age control. Such reconstructions rely on the fact that differences in the isotopic composition of rainwater set by regional rainfall patterns is preserved as the rainwater travels through cave bedrock to feed the cave drip waters forming stalagmites. Long‐term monitoring of rainwater and cave drip water isotopes ground truth the climate to stalagmite relationship across modern‐day changes in regional rainfall. Twelve years of monitoring data presented in this study identify individual El Niño–Southern Oscillation events in rainfall and cave drip water isotopic composition, providing a strong foundation for stalagmite‐based climate reconstructions from this site.Key PointsThree 12‐year‐long cave drip water δ18O time series capture El Niño and La Niña events in northern BorneoEstimates of karst residence times range from 3 to 18 months, with a secondary contribution from a longer‐term reservoir at one drip siteDrip water nonstationarity implies multiple stalagmites are required to reconstruct El Niño–Southern Oscillation variability over timePeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154266/1/grl60264-sup-0002-2019GL086363-SI.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154266/2/grl60264_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154266/3/grl60264.pd

Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica

Transformation of ENSO-related rainwater to dripwater δ^(18)O variability by vadose water mixing

Speleothem oxygen isotopes (δ^(18)O) are often used to reconstruct past rainfall δ^(18)O variability, and thereby hydroclimate changes, in many regions of the world. However, poor constraints on the karst hydrological processes that transform rainfall signals into cave dripwater add significant uncertainty to interpretations of speleothem-based reconstructions. Here we present several 6.5 year, biweekly dripwater δ^(18)O time series from northern Borneo and compare them to local rainfall δ^(18)O variability. We demonstrate that vadose water mixing is the primary rainfall-to-dripwater transformation process at our site, where dripwater δ^(18)O reflects amount-weighted rainfall δ^(18)O integrated over the previous 3–10 months. We document large interannual dripwater δ^(18)O variability related to the El Niño–Southern Oscillation (ENSO), with amplitudes inversely correlated to dripwater residence times. According to a simple stalagmite forward model, asymmetrical ENSO extremes produce significant offsets in stalagmite δ^(18)O time series given different dripwater residence times. Our study highlights the utility of generating multiyear, paired time series of rainfall and dripwater δ^(18)O to aid interpretations of stalagmite δ^(18)O reconstructions

Northern Borneo stalagmite records reveal West Pacific hydroclimate across MIS 5 and 6

Over the past decades, tropical stalagmite δ^(18)O records have provided valuable insight on glacial and interglacial hydrological variability and its relationship to a variety of natural climate forcings. The transition out of the penultimate glaciation (MIS 6) represents an important target for tropical hydroclimate reconstructions, yet relatively few such reconstructions resolve this transition. Particularly, comparisons between Termination 1 and 2 provide critical insight on the extent and influence of proposed climate mechanisms determined from paleorecords and model experiments spanning the recent deglaciation. Here we present a new compilation of western tropical Pacific hydrology spanning 0–160 ky BP, constructed from eleven different U/Th-dated stalagmite δ^(18)O records from Gunung Mulu National Park in northern Borneo. The reconstruction exhibits significant precessional power in phase with boreal fall insolation strength over the 0–160 ky BP period, identifying precessional insolation forcing as the dominant driver of hydroclimate variability in northern Borneo on orbital timescales. A comparison with a network of paleoclimate records from the circum-Pacific suggests the insolation sensitivity may arise from changes in the Walker circulation system. Distinct millennial-scale increases in stalagmite δ^(18)O, indicative of reduced regional convection, occur within glacial terminations and may reflect a response to shifts in inter-hemispheric temperature gradients. Our results imply that hydroclimate in this region is sensitive to external forcing, with a response dominated by large-scale temperature gradients

Trace metal and carbon isotopic variations in cave dripwater and stalagmite geochemistry from northern Borneo

We investigate stalagmite trace metal ratios and carbon isotopic composition (δ^(13)C) as potential paleoclimate proxies by comparing cave dripwaters, stalagmites, and bedrock composition from Gunung Mulu and Gunung Buda National Parks in northern Borneo, a tropical rainforest karst site. Three year long, biweekly time series of dripwater Mg/Ca, Sr/Ca, and δ^(13)C from several drips at our site are not correlated with rainfall variability, indicative of a relatively weak relationship between hydroclimate and dripwater geochemistry at our site. However, combining all of the dripwater geochemical data gathered over four field trips to our site (N > 300 samples), we find that drips with highly variable Mg[Sr]/Ca have relatively invariable δ^(18)O values close to the mean. We hypothesize that increased residence times translate into reduced variance in dripwater δ^(18)O through mixing in the epikarst as well as increased Mg[Sr]/Ca values through increased calcite precipitation in the epikarst. Mg/Ca, Sr/Ca, and δ^(13)C time series from three overlapping stalagmites that grew over the last 27 kyrs are characterized by strong centennial-scale variations, and bear little resemblance to previously published, well-reproduced δ^(18)O time series from the same stalagmites. The only shared signal among the three stalagmites' geochemical time series is a relative decrease of 1‰ in δ^(13)C from the Last Glacial Maximum to the Holocene, consistent with a transition from savannah (C4) to rainforest (C3) conditions documented in nearby records. Taken together, our study indicates that stalagmite Mg[Sr]/Ca ratios are poor indicators of hydroclimate conditions at our site, while stalagmite δ^(13)C exhibits some reproducible signals on glacial-interglacial timescales