A Global lake ecological observatory network (GLEON) for synthesising high-frequency sensor data for validation of deterministic ecological models

A Global Lake Ecological Observatory Network (GLEON; www.gleon.org) has formed to provide a coordinated response to the need for scientific understanding of lake processes, utilising technological advances available from autonomous sensors. The organisation embraces a grassroots approach to engage researchers from varying disciplines, sites spanning geographic and ecological gradients, and novel sensor and cyberinfrastructure to synthesise high-frequency lake data at scales ranging from local to global. The high-frequency data provide a platform to rigorously validate processbased ecological models because model simulation time steps are better aligned with sensor measurements than with lower-frequency, manual samples. Two case studies from Trout Bog, Wisconsin, USA, and Lake Rotoehu, North Island, New Zealand, are presented to demonstrate that in the past, ecological model outputs (e.g., temperature, chlorophyll) have been relatively poorly validated based on a limited number of directly comparable measurements, both in time and space. The case studies demonstrate some of the difficulties of mapping sensor measurements directly to model state variable outputs as well as the opportunities to use deviations between sensor measurements and model simulations to better inform process understanding. Well-validated ecological models provide a mechanism to extrapolate high-frequency sensor data in space and time, thereby potentially creating a fully 3-dimensional simulation of key variables of interest

A Contour Integral Representation for the Dual Five-Point Function and a Symmetry of the Genus Four Surface in R6

The invention of the "dual resonance model" N-point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic continuation formulas such as the contour-integral representation obtained by Pochhammer in 1890. Here we explore the geometry underlying the dual five-point function B5, the simplest generalization of the Euler Beta function. Analyzing the B5 integrand leads to a polyhedral structure for the five-crosscap surface, embedded in RP5, that has 12 pentagonal faces and a symmetry group of order 120 in PGL(6). We find a Pochhammer-like representation for B5 that is a contour integral along a surface of genus five. The symmetric embedding of the five-crosscap surface in RP5 is doubly covered by a symmetric embedding of the surface of genus four in R6 that has a polyhedral structure with 24 pentagonal faces and a symmetry group of order 240 in O(6). The methods appear generalizable to all N, and the resulting structures seem to be related to associahedra in arbitrary dimensions.Comment: 43 pages and 44 figure

A multi-lake comparative analysis of the General Lake Model (GLM): Stress-testing across a global observatory network

The modelling community has identified challenges for the integration and assessment of lake models due to the diversity of modelling approaches and lakes. In this study, we develop and assess a one-dimensional lake model and apply it to 32 lakes from a global observatory network. The data set included lakes over broad ranges in latitude, climatic zones, size, residence time, mixing regime and trophic level. Model performance was evaluated using several error assessment metrics, and a sensitivity analysis was conducted for nine parameters that governed the surface heat exchange and mixing efficiency. There was low correlation between input data uncertainty and model performance and predictions of temperature were less sensitive to model parameters than prediction of thermocline depth and Schmidt stability. The study provides guidance to where the general model approach and associated assumptions work, and cases where adjustments to model parameterisations and/or structure are required

Does lake size matter? Combining morphology and process modeling to examine the contribution of lake classes to population-scale processes

With lake abundances in the thousands to millions, creating an intuitive understanding of the global distribution of morphology and processes in lakes is challenging. To improve researchers’ understanding of large-scale lake processes, we developed a parsimonious mathematical model based on the Pareto distribution to describe the distribution of lake morphology (area, perimeter, and volume). While debate continues over which mathematical representation best fits any one distribution of lake morphometric characteristics, we recognize the need for a simple, flexible model to advance understanding of how the interaction between morphometry and function dictates scaling across large populations of lakes. These models make clear the relative contribution of individual lakes to the total amount of lake surface area, volume, and perimeter. They also highlight the critical thresholds at which total perimeter, area, and volume would be evenly distributed across lake-size classes having Pareto slopes of 0.63, 1.00, and 1.12, respectively. These morphological models can be used in combination with process models to create overarching “lake population” level models of process. To illustrate this potential, we combined the model of surface area distribution with a model of carbon mass accumulation rate. We found that even if smaller lakes contribute relatively less to total surface area than larger lakes, the increasing carbon accumulation rate with decreasing lake size is strong enough to bias the distribution of carbon mass accumulation toward smaller lakes. This analytical framework provides a relatively simple approach to upscaling morphology and process that can be easily generalized to other ecosystem processes

Lake-size dependency of wind shear and convection as controls on gas exchange

High-frequency physical observations from 40 temperate lakes were used to examine the relative contributions of wind shear (u*) and convection (w*) to turbulence in the surface mixed layer. Seasonal patterns of u* and w* were dissimilar; u* was often highest in the spring, while w * increased throughout the summer to a maximum in early fall. Convection was a larger mixed-layer turbulence source than wind shear (u */w*-1 for lakes* and w* differ in temporal pattern and magnitude across lakes, both convection and wind shear should be considered in future formulations of lake-air gas exchange, especially for small lakes. © 2012 by the American Geophysical Union.Jordan S. Read, David P. Hamilton, Ankur R. Desai, Kevin C. Rose, Sally MacIntyre, John D. Lenters, Robyn L. Smyth, Paul C. Hanson, Jonathan J. Cole, Peter A. Staehr, James A. Rusak, Donald C. Pierson, Justin D. Brookes, Alo Laas, and Chin H. W

Influence of a Random Telegraph Process on the Transport through a Point Contact

We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by mapping them on matrix products. The result is used to obtain the generating function of the full counting statistics of a classical point contact subject to a classical fluctuator, including extensions to a pair of two-level fluctuators as well as to a quantum point contact. We show that the noise in the quantum point contact is a sum of the (quantum) partitioning noise and the (classical) noise due to the two-level fluctuator. As a side result, we obtain the full counting statistics of a quantum point contact with time-dependent transmission probabilities.Comment: 8 pages, 2 figure; a new section about experiments and a figure showing the crossover from sub- to superpoissonian noise have been adde

Radar absorption, basal reflection, thickness and polarization measurements from the Ross Ice Shelf, Antarctica

Radio-glaciological parameters from the Moore’s Bay region of the Ross Ice Shelf, Antarctica, have been measured. The thickness of the ice shelf in Moore’s Bay was measured from reflection times of radio-frequency pulses propagating vertically through the shelf and reflecting from the ocean, and is found to be 576 ± 8 m. Introducing a baseline of 543 ± 7m between radio transmitter and receiver allowed the computation of the basal reflection coefficient, R, separately from englacial loss. The depth-averaged attenuation length of the ice column, 〈L〉 is shown to depend linearly on frequency. The best fit (95% confidence level) is 〈L(ν)〉= (460±20) − (180±40)ν m (20 dB km−1), for the frequencies ν = [0.100–0.850] GHz, assuming no reflection loss. The mean electric-field reflection coefficient is (1.7 dB reflection loss) across [0.100–0.850] GHz, and is used to correct the attenuation length. Finally, the reflected power rotated into the orthogonal antenna polarization i