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Phytoplankton biomass and production regulates key aspects of freshwater ecosystems yet its variability and subsequent predictability is poorly understood. We estimated within-lake variation in biomass using high-frequency chlorophyll fluorescence data from 18 globally distributed lakes. We tested how variation in fluorescence at monthly, daily, and hourly scales was related to high-frequency variability of wind, water temperature, and radiation within lakes as well as productivity and physical attributes among lakes. Within lakes, monthly variation dominated, but combined daily and hourly variation were equivalent to that expressed monthly. Among lakes, biomass variability increased with trophic status while, within-lake biomass variation increased with increasing variability in wind speed. Our results highlight the benefits of high-frequency chlorophyll monitoring and suggest that predicted changes associated with climate, as well as ongoing cultural eutrophication, are likely to substantially increase the temporal variability of algal biomass and thus the predictability of the services it provides.
Although quantitative isotope data from speleothems has been used to evaluate isotope-enabled model simulations, currently no consensus exists regarding the most appropriate methodology through which to achieve this. A number of modelling groups will be running isotope-enabled palaeoclimate simulations in the framework of the Coupled Model Intercomparison Project Phase 6, so it is timely to evaluate different approaches to using the speleothem data for data–model comparisons. Here, we illustrate this using 456 globally distributed speleothem δ18O records from an updated version of the Speleothem Isotopes Synthesis and Analysis (SISAL) database and palaeoclimate simulations generated using the ECHAM5-wiso isotope-enabled atmospheric circulation model. We show that the SISAL records reproduce the first-order spatial patterns of isotopic variability in the modern day, strongly supporting the application of this dataset for evaluating model-derived isotope variability into the past. However, the discontinuous nature of many speleothem records complicates the process of procuring large numbers of records if data–model comparisons are made using the traditional approach of comparing anomalies between a control period and a given palaeoclimate experiment. To circumvent this issue, we illustrate techniques through which the absolute isotope values during any time period could be used for model evaluation. Specifically, we show that speleothem isotope records allow an assessment of a model's ability to simulate spatial isotopic trends. Our analyses provide a protocol for using speleothem isotope data for model evaluation, including screening the observations to take into account the impact of speleothem mineralogy on δ18O values, the optimum period for the modern observational baseline and the selection of an appropriate time window for creating means of the isotope data for palaeo-time-slices.
It is often claimed that the entropy of a network's degree distribution is a proxy for its robustness. Here, we clarify the link between degree distribution entropy and giant component robustness to node removal by showing that the former merely sets a lower bound to the latter for randomly configured networks when no other network characteristics are specified. Furthermore, we show that, for networks of fixed expected degree that follow degree distributions of the same form, the degree distribution entropy is not indicative of robustness. By contrast, we show that the remaining degree entropy and robustness have a positive monotonic relationship and give an analytic expression for the remaining degree entropy of the log-normal distribution. We also show that degree-degree correlations are not by themselves indicative of a network's robustness for real networks. We propose an adjustment to how mutual information is measured which better encapsulates structural properties related to robustness.