Simplified model of spectral absorption by non-algal particles and dissolved organic materials in aquatic environments

Absorption by non-algal particles (NAP, ad) and colored dissolved organic matter (CDOM, ag) are frequently modeled by exponential functions of wavelength, either separately or as a sum. We present a new representation of NAP-plus-CDOM absorption adg based on the stretched exponential function adg(λ) = A exp{−[s(λ − λo)]β}, whose parameter β can be considered a measure of optical heterogeneity. A double exponential representation of adg can be fit extremely well by a stretched exponential for all plausible parameter combinations, despite having one fewer free parameter than a double exponential. Fitting two published compilations of in situ adg data – one at low spectral resolution (n = 5, λ = 412–555 nm) and one at high spectral resolution (n = 201, λ = 300–700 nm) – the stretched exponential outperforms the single exponential, double exponential, and a power law. We thereby conclude that the stretched exponential is the preferred model for adg absorption in circumstances when NAP and CDOM cannot be separated, such as in remote sensing inversions

Variability‐based constraint on ocean primary production models

Primary production (PP) is fundamental to ocean biogeochemistry, but challengingly variable. Satellite models are unique tools for investigating PP, but are difficult to compare and validate because of the scale separation between in situ and remote measurements, which also are rarely coincident. Here, I argue that satellite estimates should be log-skew-normally distributed, because of this scale separation and because PP measurements are log-normally distributed. Whether they conform to this distributional shape is therefore a powerful variability-based constraint on such models. Satellite models that do follow a log-skew-normal may then also be concisely characterized by three parameters (log-mean, log-standard deviation, and log-skewness). I show that the output from a recent satellite model (CAFE) over 2019 agrees excellently with the log-skew-normal, globally and for most spatiotemporal subsets investigated here. The exception is the Northern Hemisphere winter, which may suggest future model improvements. PP by plankton is essential to ocean ecology and biogeochemistry, so satellite models that estimate PP from remote sensing data are indispensable in numerous scientific applications. However, because the corresponding in situ data are rarely measured when a satellite passes overhead, are measured on a much smaller spatial scale, and are highly variable, it is very difficult to compare different satellite models, evaluate how accurate they are, or to constrain their parameters. Here, a different approach to evaluating, comparing, and constraining these models is described, which accounts for or avoids all of these issues with the standard approach. This approach finds excellent agreement overall with a recent satellite model, while also identifying room for improvement

Ocean heat uptake efficiency increase since 1970

The ocean stores the bulk of anthropogenic heat in the Earth system. The ocean heat uptake efficiency (OHUE) -- the flux of heat into the ocean per degree of global warming -- is therefore a key factor in how much warming will occur in the coming decades. In climate models, OHUE is well-characterised, tending to decrease on centennial timescales; in contrast, OHUE is not well-constrained from Earth observations. Here OHUE and its rate of change are diagnosed from global temperature and ocean heat content records. OHUE increased over the past five decades by 0.19$\pm$0.04 W/m$^2$K, and was on average 0.58$\pm$0.08 W/m$^2$K during this period. This increase is attributed to steepening anthropogenic heat gradients in the ocean, and corresponds to several years' difference in when temperature targets such as 1.5$^\circ$C or 2$^\circ$C are exceeded

On freshwater fluxes and the Atlantic meridional overturning circulation

We address the role of freshwater forcing in the modern day ocean. Specifically, we ask the question of whether an amplification of the global freshwater forcing pattern leads to a strengthening or weakening of the steady‐state Atlantic Meridional Overturning Circulation (AMOC). While the role of freshwater forcing in the AMOC has received much attention, this question remains unresolved, in part because past studies have primarily investigated idealized models, large regime shifts away from the modern ocean state, or coupled atmosphere–ocean simulations on shorter timescales than required for the deep ocean to equilibrate. Here we study the AMOC's sensitivity at equilibrium to small perturbations in the magnitude of the global freshwater fluxes in simulations performed with a realistically configured ocean circulation model. Our results robustly suggest that for the equilibrium state of the modern ocean, freshwater fluxes strengthen the AMOC, in the sense that an amplification of the existing freshwater flux‐forcing pattern leads to a strengthening of the AMOC and vice versa. A simple physical argument explains these results: the North Atlantic is anomalously salty at depth and increased freshwater fluxes act to amplify that salinity pattern, resulting in enhanced AMOC transport

Pond fractals in a tidal flat

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces

Bayesian estimation of Earth’s climate sensitivity and transient climate response from observational warming and heat content datasets

Future climate change projections, impacts and mitigation targets are directly affected by how sensitive Earth’s global mean surface temperature is to anthropogenic forcing, expressed via the effective climate sensitivity (ECS) and transient climate response (TCR). However, the ECS and TCR are poorly constrained, in part because historic observations and future climate projections consider the climate system under different response timescales with potentially different climate feedback strengths. Here, we evaluate ECS and TCR by using historic observations of surface warming, since the mid-19th century, and ocean heat uptake, since the mid 20th century, to constrain a model with independent climate feedback components acting over multiple response timescales. Adopting a Bayesian approach, our prior uses a constrained distribution for the instantaneous Planck feedback combined with wide-ranging uniform distributions of the strengths of the fast feedbacks (acting over several days) and slow feedbacks (acting over decades). We extract posterior distributions by applying likelihood functions derived from different combinations of observational datasets. The resulting TCR distributions are similar when using different historic datasets: from a TCR of 1.5 (1.3 to 1.7 at 5–95 % range) °C, up to 1.7 (1.4 to 2.0) °C. However, the posterior probability distribution for ECS on a 100-year response timescale varies depending on which combinations of temperature and heat content anomaly datasets are used: from ECS of 2.2 (1.5 to 4.5) °C, for datasets with less historic warming, up to 2.8 (1.8 to 6.1) °C, for datasets with more historic warming. Our results demonstrate how differences between historic climate reconstructions imply significant differences in expected future global warming

Bias in the shoreline development index: Ecological implications illustrated with an analysis of littoral-pelagic habitat coupling

We reexamined the relationship between the shoreline development index and metrics of habitat coupling using a bias-corrected variant of the shoreline development index. Our findings suggest that previously reported correlations may be artifacts of scale-dependent bias in shoreline development index measurements. The results highlight the need for careful measurement when seeking to understand links between lake morphology and ecological processes

Simple model of morphometric constraint on carbon burial in boreal lakes

A geometric theory was developed to explain the empirical relationship between carbon burial and lake shape in boreal lakes. The key feature of this model is an attenuation length scale, analogous to models of marine organic carbon fluxes. This length scale is the ratio of how fast carbon is displaced vertically versus how fast it is respired and engenders a simple model with a single easily constrained free parameter. Lake depths are modeled based on fractal area–volume relationships that reflect the approximate scale invariance of Earth’s topography on idealized lake geometries. Carbon burial is estimated by applying the attenuation length scale to these depths. Using this model, we demonstrate the relationship between the dynamic ratio—a metric of lake morphometry calculated by dividing the square root of surface area by the mean depth—and carbon burial. We use scaling relationships to predict how dynamic ratio, and by extension carbon burial, varies across the lake size spectrum. Our model also provides a basis for generalizing empirical studies to the biome scale. By applying our model to a boreal lake census, we estimate boreal lake carbon burial to be 1.8 ± 0.5 g C/m2/yr or 1.1 ± 0.3 Tg C/yr among all boreal lakes

How does lake primary production scale with lake size?

Kleiber’s 3/4-scaling law for metabolism with mass is one of the most striking regularities in biological sciences. Kleiber’s law has been shown to apply not only to individual organisms but also to communities and even the whole-ecosystem properties such as the productivity of estuaries. Might Kleiber’s law also then apply to lake ecosystems? Here, we show that for a collection of whole-lake primary production measurements, production scales to the 3/4 power of lake volume, consistent with Kleiber’s law. However, this relationship is not explicable by analogy to theories developed for individual organisms. Instead, we argue that dimensional analysis offers a simple explanation. After accounting for latitudinal gradients in temperature and insolation, whole-lake primary production scales isometrically with lake area. Because Earth’s topography is self-affine, meaning there are global-scale differences between vertical and horizontal scaling of topography, lake volume scales super-linearly with lake surface area. 3/4 scaling for primary production by volume then results from these other two scaling relationships. The identified relationship between the primary production and temperature- and insolation-adjusted area may be useful for constraining lakes’ global annual productivity and photosynthetic efficiency. More generally, this suggests that there are multiple paths to realizing the 3/4 scaling of metabolism rather than a single unifying law, at least when comparing across levels of biological organization

The size-distribution of earth’s lakes and ponds: Limits to power-law behavior

Global-scale characterizations of Earth’s lakes and ponds assume their surface areas are power-law distributed across the full size range. However, empirical power-laws only hold across finite ranges of scales. In this paper, we synthesize evidence for upper and lower limits to power-law behavior in lake and pond size-distributions. We find support for the power-law assumption in general. We also find strong evidence for a lower limit to this power-law behavior, although the specific value for this limit is highly variable (0.001–1 km2), corresponding to orders of magnitude differences of the total number of lakes and ponds. The exact mechanisms that break the power-law at this limit are unknown. The power-law extends to the size of Earth’s largest lake. There is inconsistent evidence for an upper limit at regional-scales. Explaining variations in these limits stands to improve the accuracy of global lake characterizations and shed light on the specific mechanism responsible for forming and breaking lake power-law distributions