Abstract Current estimates of carbon dioxide (CO2) evasion from Arctic lakes are highly uncertain because few studies integrate seasonal variability, specifically evasion during spring ice‐melt. We quantified annual CO2 evasion for 14 clear‐water Arctic lakes in Northern Sweden through mass balance (ice‐melt period) and high‐frequency loggers (open‐water period). On average, 80% (SD: ± 18) of annual CO2 evasion occurred within 10 d following ice‐melt. The contribution of the ice‐melt period to annual CO2 evasion was high compared to earlier studies of Arctic lakes (47% ± 32%). Across all lakes, the proportion of ice‐melt : annual CO2 evasion was negatively related to the dissolved organic carbon concentration and positively related to the mean depth of the lakes. The results emphasize the need for measurements of CO2 exchange at ice‐melt to accurately quantify CO2 evasion from Arctic lakes.

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.

Dataset to the article: "Ice-melt period dominates annual carbon dioxide evasion from clear-water Arctic lakes". The data concern the physicochemical parameters and CO2 evasion for the 14 studied lakes (sheet 1) Furthermore, ice-melt CO2 evasion, annual CO2 evasion and the ratio ice-melt:annual evasion, and DOC for the 14 studied and additional lakes from earlier publications is given (sheet 2).

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.

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.

Benthic primary production varies among lakes from 1 to 2000+ mg C m− 2 d− 1, in part owing to variations in basin shape. First principles predict an inverse correlation between benthic primary production and mean to maximum depth ratio, an index of basin shape, but reports of positive correlations suggest that current understanding is incorrect or incomplete. We develop a hypsometric (area–depth) model for littoral area that accounts for habitat disruption due to ice scouring at the lake margin. When this disruption is incorporated, the direction of the relationship between benthic primary production and depth ratio depends on water clarity—regions with clear lakes should have positive correlations, whereas regions with less water clarity should have inverse correlations. Empirical analysis of benthic primary production measurements from four eco-regions characterized by different levels of water clarity supports this prediction. Collectively, our analyses demonstrate how first principles can be used to explain heterogeneous patterns of benthic primary production at broad geographic scales.

Lakes contribute 9%–19% of global methane (CH 4 ) emissions to the atmosphere. Dissolved molecular oxygen (DO) in lakes can inhibit the production of CH 4 and promote CH 4 oxidation. DO is therefore often considered an important regulator of CH 4 emissions from lakes. Presence or absence of DO in the water above the sediments can affect CH 4 production and emissions by (a) influencing if methane production can be fueled by the most reactive organic matter in the top sediment layer or rely on deeper and less degradable organic matter, and (b) enabling CH 4 accumulation in deep waters and potentially large emissions upon water column turnover. However, the relative importance of these two DO effects on CH 4 fluxes is still unclear. We assessed CH 4 fluxes from two connected lake basins in northern boreal Sweden where one was experimentally oxygenated. Results showed no clear difference in summer CH 4 emissions attributable to water column DO concentrations. Large amounts of CH 4 accumulated in the anoxic hypolimnion of the reference basin but little of this may have been emitted because of incomplete mixing, and effective methane oxidation of stored CH 4 reaching oxic water layers. Accordingly, ≤24% of the stored CH 4 was likely emitted in the experimental lake. Overall, our results suggest that hypolimnetic DO and water column CH 4 storage might have a smaller impact on CH 4 emissions in boreal forest lakes than previous estimates, yet potential fluxes associated with water column turnover events remain a significant uncertainty in lake CH 4 emission estimates.

Lakes evade significant amounts of carbon dioxide (CO2) to the atmosphere; yet the magnitude and origin of the evasion are still poorly constrained. We quantified annual CO2 evasion and its origin (in‐lake net ecosystem production vs. lateral inputs from terrestrial ecosystems) in 14 high‐latitude lakes through high‐frequency estimates of open water CO2 flux and ecosystem metabolism and inorganic carbon mass‐balance before and after ice breakup. Annual CO2 evasion ranged from 1 to 25 g C m−2 yr−1 of which an average of 57% was evaded over a short period at ice‐breakup. Annual internal CO2 production ranged from −6 to 21 g C m−2 yr−1, of which at least half was produced over winter. The contribution of internal versus external source contribution to annual CO2 evasion varied between lakes, ranging from fully internal to fully external with most lakes having over 75% of the evasion sustained through a single source. Overall, the study stresses the large variability in magnitude and control of CO2 evasion and suggests that environmental change impacts on CO2 evasion from high‐latitude lakes are not uniform.

The shoreline development index—The ratio of a lake’s shore length to the circumference of a circle with the lake’s area—Is a core metric of lake morphometry used in Earth and planetary sciences. In this paper, we demonstrate that the shoreline development index is scale‐dependent and cannot be used to compare lakes with different areas. We show that large lakes will have higher shoreline development index measurements than smaller lakes of the same characteristic shape, even when mapped at the same scale. Specifically, the shoreline development index increases by about 14% for each doubling of lake area. These results call into question previously reported patterns of lake shape. We provide several suggestions to improve the application of this index, including a bias‐corrected formulation for comparing lakes with different surface areas.

David A. Seekell , Michael L. Pace ,* James B. Heffernan , Sally J. Holbrook 4 Climate Impacts Research Centre, Department of Ecology and Environmental Science, Umeå University, Umeå, Sweden Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia Nicholas School of the Environment, Duke University, Durham, North Carolina Department of Ecology, Evolution, and Marine Biology, University of California Santa Barbara, Santa Barbara, California

Abstract Maximum depth is crucial for many lake processes and biota, but attempts to explain its variation have achieved little predictive power. In this paper, we describe the probability distribution of maximum depths based on recent developments in the theory of fractal Brownian motions. The theoretical distribution is right‐tailed and adequately captures variations in maximum depth in a dataset of 8164 lakes (maximum depths 0.1–135 m) from the northeastern United States. Maximum depth increases with surface area, but with substantial random variation—the 95% prediction interval spans more than an order of magnitude for lakes with any specific surface area. Our results explain the observed variability in lake maximum depths, capture the link between topographic characteristics and lake bathymetry, and provide a means to upscale maximum depth‐dependent processes, which we illustrate by upscaling the diffusive flux of methane from northern lakes to the atmosphere.

Kleiber’s ¾-scaling Law for metabolism with mass is one of the most striking regularities in the biological sciences. We demonstrate that whole-lake primary production scales to the ¾-power of lake volume, consistent with Kleiber’s Law but not explicable by analogy to theories developed for individual organisms. Instead, dimensional analysis offers a simple explanation. Because Earth's topography is self-affine and whole-lake primary production scales isometrically with lake area after accounting for latitudinal gradients in temperature and insolation, sub-linear scaling for primary production by volume emerges; the ¾ scaling exponent derives from global-scale differences between vertical and horizontal scaling of topography. From these patterns we make novel inferences about lakes' global annual productivity, photosynthetic efficiency, trophic structure, and role in the carbon cycle. More generally, our study suggests there are multiple paths to realizing ¾-scaling of metabolism rather than a single unifying law, at least when comparing across levels of biological organization.

Ecological theory predicts that the relative distribution of primary production across habitats influence fish size structure and biomass production. In this study, we assessed individual, population, and community-level consequences for brown trout ( Salmo trutta ) and Arctic char ( Salvelinus alpinus ) of variation in estimated habitat specific (benthic and pelagic) and total whole lake (GPP whole ) gross primary production in 27 northern oligotrophic lakes. We found that higher contribution of benthic primary production to GPP whole was associated with higher community biomass and larger maximum and mean sizes of fish. At the population level, species-specific responses differed. Increased benthic primary production (GPP Benthic ) correlated to higher population biomass of brown trout regardless of being alone or in sympatry, while Arctic char responded positively to pelagic primary production (GPP Pelagic ) in sympatric populations. In sympatric lakes, the maximum size of both species was positively related to both GPP Benthic and the benthic contribution to GPP Whole . In allopatric lakes, brown trout mean and maximum size and Arctic char mean size were positively related to the benthic proportion of GPP Whole . Our results highlight the importance of light-controlled benthic primary production for fish biomass production in oligotrophic northern lakes. Our results further suggest that consequences of ontogenetic asymmetry and niche shifts may cause the distribution of primary production across habitats to be more important than the total ecosystem primary production for fish size, population biomass, and production. Awareness of the relationships between light availability and asymmetric resource production favoring large fish and fish production may allow for cost-efficient and more informed management actions in northern oligotrophic lakes.

Globally, the length of tributaries to lakes varies from 0 to more than 15,000 km, but scaling relationships describing this aspect of lake‐river connectivity are lacking. In this study, we describe a simple theoretical scaling relationship for tributary length based on the principle of line intercepts of topographic features, and test this theory using data from Scandinavia. Tributary length increases by 73% for each doubling of lake area. This pattern reflects the relationship between catchment and lake area, and is modified by inlet frequency, junction angle, and lake shape—factors related to specific geologic and hydrologic processes. The theory is precise (r 2 = 0.74), with low bias (mean error is 14% of mean tributary length) when the characteristic junction angle (∼76°) is estimated statistically. Our study bridges the gap between geomorphic and large‐scale statistical relationships to provide simple rules for understanding complex patterns of lake‐river connectivity.

Maximum depth varies among lakes from $<$1 to 1741 meters, but attempts to explain this variation have achieved little predictive power. In this paper, we describe the probability distribution of maximum depths based on recent developments in the theory of fractal Brownian motions. The theoretical distribution is right-tailed and adequately captures variations in maximum depth in a dataset of 8,164 lakes (maximum depths 0.1 to 135 meters) from the northeastern United States. Maximum depth increases with surface area, but with substantial random variation - the 95\% prediction interval spans more than an order of magnitude for lakes with any specific surface area. Our results explain the observed variability in lake maximum depths, capture the link between topographic characteristics and lake bathymetry, and provide a means to upscale maximum-depth-dependent processes, which we illustrate by upscaling the diffusive flux of methane from northern lakes to the atmosphere.

Scaling relationships provide simple rules for understanding complex ecological patterns. We evaluated scaling relationships between whole-lake (benthic + pelagic) primary production and the surface areas and volumes of 73 lakes. Whole-lake primary production scales isometrically with surface area, after accounting for latitudinal gradients of temperature and insolation. Whole-lake primary production scales to the ¾-power of lake volume, a pattern analogous to Kleiber’s Law for organismal metabolism except that its emergence is attributable to fractal characteristics of lake morphometry rather than optimal resource distribution networks. By applying our scaling relationships to a global lake database, we estimated that global lake primary production is 520 (±70) Tg C y-1. We also apply the scaling relationships to make predictions about other global lake characteristics including trophic structure and carbon cycling.

Metabolism is one of the most fundamental ecosystem processes, but the drivers of variation in metabolic rates among lakes dominated by benthic primary producers remain poorly constrained. Here, we report the magnitudes and potential drivers of whole-lake metabolism across 43 Swedish arctic-alpine lakes, based on the free-water diel oxygen technique with sondes deployed during the open-water season near the surface and bottom of the lakes. Gross primary production (GPP) and ecosystem respiration (R) were strongly coupled and ranged from 0.06 to 0.45 mg and 0.05 to 0.43 mg L-1 d(-1) among lakes. On average, GPP and R decreased eightfold from relatively shallow to deep lakes (mean depth 0.5-10.9 m) and twofold from concave to convex lakes (mean depth: maximum depth 0.2-0.5). We attribute this to light limitation and shape-specific sensitivity of benthic GPP to disturbance by lake ice. Net ecosystem production (GPP-R) ranged from -0.09 to 0.14 mg L-1 d(-1) and switched, on average, from positive to negative towards deeper lakes and lakes richer in dissolved organic carbon (DOC; 0.5-7.4 mg DOC L-1). Uncertainties in metabolism estimates were high (around one and three times mean R and GPP), especially in deep lakes with low insulation and diurnally variable wind speed. Our results confirm the role of DOC in stimulating net heterotrophy and highlight novel effects of lake shape on productivity in benthic-dominated lake ecosystems and its response to changes in lake ice cover.

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 km 2 ), 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.

Scaling relationships provide simple rules for understanding complex hydrographic patterns. Globally, river inlet abundance varies among lakes by about three orders of magnitude, but few scaling relationships describe this aspect of lake‐river connectivity. In this study, we describe a simple theoretical scaling relationship between lake surface area and river inlet abundance, and test this theory using data from Scandinavia. On average, the number of inlets increases by 67% for each doubling of lake area. However, lakes of vastly different areas can have the same number of inlets with relatively small variations of drainage density, lake shape, or junction angle ‐ characteristics that can often be linked to specific geological processes. Our approach bridges the gap between the detailed understanding of geomorphic processes and large‐scale statistical relationships, and engenders predictions about additional patterns including the relationship between lake area and water residence time.

The littoral zone varies in size among lakes from ∼3% to 100% of lake surface area. In this paper, we derive a simple theoretical scaling relationship that explains this variation, and test this theory using bathymetric data across the size spectra of freshwater lakes (surface area = 0.01–82,103 km 2 , maximum depth = 2–1,741 m). Littoral area primarily reflects the ratio of the maximum depth of photosynthesis to maximum lake depth. However, lakes that are similar in these characteristics can have different relative littoral areas because of variation in basin shape. Hypsometric (area‐elevation) models that describe these patterns for individual lakes can be generalized among lakes to accurately predict the relative size of littoral habitat when there is incomplete bathymetric information. Collectively, our results provide simple rules for understanding patterns of littoral habitat size at the regional and global scales.