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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.

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 (r2 = 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.

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.

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.

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 km2, 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.

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.

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.

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.

The original version of this Article contained errors. A subset of the global lake census was incorrectly and inadvertently used instead of the full dataset resulting in three parameters to be incorrect: power-law slope for the lake size-distribution, the area at which small lakes begin to deviate from a power-law distribution, and the fractal dimension relating lake areas to perimeters.

Global lake volume estimates are scarce, highly variable, and poorly documented. We developed a rigorous method for estimating global lake depth and volume based on the Hurst coefficient of Earth's surface, which provides a mechanistic connection between lake area and volume. Volume‐area scaling based on the Hurst coefficient is accurate and consistent when applied to lake data sets spanning diverse regions. We applied these relationships to a global lake area census to estimate global lake volume and depth. The volume of Earth's lakes is 199,000 km3 (95% confidence interval 196,000–202,000 km3). This volume is in the range of historical estimates (166,000–280,000 km3), but the overall mean depth of 41.8 m (95% CI 41.2–42.4 m) is significantly lower than previous estimates (62–151 m). These results highlight and constrain the relative scarcity of lake waters in the hydrosphere and have implications for the role of lakes in global biogeochemical cycles.

Globally, there are millions of small lakes, but a small number of large lakes. Most key ecosystem patterns and processes scale with lake size, thus this asymmetry between area and abundance is a fundamental constraint on broad-scale patterns in lake ecology. Nonetheless, descriptions of lake size-distributions are scarce and empirical distributions are rarely evaluated relative to theoretical predictions. Here we develop expectations for Earth’s lake area-distribution based on percolation theory and evaluate these expectations with data from a global lake census. Lake surface areas ≥0.46 km2 are power-law distributed with a tail exponent (τ = 2.14) and fractal dimension (d = 1.4), similar to theoretical expectations (τ = 2.05; d = 4/3). Lakes <0.46 km2 are not power-law distributed. An independently developed regional lake census exhibits a similar transition and consistency with theoretical predictions. Small lakes deviate from the power-law distribution because smaller lakes are more susceptible to dynamical change and topographic behavior at sub-kilometer scales is not self-similar. Our results provide a robust characterization and theoretical explanation for the lake size-abundance relationship, and form a fundamental basis for understanding and predicting patterns in lake ecology at broad scales.