Imperfect slope measurements drive overestimation in a geometric cone model of lake and reservoir depth

Stachelek, Jemma; Hanly, Patrick J.; Soranno, Patricia A.

doi:10.1080/20442041.2021.2006553

Cited by 6 publications

(12 citation statements)

References 32 publications

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“…We, therefore, introduce the free parameter ℓ that allows us to relate L to a according to L ¼ ℓ ffiffiffi a p . ℓ should be no larger than what it would be for a circular lake with its maximum depth at the center, that is, ℓ ¼ ffiffiffiffiffiffiffiffi 2=π p ≈ 0:8, but is likely much smaller as lakes take myriad shapes that are often very far from circular, and their maximum depths do not have to be in their center (Stachelek et al 2022). To compare the theoretical distribution to observed depths, it is further useful to use a normalized maximum depth y ¼ z= ffiffiffi 2 p L H and define the probability distribution in terms of y, that is, p(y) (that can later be recast in terms of z).…”

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confidence: 99%

A theory for the relationship between lake surface area and maximum depth

Cael

Seekell

2022

Limnol Oceanogr Letters

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Many foundational ecosystem characteristics in lakes are constrained by maximum depth. However, aquatic scientists have struggled to both explain this variation and to predict maximum depths for lakes without detailed bathymetric surveys. The morphometry of collections of lakes has previously been shown to follow theoretical predictions that assume Earth's topography approximates a fractal Browning motion. In this study, we apply these theories to the relationship between lake maximum depth and surface area, providing a solution to this problem of predicting lakes' maximum depths. Maximum depth increases with surface area, but massive lake-to-lake variation is an inherent characteristic of this pattern because the maximum depth is an extreme of a random topographic profile. The probability distribution of maximum depths used here can be leveraged to upscale the patterns and processes for many lakes at the regional or global scale. We demonstrate this for the diffusive flux of methane from temperate lakes to the atmosphere-a process that correlates strongly with maximum depth but not surface area.

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confidence: 99%

A theory for the relationship between lake surface area and maximum depth

Cael

Seekell

2022

Limnol Oceanogr Letters

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“…We calculate that the median volume development factor for lakes used in Stachelek et al (2022) was 1.2 whereas ours was 1.9. We attribute the higher number of concave lakes reported in Stachelek et al (2022) partially to the much greater prevalence of small lakes in our dataset (417,442 < 10 5 m 2 , 87%) compared to the bathymetric data in the cited study, which had relatively few small lakes (562 < 10 5 m 2 , 11%). However, this alone does not explain the entire difference between our study and the work of Stachelek et al (2022).…”

Section: Discussionmentioning

confidence: 89%

“…First, the temperature-based model described in Becker and Daw (2005) could not be replicated due to a lack of cloud-free nighttime land surface temperature imagery in the study area. Likewise, the bathymetrybased ("true slope") model of Stachelek et al (2022) could not be replicated due to insufficient bathymetric data for our lake depth dataset. Exact replication of prior work was further precluded by differing elevation data sources, processing constraints, and a lack of consistent watershed boundaries.…”

Section: Modeling Workflowmentioning

confidence: 99%

The distribution of depth, volume, and basin shape for lakes in the conterminous United States

Ganz,

Glines,

Rose

2023

Limnology & Oceanography

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Depth regulates many attributes of aquatic ecosystems, but relatively few lakes are measured, and existing datasets are biased toward large lakes. To address this, we used a large dataset of maximum (Zmax; n = 16,831) and mean (Zmean; n = 5,881) depth observations to create new depth models, focusing on lakes < 1,000 ha. We then used the models to characterize patterns in lake basin shape and volume. We included terrain metrics, water temperature and reflectance, polygon attributes, and other predictors in a random forest model. Our final models generally outperformed existing models (Zmax ; root mean square error [RMSE] = 8.0 m and Zmean ; RMSE = 3.0 m). Our models show that lake depth followed a Pareto distribution, with 2.8 orders of magnitude fewer lakes for an order of magnitude increase in depth. In addition, despite orders of magnitude variation in surface area, most size classes had a modal maximum depth of ~ 5 m. Concave (bowl‐shaped) lake basins represented 79% of all lakes, but lakes were more convex (funnel‐shaped) as surface area increased. Across the conterminous United States, 9.8% of all lake water was within the top meter of the water column, and 48% in the top 10 m. Excluding the Laurentian Great Lakes, we estimate the total volume in the conterminous United States is 1,057–1,294 km3, depending on whether Zmax or Zmean was modeled. Lake volume also exhibited substantial geographic variation, with high volumes in the upper Midwest, Northeast, and Florida and low volumes in the southwestern United States.

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“…One might think that lake depth could be estimated from the depth of nearby lakes, from a lake's origin (e.g., glacial vs. volcanic), or from the nearby terrain of the land. However, none of these factors has been shown to accurately predict lake depth; in fact, models designed to predict lake depth from these types of factors have generated lake depth predictions with very large uncertainties that do little to improve our understanding of lake depth or to inform the use of lake depth to predict other important factors (Oliver et al 2016; Stachelek et al In press). Thus, we are left with having to measure lake depth directly rather than predicting it from easily acquired data sources.…”

Section: Getting Our Feet Wetmentioning

confidence: 99%

Deeper by the Dozen: Diving into a Database of 17,675 Depths for U.S. Lakes and Reservoirs

Webster

McCullough

Soranno

2022

Limnology & Oceanogr Bull

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Depth is a fundamental property of lakes, essential for understanding and quantifying a range of biological, chemical, and physical processes of individual lakes as well as the collective functioning of the millions of lakes across the globe. Despite this importance, lake depth is rarely available for large numbers of lakes across the broad scales of regions and continents. We describe a new open-access dataset, LAGOS-US DEPTH, which contains 17,675 maximum depths and 6,137 mean depths for lakes in the conterminous United States. These data represent one of the largest compilations of lake depths in the world and are connected to other data products through the LAGOS-US research platform. Here, we describe characteristics of lake maximum depth across the conterminous United States and identify gaps in data coverage that we encourage other researchers to fill by linking their own depth datasets for lakes within the LAGOS-US spatial footprint. Extending this open-access effort to include other regions and countries across the globe to build a more comprehensive and representative database of lake depth would better position scientists to quantify and articulate the critical roles that lakes play globally in biogeochemical cycling, maintaining biodiversity, and in maintaining the many ecosystem services that lakes provide.

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Imperfect slope measurements drive overestimation in a geometric cone model of lake and reservoir depth

Cited by 6 publications

References 32 publications

A theory for the relationship between lake surface area and maximum depth

A theory for the relationship between lake surface area and maximum depth

The distribution of depth, volume, and basin shape for lakes in the conterminous United States

Deeper by the Dozen: Diving into a Database of 17,675 Depths for U.S. Lakes and Reservoirs

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