This content will become publicly available on April 28, 2027

Title: Self‐Affine Scaling of Earth's Islands
Abstract Earth's relief is approximately self‐affine, meaning a zoom‐in on a small region looks statistically similar to a large region upon rescaling. Fractional Brownian surfaces give an idealized self‐affine model of Earth's relief with one parameter, the Hurst exponent , characterizing the roughness of the surface. We compile a large data set of topographic profiles of islands (N = 131,063 with the range of areas covering approximately 8 orders of magnitude) and obtain four estimates for the Hurst exponent of Earth's surface by fitting four statistical laws from the theory of self‐affine surfaces concerning islands: (a) distribution of areas, (b) volume‐area relationship, (c) perimeter‐area relationship, and (d) maximum height‐area relationship. The estimated Hurst exponents indicate different fractal scaling behavior for different geometric features, and are sorted in order of increasing expected influence of coastal processes. This sheds light on the impact of coastal erosion and sedimentation on island geomorphology.  more » « less
Award ID(s):
2235451
PAR ID:
10686908
Author(s) / Creator(s):
 ;  ;  ;  ;  
Publisher / Repository:
AGU
Date Published:
Journal Name:
Geophysical Research Letters
Volume:
53
Issue:
8
ISSN:
0094-8276
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ABSTRACT Language is thought to have multiple sensitive periods in early childhood, but the neural basis of these sensitive periods is less understood. We leverage advances in in‐vivo neuroimaging of plasticity, measuring the neural inhibition across the brain via Hurst exponent. Using two large datasets with children ages 10 months to 18 years (Baby Connectome Project: 10m‐3y6m, 458 observations acrossn= 222 children; Human Connectome Project‐Development: 5–18y,n= 437), we characterize the development of the Hurst exponent in language‐related brain regions. In early childhood, Hurst increases in temporal and frontal language areas, and posterior regions develop earlier than anterior regions. In contrast, thalamic Hurst plateaus earlier, perhaps underlying the earliest language‐related sensitive periods. Children with higher language‐related skills show slower increases in cortical Hurst in early childhood, suggesting protracted plasticity. Later in childhood, cortical Hurst plateaus around age 9, suggesting a potential neural mechanism for age‐related declines syntax learning. These results highlight a potential neural basis for cascading language‐related sensitive periods. 
    more » « less
  2. Abstract In this work, we experimentally measured the pinch‐off of a gas bubble on a biphilic surface, which consisted of an inner circular superhydrophobic region and an outer hydrophilic region. The superhydrophobic region had a radius ofRSHvarying from 2.8 to 19.0 mm, where the largeRSHmodeled an infinitely large superhydrophobic surface. We found that during the pinch‐off, the contact line had two different behaviors: for smallRSH, the contact line was fixed at the boundary of superhydrophobic and hydrophilic regions, and the contact angle gradually increased; in contrast, for largeRSH, the contact angle was fixed, and the contact line shrank toward the bubble center. Furthermore, we found that regardless of bubble size and contact line behavior, the minimum neck radius collapsed onto a single curve after proper normalizations and followed a power–law relation where the exponent was close to that for bubble pinch‐off from a nozzle. The local surface shapes near the neck were self‐similar. Our results suggest that the surface wettability has a negligible impact on the dynamics of pinch‐off, which is primarily driven by liquid inertia. Our findings improve the fundamental understanding of bubble pinch‐off on complex surfaces. 
    more » « less
  3. The volume of a lake is a crucial component in understanding environmental and hydrologic processes. The State of Minnesota (USA) has tens of thousands of lakes, but only a small fraction has readily available bathymetric information. In this paper we develop and test methods for predicting water volume in the lake-rich region of Central Minnesota. We used three different published regression models for predicting lake volume using available data. The first model utilized lake surface area as the sole independent variable. The second model utilized lake surface area but also included an additional independent variable, the average change in land surface area in a designated buffer area surrounding a lake. The third model also utilized lake surface area but assumed the land surface to be a self-affine surface, thus allowing the surface area-lake volume relationship to be governed by a scale defined by the Hurst coefficient. These models all utilized bathymetric data available for 816 lakes across the region of study. The models explained over 80% of the variation in lake volumes. The sum difference between the total predicted lake volume and known volumes were <2%. We applied these models to predicting lake volumes using available independent variables for over 40,000 lakes within the study region. The total lake volumes for the methods ranged from 1,180,000- and 1,200,000-hectare meters. We also investigated machine learning models for estimating the individual lake volumes and found they achieved comparable and slightly better predictive performance than from the three regression analysis methods. A 15-year time series of satellite data for the study region was used to develop a time series of lake surface areas and those were used, with the first regression model, to calculate individual lake volumes and temporal variation in the total lake volume of the study region. The time series of lake volumes quantified the effect on water volume of a dry period that occurred from 2011 to 2012. These models are important both for estimating lake volume, but also provide critical information for scaling up different ecosystem processes that are sensitive to lake bathymetry. 
    more » « less
  4. Abstract Fault geometry affects the initiation, propagation, and cessation of earthquake rupture, as well as, potentially, the statistical behavior of earthquake sequences. We analyze 18,250 (−0.27 < M < 4.4) earthquakes of the 2016–2019 Cahuilla, California, swarm and, for the first time, use these high-resolution earthquake locations to map, in detail, the roughness across an active fault surface at depth. We find that the strike-slip fault is 50% rougher in the slip-perpendicular direction than parallel to slip. 3D mapping of fault roughness at seismogenic depths suggests that roughness varies by a factor of 8 for length scales of 1 km. We observe that the largest earthquake (M 4.4) occurred where there is significant fault complexity and the highest measured roughness. We also find that b-values are weakly positively correlated with fault roughness. Following the largest earthquake, we observe a distinct population of earthquakes with comparatively low b-values occurring in an area of high roughness within the rupture area of the M 4.4 earthquake. Finally, we measure roughness at multiple scales and find that the fault is self-affine with a Hurst exponent of 0.52, consistent with a Brownian surface. 
    more » « less
  5. Abstract An ongoing thrust of research focused on human gait pertains to identifying individuals based on gait patterns. However, no existing gait database supports modeling efforts to assess gait patterns unique to individuals. Hence, we introduce the Nonlinear Analysis Core (NONAN) GaitPrint database containing whole body kinematics and foot placement during self-paced overground walking on a 200-meter looping indoor track. Noraxon Ultium MotionTMinertial measurement unit (IMU) sensors sampled the motion of 35 healthy young adults (19–35 years old; 18 men and 17 women;mean ± 1 s.d. age: 24.6 ± 2.7 years; height: 1.73 ± 0.78 m; body mass: 72.44 ± 15.04 kg) over 18 4-min trials across two days. Continuous variables include acceleration, velocity, position, and the acceleration, velocity, position, orientation, and rotational velocity of each corresponding body segment, and the angle of each respective joint. The discrete variables include an exhaustive set of gait parameters derived from the spatiotemporal dynamics of foot placement. We technically validate our data using continuous relative phase, Lyapunov exponent, and Hurst exponent—nonlinear metrics quantifying different aspects of healthy human gait. 
    more » « less