Topological self-similarity on the random binary-tree model

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented

Community Workflows to Advance Reproducibility in Hydrologic Modeling: Separating Model-Agnostic and Model-Specific Configuration Steps in Applications of Large-Domain Hydrologic Models

Despite the proliferation of computer-based research on hydrology and water resources, such research is typically poorly reproducible. Published studies have low reproducibility due to incomplete availability of data and computer code, and a lack of documentation of workflow processes. This leads to a lack of transparency and efficiency because existing code can neither be quality controlled nor reused. Given the commonalities between existing process-based hydrologic models in terms of their required input data and preprocessing steps, open sharing of code can lead to large efficiency gains for the modeling community. Here, we present a model configuration workflow that provides full reproducibility of the resulting model instantiations in a way that separates the model-agnostic preprocessing of specific data sets from the model-specific requirements that models impose on their input files. We use this workflow to create large-domain (global and continental) and local configurations of the Structure for Unifying Multiple Modeling Alternatives (SUMMA) hydrologic model connected to the mizuRoute routing model. These examples show how a relatively complex model setup over a large domain can be organized in a reproducible and structured way that has the potential to accelerate advances in hydrologic modeling for the community as a whole. We provide a tentative blueprint of how community modeling initiatives can be built on top of workflows such as this. We term our workflow the “Community Workflows to Advance Reproducibility in Hydrologic Modeling” (CWARHM; pronounced “swarm”). © 2022. The Authors.Open access articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Is There Synchronicity in Nitrogen Input and Output Fluxes at the Noland Divide Watershed, a Small N-Saturated Forested Catchment in the Great Smoky Mountains National Park?

High-elevation red spruce [Picea rubens Sarg.]-Fraser fir [Abies fraseri (Pursh.) Poir] forests in the Southern Appalachians currently receive large nitrogen (N) inputs via atmospheric deposition (30 kg N ha�1 year�1) but have limited N retention capacity due to a combination of stand age, heavy fir mortality caused by exotic insect infestations, and numerous gaps caused by windfalls and ice storms. This study examined the magnitude and timing of the N fluxes into, through, and out of a small, first-order catchment in the Great Smoky Mountains National Park. It also examined the role of climatic conditions in causing interannual variations in the N output signal. About half of the atmospheric N input was exported annually in the streamwater, primarily as nitrate (NO3-N). While most incoming ammonium (NH4-N) was retained in the canopy and the forest floor, the NO3-N fluxes were very dynamic in space as well as in time. There was a clear decoupling between NO3-N input and output fluxes. Atmospheric N input was greatest in the growing season while largest NO3-N losses typically occurred in the dormant season. Also, as water passed through the various catchment compartments, the NO3-N flux declined below the canopy, increased in the upper soil due to internal N mineralization and nitrification, and declined again deeper in the mineral soil due to plant uptake and microbial processing. Temperature control on N production and hydrologic control on NO3-N leaching during the growing season likely caused the observed inter-annual variation in fall peak NO3-N concentrations and N discharge rates in the stream