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2081 hydrology Preprints

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hydrology hydro-environmental modeling soil sciences gedi driven interfaces hele-shaw flows water quality Applied computing soil physics nonequilibrium thermodynamics homemade restoration stable isotopes hydrography ecohydrology stochastic hydrology geography informatics shore and near-shore processes water balance snow geophysics satellite altimetry climatology (global change) porous media + show more keywords
isotope analog method geochemistry cryosphere rain physical oceanography flood frequency analysis climate change limnology fluid mechanics sampling remote sensing meteorology remote sensing (geology) geology snow depth environmental sciences salmonid geodesy information and computing sciences Disorder reproducibility soil moisture atmospheric optics icesat-2 atmospheric sciences topographic geography scaling streamflows precipitation isotope tracers input variable selection oceanography logistic regression uncertainty genetic algorithms waterfowl optimization bayesian
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Please note: These are preprints and have not been peer reviewed. Data may be preliminary.
Evaluating the Efficacy of Manmade Canals at Maintaining Lake Habitats for Salmon an...
Adrian A Jimenez
John Bershaw

Adrian A Jimenez

and 4 more

July 13, 2023
We investigated whether hydrologic restoration at Sturgeon Lake, Oregon, USA has sufficiently increased water flux and reduced stagnation, improving environmental conditions for juvenile salmon and waterfowl. This 19.2km2 lake is a pivotal environmental feature in the area, providing a haven for salmon on the Columbia River before reaching the Pacific Ocean and winter habitat for hundreds of thousands of waterfowl and migratory birds on the Pacific Flyway. The Oregon Conservation Strategy names restoring natural hydrology to Sturgeon Lake as a key step toward conservation in this area. We use stable isotopes of water from the lake, surrounding water bodies, and precipitation to understand the restoration work’s efficacy and whether further efforts are necessary to restore healthy habitats. Because of its importance to bird migration and salmon spawning, we focus on seasonal patterns in lake hydrology. We determined that approximately 36.5% and 9.5% of water input was lost to evaporation during the summer and winter, respectively, after restoration. We estimate the residence time of water in the lake to average ~43.2 days during the study period. Based on these results, we determined that the lake habitat is being adequately maintained in the winter, when it is most valuable to local fauna, but that some stagnation and potential ecosystem degradation occurs in the summer. Neither juvenile salmonids nor migratory birds utilize the lake during the summer, therefore the restoration work is effective at maintaining habitat for these species, but further summer-focused work could be beneficial.
LiDAR Uncertainty Quantification for Topo-Bathymetric Earth Science using Generalized...
Alexandra Katherine Wise
Kevin Sacca

Alexandra Katherine Wise

and 2 more

July 20, 2023
Though precise, most LiDARs are vulnerable to position and pointing errors as deviations from the expected principal axis lead to projection errors on target. While fidelity of location/pointing solutions can be high, determination of uncertainty remains relatively limited. As a result, NASA’s 2021 Surface Topography and Vegetation Incubation Study Report lists vertical (horizontal, geolocation) accuracy as an associated parameter for all (most) identified Science and Application Knowledge Gaps, and identifies maturation of Uncertainty Quantification (UQ) methodologies on the STV Roadmap for this decade. The presented generalized Polynomial Chaos Expansion (gPCE) based method has wide ranging applicability to improve positioning, geolocation uncertainty estimates for all STV disciplines, and is extended from the bare earth to the bathymetric lidar use case, adding complexity introduced by entry angle, wave structure, and sub-surface roughness. This research addresses knowledge gaps in bathy-LiDAR measurement uncertainty through a more complete description of total aggregated uncertainties, from system level to geolocation, by applying a gPCE-UQ approach. Currently, the standard approach is the calculation of the Total Propagated Uncertainty, which is often plagued by simplifying approximations (e.g. strictly Gaussian uncertainty sources) and ignored covariances. gPCE intrinsically accounts for covariance between variables to determine uncertainty in a measurement, without manually constructing a covariance matrix, through a surrogate model of system response. Additionally, gPCE allows arbitrarily high order uncertainty estimates (limited only by the one-time computational cost of computing gPCE coefficients), accurate representation of non-Gaussian sources of error (e.g. wave height energy distributions), and direct integration of measurement requirements into the design of LiDAR systems, by trivializing the computation of global sensitivity analysis.
Affordable event and monthly rain samplers: Improving isotopic datasets to understand...
Cécile Carton
Florent Barbecot

Cécile Carton

and 6 more

July 10, 2023
Stable isotopes of the water molecule have emerged as powerful tracers of the sources and trajectories of water leading to precipitation, at different spatial and temporal scales. However, the high cost of commercially available rain samplers for isotopic analysis, have made using them for high spatial resolution networks and for studies being conducted in developing countries prohibitively expensive. We have designed a low-cost, simple, and robust rain sampler capable of sampling precipitation for isotopic analysis on the event and monthly scale, based on the existing designs provided in the literature. The event rain samplers were tested to determine the minimum amount of rainfall to minimize isotopic fractionation, both from post-sampling evaporation and equilibration. These new rain samplers will enable isotopic sampling of precipitation at high spatial resolutions. All the instructions for constructing and using these samplers are made openly accessible to the scientific community so they can easily be repeated and adapted to the needs of each project. This open access and low-cost methodology will help democratize the use of isotopes for hydrological studies in developing countries.
Automated Input Variable Selection for Analog Methods Using Genetic Algorithms
Pascal Horton
Olivia Martius

Pascal Horton

and 2 more

July 31, 2023
Analog methods (AMs) have long been used for precipitation prediction and climate studies. However, they rely on manual selections of parameters, such as the predictor variables and analogy criterion. Previous work showed the potential of genetic algorithms (GAs) to optimize most parameters of AMs. This research goes one step further and investigates the potential of GAs for automating the selection of the input variables and the analogy criteria (distance metric between two data fields) in AMs. Our study focuses on daily precipitation prediction in central Europe, specifically Switzerland, as a representative case. Comparative analysis against established reference methods demonstrates the superiority of the GA-optimized AM in terms of predictive accuracy. The selected input variables exhibit strong associations with key meteorological processes that influence precipitation generation. Further, we identify a new analogy criterion inspired by the Teweles-Wobus criterion, but applied directly to grid values, which consistently performs better than other Euclidean distances. It shows potential for further exploration regarding its unique characteristics. In contrast to conventional stepwise selection approaches, the GA-optimized AM displays a preference for a flatter structure, characterized by a single level of analogy and an increased number of variables. Although the GA optimization process is computationally intensive, we highlight the use of GPU-based computations to significantly reduce computation time. Overall, our study demonstrates the successful application of GAs in automating input variable selection for AMs, with potential implications for application in diverse locations and data exploration for predicting alternative predictands.
Simultaneous Determination of Relative Permeability and Capillary Pressure from an Un...
Steffen Berg

Steffen Berg

and 5 more

July 08, 2023
A document by Steffen Berg. Click on the document to view its contents.
Stochastic in Space and Time: Part 1, Characterizing Orographic Gradients in Mean Run...
Adam Matthew Forte
Matthew W. Rossi

Adam Matthew Forte

and 1 more

July 08, 2023
Mountain topography alters the phase, amount, and spatial distribution of precipitation. Past efforts focused on how orographic precipitation alters runoff spatial distribution, but with less emphasis on how stochastic runoff generation is also patterned on topography. Given the importance of the magnitude and frequency of stochastic runoff events to fluvial erosion, we evaluate whether orographic patterns in mean runoff and daily runoff variability can be constrained using the global WaterGAP3 water model data. Model runoff data is validated against observational data in the contiguous United States, showing agreement with mean runoff in all settings and daily runoff variability in settings where rainfall-runoff predominates. In snowmelt-influenced settings, runoff variability is overestimated by the water model data. Cognizant of these limitations, we use the water model data to develop relationships between mean runoff and daily runoff variability and how these are mediated by snowmelt fraction in mountain topography globally. Attempts to explain topographic controls on hydro-climatic variables using a Random Forest Regression model were less clear. Instead, relationships between topography and runoff parameters are better assessed at mountain range scale. Rulesets linking topography to mean runoff and snowmelt fraction are developed for three mid-latitude mountain landscapes—British Columbia, European Alps, and Greater Caucasus. Increasing topographic elevation and relief together lead to higher mean runoff and lower runoff variability due to the increasing contribution of snowmelt. The three sets of empirical relationships developed here serve as the basis for a suite of numerical experiments in our companion manuscript to this one (Part 2).
Stochastic in Space and Time: Part 2, Effects of Simulating Orographic Gradients in D...
Adam Matthew Forte
Matthew W. Rossi

Adam Matthew Forte

and 1 more

July 08, 2023
Understanding the extent to which climate and tectonics can be coupled requires knowing both the form of topography and erosion rate relationships, but also the underlying mechanistic controls on those forms. The stream power incision model (SPIM) is commonly used to interpret such topography erosion rate relationships, but is limited in terms of probing mechanisms. A promising modification is a stochastic-threshold incision model (STIM) which incorporates both variability in discharge and a threshold to erosion, and in which the form of the topography erosion rate relationship is largely controlled by the variability of runoff. However, as applied STIM assumes temporally variable, but spatially constant runoff generating events, an assumption that is likely broken in regions with complicated orography. In response, we develop a unique 1D STIM based profile model that allows for stochasticity in both time and space and is driven by empirical relations between topography and runoff statistics. Testing the development of steady-state topography using spatial-STIM over a range of uplift rates highlights that coupling between mean runoff, runoff variability, and topography suggest that the development of highly nonlinear topography erosion rates should be expected. Further, we find that whether the daily statistics of runoff generating events are spatially linked or unlinked is a primary control on landscape evolution and the final resulting topography. As many empirical topography – erosion rate datasets likely sample across ranges of linked vs unlinked behavior, it is questionable whether single SPIM relationships fit to those data, without considerations of the hydroclimatology, are meaningful.
Snow depth from satellite laser altimetry (AGU 2021 presentation)
David Shean

David Shean

July 07, 2023
A document by David Shean. Click on the document to view its contents.
Rainfall frequency Analysis Based in Long-Term High-Resolution Radar Rainfall Fields:...
James A Smith
Mary Lynn Baeck

James A Smith

and 3 more

June 29, 2023
Rainfall frequency analyses are presented for the Baltimore Metropolitan region based on a 22-year, high-resolution radar rainfall data set. Analyses focus on spatial heterogeneities and time trends in sub-daily rainfall extremes. The rainfall data set covers a domain of 4900 $km^2$, has a spatial resolution of approximately 1 km and a time resolution of 15 minutes. The data set combines reflectivity-based rainfall fields during the period from 2000 - 2015 and operational polarimetric rainfall fields for the period from 2012 - 2021. Analyses of rainfall fields during the 2012 - 2015 overlap period provide grounding for assessing time trends in rainfall frequency. There are pronounced spatial gradients in short-duration rainfall extremes over the study region, with peak values of rainfall between Baltimore City and Chesapeake Bay. Rainfall frequency analyses using both peaks-over-threshold and annual peak methods point to increasing trends in short-duration rainfall extremes over the period from 2000 to 2021. Intercomparisons of sub-daily rainfall extremes with daily extremes show significant differences. Less than 50$\% $ of annual maximum hourly values occur on the same day as the daily maximum and there is relatively weak correlation between magnitudes when the hourly and daily maximum overlap. Changing measurement properties are a key challenge for application of radar rainfall data sets to detection of time trends. Mean field bias correction of radar rainfall fields using rain gauge observations is both an important component of the 22-year rainfall data set and a useful tool for addressing problems associated with changing radar measurement properties.
Projected Changes in Mean and Extreme Precipitation Over Northern Mexico
Robert Nazarian

Robert Nazarian

and 5 more

June 29, 2023
A document by Robert Nazarian. Click on the document to view its contents.
Considering Uncertainty of Historical Ice Jam Flood Records in a Bayesian Frequency A...
Jared D. Smith

Jared D. Smith

and 2 more

June 25, 2023
The Peace-Athabasca Delta in Alberta, Canada has numerous perched basins that are primarily recharged after large ice jams cause floods (an ecological benefit). Previous studies have estimated that such large floods are likely to decrease in frequency under various climate projections. However, there is a sizeable uncertainty range in these predicted flood probabilities, in part due to the short 60-year systematic record that contained few large ice jam floods. An additional 50 years of historical data are available from various sources, with expert-interpreted flood categories; however, these categorizations are uncertain in magnitude and occurrence. We developed a Bayesian framework that considers magnitude and occurrence uncertainties within a logistic regression model that predicts the annual probability of a large flood. The Bayesian regression estimates the joint distribution of parameters describing the effects of climatic factors and parameters that describe the probability that historical flood magnitudes were recorded as large (or not) when a truly large (or not) flood occurred. We compare four models for hindcasting and projecting large ice jam flood probabilities in future climates. The models consider: 1) historical data uncertainty, 2) no historical data uncertainty, 3) only the systematic record, and 4) the systematic record with a different model structure. Neglecting historical data uncertainty provides inaccurate estimates, while using only the systematic record provides wider prediction intervals than considering the full record with uncertain historical data. Thus, we demonstrate that including uncertain historical information can effectively extend the record length and improve flood frequency analyses.
A multi-chemistry modelling framework to enable flexible and reproducible water quali...
Diogo Costa
Kyle Klenk

Diogo Costa

and 5 more

June 19, 2023
This work advances the incorporation and cross-model deployment of multi-biogeochemistry and ecological simulations in existing process-based hydro-modelling tools. It aims to transform the current practice of water quality modelling as an isolated research effort into a more integrated and collaborative activity between science communities. Our approach, which we call “Open Water Quality” (OpenWQ), enables existing hydrological, hydrodynamic, and groundwater models to extend their capabilities to water quality simulations, which can be set up to examine a variety of water-related pollution problems. OpenWQ’s objective is to provide a flexible biogeochemical model representation that can be used to test different modelling hypotheses in a multi-disciplinary co-creative process. In this paper, we introduce the general approach used in OpenWQ. We detail aspects of its architecture that enable its coupling with existing models. This integration enables water quality models to benefit from advances made by hydrologic- and hydrodynamic-focused groups, strengthening collaboration between the hydrological, biogeochemistry, and soil science communities. We also detail innovative aspects of OpenWQ’s modules that enable biogeochemistry lab-like capabilities, where modellers can define the pollution problem(s) of interest, the appropriate complexity of the biogeochemistry routines, and test different modelling hypotheses. In a companion paper, we demonstrate how OpenWQ has been coupled to two hydrological models, the “Structure for Unifying Multiple Modelling Alternatives” (SUMMA) and the “Cold Regions Hydrological Model” (CRHM), demonstrating the innovative aspects of OpenWQ, the flexibility of its couplers and internal spatiotemporal data structures, and the versatile eco-modelling lab capabilities that can be used to study different pollution problems.
A multi-chemistry modelling framework to enable flexible and reproducible water quali...
Diogo Costa
Kyle Klenk

Diogo Costa

and 5 more

June 11, 2023
This work advances the cross-model deployment of ecological and biogeochemical simulation capabilities in existing process-based hydro-modeling tools, which we term “Open Water Quality” (OpenWQ). The companion paper details aspects of the OpenWQ architecture that enables its plug-in type incorporation into existing models, along with its innovative aspects that enable biogeochemistry lab-like capabilities. OpenWQ’s innovative aspects allow modelers to define the pollution problem(s) of interest, the appropriate complexity of the biogeochemistry routines, test different modeling hypotheses, and deploy them across different hydro-models. In this second paper, we implemented the coupling recipe described in the first paper to integrate OpenWQ into two hydro-models, SUMMA and CRHM. Here we explain how the implemented coupling interface between the two models provides water quality simulation capacities in the host hydro-models but, more importantly, establishes a direct and permanent link for the transfer of innovation between the modeling communities. Example applications of different pollution studies enabled by our coupling recipe are also provided to address some of these fundamental water quality modeling challenges.
STOCHASTIC INVERSION WITH MAXIMAL UPDATED DENSITIES FOR STORM SURGE WIND DRAG PARAMET...
Carlos del-Castillo-Negrete

Carlos del-Castillo-Negrete

and 4 more

June 06, 2023
A document by Carlos del-Castillo-Negrete. Click on the document to view its contents.
A Novel Deep Learning Approach for Data Assimilation of Complex Hydrological Systems
Jiangjiang Zhang
Chenglong Cao

Jiangjiang Zhang

and 5 more

June 01, 2023
In hydrological research, data assimilation (DA) is widely used to fuse the information contained in process-based models and observational data to reduce simulation uncertainty. However, many popular DA methods are limited by low computational efficiency or their reliance on the Gaussian assumption. To address these limitations, we propose a novel DA method called DA(DL), which leverages the capabilities of deep learning (DL) to model non-linear relationships and recognize complex patterns. DA(DL) first generates a large volume of training data from the prior ensemble, and then trains a DL model to update the system knowledge (e.g., model parameters in this study) from multiple predictors. For highly non-linear models, an iterative form of DA(DL) can be implemented. Additionally, strategies of data augmentation and local updating are proposed to enhance DA(DL) for problems involving small ensemble size and the equifinality issue, respectively. In two hydrological DA cases involving Gaussian and non-Gaussian distributions, DA(DL) shows promising performance compared to two ensemble smoother (ES) methods, i.e., ES(K) and ES(DL), which respectively apply the Kalman- and DL-based updates. Potential improvements to DA(DL) can be made by designing better DL model architectures, imposing physical constraints to the training of the DL model, and further updating other important variables like model states, forcings and error terms.
Improved EPANET Hydraulic Model with Optimized Roughness Coefficient using Genetic Al...

May 25, 2023
A document by SHIU CHIA-CHENG. Click on the document to view its contents.
Synthetic simulation of spatially-correlated streamflows: Weighted-modified Fractiona...
Cristian Chadwick
Frederic Babonneau

Cristian Chadwick

and 3 more

May 25, 2023
Stochastic methods have been typically used for the design and operations of hydraulic infrastructure. They allow decision makers to evaluate existing or new infrastructure under different possible scenarios, giving them the flexibility and tools needed in decision making. In this paper, we present a novel stochastic streamflow simulation approach able to replicate both temporal and spatial dependencies from the original data in a multi-site basin context. The proposed model is a multi-site extension of the modified Fractional Gaussian Noise (mFGN) model which is well-known to be efficient to maintain periodic correlation for several time lags, but presents shortcomings in preserving the spatial correlation. Our method, called Weighted-mFGN (WmFGN), incorporates spatial dependency into streamflows simulated with mFGN by relying on the Cholesky decomposition of the spatial correlation matrix of the historical streamflow records. As the order in which the decomposition steps are performed (temporal then spatial, or vice-versa) affects the performance in terms of preserving the temporal and spatial correlation, our method searches for an optimal convex combination of the resulting correlation matrices. The result is a Pareto-curve that indicates the optimal weights of the convex combination depending on the importance given by the user to spatial and temporal correlations. The model is applied to Bio-bio River basin (Chile), where the results show that the WmFGN maintains the qualities of the single-site mFGN, while significantly improving spatial correlation.
Convection-Permitting Simulations of Precipitation over the Peruvian Central Andes: S...
Yongjie Huang

Yongjie Huang

and 7 more

May 25, 2023
A document by Yongjie Huang. Click on the document to view its contents.
Pore-scale fluid dynamics resolved in pressure fluctuations at the Darcy scale
Catherine Spurin
Samuel Krevor

Catherine Spurin

and 6 more

May 19, 2023
Complex flow dynamics have been observed, at the pore-scale, during multiphase through porous rocks. These dynamics are not captured in large scale models exploring the migration and trapping of subsurface fluids e.g., CO2 or hydrogen. Due to limitations in imaging capabilities, these dynamics cannot be observed directly at the larger, Darcy scale. Instead, by using pressure data from pore-scale (mm-scale) and core-scale (cm-scale) experiments, we show that fluctuations in pressure measured at the core-scale reflect specific fluid displacement events taking place at the pore-scale. The spectral characteristics of the pressure data depends on the flow dynamics, size of the rock sample, and heterogeneity of pore space. While high resolution imaging of large samples would be useful in assessing flow dynamics across many of the scales of interest, such an approach is currently infeasible. We suggest an alternative, pragmatic, approach examining pressure data in the time-frequency domain using wavelet transformation.
Title: Addition of Alkalinity to Rivers: a new CO2 Removal Strategy
Shannon Sterling

Shannon Sterling

and 5 more

May 11, 2023
A document by Shannon Sterling. Click on the document to view its contents.
Inverse modelling of core flood experiments for predictive models of sandstone and ca...
Senyou An
Nele Wenck

Senyou An

and 6 more

May 02, 2023
Field-scale observations suggest that rock heterogeneities control subsurface fluid flow, and these must be characterised for accurate predictions of fluid migration, such as during \CO2 sequestration. Recent efforts have focused on simulation-based inversion of laboratory observations with X-ray imaging, but models produced in this way have been limited in their predictive ability for heterogeneous rocks. We address the main challenges in this approach through an algorithm that combines: a 3-parameter capillary pressure model, spatial heterogeneity in absolute permeability, the constraint of history match iterations based on marginal error improvement, and image processsing that incorporates more of the experimental data in the calibration. We demonstrate the improvements on five rocks (two sandstones and three carbonates), representing a range of heterogeneous properties, some of which could not be previously modelled. The algorithm results in physically representative models of the rock cores, reducing non-systematic error to a level comparable to the experimental uncertainty.
The relation between dissipation and memory in two-fluid displacements in disordered...
Ran Holtzman

Ran Holtzman

and 3 more

April 16, 2023
We show that the return-point memory of cyclic macroscopic trajectories enables the derivation of a thermodynamic framework for quasistatically driven dissipative systems with multiple metastable states. We use this framework to sort out and quantify the energy dissipated in quasistatic fluid-fluid displacements in disordered media. Numerical computations of imbibition--drainage cycles in a quasi-2D medium with gap thickness modulations (imperfect Hele-Shaw cell) show that energy dissipation in quasistatic displacements is due to abrupt changes in the fluid-fluid configuration between consecutive metastable states (Haines jumps), and its dependence on microstructure and gravity. The relative importance of viscous dissipation is deduced from comparison with quasistatic experiments.
Quantifying geomorphically effective floods using satellite observations of river mob...
Anya S Leenman
Louise J. Slater

Anya S Leenman

and 4 more

April 20, 2023
Geomorphologists have long debated the relative importance of disturbance magnitude, duration and frequency in shaping landscapes. For river-channel adjustment during floods, some argue that cumulative flood ‘power’, rather than magnitude or duration, matters most. However, studies of flood-induced river-channel change often draw upon small datasets. Here, we combine Sentinel-2 imagery with flow data from laterally-active rivers to address this question using a larger dataset. We apply automated algorithms in Google Earth Engine to map rivers and detect their lateral shifting; we generate a large dataset to quantify channel change during 160 floods across New Zealand, Russia, and South America. Widening during these floods is best explained by their duration and cumulative hydrograph. We use a random forest regression model to predict flood-induced channel widening, with potential applications for hazard management. Ultimately, better global data on sediment supply and caliber would help us to understand flood-driven change to river planforms.
Preferential Hydrologic States and Tipping Characteristics of Global Surface Soil Moi...
Vinit Sehgal

Vinit Sehgal

and 1 more

March 09, 2023
A dynamic transition in soil hydrologic states through climate perturbations and terrestrial feedbacks governs soil-vegetation-climate (SVC) interactions, constrained by critical soil moisture (SM) thresholds. Observational and scaling constraints limit critical SM threshold estimation at the remote-sensing (RS) footprint scale. Using global surface SM (θRS) from NASA’s Soil Moisture Active Passive (SMAP) satellite, we characterize seasonal preferential hydrologic states of θRS and derive three tipping characteristics to estimate the intensity (Mean Tipping Depth, \(\overline{{\varepsilon}}\) ), frequency (Tipping Count, \(\eta\) ), and duration (Mean Tipped Time, \(\overline{{\tau}}\) ) of the excursion of θRS from wet- to dry-average conditions. The preferential state provides the seasonally dominant hydrological states of θRS, while tipping characteristics capture the ecosystem linkages of the dynamic transition in θRS hydrologic states. Globally, θRS predominantly exhibit a (unimodal) dry-preferential state, especially over arid/semi-arid drylands and a unimodal wet-preferential θRS state in high-latitude boreal forests and tundra biomes. Prevalence of (bimodal) bistable θRS state overlaps with regions of strong positive SM-precipitation coupling and monsoonal climate in semi-arid/ subhumid climates. Seasonal preferential hydrologic states co-vary with the regional variability in plant water stress threshold and land-atmospheric coupling strength. Tipping characteristics of θRS show sensitivity to intra-biome variability in SVC coexistence patterns and display high skill in partitioning global ecoregions. While \(\overline{{\varepsilon}}\)  and \(\eta\)  are climate-controlled, \(\overline{{\tau}}\)  is moderated by soil and vegetation through their influence over θRS drydown during Stage II evapotranspiration. Preferential states and tipping characteristics find applications in quantifying SVC coexistence patterns, climate model diagnosis, and assessing ecosystem sensitivity to climate change.
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