Results for “Integrated hydrologic modeling” — Page 9

DOE OSTI2024

Evaluating SWAT + model uncertainties for human and natural outcomes: Application in a Great Lakes agricultural watershed

Nutrient exports from agricultural lands in the Great Lakes Region pose significant threats to water quality and ecological health through eutrophication, hypoxia, and harmful algal blooms. Climate change and agricultural adaptation practices complicate future nutrient loading due to intensified hydrologic cycles and land use decisions. Our research focuses on evaluating the Soil and Water Assessment Tool (SWAT) plus model parametric uncertainties for human and natural outcomes across different scales. These factors are integral to ensuring a balance between productive agricultural practices and maintaining the health of watershed hydrology. However, uncertainties in modeling such complex interactions pose significant challenges, limiting our ability to precisely determine critical factors that influence crop yield and soil moisture. Our analysis employs Sobol global sensitivity analysis to evaluate first-order, second order, and total-order indices for SWAT crop growth parameter, ensuring comprehensive assessment of individual and interactive effects on model outputs. The objective is to identify the parameters that significantly affect model outputs for crop yield and soil moisture and improve our understanding of their interactions at the basin and hydrological response unit (HRU) scale. Our case study, the Portage River Watershed, which drains into Lake Erie, is chosen to better capture finer scale interactions crucial for predicting nutrient loading under future climate scenarios. This foundational work is aimed at setting the stage for the future development of an agent-based model (ABM). The ABM model would incorporate SWAT outputs to dynamically simulate decision-making processes.

Bunyon, Enock↗

DOE OSTI2024

Impact of Hydrological Data on Power System Operational Studies: Preprint

Hydropower is expected to play an important role in maintaining grid reliability and flexibility as the share of of variable renewable energy increases. While the current hydropower operational models have been studied and used widely, they haven't been updated for decades to meet new performance standards. For example, current steady state and dynamic models often neglect hydrological conditions, which may lead to unrealistic expectations when relying on hydropower for energy and ancillary services. To study this impact, a multi-timescale hydrological model was created by leveraging the National Renewable Energy Laboratory-developed Multi-timescale Integrated Dynamics and Scheduling (MIDAS) tool. Using MIDAS, we compare the impact of considering hydrological conditions in a day-ahead unit commitment (DAUC) schedule on the reduced 240-bus Western Interconnect (WI) test system under winter and summer case studies. We show that neglecting current hydrological conditions of hydropower plants in power system models can lead to an overestimation of hydropower capabilities, which could lead to power balancing issues. For example, power system DAUC simulation results of our reduced test system show that in the case where hydrological conditions are not considered in the model, an approximate 31% overestimation of hydropower capabilities occurs in the summer case and approximately 60% occurs in the winter case compared to what is available. Additionally, results show an underestimation of WI day-ahead power system generation costs by approximately $54M - $80M in the weekly summer scenario and $116M - $126M in the weekly winter scenario. This analysis helps to underscore the importance of considering hydrological data in power system operational studies.

ENERGY PLANNING, POLICY, AND ECONOMY,HYDRO ENERGY↗

DOE OSTI2022

Modeling the topographic influence on aboveground biomass using a coupled model of hillslope hydrology and ecosystem dynamics

Abstract. Topographic heterogeneity and lateral subsurface flow at the hillslope scale of ≤1 km may have outsized impacts on tropical forest through their impacts on water available to plants under water-stressed conditions. However, vegetation dynamics and finer-scale hydrologic processes are not concurrently represented in Earth system models. In this study, we integrate the Energy Exascale Earth System Model (E3SM) land model (ELM) that includes the Functionally Assembled Terrestrial Ecosystem Simulator (FATES), with a three-dimensional hydrology model (ParFlow) to explicitly resolve hillslope topography and subsurface flow and perform numerical experiments to understand how hillslope-scale hydrologic processes modulate vegetation along water availability gradients at Barro Colorado Island (BCI), Panama. Our simulations show that groundwater table depth (WTD) can play a large role in governing aboveground biomass (AGB) when drought-induced tree mortality is triggered by hydraulic failure. Analyzing the simulations using random forest (RF) models, we find that the domain-wide simulated AGB and WTD can be well predicted by static topographic attributes, including surface elevation, slope, and convexity, and adding soil moisture or groundwater table depth as predictors further improves the RF models. Different model representations of mortality due to hydraulic failure can change the dominant topographic driver for the simulated AGB. Contrary to the simulations, the observed AGB in the well-drained 50 ha forest census plot within BCI cannot be well predicted by the RF models using topographic attributes and observed soil moisture as predictors, suggesting other factors such as nutrient status may have a larger influence on the observed AGB. The new coupled model may be useful for understanding the diverse impact of local heterogeneity by isolating the water availability and nutrient availability from the other external and internal factors in ecosystem modeling.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Machine Learning Analysis of Hydrologic Exchange Flows and Transit Time Distributions in a Large Regulated River

Hydrologic exchange between river channels and adjacent subsurface environments is a key process that influences water quality and ecosystem function in river corridors. High-resolution numerical models were often used to resolve the spatial and temporal variations of exchange flows, which are computationally expensive. In this study, we adopt Random Forest (RF) and Extreme Gradient Boosting (XGB) approaches for deriving reduced order models of hydrologic exchange flows and associated transit time distributions, with integrated field observations (e.g., bathymetry) and hydrodynamic simulation data (e.g., river velocity, depth). The setup allows an improved understanding of the influences of various physical, spatial, and temporal factors on the hydrologic exchange flows and transit times. The predictors also contain those derived using hybrid clustering, leveraging our previous work on river corridor system hydromorphic classification. The machine learning-based predictive models are developed and validated along the Columbia River Corridor, and the results show that the top parameters are the thickness of the top geological formation layer, the flow regime, river velocity, and river depth; the RF and XGB models can achieve 70% to 80% accuracy and therefore are effective alternatives to the computational demanding numerical models of exchange flows and transit time distributions. Each machine learning model with its favorable configuration and setup have been evaluated. The transferability of the models to other river reaches and larger scales, which mostly depends on data availability, is also discussed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A Multiscale Deep Learning Model for Soil Moisture Integrating Satellite and In Situ Data

Deep learning (DL) models trained on hydrologic observations can perform extraordinarily well, but they can inherit deficiencies of the training data, such as limited coverage of in situ data or low resolution/accuracy of satellite data. In this work, we propose a novel multiscale DL scheme learning simultaneously from satellite and in situ data to predict 9 km daily soil moisture (5 cm depth). Based on spatial cross-validation over sites in the conterminous United States, the multiscale scheme obtained a median correlation of 0.901 and root-mean-square error of 0.034 m 3 /m 3 . It outperformed the Soil Moisture Active Passive satellite mission's 9 km product, DL models trained on in situ data alone, and land surface models. Our 9 km product showed better accuracy than previous 1 km satellite downscaling products, highlighting limited impacts of improving resolution. Not only is our product useful for planning against floods, droughts, and pests, our scheme is generically applicable to geoscientific domains with data on multiple scales, breaking the confines of individual data sets.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Machine Learning Calibration of Groundwater Table Depth in ELM: Impact on Land Surface Hydrology and Land‐Atmosphere Fluxes

Accurate representation of groundwater table depth (GWTD) is crucial for simulating hydrological cycling in Earth system models (ESM). Nevertheless, there is a notable gap in the literature regarding the validation of GWTD simulations in ESMs and their subsequent impact on downstream hydrological components. This study explores the calibration of parameterization of global GWTD using machine learning within the Energy Exascale Earth System Model (E3SM) Land Model (ELM). Despite achieving significant gains in simulating GWTD through calibration, offline ELM simulations unexpectedly show that these improvements do not translate to substantial enhancements in model performance for other key hydrological variables, including soil moisture (SM), runoff, groundwater contribution to runoff or base flow index (BFI), and evapotranspiration and its partitioning. The performance in SM and runoff was even degraded in some regions, while BFI was mostly overestimated. Although there is significant improvement in GWTD within the critical range of 1–5 m, where groundwater traditionally influences land surface energy fluxes, these improvements occurred mostly in humid areas where the impact of GWTD on surface processes is minimal. Although the impacts of model calibration are generally small in offline ELM simulations, coupled land-atmosphere simulations exhibit much stronger responses to GWTD calibration, highlighting the role of land-atmosphere feedbacks in Earth system modeling. These findings underscore the need for integrated calibration strategies that simultaneously optimize multiple hydrological variables. However, if a single-variable approach is necessary, it is crucial to establish clear priorities for calibration, identifying the most critical variables that have the greatest impact on overall model performance.

Fang, Yilin [Pacific Northwest National Laboratory↗

NASA NTRS2024

Improving the Fire Weather Index System for Peatlands Using Peat-Specific Hydrological Input Data

The Canadian Fire Weather Index (FWI) system, even though originally developed and calibrated for an upland Jack pine forest, is used globally to estimate fire danger for any fire environment. However, for some environments, such as peatlands, the applicability of the FWI in its current form, is often questioned. In this study, we replaced the original moisture codes of the FWI with hydrological estimates resulting from the assimilation of satellite-based L-band passive microwave observations into a peatland-specific land surface model. In a conservative approach that maintains the integrity of the original FWI structure, the distributions of the hydrological estimates were first matched to those of the corresponding original moisture codes before replacement. The resulting adapted FWI, hereafter called FWIpeat, was evaluated using satellite-based information on fire presence over boreal peatlands from 2010 through 2018. Adapting the FWI with model- and satellite-based hydrological information was found to be beneficial in estimating fire danger, especially when replacing the deeper moisture codes of the FWI. For late-season fires, further adaptations of the fine fuel moisture code show even more improvement due to the fact that late-season fires are more hydrologically driven. The proposed FWIpeat should enable improved monitoring of fire risk in boreal peatlands.

Canadian Fire Weather Index↗

NASA NTRS2011

Combining Space-Based and In-Situ Measurements to Track Flooding in Thailand

We describe efforts to integrate in-situ sensing, space-borne sensing, hydrological modeling, active control of sensing, and automatic data product generation to enhance monitoring and management of flooding. In our approach, broad coverage sensors and missions such as MODIS, TRMM, and weather satellite information and in-situ weather and river gauging information are all inputs to track flooding via river basin and sub-basin hydrological models. While these inputs can provide significant information as to the major flooding, targetable space measurements can provide better spatial resolution measurements of flooding extent. In order to leverage such assets we automatically task observations in response to automated analysis indications of major flooding. These new measurements are automatically processed and assimilated with the other flooding data. We describe our ongoing efforts to deploy this system to track major flooding events in Thailand.

Flooding↗

NASA NTRS2019

Utilizing Satellite Based Observations and Physical Hydrological Modeling for Freshwater Ecosystem Health in the Lower Mekong River Basin

Freshwater availability is necessary to promote economic growth through agriculture, fisheries, transport, environmental health, and social equity.The National Aeronautics and Space Administration (NASA) and the Conservation International (CI) are partnering to use remote sensing Earth observations to improve regional efforts that assess natural resources for conservation and sustainable management. (Vollmer et al.,2018) have presented the social-ecological framework named the Freshwater Health Index (FHI), which takes account of the interplay between governance, stakeholders, freshwater ecosystems and the ecosystem services they provide.In this work, we develop decision support and making tools for natural resources conservation in the Lower Mekong by leveraging the FHI framework, multiple data products, and hydrological modeling capabilities (Mohammed et al., 2018). Modeling capabilities enable the integration of satellite-based daily gridded precipitation, air temperature, digital elevation model, soil characteristics, and land cover and land use information to simulate water flux framework.

Mohammed, Ibrahim N.↗

DOE OSTI2025

Supporting Information - How Can Crop Production Adapt to growing groundwater restrictions in the West?

Abstract This data plan outlines the structure and content of datasets generated and utilized in the research presented in the manuscript abstract. Groundwater overdraft has led to serious water supply issues in the US West. Most western states manage groundwater use through a permitting system, but California has only recently begun to restrict groundwater use statewide with the 2014 passage of groundwater restrictions which target the elimination of groundwater overdraft practices by 2042. With groundwater extraction curtailed, crop production in the US West (a $95 billion industry annually) will be affected, and appropriate response strategies will be needed to ensure minimal disruption to food production and the regional economy. In this paper, we explore the adoption of alternative adaptive responses: (a) deficit irrigation; (b) switching to less water-intensive crops; (c) changing the extent of irrigated land (including fallowing); and (d) geographically shifting crop production. Employing an integrated modeling approach, we explicitly capture the interactions and feedbacks between local hydrology, changes in crop yields, crop and land use decision-making, changes in crop prices, and regional shifts in crop production. We find that the optimal adaptive response is spatially heterogeneous and comprises a portfolio of strategies. Southwestern states and California will be the most impacted by groundwater restrictions. The optimal responses in these states are to both adopt deficit irrigation strategies and reduce a portion of their irrigated croplands, resulting in a shift in crop production to northwestern states with a larger supply of water. The datasets detailed in this repository represent the output from these integrated models, specifically designed to support the analysis and visualization presented in the manuscript and supplemental information. These datasets, used in conjunction with the scripts available at our associated GitHub repository (https://github.com/pches/Femeena_etal_How_can_crop_production_adapt), enable the reproduction of figures and facilitate a comprehensive understanding of the optimal adaptive strategies in agriculture for mitigating water stress under varying groundwater extraction scenarios, as outlined in the abstract.

DNDCe↗

DOE OSTI2025

Supporting Information - How Can Crop Production Adapt to growing groundwater restrictions in the West?

Abstract This data plan outlines the structure and content of datasets generated and utilized in the research presented in the manuscript abstract. Groundwater overdraft has led to serious water supply issues in the US West. Most western states manage groundwater use through a permitting system, but California has only recently begun to restrict groundwater use statewide with the 2014 passage of groundwater restrictions which target the elimination of groundwater overdraft practices by 2042. With groundwater extraction curtailed, crop production in the US West (a $95 billion industry annually) will be affected, and appropriate response strategies will be needed to ensure minimal disruption to food production and the regional economy. In this paper, we explore the adoption of alternative adaptive responses: (a) deficit irrigation; (b) switching to less water-intensive crops; (c) changing the extent of irrigated land (including fallowing); and (d) geographically shifting crop production. Employing an integrated modeling approach, we explicitly capture the interactions and feedbacks between local hydrology, changes in crop yields, crop and land use decision-making, changes in crop prices, and regional shifts in crop production. We find that the optimal adaptive response is spatially heterogeneous and comprises a portfolio of strategies. Southwestern states and California will be the most impacted by groundwater restrictions. The optimal responses in these states are to both adopt deficit irrigation strategies and reduce a portion of their irrigated croplands, resulting in a shift in crop production to northwestern states with a larger supply of water. The datasets detailed in this repository represent the output from these integrated models, specifically designed to support the analysis and visualization presented in the manuscript and supplemental information. These datasets, used in conjunction with the scripts available at our associated GitHub repository (https://github.com/pches/Femeena_etal_How_can_crop_production_adapt), enable the reproduction of figures and facilitate a comprehensive understanding of the optimal adaptive strategies in agriculture for mitigating water stress under varying groundwater extraction scenarios, as outlined in the abstract.

DNDCe↗

DOE OSTI2025

Supporting Information - How Can Crop Production Adapt to growing groundwater restrictions in the West?

Abstract This data plan outlines the structure and content of datasets generated and utilized in the research presented in the manuscript abstract. Groundwater overdraft has led to serious water supply issues in the US West. Most western states manage groundwater use through a permitting system, but California has only recently begun to restrict groundwater use statewide with the 2014 passage of groundwater restrictions which target the elimination of groundwater overdraft practices by 2042. With groundwater extraction curtailed, crop production in the US West (a $95 billion industry annually) will be affected, and appropriate response strategies will be needed to ensure minimal disruption to food production and the regional economy. In this paper, we explore the adoption of alternative adaptive responses: (a) deficit irrigation; (b) switching to less water-intensive crops; (c) changing the extent of irrigated land (including fallowing); and (d) geographically shifting crop production. Employing an integrated modeling approach, we explicitly capture the interactions and feedbacks between local hydrology, changes in crop yields, crop and land use decision-making, changes in crop prices, and regional shifts in crop production. We find that the optimal adaptive response is spatially heterogeneous and comprises a portfolio of strategies. Southwestern states and California will be the most impacted by groundwater restrictions. The optimal responses in these states are to both adopt deficit irrigation strategies and reduce a portion of their irrigated croplands, resulting in a shift in crop production to northwestern states with a larger supply of water. The datasets detailed in this repository represent the output from these integrated models, specifically designed to support the analysis and visualization presented in the manuscript and supplemental information. These datasets, used in conjunction with the scripts available at our associated GitHub repository (https://github.com/pches/Femeena_etal_How_can_crop_production_adapt), enable the reproduction of figures and facilitate a comprehensive understanding of the optimal adaptive strategies in agriculture for mitigating water stress under varying groundwater extraction scenarios, as outlined in the abstract.

DNDCe↗

NASA NTRS2011

Evaluating the Application of Multi-Satellite Observations in Hydrologic Modeling

When monitoring local or regional hydrosphere dynamics for applications such as agricultural productivity or drought and flooding events, it is necessary to have accurate, high-resolution estimates of terrestrial water and energy storages. Though in-situ observations provide reliable estimates of hydrologic states and fluxes, they are only capable of accurately capturing the dynamics at relatively discrete points in space and time, which makes them inadequate for characterizing the variability of the water budget across scales. In contrast, satellite-based remote sensing is ideal for providing observations of hydrological states and fluxes because it provides spatially-distributed observations at spatial and temporal scales required for regional land surface process modeling. Due to the continued progress in algorithm development and emerging satellite technology, we now have near-real time monitoring of several components of the water cycle including precipitation, soil moisture, lake and river height, terrestrial water storage, snow cover, and evapotranspiration. As these data become more readily available, their application to hydrologic modeling is becoming more common, however there remains little consensus on the most appropriate method for optimal integration and evaluation in regard to hydrological applications. Here we present two case studies operationally applying several remotely sensed products from AMSR-E, GRACE, and MODIS and discuss assimilation strategies, ease of integration and interpretation, and methods for quantifying the success of the application methodology.

Bolten, John↗

DOE OSTI2020

Understanding Contaminant Migration within a Dynamic River Corridor through Field Experiments and Reactive Transport Modeling

The behavior of a persistent uranium plume within an extended river corridor at the DOE Hanford site is dominantly controlled by river stage fluctuations in the adjacent Columbia River. The plume behavior is further complicated by substantial heterogeneity in physical and geochemical properties of the host aquifer sediments. Multi-scale field and laboratory experiments and reactive transport modeling were integrated to understand the complex plume behavior influenced by highly variable hydrologic and geochemical conditions in time and space. In this paper, we (1) describe multiple data sets from field-scale uranium adsorption and desorption experiments performed at our experimental well-field, (2) develop a reactive transport model that incorporates hydrologic and geochemical heterogeneities characterized from multi-scale and multi-type datasets and a surface complexation reaction network based on laboratory studies, and (3) compare the modeling and observation results to provide insights on how to refine the conceptual model and reduce prediction uncertainties. The experimental results revealed significant spatial variability in uranium adsorption/desorption behavior, while modeling demonstrated that ambient hydrologic and geochemical conditions and heterogeneities in sediment physical and chemical properties both contributed to complex plume behavior and its persistence. This research underscores the great challenges in adequately characterizing this type of site to model the reactive transport processes over scales of 10 m or more. Our analysis provides important insights into the characterization, understanding, modeling, and remediation of groundwater contaminant plumes influenced by dynamic surface water and groundwater interactions.

Chen, Xingyuan↗

DOE OSTI2026

Assessing shellfish water exposure to fecal bacteria pollution in Salish Sea: three-dimensional modeling and implications for monitoring

Fecal bacteria (FB) contamination poses significant risks to shellfish safety and management in coastal and estuarine waters. Despite extensive pollution identification and correction efforts, FB contamination in shellfish-growing areas persists in the Salish Sea, highlighting the need to identify overlooked sources and better understand FB transport from riverine and shoreline inputs to shellfish beds. To address this, a high-resolution three-dimensional hydrodynamic model coupled with FB kinetics was developed and applied to a case study site in Salish Sea—Portage Bay—to simulate freshwater plume circulation, flushing dynamics, and bacterial transport. Daily FB loading from the major freshwater inflow—Nooksack River was generated by both linear interpolation and integrating a machine learning approach (XGBoost), trained on historical hydrological and meteorological data. The model successfully reproduced both the magnitude and seasonal variation of FB concentrations in Portage Bay for the year of 2021, demonstrating that simplified FB kinetics with first-order decay due to mortality was effective in this dynamic coastal environment with short flushing time. Model results identified the Nooksack River as the dominant far-field FB source, while scenario simulations showed that near-field coastal stormwater outfalls elevated local FB levels following rainfall, particularly under low-flow conditions. The XGBoost prediction provided comparable or superior accuracy to linear interpolation, particularly during periods of missing observational data, by capturing short-term variability and event-driven loading more effectively. Integrating data-driven riverine FB inputs with mechanistic coastal numerical modeling provides a robust framework for operational forecasting of shellfish bed exposure risk and supports adaptive monitoring and management of shellfish growing areas in the Salish Sea and similar coastal systems.

Salish Sea↗

NASA NTRS2011

Integrating Gridded NASA Hydrological Data into CUAHSI HIS

The amount of hydrological data available from NASA remote sensing and modeling systems is vast and ever-increasing;but, one challenge persists:increasing the usefulness of these data for, and thus their use by, end user communities. The Hydrology Data and Information Services Center (HDISC), part of the Goddard Earth Sciences DISC, has continually worked to better understand the hydrological data needs of different end users, to thus better able to bridge the gap between NASA data and end user communities. One effective strategy is integrating the data in to end user community tools and environments. There is an ongoing collaborative effort between NASA HDISC, NASA Hydrological Sciences Branch, and CUAHSI to integrate NASA gridded hydrology data in to the CUAHSI Hydrologic Information System (HIS).

Rui, Hualan↗

DOE OSTI2024

Snow Distribution Patterns Revisited: A Physics-Based and Machine Learning Hybrid Approach to Snow Distribution Mapping in the Sub-Arctic

Snowpack distribution in Arctic and alpine landscapes often occurs in repeating, year-to-year patterns due to local topographic, weather, and vegetation characteristics. Previous studies have suggested that with years of observational data, these snow distribution patterns can be statistically integrated into a snow process modeling workflow. Recent advances in snow hydrology and machine learning (ML) have increased our ability to predict snowpack distribution using in-situ observations, remote sensing data sets, and simple landscape characteristics that can be easily obtained for most environments. Here, we propose a hybrid approach to couple a ML snow distribution pattern (MLSDP) map with a physics-based, snow process model. We trained a random forest ML algorithm on tens of thousands of snow survey observations from a subarctic study area on the Seward Peninsula, Alaska, collected during peak snow water equivalent (SWE). We validated hybrid model outputs using in-situ snow depth and SWE observations, as well as a light detection and ranging data set and a distributed temperature profiling sensor data set. When the hybrid results were compared with the physics-based method, the hybrid method more accurately depicted the spatial patterns of the snowpack, areas of drifting snow, and years when no in-situ observations were used in the random forest ML training data set. The hybrid method also showed improvements in root mean squared error at 61% of locations where time-series estimations of snow depth were observed. These results can be applied to any physics-based model to improve the snow distribution patterning to reflect observed conditions in high latitude and high elevation cold region environments.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1995

Thermal remote sensing of surface soil water content with partial vegetation cover for incorporation into climate models

This study outlines a method for the estimation of regional patterns of surface moisture availability (M(sub 0)) and fractional vegetation (Fr) in the presence of spatially variable vegetation cover. The method requires relating variations in satellite-derived (NOAA, Advanced Very High Resolution Radiometer (AVHRR)) surface radiant temperature to a vegetation index (computed from satellite visible and near-infrared data) while coupling this association to an inverse modeling scheme. More than merely furnishing surface soil moisture values, the method constitues a new conceptual and practical approach for combining thermal infrared and vegetation index measurements for incorporating the derived values of M(sub 0) into hydrologic and atmospheric prediction models. Application of the technique is demonstrated for a region in and around the city of Newcastle upon Tyne situated in the northeast of England. A regional estimate of M(sub 0) is derived and is probabbly good for fractional vegetation cover up to 80% before errors in the estimated soil water content become unacceptably large. Moreover, a normalization scheme is suggested from which a nomogram, `universal triangle,' is constructed and is seen to fit the observed data well. The universal triangle also simplifies the inclusion of remotely derived M(sub 0) in hydrology and meteorological models and is perhaps a practicable step toward integrating derived data from satellite measurements in weather forecasting.

Gillies, Robert R.↗