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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Hybrid Uses of High-Temperature Reservoir Thermal Energy Storage: Lessons Learned from Previous Projects

One of the critical challenges of the green energy transition is resolving the mismatch between energy generation provided by intermittent renewable energy sources such as solar and wind and the demand for energy. There is a need for large amounts of energy storage over a range of time scales (diurnal to seasonal) to better balance energy supply and demand. Subsurface geologic reservoirs provide the potential for storage of hot water that can be retrieved when needed and used for power generation or direct-use applications, such as district heating. It is important to identify potential issues associated with high-temperature reservoir thermal energy storage (HT-RTES) systems so that they can be mitigated, thus reducing the risks of these systems. This paper reviews past experiences from moderate and high-temperature reservoir thermal energy storage (RTES) projects, along with hot water and steam flood enhanced oil recovery (EOR) operations, to identify technical challenges encountered and evaluate possible ways to address them. Some of the identified technical problems that have impacted system performance include: 1) insufficient site characterization that failed to identify reservoir heterogeneity; 2) scaling resulting from precipitation of minerals having retrograde solubility that form with heating of formation brines; 3) corrosion from low pH or high salinity brines; 4) thermal breakthrough between hot and cold wells due to insufficient spacing. Proper design, characterization, construction, and operational practices can help reduce the risk of technical problems that could lead to reduced performance of these thermal energy storage systems.

energy storage↗
NASA NTRS2012

Links Between Acceleration, Melting, and Supraglacial Lake Drainage of the Western Greenland Ice Sheet

The impact of increasing summer melt on the dynamics and stability of the Greenland Ice Sheet is not fully understood. Mounting evidence suggests seasonal evolution of subglacial drainage mitigates or counteracts the ability of surface runoff to increase basal sliding. Here, we compare subdaily ice velocity and uplift derived from nine Global Positioning System stations in the upper ablation zone in west Greenland to surface melt and supraglacial lake drainage during summer 2007. Starting around day 173, we observe speedups of 6-41% above spring velocity lasting approximately 40 days accompanied by sustained surface uplift at most stations, followed by a late summer slowdown. After initial speedup, we see a spatially uniform velocity response across the ablation zone and strong diurnal velocity variations during periods of melting. Most lake drainages were undetectable in the velocity record, and those that were detected only perturbed velocities for approximately 1 day, suggesting preexisting drainage systems could efficiently drain large volumes of water. The dynamic response to melt forcing appears to 1) be driven by changes in subglacial storage of water that is delivered in diurnal and episodic pulses, and 2) decrease over the course of the summer, presumably as the subglacial drainage system evolves to greater efficiency. The relationship between hydrology and ice dynamics observed is similar to that observed on mountain glaciers, suggesting that seasonally large water pressures under the ice sheet largely compensate for the greater ice thickness considered here. Thus, increases in summer melting may not guarantee faster seasonal ice flow.

Hoffman, M. J.↗
NASA NTRS2011

Links Between Acceleration, Melting, and Supraglacial Lake Drainage of the Western Greenland Ice Sheet

The impact of increasing summer melt on the dynamics and stability of the Greenland Ice Sheet is not fully understood. Mounting evidence suggests seasonal evolution of subglacial drainage mitigates or counteracts the ability of surface runoff to increase basal sliding. Here, we compare subdaily ice velocity and uplift derived from nine Global Positioning System stations in the upper ablation zone in west Greenland to surface melt and supraglacial lake drainage during summer 2007. Starting around day 173, we observe speedups of 6-41% above spring velocity lasting 40 days accompanied by sustained surface uplift at most stations, followed by a late summer slowdown. After initial speedup, we see a spatially uniform velocity response across the ablation zone and strong diurnal velocity variations during periods of melting. Most lake drainages were undetectable in the velocity record, and those that were detected only perturbed velocities for approx 1 day, suggesting preexisting drainage systems could efficiently drain large volumes of water. The dynamic response to melt forcing appears to (1) be driven by changes in subglacial storage of water that is delivered in diurnal and episodic pulses, and (2) decrease over the course of the summer, presumably as the subglacial drainage system evolves to greater efficiency. The relationship between hydrology and ice dynamics observed is similar to that observed on mountain glaciers, suggesting that seasonally large water pressures under the ice sheet largely compensate for the greater ice thickness considered here. Thus, increases in summer melting may not guarantee faster seasonal ice flow.

Hoffman, M. J.↗
DOE OSTI2021

Evaluation of Energy Storage Potential of Unconventional Shale Reservoirs Using Numerical Simulation of Cyclic Gas Injection

Compressed air energy storage (CAES) stores energy as compressed air in underground formations, typically salt dome caverns. When electricity demand grows, the compressed air is released through a turbine to produce electricity. CAES in the US is limited to one plant built in 1991, due in part to the inherent risk and uncertainty of developing subsurface storage reservoirs. As an alternative to CAES, we propose using some of the hundreds of thousands of hydraulically fractured horizontal wells to store energy as compressed natural gas in unconventional shale reservoirs. To store energy, produced or “sales” natural gas is injected back into the formation using excess electricity and is later produced through an expander to generate electricity. To evaluate this concept, we performed numerical simulations of cyclic natural gas injection into unconventional shale reservoirs using cmg-gem commercial reservoir modeling software. We tested short-term (diurnal) and long-term (seasonal) energy storage potential by modeling well injection and production gas flowrates as a function of bottom-hole pressure. First, we developed a conceptual model of a single fracture stage in an unconventional shale reservoir to characterize reservoir behavior during cyclic injection and production. Next, we modeled cyclic injection in the Marcellus shale gas play using published data. Results indicate that Marcellus unconventional shale reservoirs could support both short- and long-term energy storage at capacities of 100–1000 kWe per well. The results indicate that energy storage in unconventional shale gas wells may be feasible and warrants further investigation.

25 ENERGY STORAGE↗
DOE OSTI2023

Nepal Himalaya offers considerable potential for pumped storage hydropower

There is a pressing need for a transition from fossil fuel to renewable energy to meet the increasing energy demands and reduce greenhouse gas emissions. The Himalayan region, with its unique topography and abundant water resources, offers substantial renewable energy potential, particularly through hydropower generation. However, the current exploitation rate is low owing to the predominance of run-of-river hydropower systems to support the power system. The utility-scale storage facility is crucial in the load scenario of an integrated power system to manage diurnal variation, peak demand, and penetration of intermittent energy sources. In this study, we assess the potential of pumped storage hydropower across Nepal, a central Himalayan country, under multiple configurations by pairing lakes, rivers, and available flat terrains. We then identify technically feasible pairs from those of potential locations. Infrastructural, environmental, operational, and other technical constraints govern the choice of feasible locations. Here, we show that 42% of the theoretical potential of 3000 GWh is technically feasible. We find the flat land-to-river configuration more promising than other configurations. Our findings provide insight into the potential of pumped storage hydropower and are of practical importance in planning sustainable power systems in the Himalayas and beyond.

13 HYDRO ENERGY↗
DOE OSTI2020

Benefit Analysis of Long-Duration Energy Storage in Power Systems with High Renewable Energy Shares

The integration of high shares of variable renewable energy raises challenges for the reliability and cost-effectiveness of power systems. The value of long-duration energy storage, which helps address variability in renewable energy supply across days and seasons, is poised to grow significantly as power systems shift to larger shares of variable generation such as wind and solar. This study explores the system-level services and associated benefits of long-duration energy storage on the 2050 Western Interconnection (WI). The operation of the future WI system with 85% renewable penetration is simulated using a two-stage production cost model. The impact of long duration energy storage on systemwide operations is examined for the 2050 WI system, using a range of round-trip efficiencies corresponding to four different energy storage technologies. The analysis projects the energy storage dispatch profile, system-wide production cost savings (from both diurnal and seasonal operation), and impacts on generation mix, and change in renewable generation curtailment.

25 ENERGY STORAGE↗
DOE OSTI2023

Demand reduction and energy saving potential of thermal energy storage integrated heat pumps [Réduction de la demande et potentiel d'économie d'énergie des pompes à chaleur avec stockage d'énergie thermique intégré]

A heat pump (HP) moves heat from a low-temperature source to a high-temperature sink with an input of energy. Often, one temperature body fluctuates with time (e.g., diurnal ambient temperature), causing the HP efficiency to vary. Integrating thermal energy storage (TES) into a HP system adds a third temperature body, enabling the HP to be advantageously coupled to any two: the application, the ambient, or the TES at strategic times. Although TES integration with HPs is an important emerging technology to lower energy consumption and decrease energy demand during critical times, the favorable circumstances for TES integration are poorly understood. Here, this paper establishes the energy reduction and demand reduction potential of TES-integrated HPs with both analytical and numerical HP models. All possible temperature arrangements are considered for HP-TES systems with two fixed temperature bodies (application and TES) and one variable temperature (ambient). Results show that overall energy savings are most attainable when the TES temperature is near the application temperature, whereas a large temperature difference between the TES and the application leads to the most peak demand reduction. The potential for overall energy savings increases as the magnitude of ambient temperature fluctuations increases.

25 ENERGY STORAGE↗
NASA NTRS1994

Effects of several environmental factors on sweetpotato growth

Effects of relative humidity, light intensity and photoperiod on growth of 'Ga Jet' and TI-155' sweetpotato cultivars, using the nutrient film technique (NFT), have been reported. In this study, the effect of ambient temperature regimes (constant 28 C and diurnal 28:222 C day:night) and different CO2 levels (ambient, 400, 1 000 and 10 000 microL/L-400, 1 000 and 10 000 ppm) on growth of one or both of these cultivars in NFT are reported. For a 24-h photoperiod, no storage roots were prodcued for either cultivar in NFT when sweetpotato plants were grown at a constant temperature of 28 C. For the same photoperiod, when a 28:22 C diurnal temperature variation was used, there were still no storage roots for 'TI-155' but the cv. 'Ga Jet' produced 537 g/plant of storage roots. For both a 12-h and 24-h photoperiod. 'Ga Jet' storage root fresh and dry weight tended to be higher with a 28:22 C diurnal temperature variation than with a constant 28 C temperature regime. Preliminary results with both 'Ga Jet' and 'TI-155' cultivars indicate a distinctive diurnal stomatal response for sweetpotato grown in NFT under an ambient CO2 level. The stomatal conductance values observed for 'Ga Jet' at elevated CO2 levels indicated that the difference between the light- and dark-period conductance rates persisted at 400, 1 000, and 10 000 microL/L.

Loretan, P. A.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-10735-DND

The Clouds and the Earth's Radiant Energy System (CERES) project has now surpassed the 10-year mark, has combined rigorous calibration, improved scene identification, and multi-satellite data fusion to produce a climate-accuracy data set of global 1° gridded radiative surface and TOA fluxes, and cloud properties. CERES provides the climate community with four observed TOA flux products. The ERBE-like product uses the same algorithms as ERBE in order to be compared with the ERBE time period. The SSF product uses the improved scene identification and radiance to flux conversion. The SYN product uses GEO derived clouds and fluxes to provide diurnally complete TOA fluxes. The EBAF product provides net balanced fluxes tied to the ocean heat storage term. This product is suited for climate modelers estimating the global mean energy budget. Each successive CERES flux product applies the improvements over the previous product. This presentation will focus on the diurnal averaging improvements by the inclusion of imager radiances from 5 geostationary (GEO) satellites at 3-hourly intervals to estimate the flux in between CERES observations. The regional monthly mean flux differences based on SYN (CERES/GEO) and SSF (CERES-only) can exceed 20 Wm^-2. CERES shortwave and longwave fluxes have been rigorously validated and are key elements in evaluating the ability of climate models to predict both past and future climate states. The CERES normalization of GEO derived fluxes in order to maintain the CERES instrument calibration and are consistent globally within 0.1 Wm^-2, even if the GEO calibration is artificially altered by ±5%, twice the anticipated calibration error. The predicted GEO TOA fluxes normalized to Terra have been compared at Aqua times to Aqua flux observations, as well as with GERB hourly fluxes over the METEOSAT domain. Similarly ground based radiometers have been used to validate the CERES radiative transfer computed surface fluxes and have confirmed that the CERES/GEO fluxes have improved the computed surface flux product. Although the GEO based fluxes are of inferior quality then the CERES observed fluxes, they capture the diurnal signal more effectively than using constant meteorology between CERES measurements. The validation of the GEO derived fluxes and clouds will be shown.

D. R. Doelling↗
DOE OSTI2026

Enhancing SWAT with mechanistic plant hydraulics: development and application in the Hanjiang River Basin

Plant transpiration plays a critical role in global water and energy cycles, requiring better process understanding as climate change intensifies drought stress and alters plant responses. Most hydrological models such as the widely-used SWAT lack representation of plant hydraulics, the mechanistic processes controlling plant water regulation and transpiration. Here, this study developed SWAT-PHS by integrating a plant hydraulics scheme (PHS) into SWAT hydrological model, enabling explicit simulation of root water uptake, sap flow, storage and transpiration at 30-minute timescales for watershed-scale modeling. In the Hanjiang River Basin, SWAT-PHS mitigated overestimation of runoff during the rainy season and underestimation during the dry season, reducing the overall simulation error by 29% across the entire simulation period. The model can simulate reasonable plant water dynamics, including diurnal transpiration patterns and drought responses showing declining transpiration flux, hydraulic buffering through stem water storage, and depth-dependent root water uptake strategies. Sensitivity analysis shows that SWAT-PHS captured mechanistic relationships between plant hydraulic traits and transpiration, with root distribution and stem capacitance positively affecting annual transpiration while vulnerability parameters showed negative effects. This work provides a pathway for improving hydrologic modeling and water resource management by better representing plant water regulation under climate change and expected intensifying water stress conditions.

China↗
DOE OSTI2026

Modeling the Potential Impact of Storage on the US Power Sector in a Multisector Dynamic Context

The electric power sector is expected to grow in size, importance, and complexity around the world as economies expand and electric supply technologies and demand patterns evolve in significant ways. At the same time the electric power sector may see substantial increases in VRE generating technologies which can add variability and uncertainty to the diurnal and seasonal profile of electric supply. With these forces in play, the emergence of modular, flexible electricity storage technologies may have profound impacts on the operation of electric power systems. Here we reduce a storage modeling gap in MSD models by incorporating grid-based electricity storage into the electric sector dynamics of the Global Change Analysis Model-USA (GCAM-USA) with improved power sector representation. We find a potentially significant role for storage technologies in the future of the U.S. power system, with storage capacity ranging from 7.7 to 14.7 GW in 2050 and 13.9 to 31.6 GW in 2100 across several techno-economic scenarios. We also find that storage can help to smooth variability in residual load arising from evolving electricity demands and the introduction of high shares of VRE to the electric grid. This reduces reliance on high-cost peaking generators, improves system-wide capacity factors, and limits curtailment of VRE.

Patel, Pralit L.↗
NASA NTRS1997

Thermal and Hydrologic Signatures of Soil Controls on Evaporation: A Combined Energy and Water Balance Approach with Implications for Remote Sensing of Evaporation

The overall goal of this research is to examine the feasibility of applying a newly developed diagnostic model of soil water evaporation to large land areas using remotely sensed input parameters. The model estimates the rate of soil evaporation during periods when it is limited by the net transport resulting from competing effects of capillary rise and drainage. The critical soil hydraulic properties are implicitly estimated via the intensity and duration of the first stage (energy limited) evaporation, removing a major obstacle in the remote estimation of evaporation over large areas. This duration, or "time to drying" (t(sub d)), is revealed through three signatures detectable in time series of remote sensing variables. The first is a break in soil albedo that occurs as a small vapor transmission zone develops near the surface. The second is a break in either surface to air temperature differences or in the diurnal surface temperature range, both of which indicate increased sensible heat flux (and/or storage) required to balance the decrease in latent heat flux. The third is a break in the temporal pattern of near surface soil moisture. Soil moisture tends to decrease rapidly during stage 1 drying (as water is removed from storage), and then become more or less constant during soil limited, or "stage 2" drying (as water is merely transmitted from deeper soil storage). The research tasks address: (1) improvements in model structure, including extensions to transpiration and aggregation over spatially variable soil and topographic landscape attributes; and (2) applications of the model using remotely sensed input parameters.

Salvucci, Guido D.↗
NASA NTRS2000

Thermal and Hydrologic Signatures of Soil Controls on Evaporation: A Combined Energy and Water Balance Approach with Implications for Remote Sensing of Evaporation

The overall goal of this research is to examine the feasibility of applying a newly developed diagnostic model of soil water evaporation to large land areas using remotely sensed input parameters. The model estimates the rate of soil evaporation during periods when it is limited by the net transport resulting from competing effects of capillary rise and drainage. The critical soil hydraulic properties are implicitly estimated via the intensity and duration of the first stage (energy limited) evaporation, removing a major obstacle in the remote estimation of evaporation over large areas. This duration, or 'time to drying' (t(sub d)) is revealed through three signatures detectable in time series of remote sensing variables. The first is a break in soil albedo that occurs as a small vapor transmission zone develops near the surface. The second is a break in either surface to air temperature differences or in the diurnal surface temperature range, both of which indicate increased sensible heat flux (and/or storage) required to balance the decrease in latent heat flux. The third is a break in the temporal pattern of near surface soil moisture. Soil moisture tends to decrease rapidly during stage I drying (as water is removed from storage), and then become more or less constant during soil limited, or 'stage II' drying (as water is merely transmitted from deeper soil storage). The research tasks address: (1) improvements in model structure, including extensions to transpiration and aggregation over spatially variable soil and topographic landscape attributes; and (2) applications of the model using remotely sensed input parameters.

Salvucci, Guido D.↗
DOE OSTI2022

Assessment of Wind Energy Resource Potential for Future Human Missions to Mars

Energy sustainability and redundancy for surface habitats, life support systems and scientific instrumentation represent one of the highest-priority issues for future crewed missions to Mars. However, power sources utilized for the current class of robotic missions to Mars may be potentially dangerous near human surface habitats (for example, nuclear) or lack stability on diurnal or seasonal timescales (for example, solar) that cannot be easily compensated for by power storage. Here, we evaluate the power potential for wind turbines as an alternative energy resource on the Mars surface. Using a state-of-the-art Mars global climate model, we analyse the total planetary Martian wind potential and calculate its spatial and temporal variability. We find that wind speeds at some proposed landing sites are sufficiently fast to provide a stand-alone or complementary energy source to solar or nuclear power. While several regions show promising wind energy resource potential, other regions of scientific interest can be discarded based on the natural solar and wind energy potential alone. We demonstrate that wind energy compensates for diurnal and seasonal reductions in solar power particularly in regions of scientific merit in the midlatitudes and during regional dust storms. Critically, proposed turbines stabilize power production when combined with solar arrays, increasing the percent time that power exceeds estimated mission requirements from ~40% for solar arrays alone to greater than 60-90% across a broad fraction of the Mars surface. We encourage additional study aimed at advancing wind turbine technology to operate efficiently under Mars conditions and to extract more power from Mars winds.

atmospheric dynamics↗
NASA NTRS1993

Measurements of dimethyl sulfide and SO2 during GTE/CITE 3

As part of NASA's Tropospheric Experiment Chemical Instrumentation Test and Evaluation (GTE/CITE 3) Sulfur Gas Intercomparison, we conducted measurements of dimethyl sulfide (DMS) and SO2 using two techniques well suited for sampling from an aircraft due to their simplicity of design. DMS was collected by preconcentration on gold wire preceded by a KOH-impregnated filter oxidant scrubber, and analyzed by gas chromatography with flame photometric detection. SO2 was collected on K2CO3/glycerol-impregnated filters and analyzed by ion chromatography. In blind tests, both techniques produced excellent agreement with National Institutes of Standards and Technology (NIST) standards. For field measurements, the DMS technique produced excellent correlation with the mean of the six different techniques intercompared. For SO2, the five techniques intercompared were rather poorly correlated, but correlations between the three techniques which passed NIST standards tests were somewhat better. Our SO2 filter measurements exhibited rather large uncertainties due to higher than normal variabiltiy of the filter blanks, which we believe was caused by extended storage in the field. In measurements conducted off the coast of Natal, Brazil, a diurnal afternoon minimum in DMS concentrations accompanied by a corresponding maximum in SO2 concentrations was observed. However, due to rather large uncertainties in the SO2 measurements, any conclusions about the SO2 trend must by considered tentative.

Ferek, Ronald J.↗
NASA NTRS1981

Modeling the terrestrial hydrology for the global atmosphere - The future role of satellite data

A global terrestrial hydrology model has been developed for the transport and storage of moisture and heat in the ground surface layer where the hydrological parameters react to diurnal and seasonal changes in the atmosphere. The spatial and temporal variability of land surface features is considered in the model by means of large scale parameterizations. The model can be either forced by the atmosphere using conventional meteorological data or coupled to an atmospheric general circulation model (GCM) for interactive studies. The global surface is divided into 4 deg longitude by 5 deg latitude cells while the ground is represented by a thin surface layer, a bulk layer (the root zone), and a deep layer (the ground water zone). Results are presented from a seven-day global experiment which was conducted utilizing the GLAS GCM (NASA Goddard Laboratory for Atmospheric Sciences). The model has demonstrated its capability to predict, over a large region, the overall soil moisture storage and major flux exchanges with the atmosphere above and the ground water below.

Lin, J. D.↗
NASA NTRS1994

Growing season boundary layer climate and surface exchanges in a subarctic lichen woodland

Between June and August 1990, observations were made at two surface micrometeorological towers near Schefferville Quebec (54 deg 52 min N, 66 deg 40.5 min W), one in a fen and one in the subarctic lichen woodland, and at four surface climatological stations. Data from these surface stations were supplemented by regular radiosonde launches. Supporting measurements of radiative components and soil temperatures allowed heat and moisture balances to be obtained at two sites. The overall surface meteorological experiment design and results of micrometeorological observations made on a 30-m tower in the lichen woodland are presented here. Seasonal variation in the heat and water vapor transport characteristics illustrate the marked effect of the late summer climatological shift in air mass type. During the first half of the summer, average valley sidewalls only 100 m high are sufficient to channel winds along the valley in the entire convective boundary layer. Channeling effects at the surface, known for some time at the long-term climate station in Schefferville, are observed both at ridge top and in the valley, possibly the response of the flow to the NW-SE orientation of valleys in the region. Diurnal surface temperature amplitude at ridge top (approximately equal to 10 C) was found to be half that observed in the valley. Relatively large differences in precipitation among these stations and the climatological station at Schefferville airport were observed and attributed to the local topography. Eddy correlation observations of the heat, moisture and momentum transports were obtained from a 30-m tower above a sparse (approximately equal to 616 stems/ha) black spruce lichen woodland. Properties of the turbulent surface boundary layer agree well with previous wind tunnel studies over idealized rough surfaces. Daytime Bowen ratios of 2.5-3 are larger than those reported in previous studies. Surface layer flux data quality was assessed by looking at the surface layer heat balance. Diurnal and seasonal scale heat budget imbalances were found. We suggest that unmeasured surface heat storage may be responsible for some of the observed imbalance. The presence of the unexplained residual in this and other studies of energy balance over forests casts a note of caution on the interpretation of energy balance components obtained using heat residual methods.

Fitzjarrald, David R.↗
NASA NTRS2020

Intercomparison of surface meltwater routing models for the Greenland ice sheet and influence on subglacial effective pressures

Each summer, large volumes of surface meltwater drain off the Greenland ice sheet (GrIS) surface through moulins to the bed, impacting subglacial hydrology and ice flow dynamics. Supraglacial surface routing delays may propagate to englacial and subglacial hydrologic systems, requiring accurate assessment to correctly estimate subglacial effective pressures. We compare hourly supraglacial moulin discharge simulations from three surface meltwater routing models – the synthetic unit hydrograph (SUH), the bare-ice component of surface routing and lake filling (SRLF), and the rescaled width function (RWF) – for four internally drained catchments on the southwestern Greenland ice sheet surface. The routing models are forced identically using surface runoff from the Modèle Atmosphérique Régionale regional climate model (RCM). For each catchment, simulated moulin hydrographs are input to the SHAKTI subglacial hydrologic model to simulate diurnally varying subglacial effective-pressure variations in the vicinity of a single moulin. Overall, all three routing models produce more realistic moulin discharges than simply using RCM runoff outputs without surface routing but produce significant differences in peak moulin discharge and time to peak. In particular, the RWF yields later, smaller peak moulin discharges than the SUH or SRLF due to its representation of slow interfluve flow between supraglacial meltwater channels, and it can readily accommodate the seasonal evolution of supraglacial stream and river networks. Differences among the three routing models are reflected in a series of simple idealized subglacial hydrology simulations that yield different diurnal effective-pressure amplitudes; however, the supraglacial hydrologic system acts as short-term storage for surface meltwater, and the temporal mean effective pressure is relatively consistent across routing models.

Kang Yang↗