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At least 883 records · Page 49Linked to original sources
USGS1997

Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer

A Laplace transform solution is presented for the problem of flow to a partially penetrating well of finite diameter in a slightly compressible water table aquifer. The solution, which allows for evaluation of both pumped well and observation piezometer data, accounts for effects of well bore storage and skin and allows for the noninstantaneous release of water from the unsaturated zone. For instantaneous release of water from the unsaturated zone the solution approaches the line source solution derived by Neuman as the diameter of the pumped well approaches zero. Delayed piezometer response, which is significant during times of rapidly changing hydraulic head, is included in the theoretical treatment and shown to be an important factor in accurate evaluation of specific storage. By means of a hypothetical field example it is demonstrated that evaluations of specific storage ( S s ) using classical line source solutions may yield values of S s that are overestimated by a factor of 100 or more, depending upon the location of the observation piezometers and whether effects of delayed piezometer response are included in the analysis. Theoretical responses obtained with the proposed model are used to suggest methods for evaluating specific storage.

Water Resources Research↗
USGS1997

Strontium 87/strontium 86 as a tracer of mineral weathering reactions and calcium sources in an alpine/subalpine watershed, Loch Vale, Colorado

Sr isotopic ratios of atmospheric deposition, surface and subsurface water, and geologic materials were measured in an alpine/subalpine watershed to characterize weathering reactions and identify sources of dissolved Ca in stream water. Previous studies have noted an excess of Ca in stream water above that expected from stoichiometric weathering of the dominant bedrock minerals. Mixing calculations based on 87 Sr/ 86 Sr indicate that on an annual basis, 26 ± 7% of Ca export in streams is atmospherically derived, 23 ± 1% is from weathering of plagioclase, and the remainder is from weathering of calcite present in trace amounts in the bedrock. A potential source of error when applying Sr isotopes in catchment studies is determination of the 87 Sr/ 86 Sr of Sr released by mineral weathering, which is complicated by the wide range of mineral isotopic compositions, particularly in older rocks, and the variable rates at which the minerals weather. In this study, base-flow stream chemistry was used to represent the 87 Sr/ 86 Sr of Sr derived from mineral weathering because it effectively integrates the potentially variable isotopic composition of Sr released by weathering in the alpine environment.

Colorado↗
USGS1997

Multiphase flow modeling of a crude-oil spill site with a bimodal permeability distribution

Fluid saturation, particle-size distribution, and porosity measurements were obtained from 269 core samples collected from six boreholes along a 90-m transect at a subregion of a crude-oil spill site, the north pool, near Bemidji, Minnesota. The oil saturation data, collected 11 years after the spill, showed an irregularly shaped oil body that appeared to be affected by sediment spatial variability. The particle-size distribution data were used to estimate the permeability ( k ) and retention curves for each sample. An additional 344 k estimates were obtained from samples previously collected at the north pool. The 613 k estimates were distributed bimodal lognormally with the two population distributions corresponding to the two predominant lithologies: a coarse glacial outwash deposit and fine-grained interbedded lenses. A two-step geostatistical approach was used to generate a conditioned realization of k representing the bimodal heterogeneity. A cross-sectional multiphase flow model was used to simulate the flow of oil and water in the presence of air along the north pool transect for an 11-year period. The inclusion of a representation of the bimodal aquifer heterogeneity was crucial for reproduction of general features of the observed oil body. If the bimodal heterogeneity was characterized, hysteresis did not have to be incorporated into the model because a hysteretic effect was produced by the sediment spatial variability. By revising the relative permeability functional relation, an improved reproduction of the observed oil saturation distribution was achieved. The inclusion of water table fluctuations in the model did not significantly affect the simulated oil saturation distribution.

Water Resources Research↗
USGS1997

Experimental design for estimating parameters of rate-limited mass transfer: Analysis of stream tracer studies

Tracer experiments are valuable tools for analyzing the transport characteristics of streams and their interactions with shallow groundwater. The focus of this work is the design of tracer studies in high-gradient stream systems subject to advection, dispersion, groundwater inflow, and exchange between the active channel and zones in surface or subsurface water where flow is stagnant or slow moving. We present a methodology for (1) evaluating and comparing alternative stream tracer experiment designs and (2) identifying those combinations of stream transport properties that pose limitations to parameter estimation and therefore a challenge to tracer test design. The methodology uses the concept of global parameter uncertainty analysis, which couples solute transport simulation with parameter uncertainty analysis in a Monte Carlo framework. Two general conclusions resulted from this work. First, the solute injection and sampling strategy has an important effect on the reliability of transport parameter estimates. We found that constant injection with sampling through concentration rise, plateau, and fall provided considerably more reliable parameter estimates than a pulse injection across the spectrum of transport scenarios likely encountered in high-gradient streams. Second, for a given tracer test design, the uncertainties in mass transfer and storage-zone parameter estimates are strongly dependent on the experimental Damkohler number, DaI , which is a dimensionless combination of the rates of exchange between the stream and storage zones, the stream-water velocity, and the stream reach length of the experiment. Parameter uncertainties are lowest at DaI values on the order of 1.0. When DaI values are much less than 1.0 (owing to high velocity, long exchange timescale, and/or short reach length), parameter uncertainties are high because only a small amount of tracer interacts with storage zones in the reach. For the opposite conditions ( DaI ≫ 1.0), solute exchange rates are fast relative to stream-water velocity and all solute is exchanged with the storage zone over the experimental reach. As DaI increases, tracer dispersion caused by hyporheic exchange eventually reaches an equilibrium condition and storage-zone exchange parameters become essentially nonidentifiable.

Water Resources Research↗
USGS1997

Geochemical mole-balance modeling with uncertain data

Geochemical mole-balance models are sets of chemical reactions that quantitatively account for changes in the chemical and isotopic composition of water along a flow path. A revised mole-balance formulation that includes an uncertainty term for each chemical and isotopic datum is derived. The revised formulation is comprised of mole-balance equations for each element or element redox state, alkalinity, electrons, solvent water, and each isotope; a charge-balance equation and an equation that relates the uncertainty terms for p H, alkalinity, and total dissolved inorganic carbon for each aqueous solution; inequality constraints on the size of the uncertainty terms; and inequality constraints on the sign of the mole transfer of reactants. The equations and inequality constraints are solved by a modification of the simplex algorithm combined with an exhaustive search for unique combinations of aqueous solutions and reactants for which the equations and inequality constraints can be solved and the uncertainty terms minimized. Additional algorithms find only the simplest mole-balance models and determine the ranges of mixing fractions for each solution and mole transfers for each reactant that are consistent with specified limits on the uncertainty terms. The revised formulation produces simpler and more robust mole-balance models and allows the significance of mixing fractions and mole transfers to be evaluated. In an example from the central Oklahoma aquifer, inclusion of up to 5% uncertainty in the chemical data can reduce the number of reactants in mole-balance models from seven or more to as few as three, these being cation exchange, dolomite dissolution, and silica precipitation. In another example from the Madison aquifer, inclusion of the charge-balance constraint requires significant increases in the mole transfers of calcite, dolomite, and organic matter, which reduce the estimated maximum carbon 14 age of the sample by about 10,000 years, from 22,700 years to 12,600 years.

Water Resources Research↗
USGS1997

Soil-water movement under natural-site and waste-site conditions: A multiple-year field study in the Mojave Desert, Nevada

Soil-water movement under natural-site and simulated waste-site conditions were compared by monitoring four experimental sites in the Mojave Desert, Nevada, during a 5-year period: one vegetated soil profile, one soil profile where vegetation was removed, and two nonvegetated test trenches. Precipitation ranged from 14 to 162 mm/yr. Temporal changes in water content measured by neutron probe were limited to the upper 0.5–1 m; values ranged from 0.01 to 0.19 m 3 /m 3 . Water potential and temperature were measured by thermocouple psychrometers; 77% remained operable for ≥4.5 years. For vegetated soil, precipitation that accumulated in the upper 0.75 m of soil was removed by evapotranspiration: water potentials decreased seasonally by 4 to >8 MPa. During 2 years with below-average precipitation, water potentials below the app arent root zone decreased by 2.3 (1.2-m depth) to 0.4 MPa (5-m depth), and the gradients became predominantly upward. Water potentials then rebounded during 2 years with near- and above-average precipitation, and seasonally variant water potential gradients were reestablished above the 4.2-m depth. Under nonvegetated waste-site conditions, data indicated the long-term accumulation and shallow, but continued, penetration of precipitation: water potentials showed moisture penetration to depths of 0.75−1.85 m. The method of simulated-waste drum placement (stacked versus random) and the associated differences in subsidence showed no measurable influence on the water balance of the trenches: subsidence totaled ≤13 mm during the study. Water potentials below the trenches and below the 2-m depth for the nonvegetated soil remained low (≈−5.5 to −7.5 MPa) and indicated the persistence of typically upward driving forces for isothermal water flow. Water fluxes estimated from water potential and temperature data suggested that isothermal liquid, isothermal vapor, and nonisothermal vapor flow need to be considered in the conceptualization of unsaturated flow at the field sites. Below the depth of temporal water content change, the estimated liquid fluxes ranged from 10 −10 to 10 −15 cm/s, isothermal vapor fluxes ranged from 10 −10 to 10 −13 cm/s, and the nonisothermal vapor fluxes ranged from 10 −8 to 10 −10 cm/s.

Nevada↗
USGS1997

Methods for predicting peak discharge of floods caused by failure of natural and constructed earthen dams

Floods from failures of natural and constructed dams constitute a widespread hazard to people and property. Expeditious means of assessing flood hazards are necessary, particularly in the case of natural dams, which may form suddenly and unexpectedly. We revise statistical relations (derived from data for past constructed and natural dam failures) between peak discharge ( Q p ) and water volume released ( V 0 ) or drop in lake level ( d ) but assert that such relations, even when cast into a dimensionless form, are of limited utility because they fail to portray the effect of breach-formation rate. We then analyze a simple, physically based model of dam-breach formation to show that the hydrograph at the breach depends primarily on a dimensionless parameter η= kV 0 / g l/2 d 7/2 , where k is the mean erosion rate of the breach and g is acceleration due to gravity. The functional relationship between Q p and η takes asymptotically distinct forms depending on whether η ≪ 1 (relatively slow breach formation or small lake volume) or η ≫ 1 (relatively fast breach formation or large lake volume). Theoretical predictions agree well with data from dam failures for which k , and thus η, can be estimated. The theory thus provides a rapid means of predicting the plausible range of values of peak discharge at the breach in an earthen dam as long as the impounded water volume and the water depth at the dam face can be estimated.

Water Resources Research↗
USGS1997

An algorithm for computing moments-based flood quantile estimates when historical flood information is available

This paper presents the expected moments algorithm (EMA), a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies. EMA can utilize three types of at-site flood information: systematic stream gage record; information about the magnitude of historical floods; and knowledge of the number of years in the historical period when no large flood occurred. EMA employs an iterative procedure to compute method-of-moments parameter estimates. Initial parameter estimates are calculated from systematic stream gage data. These moments are then updated by including the measured historical peaks and the expected moments, given the previously estimated parameters, of the below-threshold floods from the historical period. The updated moments result in new parameter estimates, and the last two steps are repeated until the algorithm converges. Monte Carlo simulations compare EMA, Bulletin 17B 's [ United States Water Resources Council , 1982] historically weighted moments adjustment, and maximum likelihood estimators when fitting the three parameters of the log-Pearson type III distribution. These simulations demonstrate that EMA is more efficient than the Bulletin 17B method, and that it is nearly as efficient as maximum likelihood estimation (MLE). The experiments also suggest that EMA has two advantages over MLE when dealing with the log-Pearson type III distribution: It appears that EMA estimates always exist and that they are unique, although neither result has been proven. EMA can be used with binomial or interval-censored data and with any distributional family amenable to method-of-moments estimation.

Water Resources Research↗
USGS1997

Evaluation of process errors in bed load sampling using a Dune Model

Reliable estimates of the streamwide bed load discharge obtained using sampling devices are dependent upon good at-a-point knowledge across the full width of the channel. Using field data and information derived from a model that describes the geometric features of a dune train in terms of a spatial process observed at a fixed point in time, we show that sampling errors decrease as the number of samples collected increases, and the number of traverses of the channel over which the samples are collected increases. It also is preferable that bed load sampling be conducted at a pace which allows a number of bed forms to pass through the sampling cross section. The situations we analyze and simulate pertain to moderate transport conditions in small rivers. In such circumstances, bed load sampling schemes typically should involve four or five traverses of a river, and the collection of 20–40 samples at a rate of five or six samples per hour. By ensuring that spatial and temporal variability in the transport process is accounted for, such a sampling design reduces both random and systematic errors and hence minimizes the total error involved in the sampling process.

Water Resources Research↗
USGS1997

Constant-concentration boundary condition: Lessons from the HYDROCOIN variable-density groundwater benchmark problem

In a solute-transport model, if a constant-concentration boundary condition is applied at a node in an active flow field, a solute flux can occur by both advective and dispersive processes. The potential for advective release is demonstrated by reexamining the Hydrologic Code Intercomparison (HYDROCOIN) project case 5 problem, which represents a salt dome overlain by a shallow groundwater system. The resulting flow field includes significant salinity and fluid density variations. Several independent teams simulated this problem using finite difference or finite element numerical models. We applied a method-of-characteristics model (MOCDENSE). The previous numerical implementations by HYDROCOIN teams of a constant-concentration boundary to represent salt release by lateral dispersion only (as stipulated in the original problem definition) was flawed because this boundary condition allows the release of salt into the flow field by both dispersion and advection. When the constant-concentration boundary is modified to allow salt release by dispersion only, significantly less salt is released into the flow field. The calculated brine distribution for case 5 depends very little on which numerical model is used, as long as the selected model is solving the proper equations. Instead, the accuracy of the solution depends strongly on the proper conceptualization of the problem, including the detailed design of the constant-concentration boundary condition. The importance and sensitivity to the manner of specification of this boundary does not appear to have been recognized previously in the analysis of this problem.

Water Resources Research↗
USGS1997

Regional interpretation of water-quality monitoring data

We describe a method for using spatially referenced regressions of contaminant transport on watershed attributes (SPARROW) in regional water-quality assessment. The method is designed to reduce the problems of data interpretation caused by sparse sampling, network bias, and basin heterogeneity. The regression equation relates measured transport rates in streams to spatially referenced descriptors of pollution sources and land-surface and stream-channel characteristics. Regression models of total phosphorus (TP) and total nitrogen (TN) transport are constructed for a region defined as the nontidal conterminous United States. Observed TN and TP transport rates are derived from water-quality records for 414 stations in the National Stream Quality Accounting Network. Nutrient sources identified in the equations include point sources, applied fertilizer, livestock waste, nonagricultural land, and atmospheric deposition (TN only). Surface characteristics found to be significant predictors of land-water delivery include soil permeability, stream density, and temperature (TN only). Estimated instream decay coefficients for the two contaminants decrease monotonically with increasing stream size. TP transport is found to be significantly reduced by reservoir retention. Spatial referencing of basin attributes in relation to the stream channel network greatly increases their statistical significance and model accuracy. The method is used to estimate the proportion of watersheds in the conterminous United States (i.e., hydrologic cataloging units) with outflow TP concentrations less than the criterion of 0.1 mg/L, and to classify cataloging units according to local TN yield (kg/km 2 /yr).

Water Resources Research↗
USGS1997

Hydrological and chemical estimates of the water balance of a closed-basin lake in north central Minnesota

Chemical mass balances for sodium, magnesium, chloride, dissolved organic carbon, and oxygen 18 were used to estimate groundwater seepage to and from Williams Lake, Minnesota, over a 15-month period, from April 1991 through June 1992. Groundwater seepage to the lake and seepage from the lake to groundwater were determined independently using a flow net approach using data from water table wells installed as part of the study. Hydrogeological analysis indicated groundwater seepage to the lake accounted for 74% of annual water input to the lake; the remainder came from atmospheric precipitation, as determined from a gage in the watershed and from nearby National Weather Service gages. Seepage from the lake accounted for 69% of annual water losses from the lake; the remainder was removed by evaporation, as determined by the energy budget method. Calculated annual water loss exceeded calculated annual water gain, and this imbalance was double the value of the independently measured decrease in lake volume. Seepage to the lake determined from oxygen 18 was larger (79% of annual water input) than that determined from the flow net approach and made the difference between calculated annual water gain and loss consistent with the independently measured decrease in lake volume. Although the net difference between volume of seepage to the lake and volume of seepage from the lake was 1% of average lake volume, movement of water into and out of the lake by seepage represented an annual exchange of groundwater with the lake equal to 26–27% of lake volume. Estimates of seepage to the lake from sodium, magnesium, chloride, and dissolved organic carbon did not agree with the values determined from flow net approach or oxygen 18. These results indicated the importance of using a combination of hydrogeological and chemical approaches to define volume of seepage to and from Williams Lake and identify uncertainties in chemical fluxes.

Minnesota↗
USGS1998

A nonlinear model for analysis of slug-test data

While doing slug tests in high-permeability aquifers, we have consistently seen deviations from the expected response of linear theoretical models. Normalized curves do not coincide for various initial heads, as would be predicted by linear theories, and are shifted to larger times for higher initial heads. We have developed a general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the well bore, and a Hvorslev model for the aquifer, which explains these data features. The model produces a very good fit for both oscillatory and nonoscillatory field data, using a single set of physical parameters to predict the field data for various initial displacements at a given well. This is in contrast to linear models which have a systematic lack of fit and indicate that hydraulic conductivity varies with the initial displacement. We recommend multiple slug tests with a considerable variation in initial head displacement to evaluate the possible presence of nonlinear effects. Our conclusion is that the nonlinear model presented here is an excellent tool to analyze slug tests, covering the range from the underdamped region to the overdamped region.

Water Resources Research↗
USGS1998

High-resolution Monte Carlo simulation of flow and conservative transport in heterogeneous porous media: 2. Transport results

In this, the second of two papers concerned with the use of numerical simulation to examine flow and transport parameters in heterogeneous porous media via Monte Carlo methods, results from the transport aspect of these simulations are reported on. Transport simulations contained herein assume a finite pulse input of conservative tracer, and the numerical technique endeavors to realistically simulate tracer spreading as the cloud moves through a heterogeneous medium. Medium heterogeneity is limited to the hydraulic conductivity field, and generation of this field assumes that the hydraulic-conductivity process is second-order stationary. Methods of estimating cloud moments, and the interpretation of these moments, are discussed. Techniques for estimation of large-time macrodispersivities from cloud second-moment data, and for the approximation of the standard errors associated with these macrodispersivities, are also presented. These moment and macrodispersivity estimation techniques were applied to tracer clouds resulting from transport scenarios generated by specific Monte Carlo simulations. Where feasible, moments and macrodispersivities resulting from the Monte Carlo simulations are compared with first- and second-order perturbation analyses. Some limited results concerning the possible ergodic nature of these simulations, and the presence of non-Gaussian behavior of the mean cloud, are reported on as well.

Water Resources Research↗
USGS1998

High-resolution Monte Carlo simulation of flow and conservative transport in heterogeneous porous media: 1. Methodology and flow results

In this, the first of two papers concerned with the use of numerical simulation to examine flow and transport parameters in heterogeneous porous media via Monte Carlo methods, various aspects of the modelling effort are examined. In particular, the need to save on core memory causes one to use only specific realizations that have certain initial characteristics; in effect, these transport simulations are conditioned by these characteristics. Also, the need to independently estimate length scales for the generated fields is discussed. The statistical uniformity of the flow field is investigated by plotting the variance of the seepage velocity for vector components in the x , y , and z directions. Finally, specific features of the velocity field itself are illuminated in this first paper. In particular, these data give one the opportunity to investigate the effective hydraulic conductivity in a flow field which is approximately statistically uniform; comparisons are made with first- and second-order perturbation analyses. The mean cloud velocity is examined to ascertain whether it is identical to the mean seepage velocity of the model. Finally, the variance in the cloud centroid velocity is examined for the effect of source size and differing strengths of local transverse dispersion.

Water Resources Research↗
USGS1998

Simulation of variable-density flow and transport of reactive and nonreactive solutes during a tracer test at Cape Cod, Massachusetts

A multispecies numerical code was developed to simulate flow and mass transport with kinetic adsorption in variable-density flow systems. The two-dimensional code simulated the transport of bromide (Br − ), a nonreactive tracer, and lithium (Li + ), a reactive tracer, in a large-scale tracer test performed in a sand-and-gravel aquifer at Cape Cod, Massachusetts. A two-fraction kinetic adsorption model was implemented to simulate the interaction of Li + with the aquifer solids. Initial estimates for some of the transport parameters were obtained from a nonlinear least squares curve-fitting procedure, where the breakthrough curves from column experiments were matched with one-dimensional theoretical models. The numerical code successfully simulated the basic characteristics of the two plumes in the tracer test. At early times the centers of mass of Br − and Li + sank because the two plumes were closely coupled to the density-driven velocity field. At later times the rate of downward movement in the Br − plume due to gravity slowed significantly because of dilution by dispersion. The downward movement of the Li + plume was negligible because the two plumes moved in locally different velocity regimes, where Li + transport was retarded relative to Br − . The maximum extent of downward transport of the Li + plume was less than that of the Br − plume. This study also found that at early times the downward movement of a plume created by a three-dimensional source could be much more extensive than the case with a two-dimensional source having the same cross-sectional area. The observed shape of the Br − plume at Cape Cod was simulated by adding two layers with different hydraulic conductivities at shallow depth across the region. The large dispersion and asymmetrical shape of the Li + plume were simulated by including kinetic adsorption-desorption reactions.

Massachusetts↗
USGS1998

Nitrogen transport and transformations in a shallow aquifer receiving wastewater discharge: A mass balance approach

Nitrogen transport and transformations were followed over the initial 3 years of development of a plume of wastewater-contaminated groundwater in Cape Cod, Massachusetts. Ammonification and nitrification in the unsaturated zone and ammonium sorption in the saturated zone were predominant, while loss of fixed nitrogen through denitrification was minor. The major effect of transport was the oxidation of discharged organic and inorganic forms to nitrate, which was the dominant nitrogen form in transit to receiving systems. Ammonification and nitrification in the unsaturated zone transformed 16–19% and 50–70%, respectively, of the total nitrogen mass discharged to the land surface during the study but did not attenuate the nitrogen loading. Nitrification in the unsaturated zone also contributed to p H decrease of 2 standard units and to an N 2 O increase (46–660 µg N/L in the plume). Other processes in the unsaturated zone had little net effect: Ammonium sorption removed <1% of the total discharged nitrogen mass; filtering of particulate organic nitrogen was less than 3%; ammonium and nitrate assimilation was less than 6%; and ammonia volatilization was less than 0.25%. In the saturated zone a central zone of anoxic groundwater (DO ≤ 0.05 mg/L) was first detected 17 months after effluent discharge to the aquifer began, which expanded at about the groundwater-flow velocity. Although nitrate was dominant at the water table, the low, carbon-limited rates of denitrification in the anoxic zone (3.0–9.6 (ng N/cm 3 )/d) reduced only about 2% of the recharged nitrogen mass to N 2 . In contrast, ammonium sorption in the saturated zone removed about 16% of the recharged nitrogen mass from the groundwater. Ammonium sorption was primarily limited to anoxic zone, where nitrification was prevented, and was best described by a Langmuir isotherm in which effluent ionic concentrations were simulated. The initial nitrogen load discharged from the groundwater system may depend largely on the growth and stability of the sorbed ammonium pool, which in turn depends on effluent-loading practices, subsurface microbial processes, and saturation of available exchange sites.

Water Resources Research↗
USGS1998

Tritium-helium 3 dating under complex conditions in hydraulically stressed areas of a buried-valley aquifer

The 3 H- 3 He dating method is applied in a buried-valley aquifer near Dayton, Ohio. The study area is large, not all sampling locations lie along well-defined flow paths, and existing wells with variable screen lengths and diameters are used. Reliable use of the method at this site requires addressing several complications: (1) The flow system is disturbed because of high pumping rates and induced infiltration; (2) tritium contamination is present in several areas of the aquifer; and (3) radiogenic helium concentrations are elevated in a significant number of the wells. The 3 H- 3 He ages are examined for self-consistency by comparing the reconstructed tritium evolution to the annual weighted tritium measured in precipitation; deviations result from dispersion, tritium contamination, and mixing. 3 H- 3 He ages are next examined for consistency with chlorofluorocarbon ages; the agreement is poor because of degradation of CFCs. Finally, the 3 H- 3 He ages are examined for consistency with the current understanding of local hydrologic processes; the ages are generally supported by hydrogeologic data and the results of groundwater flow modeling coupled with particle-tracking analyses.

Ohio↗