Hydrogeochemical and Isotopic Investigations on Groundwater Salinization in the Datong Basin,Northern China1

Abstract: Analyses of major elements, environmental isotope ratios (δ¹⁸O, δ²H), and PHREEQC inverse modeling investigations were conducted to understand the processes controlling the salinization of groundwater within the Datong Basin. The hydrochemical results showed that groundwater with high total dissolved solid (TDS) concentrations was dominated by sodium bicarbonate (Na‐HCO₃), sodium chlorite (Na‐Cl), and sodium sulfate (Na‐SO₄) type waters, whereas low‐TDS groundwater from near mountain areas was dominated by calcium bicarbonate (Ca‐HCO₃) and magnesium bicarbonate (Mg‐HCO₃) type waters. The characterization of the major components of groundwater and PHREEQC inverse modeling indicated that the aluminosilicate hydrolysis, cation exchange, and dissolution of evaporites (halite, mirabilite, and gypsum) governed the salinization of groundwater within the Datong Basin. The environmental isotope (δ¹⁸O, δ²H) and Cl^?/Br^? ratios revealed the impact of fast vertical recharge by irrigation returns and salt‐flushing water on the groundwater salinization. According to the analyses of major hydrochemical components and PHREEQC inverse modeling, evaporite dissolution associated with irrigation and salt‐flushing practice was probably the dominant controlling factor for the groundwater salinization, especially in the central part of the basin. Therefore, groundwater pumping for irrigation and salt‐flushing should be controlled to protect groundwater quality in this area.     

Comparison of 85Kr and 3H Apparent Ground‐Water Ages for Source Water Vulnerability in the Collyer River Catchment,Maine1

Abstract: Apparent ground‐water ages as determined by the noble gas isotope ⁸⁵Kr and the water isotope ³H are compared. Refined gas extraction methodology at the wellhead permits efficient collection of Kr for ⁸⁵Kr isotope enrichment. ⁸⁵Kr isochrones elucidate areas of much younger ground‐water ages than ³H. Declining ³H activities in the catchment prevent its correlation with the youngest measured ⁸⁵Kr ages. Source water for most drinking water supplies in the Collyer River catchment is recharged within 40 years BP (2004). Mean‐age (τ) transport modeling suggests uncertainty of ground‐water ages is greatest in the central basin area.     

The Use of Carbon and Nitrogen Isotopes to Study Watershed Erosion Processes1

Abstract:  Tracer studies are needed to better understand watershed soil erosion and calibrate watershed erosion models. For the first time, stable nitrogen and carbon isotopes (δ¹⁵N and δ¹³C) and the carbon to nitrogen atomic ratio (C/N) natural tracers are used to investigate temporal and spatial variability of erosion processes within a sub‐watershed. Temporal variability was assessed by comparing δ¹⁵N, δ¹³C, and C/N of eroded‐soils from a non‐equilibrium erosion event immediately following freezing and thawing of surface soils with two erosion events characterized by equilibrium conditions with erosion downcutting. Spatial variability was assessed for the equilibrium events by using the δ¹⁵N and δ¹³C signatures of eroded‐soils to measure the fraction of eroded‐soil derived from rill/interrill erosion on upland hillslopes as compared to headcut erosion on floodplains. In order to perform this study, a number of tasks were carried out including: (1) sampling source‐soils from upland hillslopes and floodplains, (2) sampling eroded‐soils with an in situ trap in the stream of the sub‐watershed, (3) isotopic and elemental analysis of the samples using isotope ratio mass spectrometry, (4) fractioning eroded‐soil to its upland rill/interrill and floodplain headcut end‐members using an unmixing model within a Bayesian Markov Chain Monte Carlo framework, and (5) evaluating tracer unmixing model results by comparison with process‐based erosion prediction models for rill/interrill and headcut erosion processes. Results showed that finer soil particles eroded during the non‐equilibrium event were enriched in δ¹⁵N and δ¹³C tracers and depleted in C/N tracer relative to coarser soil particles eroded during the equilibrium events. Correlation of tracer signature with soil particle size was explainable based on known biogeochemical processes. δ¹⁵N and δ¹³C were also able to distinguish between upland rill/interrill erosion and floodplain headcut erosion, which was due to different plant cover at the erosion sources. Results from the tracer unmixing model highlighted future needs for coupling rill/interrill and headcut erosion prediction models.     

ISOTOPE HYDROLOGY DYNAMICS OF RIVERINE WETLANDS IN THE KANKAKEE WATERSHED,INDIANA1

ABSTRACT: Wetland restoration activities may disturb shallow ground‐water flow dynamics. There may be unintentional sources of water flowing into a constructed wetland that could compromise the long‐term viability of a wetland function. Measurement of naturally‐occurring isotopes in the hydrosphere can provide an indication of provenance, flow paths or components, and residence times or ages of wetland ground‐water flow systems. Hydraulic head measurements may not provide sufficient detail of shallow flow disturbances and can be complemented by analyzing isotopes in waters flowing through the wetland. Two north‐central Indiana wetlands in the Kankakee watershed are being studied to determine the adequacy of wetland restoration activities. The native LaSalle wetland and the restored Hog Marsh wetland have contrasting ground‐water flow regimes. The conservative water isotopes ¹⁸O, ²H, and ³H, and selected solute isotopes ¹³C, ¹⁴C, ¹⁵N, ³⁴S, ⁸⁷Sr, and 206–208Pb, demonstrate the complexity of ground‐water flow in Hog Marsh compared to the established flow regime at the LaSalle wetland.     

Estimating Nitrogen Loading to Ground Water and Assessing Vulnerability to Nitrate Contamination in a Large Karstic Springs Basin,Florida1

Abstract: A nitrogen (N) mass‐balance budget was developed to assess the sources of N affecting increasing ground‐water nitrate concentrations in the 960‐km² karstic Ichetucknee Springs basin. This budget included direct measurements of N species in rainfall, ground water, and spring waters, along with estimates of N loading from fertilizers, septic tanks, animal wastes, and the land application of treated municipal wastewater and residual solids. Based on a range of N leaching estimates, N loads to ground water ranged from 262,000 to 1.3 million kg/year; and were similar to N export from the basin in spring waters (266,000 kg/year) when 80‐90% N losses were assumed. Fertilizers applied to cropland, lawns, and pine stands contributed about 51% of the estimated total annual N load to ground water in the basin. Other sources contributed the following percentages of total N load to ground water: animal wastes, 27%; septic tanks, 12%; atmospheric deposition, 8%; and the land application of treated wastewater and biosolids, 2%. Due to below normal rainfall (97.3 cm) during the 12‐month rainfall collection period, N inputs from rainfall likely were about 30% lower than estimates for normal annual rainfall (136 cm). Low N‐isotope values for six spring waters (δ¹⁵N‐NO₃ = 3.3 to 6.3‰) and elevated potassium concentrations in ground water and spring waters were consistent with the large N contribution from fertilizers. Given ground‐water residence times on the order of decades for spring waters, possible sinks for excess N inputs to the basin include N storage in the unsaturated zone and parts of the aquifer with relatively sluggish ground‐water movement and denitrification. A geographical‐based model of spatial loading from fertilizers indicated that areas most vulnerable to nitrate contamination were located in closed depressions containing sinkholes and other dissolution features in the southern half of the basin.     

Predicting Sustainable Ground Water to Constructed Riparian Wetlands: Shaker Trace,Ohio, USA

Water isotopy is introduced as a tool to design, locate, and select storm water best management practices for the prediction of sustained ground water inflows to prospective constructed wetlands. A primer and application of the stable isotopes, ¹⁸O and ²H, are discussed for riparian wetland restoration areas among an agricultural landscape in southwestern Ohio. Conventional piezometric measurements were ambiguous in identifying groundwater mounding across a transect which includes numerous agricultural tile drains. Instead evaporative potential data represented by δ¹⁸O values indicated a well delineated zone for prospective constructed wetlands. All successful constructed wetland areas thus far at Shaker Trace are represented by ground water with depleted δ¹⁸O values below −9.0‰ VSMOW. Such areas of sustainable ground water inflow could either be due to perched units at depth or simply the result of an increased flow gradient.     

利用氮、氧稳定同位素识别地下水硝酸盐污染源研究进展

氮污染特别是地下水硝酸盐污染已成为一个相当普遍而重要的环境问题。地下水硝酸盐污染与人类健康和环境安全密切相关。为控制地下水硝酸盐污染,最根本的解决办法就是找到硝酸盐的来源,减少硝态氮向地下水的输送。由于不同来源的硝酸盐具有不同的氮、氧同位素组成,人们利用NO3-中δ15N和δ18O开展了硝酸盐污染源识别研究。本文综述了利用氮、氧同位素识别地下水硝酸盐污染源及定量硝酸盐污染源输入的研究进展及目前存在的问题,并提出几个值得重视的研究方向。     

Impact of an Invasive Exotic Species on Stream Nitrogen Levels in Southern Illinois1

Abstract: Autumn‐olive (Elaeagnus umbellata Thunb.) is an invasive, exotic shrub that has become naturalized in the eastern United States. Autumn‐olive fixes nitrogen (N) via a symbiotic relationship with the actinomycete Frankia. At the plot scale, the presence of autumn‐olive has been related to elevated soil water nitrate‐N (NO₃^?‐N) concentrations. This study examined the relationship between autumn‐olive cover in a watershed and stream water quality. Stream water nitrate‐N (NO₃^?‐N) and ammonium‐N (NH₄⁺‐N) concentrations were measured in 12 first order ephemeral streams draining watersheds with mixed forest cover and a range of 0‐35% autumn‐olive cover. Percent autumn‐olive cover was positively correlated with mean stream NO₃^?‐N concentrations, but was not correlated with mean stream NH₄⁺‐N concentrations. While other studies have demonstrated a significant relationship between native N‐fixers and stream NO₃^?‐N, this is the first study to document a relationship for an invasive, exotic N‐fixing species. Results suggest that this exotic species can be an additional source of NO₃^? in local and regional water bodies and demonstrates an additional negative ecosystem consequence of invasion beyond losses in biodiversity.     

Spatiotemporal Variability in Water Sources Controls Chemical and Physical Properties of a Semi‐arid Urban River System

We conducted synoptic surveys over three seasons in one year to evaluate the variability in water sources and geochemistry of an urban river with complex water infrastructure in the state of Utah. Using stable isotopes of river water (δ¹⁸O and δ²H) within a Bayesian mixing model framework and a separate hydrologic mass balance approach, we quantified both the proportional inputs and magnitude of discharge associated with “natural” (lake, groundwater, and tributary inputs) and “engineered” (effluent and canal inflows) sources. The relative importance of these major contributors to streamflow varied both spatially and seasonally. Spatiotemporal patterns of dissolved oxygen, temperature, pH, calcium, chloride, nitrate, and orthophosphate indicated seasonal shifts in dominant sources of river water played an important role in determining water quality. We show although urban rivers are clearly influenced by novel water sources created by water infrastructure, they continue to reflect the imprint of “natural” water sources, including diffuse groundwater. Resource managers thus may need to account for the quantity of both surface waters and also historically overlooked groundwater inputs to address water quality concerns in urban rivers.     

IDENTIFYING DISCHARGE ZONES OF ARSENIC IN THE GOOSE RIVER BASIN,MAINE1

ABSTRACT: Water balance modeling and the analysis of stable water isotopes in ground water were conducted to aid the location of ground water discharge areas within the Goose River basin, in mid‐coastal Maine. Previous investigations of drinking water from wells in the fractured crystalline bedrock encountered persistent elevated total arsenic. Such contamination may be related to discharging ground water from fractured zones in the basin. Modeled discharge rates greater than +10 cm/yr and ¹⁸O values lighter than‐9.5 per mil VSMOW may indicate recent recharge is mixing with deeper ground water and is focused along some fractured zones in arsenic bearing crystalline rocks.     

Nitrate loading and isotopic signatures in subsurface agricultural drainage systems

Artificially draining soils using subsurface tiles is a common practice on many agricultural fields. High levels of nitrate-nitrogen (NO-N) are often released from these systems; therefore, knowledge on the sources and processes controlling NO-N in drainage systems is needed. A dual isotope study (δN and δO) was used to investigate three subsurface drainage systems (shallow, conventional, and controlled) in Onslow, Nova Scotia, Canada. The objectives of this study were (i) to identify which drainage system more effectively reduced the NO-N loading, (ii) to examine differences in isotopic signatures under identical nutrient and cropping regimes for a fixed soil type, and (iii) to identify the utility of different drainage systems in controlling nutrient flows. Nitrate concentrations measured ranged from 0.92 to 11.8, from 2.3 to 17.3, and from 2.1 to 19.8 mg L for the shallow, conventional, and controlled drains, respectively. Total NO-N loading from shallow and controlled drains were 20 and 5.6 kg ha, respectively, lower than conventional (39.1 kg ha). The isotopic composition of NO-N for all drainage types appeared to be a mixture of two organic sources (manure and soil organic matter) via the process of nitrification. There was no evidence that denitrification played a significant role in removing NO-N during transport. Overall, shallow drainage reduced NO-N loading but offered no water conservation benefits. Combining the benefits of decreased NO-N loading from shallow systems with water control capability may offer the best solution to reducing nutrient loadings into water systems, achieving optimal crop yield, and decreasing drainage installation costs.     

Estimating Annual Groundwater Evapotranspiration from Phreatophytes in the Great Basin Using Landsat and Flux Tower Measurements

Escalating concerns about water supplies in the Great Basin have prompted numerous water budget studies focused on groundwater recharge and discharge. For many hydrographic areas (HAs) in the Great Basin, most of the recharge is discharged by bare soil evaporation and evapotranspiration (ET) from phreatophyte vegetation. Estimating recharge from precipitation in a given HA is difficult and often has significant uncertainty, therefore it is often quantified by estimating the natural discharge. As such, remote sensing applications for spatially distributing flux tower estimates of ET and groundwater ET (ET_g) across phreatophyte areas are becoming more common. We build on previous studies and develop a transferable empirical relationship with uncertainty bounds between flux tower estimates of ET and a remotely sensed vegetation index, Enhanced Vegetation Index (EVI). Energy balance‐corrected ET measured from 40 flux tower site‐year combinations in the Great Basin was statistically correlated with EVI derived from Landsat imagery (r² = 0.97). Application of the relationship to estimate mean‐annual ET_g from four HAs in western and eastern Nevada is highlighted and results are compared with previous estimates. Uncertainty bounds about the estimated mean ET_g allow investigators to evaluate if independent groundwater discharge estimates are “believable” and will ultimately assist local, state, and federal agencies to evaluate expert witness reports of ET_g, along with providing new first‐order estimates of ET_g.     

Identification of the source of nitrate contamination in ground water below an agricultural site, Jeungpyeong, Korea

This study applied hydrogeological characterization and isotope investigation to identify source locations and to trace a plume of ground water contaminated by nitrate. Most of the study site is agricultural fields with the remainder being residential. A poultry farm is also within the study area, so that potential point and nonpoint sources were present. Estimates of seasonal ground water recharge from irrigation and precipitation, leakage of sewage, and the regional ground water flow were linked to the seasonal changes in isotopic values. Ground water recharge largely occurred in spring and summer following precipitation or irrigation, depending on the locations. Natural and fertilized soils were identified as nonpoint sources of nitrate contamination in this area, while septic and animal wastes were identified as small point sources. The seasonal changes in the relative impact of these sources on ground water contamination were related to such factors as source distribution, the aquifer confining condition, precipitation rate, infiltration capacity, recharge rate, and the land use pattern.     

Predicting δCDIC dynamics in CCS: A scheme based on a review of inorganic carbon chemistry under elevated pressures and temperatures

Stable carbon isotopes are important tools to assess potential storage sites for CO₂, as they allow the quantification of ionic trapping via isotope mass balances. In deep geological formations high p/T conditions need to be considered, because CO₂ dissolution, equilibrium constants and isotope fractionation of dissolved inorganic carbon (DIC) depend on temperature, pressure and solute composition. After reviewing different approaches to account for these dependencies, an expanded scheme is presented for speciation and carbon isotope fractionation of DIC and dissolution of CaCO₃ for pCO₂ up to 100 bar, pH down to 3 and temperatures of up to 200 °C. The scheme evaluates the influence of respective parameters on isotope ratios during CO₂ sequestration. The pCO₂ and pH are the dominant controlling factors in the DIC/δ¹³C/pH system. The fugacity of CO₂ has major impact on DIC concentrations at temperatures below 100 °C at high pCO₂. Temperature dependency of activities and equilibrium dominates at temperatures above 100 °C. Isotope ratios of DIC are expected to be about 1–2‰ more depleted in ¹³C compared to the free CO₂ at pCO₂ values above 10 bar. This depletion is controlled by carbon isotope fractionation between CO₂ and H₂CO₃* which is the dominant species of DIC at the resulting pH below 5.     

DISSOLVED GAS ANALYSIS FOR ASSESSING THE FATE OF NITRATE IN WETLANDS1

ABSTRACT: Dissolved gas analysis permits direct detection of ground water denitrification, a technique we used in this study to assess the fate of nitrate in a riparian wetland. Dissolved argon (Ar) and dinitrogen (N₂) were measured in transects of nested piezometers installed at different depths within upwelling regions of a riparian wetland. The method uses the Ar content in the water as a natural inert tracer for assessing background content of N₂ from the previous air/water equilibrium. Within the wetland under study, anoxic to suboxic ground water became more oxic in piezometers close to the aquifer layer, indicating upwelling of oxic ground water. Assessment of loss of nitrate and Ar in ground water within an upwelling zone indicated that shallow piezometers had significant N₂ loss through degassing. Most of the measured nitrate‐nitrogen (NO₃^?‐N) loss of 205 μM in a piezometer nest could be accounted for by total N₂‐N produced (169 μM N), calculated from changes in dissolved N₂ and estimated N₂ degassed. Degassing due to methane (CH₄) production was also detected in some shallow piezometers within nests. This technique for analysis of dissolved gases in ground water can be applied to detect small changes in N gas concentration and aids in assessing the fate of nitrate along a ground water flow path.     

STREAM WATER CHEMISTRY IN WATERSHEDS RECEIVING DIFFERENT ATMOSPHERIC INPUTS OF H+, NH4, NO3−, AND SO42−1

ABSTRACT: Weekly precipitation and stream water samples were collected from small watersheds in Denali National Park, Alaska, the Fraser Experimental Forest, Colorado, Isle Royale National Park, Michigan, and the Calumet watershed on the south shore of Lake Superior, Michigan. The objective was to determine if stream water chemistry at the mouth and upstream stations reflected precipitation chemistry across a range of atmospheric inputs of H⁺, NH₄⁺, NO₃^?_?, and SO₄^2?. Volume-weighted precipitation H⁺, NH₄⁺, NO₃^?_?, and SO₄^2? concentrations varied 4 to 8 fold with concentrations highest at Calumet and lowest in Denali. Stream water chemistry varied among sites, but did not reflect precipitation chemistry. The Denali watershed, Rock Creek, had the lowest precipitation NO₃^?_? and SO₄^2? concentrations, but the highest stream water NO₃^?and SO₄^2? concentrations. Among sites, the ratio of mean monthly upstream NO₃^?_? concentration to precipitation NO₃^?_- concentration declined (p < 0.001, R²= 0.47) as precipitation NO₃^?_? concentration increased. The ratio of mean monthly upstream to precipitation SO₄^2? concentration showed no significant relationship to change in precipitation SO₄^2? concentration. Watersheds showed strong retention of inorganic N (> 90 percent inputs) across inputs ranging from 0.12 to > 6 kg N ha^?1 y^?1. Factors possibly accounting for the weak or non-existent signal between stream water and precipitation ion concentrations include rapid modification of meltwater and precipitation chemistry by soil processes, and the presence of unfrozen soils which permits winter mineralization and nitrification to occur.     

Long-term effects of nitrogen fertilizer use on ground water nitrate in two small watersheds

Changes in agricultural management can minimize NO3-N leaching, but then the time needed to improve ground water quality is uncertain. A study was conducted in two first-order watersheds (30 and 34 ha) in Iowa's Loess Hills. Both were managed in continuous corn (Zea mays L.) from 1964 through 1995 with similar N fertilizer applications (average 178 kg ha(-1) yr(-1)), except one received applications averaging 446 kg N ha(-1) yr(-1) between 1969 and 1974. This study determined if NO3-N from these large applications could persist in ground water and baseflow, and affect comparison between new crop rotations implemented in 1996. Piezometer nests were installed and deep cores collected in 1996, then ground water levels and NO3-N concentrations were monitored. Tritium and stable isotopes (2H, 18O) were determined on 33 water samples in 2001. Baseflow from the heavily N-fertilized watershed had larger average NO3-N concentrations, by 8 mg L(-1). Time-of-travel calculations and tritium data showed ground water resides in these watersheds for decades. "Bomb-peak" precipitation (1963-1980) most influenced tritium concentrations near lower slope positions, while deep ground water was dominantly pre-1953 precipitation. Near the stream, greater recharge and mixed-age ground water was suggested by stable isotope and tritium data, respectively. Using sediment-core data collected from the deep unsaturated zone between 1972 and 1996, the increasing depth of a NO3-N pulse was related to cumulative baseflow (r2 = 0.98), suggesting slow downward movement of NO3-N since the first experiment. Management changes implemented in 1996 will take years to fully influence ground water NO3-N. Determining ground water quality responses to new agricultural practices may take decades in some watersheds.     

Intensification of treatment processes for oily wastewater: Theoretical foundations for calculating the hydrodynamic characteristics of tube coalescers

We present the results of theoretical studies of the pressure fluid flow fundamental characteristics in tube coalescers used in the treatment processes for oily wastewater. It is shown that three different regions of flow (wall sublayer, transition sublayer, and flow kernel), having their own hydrodynamic characteristics, are formed in a cross section of the tube coalescer. In the viscous wall sublayer (of thickness δ_*), viscous frictional forces exceed inertial forces (Re_δ* < 1), and “creeping flow” is observed. This region borders on the transition sublayer (of thickness δ_** = δ_*), in which inertial forces exceed viscous frictional forces (Re_δ** > 1). For both laminar and turbulent flow, distribution laws of local velocities and velocity gradients along the pipe radius are obtained in each of the three regions. In the flow kernel, the linear distribution law of velocity gradients gives a square distribution law of velocities for both types of flow, but for the turbulent flow, the correction coefficients A = β and B = 2β ? 1 must be introduced.     

BIOGEOCHEMICAL EFFECTS OF GLOBAL CHANGE ON U.S. NATIONAL PARKS1

ABSTRACT: Federal parks and other public lands have unique mandates and rules regulating their use and conservation. Because of variation in their response to local, regional, and global‐scale disturbance, development of mitigation strategies requires substantial research in the context of long‐term inventory and monitoring. In 1982, the National Park Service began long‐term, watershed‐level studies in a series of national parks. The objective was to provide a more comprehensive database against which the effects of global change and other issues could be quantified. A subset of five sites in North Carolina, Texas, Washington, Michigan, and Alaska, is examined here. During the last 50 years, temperatures have declined at the southern sites and increased at the northern sites with the greatest increase in Alaska. Only the most southern site has shown an increase in precipitation amount. The net effect of these trends, especially for the most northern and southern sites, would likely be an increase in the growing season and especially the time soil processes could continue without moisture or temperature limitations. During the last 18 years, there were few trends in atmospheric ion inputs. The most evident was the decline in SO₄² deposition. There were no significant relationships between ion input and stream water output. This finding suggests other factors as modification of precipitation or canopy throughfall by soil processes, hydrologic flow path, and snowmelt rates are major processes regulating stream water chemical outputs.     

Detecting the Dynamic Linkage between Landscape Characteristics and Water Quality in a Subtropical Coastal Watershed, Southeast China

Geospatial analysis and statistical analysis are coupled in this study to determine the dynamic linkage between landscape characteristics and water quality for the years 1996, 2002, and 2007 in a subtropical coastal watershed of Southeast China. The landscape characteristics include Percent of Built (%BL), Percent of Agriculture, Percent of Natural, Patch Density and Shannon’s Diversity Index (SHDI), with water quality expressed in terms of COD_Mn and NH₄ ⁺–N. The %BL was consistently positively correlated with NH₄ ⁺–N and COD_Mn at time three points. SHDI is significantly positively correlated with COD_Mn in 2002. The relationship between NH₄ ⁺–N, COD_Mn and landscape variables in the wet precipitation year 2007 is stronger, with R² = 0.892, than that in the dry precipitation years 1996 and 2002, which had R² values of 0.712 and 0.455, respectively. Two empirical regression models constructed in this study proved more suitable for predicting COD_Mn than for predicting NH₄ ⁺–N concentration in the unmonitored watersheds that do not have wastewater treatment plants. The calibrated regression equations have a better predictive ability over space within the wet precipitation year of 2007 than over time during the dry precipitation years from 1996 to 2002. Results show clearly that climatic variability influences the linkage of water quality-landscape characteristics and the fit of empirical regression models.