The response of sediment transport and morphological evolution to storms with different characteristics.

Strong wave-current interaction under the impact of storm events can induce a series of complex sedimentary processes of sediment resuspension and transport and morphology changes, significantly changing the topography of coastal zones. However, coastal sedimentary processes during storm events have not been fully understood. In this study, we developed a wave-current-sediment coupled model to investigate the response of dynamical processes to extreme storm events. The model was first validated against the observed data for both storm conditions during the 2007 Typhoon Wipha and fair-weather conditions in 2016 in the Haizhou Bay (HZB) of the Yellow Sea. The simulated results indicated that the longshore sediment transport was dominated originally by tidal effects which were significantly enhanced by wind-induced waves during the passage of the Typhoon Wipha. Storms with different characteristics correspond to two typical sedimentary dynamic response modes based on a series of numerical experiments. The tidal pumping effect (T3 + T4 + T5) and gravitational circulation term (T6) controlled the total storm-induced sediment flux, and T6 played a crucial and special role, typically in the opposite direction of the dominant wind of the storm. The strong wind could lead to the stratification of the water column, causing the down-slope or up-slope cross-shore sediment transport, resulting in coastal seabed erosion/deposition. In addition, the onshore wind was found to have a stronger impact on the sedimentary process. The methodology and findings of this study provide a scientific basis for understanding the response mechanism of sediment transport during storm events in coastal areas.

Risk prediction models for postoperative delirium in elderly patients with hip fracture: a systematic review.

Objectives: To systematically evaluate the risk prediction models for postoperative delirium in older adult hip fracture patients. Methods: Risk prediction models for postoperative delirium in older adult hip fracture patients were collected from the Cochrane Library, PubMed, Web of Science, and Ovid via the internet, covering studies from the establishment of the databases to March 15, 2023. Two researchers independently screened the literature, extracted data, and used Stata 13.0 for meta-analysis of predictive factors and the Prediction Model Risk of Bias Assessment Tool (PROBAST) to evaluate the risk prediction models for postoperative delirium in older adult hip fracture patients, evaluated the predictive performance. Results: This analysis included eight studies. Six studies used internal validation to assess the predictive models, while one combined both internal and external validation. The Area Under Curve (AUC) for the models ranged from 0.67 to 0.79. The most common predictors were preoperative dementia or dementia history (OR = 3.123, 95% CI 2.108-4.626, p < 0.001), American Society of Anesthesiologists (ASA) classification (OR = 2.343, 95% CI 1.146-4.789, p < 0.05), and age (OR = 1.615, 95% CI 1.387-1.880, p < 0.001). This meta-analysis shows that these were independent risk factors for postoperative delirium in older adult patients with hip fracture. Conclusion: Research on the risk prediction models for postoperative delirium in older adult hip fracture patients is still in the developmental stage. The predictive performance of some of the established models achieve expectation and the applicable risk of all models is low, but there are also problems such as high risk of bias and lack of external validation. Medical professionals should select existing models and validate and optimize them with large samples from multiple centers according to their actual situation. It is more recommended to carry out a large sample of prospective studies to build prediction models. Systematic review registration: The protocol for this systematic review was published in the International Prospective Register of Systematic Reviews (PROSPERO) under the registered number CRD42022365258.

Identification and assessment of the drift velocity of green tides using the maximum cross-correlation method in the Yellow Sea.

The green tides outbreak events seriously threaten the ecological balance of the coastal areas. Quickly and accurately obtaining the spatial distribution and drift state of green tides is key to early warning. Based on Landsat 8 (L8) and Sentinel-2 (S2) image pair, the green tides drift velocity was extracted using the maximum cross-correlation (MCC) method, and windage was calculated by combining ocean current and wind data. The results of the MCC method were validated. Ulva's drift in the Yellow Sea is shaped by both ocean currents and wind, closely aligning with the direction of the currents. Notably, the northward drift velocity of Ulva exhibits a clear boundary around 34°40'N. Windage shows similar characteristics with the Ulva drift velocity, as its values vary with time and space. This study will enhance our comprehension of the dynamic mechanism of green tides drift.

Development and Validation of a Risk Prediction Model for Ketosis-Prone Type 2 Diabetes Mellitus Among Patients Newly Diagnosed with Type 2 Diabetes Mellitus in China.

Background: We established a nomogram for ketosis-prone type 2 diabetes mellitus (KP-T2DM) in the Chinese adult population in order to identify high-risk groups early and intervene in the disease progression in a timely manner. Methods: We reviewed the medical records of 924 adults with newly diagnosed T2DM from January 2018 to June 2021. All patients were randomly divided into the training and validation sets at a ratio of 7:3. The least absolute shrinkage and selection operator regression analysis method was used to screen the predictors of the training set, and the multivariable logistic regression analysis was used to establish the nomogram prediction model. We verified the prediction model using the receiver operating characteristic (ROC) curve, judged the model's goodness-of-fit using the Hosmer-Lemeshow goodness-of-fit test, and predicted the risk of ketosis using the decision curve analysis. Results: A total of 21 variables were analyzed, and four predictors-hemoglobin A1C, 2-hour postprandial blood glucose, 2-hour postprandial C-peptide, and age-were established. The area under the ROC curve for the training and validation sets were 0.8172 and 0.8084, respectively. The Hosmer-Lemeshow test showed that the prediction model and validation set have a high degree of fit. The decision curve analysis curve showed that the nomogram had better clinical applicability when the threshold probability of the patients was 0.03-0.79. Conclusion: The nomogram based on hemoglobin A1C, 2-hour postprandial blood glucose, 2-hour postprandial C-peptide, and age has good performance and can serve as a favorable tool for clinicians to predict KP-T2DM.

[Effect of neuromuscular electrical stimulation on muscle strength in patients with mechanical ventilation in intensive care unit: cumulative Meta-analysis and trial sequential analysis].

OBJECTIVE: To evaluate the effect of neuromuscular electrical stimulation (NMES) on muscle strength and duration of mechanical ventilation through cumulative Meta-analysis and sequential trial analysis (TSA). METHODS: Randomized controlled trial (RCT) of NMES intervention in intensive care unit (ICU) patients with mechanical ventilation were searched from PubMed database of US National Library of Medicine, EMbase database of Netherlands Medical Abstract, Web of Science, SinoMed database of China, CNKI, Wanfang data, VIP and other Chinese and English databases from database construction to July 15, 2021. The control group received ICU routine nursing or rehabilitation exercise; the experimental group received NMES (low frequency electric current through electrode stimulation to make muscle groups twitch or contract) based on routine care in ICU. Relevant data were screened, evaluated and extracted by two researchers independently. After extracting data, STATA 15.0 and TSA software were used to analyze the data and evaluate the research results. RESULTS: A total of 9 studies were enrolled, including 619 subjects. Among the 9 articles included, 2 were grade A and 7 were grade B, indicating good overall quality. Cumulative Meta-analysis showed that compared with ICU routine care, NMES improved muscle strength of patients undergoing mechanical ventilation [standardized mean difference (SMD) = 0.64, 95% confidence interval (95%CI) was 0.07 to 1.21] and shortened the duration of mechanical ventilation (SMD = -1.84, 95%CI was -2.58 to -1.10). TSA analysis of the two outcomes showed that the sample size of muscle strength outcome index (n = 518) and mechanical ventilation outcome index (n = 419) did not meet the expected information (RIS; n values of 618 and 685); the cumulative Z-value line of the muscle strength outcome index crossed the traditional boundary line and TSA boundary line, indicating that more tests were not needed to verify this result. In the outcome index of mechanical ventilation duration, it was found that the cumulative Z-value line only crossed the traditional boundary line, but did not cross the TSA boundary line, indicating that further studies in this area should be carried out in the future to demonstrate this result. CONCLUSION: NMES can improve ICU patients' muscle strength and reduce the duration of mechanical ventilation.

Sensitivity analysis of greenhouse gas emissions at farm level: case study of grain and cash crops.

Sensitivity analysis is useful to downgrade/upgrade the number of inputs to limit greenhouse emissions and enhance crop yield. The primary data from the 300 rice (grain crop) and 300 cotton (cash crop) farmers were gathered in face-to-face interviews by applying a multistage random sampling technique using a well-structured pretested questionnaire. Energy use efficiency was estimated with data envelopment analysis (DEA) model, and a second-stage regression analysis was conducted by applying Cobb-Douglas production function to evaluate the influencing factors affecting. The results exhibit that chemical fertilizers, diesel fuel and water for irrigation are the major energy inputs that are accounted to be 15,721.55, 10,787.50 and 6411.08 MJ ha-1 for rice production, while for cotton diesel fuel, chemical fertilizer and water for irrigation were calculated to be 13,860.94, 12,691.10 and 4456.34 MJ ha-1, respectively. Total GHGs emissions were found to be 920.69 and 954.71 kg CO2eq ha-1 from rice and cotton productions, respectively. Energy use efficiency (1.33 and 1.53), specific energy (11.03 and 7.69 MJ ha-1), energy productivity (0.09 and 0.13 kg MJ-1) and energy gained (14,497.85 and 20,047.56 MJ ha-1) for rice and cotton crop, respectively. Moreover, the results obtained through the second-stage regression analysis revealed that excessive application of fertilizer had a negative impact on the yield of rice and cotton, while farm machinery, diesel fuel and biocides had a positive effect. We hope that these findings could help in the management of the energy budget that we believe will reduce the high emissions of GHGs to address the growing environmental hazards.

Impacts of climate change on vegetation phenology and net primary productivity in arid Central Asia.

Vegetation is highly sensitive to climate changes in arid regions. The relationship between vegetation and climate changes can be effectively characterized by vegetation phenology. However, few studies have examined the vegetation phenology and productivity changes in arid Central Asia (ACA). The vegetation phenological information of ACA was extracted using MODIS NDVI (Normalized Difference Vegetation Index) data, and the dynamics of vegetation phenological changes under spatiotemporal variations were quantitatively assessed. Moreover, the impacts of climate change on vegetation phenology and net primary productivity were analyzed by combining meteorological data with that of MODIS NPP (Net Primary Productivity) during the same period. The results demonstrated that the start of the season (SOS) of vegetation in the study was concentrated from mid-February to mid-April, while the end of the season (EOS) was concentrated from early October to mid-December. The length of growing season (LOS) ranged from 6 to 10 months. The SOS of vegetation was gradually postponed at a rate of 0.16 d·year-1. The EOS advanced at a rate of 0.69 d·year-1. The LOS was gradually shortened at a rate of 0.89 d·year-1. For each per 1000 m increase in elevation, the SOS of vegetation was postponed by 12.40 d; the EOS advanced by 0.40 d, and the LOS was shortened by 11.70 d. For the impacts of climate changes on vegetation phenology and NPP, the SOS of vegetation phenology negatively correlated with temperature but positively correlated with precipitation and NPP. The EOS and LOS positively correlated with temperature but negatively with precipitation and NPP. Results indicated that the SOS was not moved ahead but was delayed, while the EOS advanced rather than being postponed under climate change. These results can offer new insights on the phenological response to climate change in arid regions and on non-systematic changes in phenology under global warming.

Effects of different aerobic exercise training on glycemia in patients with type 2 diabetes: A protocol for systematic review and meta analysis.

BACKGROUND: Type 2 diabetes is an emergent worldwide health crisis, and rates are growing globally. Aerobic exercise is an essential measure for patients with diabetes, which has the advantages of flexible time and low cost. Aerobic exercise is a popular method to reduce blood glucose. Due to the lack of randomized trials to compare the effects of various aerobic exercises, it is difficult to judge the relative efficacy. Therefore, we intend to conduct a network meta-analysis to evaluate these aerobic exercises. METHODS: According to the retrieval strategies, randomized controlled trials on different aerobic exercise training will be obtained from China National Knowledge Infrastructure, WanFang, SinoMed, PubMed, Web of Science, EMBASE, and Cochrane Library, regardless of publication date or language. Studies were screened based on inclusion and exclusion criteria, and the Cochrane risk bias assessment tool will be used to evaluate the quality of the literature. The network meta-analysis will be performed in Markov Chain Monte Carlo method and carried out with Stata14 and OpenBUGS software. Ultimately, the evidentiary grade for the results will be evaluated. RESULTS: Eighteen literatures with a total of 1134 patients were included for the meta-analysis. In glycemia assessment, Tennis (standard mean difference = 3.59, credible interval 1.52, 5.65), had significantly better effects than the named control group. Tennis (standard mean difference = 3.50, credible interval 1.05, 5.59), had significantly better effects than the named Taiji group. CONCLUSION: All together, these results suggest that tennis may be the best way to improve blood glucose in patients with type 2 diabetes. This study may provide an excellent resource for future control glycemia and may also serve as a springboard for creative undertakings as yet unknown.

Projections of desertification trends in Central Asia under global warming scenarios.

Central Asia (CA) is a core area of global desertification, but the effect of the intensifying "global greening" policy on the desertification process under global warming scenarios in CA remains unclear. Based on multi-source remote sensing data and Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) 2b climate data, this study investigated desertification in CA using actual evapotranspiration (ETa), temperature and precipitation as driving factors. Coupling with the CA-Markov model, the inversion method of desertification was improved, and the evolution normal form of desertification in CA was proposed. Finally, spatio-temporal variations of desertification in CA were quantified. The results indicate that temperature, precipitation, and normalized difference vegetation index (NDVI) in CA increased during the historical period (1980-2015), with sudden changes in 1994. In contrast, although ETa exhibited fluctuating increases (7.41 mm/10 yr) during this period, no sudden changes were observed in 1994. In the future (2006-2099), the climate of CA will become warmer and wetter. With reference to 1980-2005, precipitation under global warming of 2.0 °C (GW2.0) will be higher than that under global warming of 1.5 °C (GW1.5) by 10.3 mm, and ETa will increase by 20.88 mm and 27.54 mm under GW1.5 and GW2.0, respectively. Although the area of desert lands has decreased (5.94 × 104 km2/10 yr), the area of potential desert lands has increased (0.17 × 104 km2/10 yr). With global warming, this situation will continue to intensify, mainly in Xinjiang of China, and Kazakhstan. The Aral Sea plays an important role in the desertification of CA. The potential increase in desert land under GW2.0 is equivalent to the current water area of the Aral Sea. The findings could provide policy support for combating desertification in CA and promoting the achievement of the Sustainable Development Goals.

Multiple Wavelet Coherence to Evaluate Local Multivariate Relationships in a Groundwater System.

Groundwater level fluctuations are affected by surface properties due to complex correlations of groundwater-surface water interaction and/or other surface processes, which are usually hard to be accurately quantified. Previous studies have assessed the relationship between groundwater level fluctuations and specific controlling factors. However, few studies have been conducted to explore the impact of the combination of multiple factors on the groundwater system. Hence, this paper tries to explore the localized and scale-specific multivariate relationships between the groundwater level and controlling factors (such as hydrologic and meteorological factors) using bivariate wavelet coherence and multiple wavelet coherence. The groundwater level fluctuations of two wells in areas covered by different plant densities (i.e., the riparian zone of the Colorado River, USA) are analyzed. Main findings include three parts. First, barometric pressure and river stage are the best factors to interpret the groundwater level fluctuations at small scales (<1 day) and large scales (>1 day) at the well of low-density plants stand, respectively. Second, at the well of high-density plants stand, the best predictors to control the groundwater level fluctuations include barometric pressure (<1 day), the combination of barometric pressure and temperature (1-7 days), temperature (7-30 days), and the combination of barometric pressure, temperature, and river stage (>30 days). The best predictor of groundwater head fluctuations depends on the variance of the vegetation coverage and hydrological processes. Third, these results provide a suite of factors to explain the groundwater level variations, which is an important topic in water-resource prediction and management.

Fractal nature of groundwater level fluctuations affected by riparian zone vegetation water use and river stage variations.

Groundwater systems affected by various factors can exhibit complex fractal behaviors, whose reliable characterization however is not straightforward. This study explores the fractal scaling behavior of the groundwater systems affected by plant water use and river stage fluctuations in the riparian zone, using multifractal detrended fluctuation analysis (MFDFA). The multifractal spectrum based on the local Hurst exponent is used to quantify the complexity of fractal nature. Results show that the water level variations at the riparian zone of the Colorado River, USA, exhibit multifractal characteristics mainly caused by the memory of time series of the water level fluctuations. The groundwater level at the monitoring well close to the river characterizes the season-dependent scaling behavior, including persistence from December to February and anti-persistence from March to November. For the site with high-density plants (Tamarisk ramosissima, which requires direct access to groundwater as its source of water), the groundwater level fluctuation becomes persistent in spring and summer, since the plants have the most significant and sustained influence on the groundwater in these seasons, which can result in stronger memory of the water level fluctuation. Results also show that the high-density plants weaken the complexity of the multifractal property of the groundwater system. In addition, the groundwater level variations at the site close to the river exhibit the most complex multifractality due to the influence of the river stage fluctuation.

Projections of actual evapotranspiration under the 1.5 °C and 2.0 °C global warming scenarios in sandy areas in northern China.

Actual evapotranspiration (ETa) is an essential component of Earth's global energy balance and water cycle. The Paris Agreement aspires to limit global mean surface warming to <2 °C and no >1.5 °C relative to preindustrial levels. However, it is uncertain how this global level will impact the shifts in the extents of sandy areas caused by global desertification. Using Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) datasets and advection-aridity models, we investigated the spatiotemporal features of ETa in sandy areas in northern China under global warming scenarios of 1.5 °C and 2.0 °C. The four climate models indicated significant increases in ETa in arid areas across northwestern China. Over time, the ETa value under only the representative concentration pathway 2.6 (RCP2.6) emission scenario increased towards a plateau and significantly increased in the other three emission scenarios (P < 0.01) under global warming of 1.5 °C and 2.0 °C. In terms of the spatial variations, ETa showed an increasing trend in all seasons except winter. The maximum ETa was 84.61 mm, and high values were mainly located in the southeast of the study area. Precipitation and the normalized difference vegetation index (NDVI) showed good correlations with ETa in the sandy areas in northern China. The sandy areas in northern China showed decreasing trends (0.45 km2/a) from 1980 to 2015. Under global warming of 2.0 °C (2040-2059) relative to that of 1.5 °C (2020-2039), the area of sandy land will increase at a rate of 27.04 km2 per decade (P < 0.01); after this period, the sandy land area in northern China may gradually stabilize, with a trend of 0.02 km2/a (2047-2100). Early efforts to achieve the 1.5 °C temperature goal could therefore markedly reduce the likelihood that large regions will face substantial global desertification and the related impacts.

Significance of groundwater flux on contaminant concentration and mass discharge in the nonaqueous phase liquid (NAPL) contaminated zone.

Groundwater flowing through residual nonaqueous phase liquid (NAPL) source zone will cause NAPL dissolution and generate large contaminant plume. The use of contaminant mass discharge (CMD) measurements in addition to NAPL aqueous phase concentration to characterize site conditions and assess remediation performance is becoming popular. In this study, we developed new and generic numerical models to investigate the significance of groundwater flux temporal variations on the NAPL source dynamics. The developed models can accommodate any temporal variations of groundwater flux in the source zone. We examined the various features of groundwater flux using a few selected functional forms of linear increase/decrease, gradual smooth increase/decrease, and periodic fluctuations with a general trend. Groundwater flux temporal variations have more pronounced effects on the contaminant mass discharge dynamics than the aqueous concentration. If the groundwater flux initially increases, then the reduction in contaminant mass discharge (CMDR) vs. NAPL mass reduction (MR) relationship is mainly downward concave. If the groundwater flux initially decreases, then CMDR vs. MR relationship is mainly upward convex. If the groundwater flux variations are periodic, the CMDR vs. MR relationship tends to also have periodic variations ranging from upward convex to downward concave. Eventually, however, the CMDR vs. MR relationship approaches 1:1 when majority of the NAPL mass becomes depleted.

Storage and Drainage Characteristics of a Highly Heterogeneous Karst Aquifer in Houzhai Basin.

The characteristics of karst aquifers are difficult to be determined due to their heterogeneous physical properties and lack of hydrogeological information. In this case study, we applied two methods for a comparative analysis of storage and drainage characteristics in upstream, midstream, and downstream of Houzhai cave stream basin. In the first method, Minimum Smoothed Method (MSM) is used to determine the proportion of baseflow to the total flow (Baseflow Index, BFI). In the second method, a bicarbonate-base two-end member mixing model is used to quantify the slow flow component and fast flow component. For both methods, slow flow and quick flow are quantified at three sampling sites, which provide useful information for the analysis of storage and drainage characteristics. The results from flow separation method and hydrogeochemical analysis show a consistently increasing trend of the proportion of slow flow to total flow from the upstream to downstream which indicates that the voids of highly conductive conduits and well-connected fissures decrease along the flow paths in the Houzhai cave stream basin in southwest China. The upstream areas have a low proportion of baseflow which indicates a high drainage capacity due to high permeable conduits and well-connected fissures. The downstream areas, on the contrary, have a high proportion of baseflow which indicates a high storage capacity and slow infiltration due to the predominant presence of matrix and poorly-connected fissures. These numerical methods provide alternative ways to investigate the storage and drainage characteristics of karst aquifers where direct measurement are not available.

A fractal Richards' equation to capture the non-Boltzmann scaling of water transport in unsaturated media.

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scaling, attributed to the fractal nature of heterogeneous media. Several applications are presented, fitting the FRE to water content curves from previous literature.

Sensitivity of solute advective travel time to porosities of hydrogeologic units.

An integral approach is proposed to quantify uncertainty and sensitivity of advective travel time to the effective porosities of hydrogeologic units (HGUs) along groundwater flow paths. The approach is applicable in situations where a groundwater flow model exists, but a full solute transport model is not available. The approach can be used to: (1) determine HGUs whose porosities are influential to the solute advective travel time; and (2) apportion uncertainties of solute advective travel times to the uncertainty contributions from individual HGU porosities. A simple one-dimensional steady-state flow example is used to illustrate the approach. Advective travel times of solutes are obtained based on the one-dimensional steady-state flow results in conjunction with the HGU porosities. The approach can be easily applicable to more complex multi-dimensional cases where advective solute travel time can be calculated based on simulated flow results from groundwater flow models. This approach is particularly valuable for optimizing limited resources when designing field characterization programs for uncertainty reduction by identifying HGUs that contribute most to the estimation uncertainty of advective travel times of solutes.

Incorporating layer- and local-scale heterogeneities in numerical simulation of unsaturated flow and tracer transport.

This study characterizes layer- and local-scale heterogeneities in hydraulic parameters (i.e., matrix permeability and porosity) and investigates the relative effect of layer- and local-scale heterogeneities on the uncertainty assessment of unsaturated flow and tracer transport in the unsaturated zone of Yucca Mountain, USA. The layer-scale heterogeneity is specific to hydrogeologic layers with layerwise properties, while the local-scale heterogeneity refers to the spatial variation of hydraulic properties within a layer. A Monte Carlo method is used to estimate mean, variance, and 5th, and 95th percentiles for the quantities of interest (e.g., matrix saturation and normalized cumulative mass arrival). Model simulations of unsaturated flow are evaluated by comparing the simulated and observed matrix saturations. Local-scale heterogeneity is examined by comparing the results of this study with those of the previous study that only considers layer-scale heterogeneity. We find that local-scale heterogeneity significantly increases predictive uncertainty in the percolation fluxes and tracer plumes, whereas the mean predictions are only slightly affected by the local-scale heterogeneity. The mean travel time of the conservative and reactive tracers to the water table in the early stage increases significantly due to the local-scale heterogeneity, while the influence of local-scale heterogeneity on travel time gradually decreases over time. Layer-scale heterogeneity is more important than local-scale heterogeneity for simulating overall tracer travel time, suggesting that it would be more cost-effective to reduce the layer-scale parameter uncertainty in order to reduce predictive uncertainty in tracer transport.

Simple screening models of NAPL dissolution in the subsurface.

Three simple screening models of nonaqueous phase liquid (NAPL) dissolution in the subsurface are proposed based on the NAPL mass conservation and the assumption of proportionality between the residual NAPL source zone concentration and the remaining residual NAPL mass. The purpose of the proposed models is to predict the solute concentration in the zone of the residual NAPL as a result of dissolution. The predicted source zone concentration decrease is used to simulate and account for the decrease of dissolution rate with time. The proposed simple NAPL dissolution models enable the pseudo-equilibrium formulation to be used and therefore the numerical simulations for field application problems can be simplified compared to the non-equilibrium counterpart. With proper choice of empirical parameters, the proposed simple screening models can work as well as more complex dissolution rate correlation models, such as that of Imhoff et al. [Water Resour. Res. 30 (1994) 307-320]. It is found that the proposed models are very good for quantifying non-equilibrium dissolution, which is characterized by tailing of breakthrough curves. The models are especially useful for situations of small residual NAPL saturation, which are typical for many field applications.