Multi-objective fitting of concentration-discharge relationships

Concentration–discharge ($C–Q$) relationships are widely used to assess the link between hydrological and biogeochemical processes at the catchment scale. $C–Q$ relationships are mainly calibrated using mono-objective methods to represent, either concentrations or discharge-weighted concentrations (i.e., load). Based on its wide use in hydrological modelling, we test a multi-objective calibration for the $C–Q$ relationship parameters, using both concentration and load, and compare it to a mono-objective calibration applied on either concentrations or load. This work is carried out on a high-frequency dataset (ORACLE-Orgeval Observatory, France). Our findings show that the multi-objective calibration yield a better representation of $C–Q$ relationships parameters during the high and low-flow events. The multi-objective calibration can be used for all forms of $C–Q$ relationships and avoids issues of under-representation of dilution processes characterized by high-discharge, low-concentration periods.     

The role of bathymetry and directional wave conditions on observed crescentic bar dynamics

Nearshore sandbars are important features in the surf zone of many beaches because they strongly influence the mean circulation and evolving morphology. Due to variations in wave conditions, sandbars can experience cross-shore migration and vary in shape from alongshore uniform (shore-parallel) to alongshore rhythmic (crescentic). Sandbar dynamics have been studied extensively, but existing observational studies usually do not quantify the processes leading to crescentic bar formation and straightening. This study analyses the dynamics of crescentic bar events at the fetch-limited beach of Castelldefels (northwestern Mediterranean Sea, Spain) using 7.5 years of hourly time-exposure video images and detailed wave conditions. The results show that, despite the generally calm wave conditions, the sandbars were very dynamic in the cross-shore and longshore directions. They often migrated rapidly offshore during storms (up to 70 m in one day) and more slowly onshore during post-storm conditions. Crescentic bars were often present at the study site (48% of the time), but only when the sandbar was at least 10 m from the shoreline. They displayed a large variability in wavelengths (100–700 m), alongshore migration speeds (0–50 m/day) and cross-shore amplitudes (5–20 m). Wavelengths increased for larger bar–shoreline distances and the alongshore migration speeds were strongly correlated with the alongshore component of the radiation stresses. Crescentic patterns typically developed during low–medium energetic waves with limited obliquity ( $\theta \lesssim 20$° at 10 m depth), while bar straightening occurred during medium–high energetic waves with strong oblique angles of incidence ( $\theta \gtrsim 15$°). Overall, this study provides further proof for the important role of wave direction in crescentic bar dynamics and highlights the strong dependence of crescentic bar development on the initial bathymetric configuration.     

Impact of evaporation on field capacity during water drainage redistribution in a soil

To this day, field capacity (FC) is rarely defined in the context of soil properties, and the use of non-physical simplistic models is the common way to normalize water content at FC. In this study, the problem of water drainage redistribution in a soil column with and without the presence of evaporation (EV) was extensively studied. Analytical solutions for the Richards equation were established for the case of water drainage redistribution through a deeply wetted soil water column with and without EV at FC conditions. Water retention and depth evolution curves were plotted first, using different EV values of (2 $\frac{\mathbf{mm}}{\mathbf{day}}$, 5 $\frac{\mathbf{mm}}{\mathbf{day}}$ and 8 $\frac{\mathbf{mm}}{\mathbf{day}}$) and second, for different drainage redistribution durations of (1 day, 4 days and 6 days) where EV was set to zero for the case with no EV or to a fixed value of 5 $\frac{\mathbf{mm}}{\mathbf{day}}$ for the case with EV. The results suggest that EV plays a significant role in soil water drainage suggesting that, in the presence of EV, the FC drying front reaches much higher depths in the soil water profile than if EV is turned off. It was also concluded that FC reaches deeper depths faster the stronger EV is acting at the surface of a soil water column. Additionally, the results suggest that the texture of the soil receiving drainage controls the amount of water available for EV and as a result, EV was found to play a stronger role the smaller the hydraulic conductivity of the soil is.     

Structural information derived from ambient noise tomography over a hydrocarbon-producing region in the Cachar fold belt,lower Assam,northeast India

Ambient noise tomography is a powerful tool that has found increasing application in reservoir analysis and imaging. The Cachar fold belt in lower Assam, northeast India encompasses several wells under active hydrocarbon production, along with several dry wells. To overcome the lack of active seismic data over the entire fold belt, a passive seismic study was carried out to image the concealed three-dimensional sub-surface structures. The data were recorded from February to November 2011 by a network of 65 wideband seismometers spanning an area of about 40 × 60 km². The data are crosscorrelated in the 2–5 s band, followed by phase-weighted stacking to estimate noise correlation functions with surface wave signatures. The traveltimes picked from the frequency-time analysis are utilized in a tomographic inversion for Rayleigh wave group velocities. The group velocity anomalies have a lateral resolution of ~ 3.5 × 5.5 km² and variations of up to $\pm 20\%$ for each period. The group velocities are in turn inverted for S-wave velocity distribution as a function of depth. The three-dimensional S-wave velocity tomograms reveal the tight anticlines and broad synclines, with high- and low-velocity zones corresponding to structural highs and lows, respectively. The structural interpretation is supported for the part of the region with producing wells and covered by active seismic data, wherein the post-stack time migrated seismic section shows anticlinal and synclinal features similar to those obtained from ambient noise tomography. The structures revealed by ambient noise tomography can help identify zones of interest to be targeted by active seismic surveys in the Cachar fold belt.     

Post-fire management effects on sediment (dis)connectivity in Mediterranean forest ecosystems: Channel and catchment response

Forest fires and post-fire practices influence sediment connectivity (SC). In this study, we use the ‘aggregated index of connectivity’ (AIC) to assess SC in five Mediterranean catchments (198–1090 ha) affected by a wildfire in 2012 in south-eastern Spain. Two temporal scenarios were considered, immediately after the fire and before post-fire management, and 2 years after the fire including all practices (hillslope barriers, check-dams, afforestation, salvage logging and skid trails). One LiDAR (light detection and ranging)-derived digital elevation model (DEM, 2 m × 2 m resolution) was generated, per scenario. The five catchment outlets were established as the computation target (AIC_OUT), and structural and functional SC were calculated. Index outputs were normalized to make the results of the non-nested catchments comparable (AIC_N-OUT). The output analysis includes the SC distribution along the catchments and at local scale (929 sub-catchments, 677 in the burned area), the hillslope and channel measures' effect on SC, and a sedimentological analysis using observed area-specific sediment yield (SSY) at 10 new (built after post-fire practices) concrete check-dams located in the catchments (SSY = 1.94 Mg ha⁻¹ yr⁻¹; σ = 1.22). The catchments with more circular shapes and steeper slopes were those with higher AIC_N-OUT. The structural SC maps – removing the rainfall erosivity influence – allowed evaluating the actual role played by the post-fire practices that reduced SC ( $\overline{x}$= − 1.19%; σ = 0.41); while functional SC was linked to the actual change of SC ( $\overline{x}$= + 5.32%; σ = 0.62). Hillslope treatments resulted in significant changes on AIC_N-OUT at sub-catchment scale with certain disconnectivity. A good and positive correlation was found between the SSY and the changes of AIC_N-OUT. However, the coarse DEM resolution explained the lack of effect of the rock check-dams – located on the secondary channels – on AIC_N-OUT. AIC_N-OUT proved to be a useful tool for decision making in post-fire restoration, but an optimal input data is still necessary to refine calculations.     

Homotopy scattering series for seismic forward modelling with variable density and velocity

We have derived a convergent scattering series solution for the frequency-domain wave equation in acoustic media with variable density and velocity. The convergent scattering series solution is based on the homotopy analysis of a vectorial integral equation of the Lippmann–Schwinger type. By using the Green's function and partial integration, we have derived the vectorial integral equation of the Lippmann–Schwinger type that involves the pressure gradient field as well as the pressure field from the wave equation. The vectorial Lippmann–Schwinger equation can in principle be solved via matrix inversion, but the computational cost of matrix inversion scales like $N^3$, where $N$ is the number of grid blocks. The computational cost can be significantly reduced if one solves the vectorial Lippmann–Schwinger equation iteratively. A simple iterative solution is the Born series, but it is only convergent when the scattering potential is sufficiently small. In this study, we have used the so-called homotopy analysis method to derive an iterative solution for the vectorial Lippmann–Schwinger equation which can be made convergent even in strongly scattering media. The computational cost of our convergent scattering series scales as $N^2$. Our algorithm, which is based on the homotopy analysis method, involves a convergence control operator that we select using hierarchical matrices. We use a three-layer model and a resampled version of the SEG/EAGE salt model to show the performance of the developed convergent scattering series.     

Approximation of van Genuchten Parameter Ranges from Hydraulic Conductivity Data

The use of retention function and relative conductivity function is essential for the calculation of flow in a variably saturated media using the Richards equation. A widely used mathematical model for this is the Mualem-van Genuchten model which requires the shape parameters and . These, however, are difficult to obtain. When data is scarce, and are often taken from literature and may deviate largely from actual values. The current study presents a novel mathematical model for the approximation of $$ and $$ and for the further estimation of realistic value ranges, which may be used as parameter space, for example, for the calibration of a numerical model. The model was developed for cases where data is scarce and only values of saturated hydraulic conductivity are available. It is based on a large data set from literature and it is demonstrated that the model estimates mean values from that data set with a good accuracy. In order to show the applicability of the model, a second data set has been compiled anew (provided as Supporting Information). The model is incorporated into the current version of the freeware computer program HYPAGS, which enables easy usage.     

Investigating young water fractions in a small Mediterranean mountain catchment: Both precipitation forcing and sampling frequency matter

The proportion of water younger than 2–3 months (young water fraction, F_yw) has become increasingly investigated in catchment hydrology. F_yw is typically estimated by comparing seasonal tracer cycles in precipitation and streamflow, through water sampling. However, some open research questions remain, such as: (i) whether part of the summer precipitation should be discarded because the high evapotranspiration demand, (ii) how well F_yw serves as a metric to compare catchments, and (iii) how sampling frequency affects F_yw estimates. To address these questions, we investigated F_yw in soil-, ground- and stream waters for the small Mediterranean Can Vila catchment. Rainfall was sampled at 5-mm intervals. Mobile soil water and groundwater were sampled fortnightly. Stream water was sampled depending on flow at variable time intervals (30 min to 1 week). Over 58 months, this sampling provided 1,529 δ¹⁸O determinations. Isotopic analyses results led us to include summer precipitation in the input signal. We found the highest F_yw in mobile soil waters (34%), while this was almost zero for groundwater except during wet periods. For stream waters, F_yw depended on the discharge variations, so that the flow-weighted young water fraction () was 22.6%, whereas the time-weighted F_yw was just 6.2%. Both and its discharge sensitivity (S_d) varied when different 12-month sampling periods were investigated. The young water fraction that would be obtained from a virtual thorough sampling () was estimated from the S_d and the observed stream flow. This showed an underestimation of by 25% for the frequent dynamic sampling and 66% for weekly sampling, due to missing high flows. Our results confirm that F_yw and its discharge sensitivity are metrics very sensitive to meteorological forcing during the analysed period. Thus, comparisons between catchments need long-term mean annual values and their variability. Our findings also support the dependence of F_yw estimates on the sampling rate and show the advantages of flow-weighted analysis. Finally, catchment water turnover investigations should be accompanied by the analysis of flow duration curves.     

Evaluating equilibrium and non‐equilibrium transport of ammonium in a loam soil column

Release of nitrogen compounds into groundwater, particularly those compounds from excessive agricultural fertilization, is a major concern in an aquifer recharge. Among the nitrogen compounds, ammonium ( ) is a common one. In order to assess the risk of agricultural fertilizer contamination to an aquifer through infiltration, adsorption onto a loamy agricultural soil profile (0–0.60 m depth) was studied using a soil column experiment and modelling simulation. The soil used in the experiment was drawn from an agricultural field in Xinzhen, Fangshan district, Beijing, China, and reconstituted in laboratory soil columns. Column experiments were conducted using bromide (conservative tracer) and ‐bearing aqueous solutions. The ammonium concentrations in the soil water samples were measured, and their values were plotted as the breakthrough curves. The chemical's soil–water distribution coefficients (K_d) were calculated using breakthrough curves. Then the retardation factor (R) in saturated soil was calculated. For the ‐bearing aqueous solutions, the strongest adsorption occurred at the soil depth of 0.30–0.45 m. The convection–dispersion equation model and chemical non‐equilibrium model in Hydrus‐1D were used to simulate transport in the loamy soil. The two‐site chemical non‐equilibrium model in Hydrus‐1D was best to simulate transport through the soil column. Parameter sensitivity study was conducted to investigate the influences of solute transport by K_d, the fraction of exchange sites assuming to be in equilibrium with the solution phase (f), the longitudinal dispersivity (λ), and the first‐order rate coefficients (ω). The sensitivity analysis results indicate K_d is the most critical parameter.     

Applicability of cosmic-ray neutron sensor for measuring soil moisture at the agricultural-pastoral ecotone in northwest China

Accurate monitoring of soil moisture is crucial in hydrological and ecological studies. Cosmic-ray neutron sensors (CRNS) measure area-average soil moisture at field scale, filling a spatial scale gap between in-situ observations and remote sensing measurements. However, its applicability has not been assessed in the agricultural-pastoral ecotone, a data scarce semi-arid and arid region in Northwest China (APENC). In this study, we calibrated and assessed the CRNS (the standard N₀ method) estimates of soil moisture. Results show that Pearson correlation coefficient, R_P, and the root mean square error (RMSE) between the CRNS soil moisture and the gravimetric soil moisture are 0.904 and less than 0.016 m³ m⁻³, respectively, indicating that the CRNS is able to estimate the area-average soil moisture well at our study site. Compared with the in-situ sensor network measurements (ECH2O sensors), the CRNS is more sensitive to the changes in moisture in its footprint, which overestimates and underestimates the soil moisture under precipitation and dry conditions, respectively. The three shape parameters a₀, a₁, a₂ in the standard calibration equation (N₀ method) are not well suited to the study area. The calibrated parameters improved the accuracy of the CRNS soil moisture estimates. Due to the lack of low gravimetric soil moisture data, performance of the calibrated N₀ function is still poor in the extremely dry conditions. Moreover, aboveground biomass including vegetation biomass, canopy interception and widely developed biological soil crusts adds to the uncertainty of the CRNS soil moisture estimates. Such biomass impacts need to be taken into consideration to further improve the accuracy of soil moisture estimation by the CRNS in the data scarce areas such as agricultural-pastoral ecotone in Northwest China.

     

Spatial average aquifer recharge through atmospheric chloride mass balance and its uncertainty in continental Spain

The atmospheric chloride mass balance (CMB) method allows spatial evaluations of the average diffuse aquifer recharge by rainfall () in large and varied territories when long‐term steady conditions can be assumed. Often, the distributed average CMB variables necessary to calculate have to be estimated from the available variable‐length data series, which may be of suboptimal quality and spatial coverage. This paper explains the use of these data and the reliability of the results in continental Spain, chosen as a large and varied territory. The CMB variables have been regionalized by ordinary kriging at the same 4976 nodes of a 10 km × 10 km grid. Nodal values vary from 14 to 810 mm year^–1, 90% ranging from 30 to 300 mm year^–1. The recharge‐to‐precipitation ratios vary from 0.03 in low‐permeability formations and semiarid areas to 0.65 in some carbonate massifs. Integrated average results for the whole of continental Spain yield a potential aquifer recharge of 64 km³ year^?1, the net recharge over permeable formations (40% of the territory) being 32 km³ year^?1. Two main sources of uncertainty affecting (given by the coefficient of variation, CV), induced by the inherent natural variability of the variables (CV_R) and from mapping (), have been segregated. The average CV_R is 0.13 and could be improved with longer data series. The average is 0.07 and may be decreased with better data coverage. The estimates were compared with other regional and local recharge estimates, being 4% and 1% higher, respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

Isotopic and hydrochemical insights into the groundwater characteristics along an arid to semi-humid climate gradient in China

In arid to semi-arid regions, groundwater is a critical water resource heavily relied upon, with the recharge sources and patterns being predominantly shaped by climate change and regional disparities. To compare the characteristics of groundwater in the endorheic and exorheic river basins with the climate transition zone of Gansu Province, this study uses isotopic hydrochemical analyses. This study summarizes the differences in regional groundwater recharge and evolutionary patterns. The results shows that the distribution patterns of precipitation isotopes in endorheic and exorheic river basins are opposite to those of groundwater isotopes. Specifically, the precipitation in the endorheic areas is more depleted in heavy isotopes, whereas the groundwater is more enriched. Both endorheic areas and exorheic areas exhibit similar characteristics of groundwater hydrochemical evolution, evolving from low-mineralization Mg²⁺ HC ${\mathrm{O}}_3^{-}$ recharge water to Na⁺ Cl⁻ type water with saline characteristics. The former is primarily replenished by surface water, whereas the latter is primarily replenished by precipitation. Variations in recharge patterns along with the differences in climatic conditions lead to distinct groundwater conditions in the two regions.