Ensemble and effective dispersion in three-dimensional isotropic fractal media Abstract We determine the time-dependent behavior of the dispersion coefficient for transport in formations with isotropic log-conductivity fields showing fractal behavior. We consider two different dispersion coefficients for point-like injection: (1) the ensemble dispersion coefficients, defined as half the rate of change of the second central moments of the ensemble-averaged concentration distribution and (2) the effective dispersion, which is half the rate of change of the expected second central moments. Our results show, that the two longitudinal macrodispersion coefficients steadily grow with time and remain different at all times in a fully fractal regime, indicating that no Fickian transport regime is ever reached. The resulting effective longitudinal transport model is consequently a fractional advection–dispersion equation. In the semi-fractal regime, a Gaussian transport regime is reached eventually. However, compared to the case of a classic non-fractal regime, the transient non-Gaussian regime lasts much longer. In the transverse direction, the two dispersion coefficients approach the same large-time limit also in fractal media highlighting the fundamental difference between longitudinal and transverse dispersion.

Probabilistic numerical assessment of seawater intrusion overshoot in heterogeneous coastal aquifers Abstract Seawater intrusion is considered as one of the main hazards to coastal aquifers. In coastal aquifers, an overshoot occurs when the freshwater–saltwater interface exceeds the steady state position due to sea level rise (SLR). Hence, it is considered a more critical state than the terminal state. In the present study, overshoot is characterized in an unconfined, heterogeneous two-dimensional aquifer. For a more accurate evaluation, overshoot is investigated using three indicators, seawater toe, salinized volume, and effective dispersivity. In combination with the associated land surface inundation (LSI) impact, two types of SLR are assumed, gradual SLR (GSLR) and instantaneous SLR (ISLR). For addressing the heterogeneity of the aquifer, 50 sets of log-normally-distributed conductivity fields using a spherical correlation function are generated for each of the scenarios. Heterogeneity of the aquifer is modeled using the variance of conductivity field ( \(\sigma_{{{ \ln }k}}^{2}\) ) and the longitudinal correlation length ( \(\lambda_{x}\) ). Three different values of 0.5, 1, and 2 are assumed for \(\sigma_{{{ \ln }k}}^{2}\) where two values of 20 m and 40 m are assigned to \(\lambda_{x}\) . Using Monte-Carlo simulations, it is shown that (1) in both GSLR and ISLR scenarios, the overshoot is observed for both the seawater toe and the salinized volume where LSI is not assumed; (2) the SLR impact is overshadowed by the significance of conductivity field properties in heterogeneous scenarios; (3) \(\sigma_{{{ \ln }k}}^{2}\) plays a more discernible role in the overshoot characteristics compared to \(\lambda_{x}\) ; (4) a realistic assumption of GSLR results in lower overshoot occurrence probability. These observations are interpreted using the associated behavior of the flow field in the aquifer and the time needed for hydraulic pressures in this field to re-equilibrate after SLR.

MPS-APO: a rapid and automatic parameter optimizer for multiple-point geostatistics Abstract Multiple-point statistics (MPS) have been widely used in Earth and environmental sciences because of their ability to generate realistic stochastic realizations of complex natural processes. The spatial patterns and statistical information required for MPS modeling are represented by a training image. However, each MPS algorithm has a specific set of parameters that have a direct impact on the quality of pattern reproduction and should be chosen prior to the modeling. While there are some general guidelines for some MPS algorithms, a general parameter interference methodology is currently lacking. To date, the common practice for finding optimal parameters is to carry out a sensitivity analysis, which can be cumbersome especially in complex applications. In this study, we propose the MPS Automatic Parameter Optimizer (MPS-APO), a generic method based on stochastic optimization to rapidly approximate optimal parameters for any MPS method and different types of settings. The MPS-APO formulates an objective function that quantifies spatial pattern reproduction for each set of parameters. The Simultaneous Perturbation Stochastic Approximation (SPSA) optimization method is used because of its computational efficiency, and also its ability to cope with the stochastic nature of the objective function. The optimization proceeds in two steps. The first step aims to optimize the parameters for the best quality regardless of computational cost. When no more improvement can be achieved, the second step minimizes the CPU cost without degrading the spatial structures reproduction attained in the first step. In this study, MPS-APO is performed on different pixel-based and patch-based MPS methods: SNESIM, FILTERSIM, Direct Sampling and Image Quilting. Test cases show that MPS-APO is a useful heuristic to automatically approximate optimal parameters for good patterns reproduction with minimal computational cost. Therefore, it can help non-expert users and increase the usability of MPS methods for practical applications.

Risk assessment and source identification of heavy metals in agricultural soil: a case study in the coastal city of Zhejiang Province, China Abstract Heavy metal contamination is a serious environmental problem, especially in developing countries such as China. In this study, we collected 1928 soil samples from the southeastern coastal area of China and analyzed the pollution concentration and potential ecological risk from heavy metals including arsenic (As), cadmium (Cd), chromium (Cr), lead (Pb), and mercury (Hg). The mean concentrations of Cr, Hg, and Pb were lower than their corresponding background values, whereas As and Cd were 1.31 and 1.59 times their background values, respectively. The calculation of the mean Pollution Index (PI) for these heavy metals were, in decreasing order Cd (1.59), As (1.31), Cr (0.94), Pb (0.89), and Hg (0.78) and the Nemerow Integrated Pollution Index revealed that almost one-fifth of the soil in the study area was moderately polluted. According to the ecological risk index, about 12% of the soil was at a moderate or high ecological risk, and Cd and Hg presented the highest ecological risk. The GeogDetector software was used to quantitatively assess the potential sources of these metals. The GeogDetector results showed that the soil heavy metals have various sources, including: natural processes had significant impacts on all heavy metals analyzed in this study; farmland types influenced the concentrations of As and Cr significantly; industrial activities significantly increased As, Cr, and Hg; transportation-related activities increased As, Cd, and Hg; and agricultural application of fertilizer and pesticides, had significant impacts on As, Cd, and Pb levels. Based on the results of the interaction detector, natural processes and agricultural activities were determined to be the main sources of heavy metals in the study area.

Assessment of water storage response to surface hydrological connectivity in a large floodplain system (Poyang Lake, China) using hydrodynamic and geostatistical analysis Abstract Floodplains play a significant role in affecting the transport of water, dissolved matter and sediments during wide-ranging drying and wetting. This study uses a hydrodynamic model and geostatistical method to explore the variations of water storage and its relationship with the surface hydrological connectivity, exemplified by the large Poyang Lake-floodplain system (in China). The simulations show that the floodplain storage exhibits largely similar behavior to that of the total lake water storage, but the water storage in the main lake is distinctly higher than the floodplains. The lake storage is estimated to be from 20 × 108 to 163 × 108 m3 and differs considerably between seasons, and the contribution of the floodplain to the total lake storage varies from 18 to 34%. Geostatistical analysis reveals that the degree of surface hydrological connectivity can be classified as high connectivity in summer, low connectivity in winter, and intermediate connectivity during other seasons. Higher variability of water storage and lower frequency of hydrological connectivity are found in the seasonal floodplains, whereas the lower variability and higher frequency are observed in the main lake, indicating that water storage is inextricably linked to the dynamic behaviors of surface hydrological connectivity. Additionally, the estimated water storage significantly increases from the low and intermediate conditions to the high connectivity condition, mainly due to the key process of the west–east connectivity in controlling lake-floodplain interactions. This study improves understanding of Poyang Lake floodplain behavior and other similar floodplain systems by providing knowledge of water balance, water allocation and water management. Graphic abstract

Probabilistic streamflow forecast based on spatial post-processing of TIGGE precipitation forecasts Abstract Ensemble precipitation forecast is effective in reducing the uncertainty and providing reliable probabilistic streamflow forecast. However, for operational applications, precipitation forecasts must go through bias correction in mean and spread. Although post-processing methods, such as BMA, have demonstrated good performance in ensemble-based calibration, the spatial correlation between stations may be altered after post-processing. In this research, ensemble precipitation forecasts of four NWP models, including ECMWF, UKMO, NCEP, and CMA within the TIGGE database, was bias-corrected and post-processed using quantile mapping and BMA for a case study basin in Iran. The ECC method was then used to recover the spatial correlation of ensemble forecasts. Subsequently, probabilistic streamflow forecast was conducted using post-processed precipitation forecasts. The results showed that the errors in the mean and spread of ensemble precipitation forecasts were corrected for each of the four NWP models while the ECC method was effective in maintaining spatial correlation. Furthermore, the results of probabilistic streamflow forecast showed that the performance of the forecast models improved after post processing, with the ECMWF model providing the best forecasts. More work is recommended to improve the impact of the ECC method on NWP models’ performance.

Hybrid model of the near-ground temperature profile Abstract The topic of the paper is modelling and prediction of atmospheric variables that are further used for prediction of the consequences of radioactive-material release to the atmosphere. Physics-based models of atmospheric dynamics provide an approximate description of the true nature of a dynamic system. However, the accuracy of the model’s short-term predictions and long-term forecasts, especially over complex terrain, decreases when the information at a micro-location is sought. Integration of a physics-based model with a statistical model for enhancing the prediction power is proposed in the paper. Gaussian Processes models can be used to identify the mapping between the system input and output measured values. With the given mapping function, we can provide one-step ahead prediction of the system output values together with its uncertainty, which can be used advantageously. In this paper, we combine a physics-based model with a Gaussian-process model to identify air temperature from measurements at different atmospheric surface layers as a dynamic system and to make short-term predictions as well as long-term forecasts.

Water and energy circulation characteristics and their impacts on water stress at the provincial level in China Abstract Water and energy circulate between provinces and sectors through products and services. The multi-scale input–output method can quantify the resources embodied in direct consumption, domestic trade and foreign trade and the resources in intermediate input and final consumption. In this study, this method is used to calculate the embodied water intensity and embodied energy intensity at the provincial level in China. The impacts of interprovincial water and energy transfers on provincial water stress were analyzed with reference to their water stress index. The results show that direct consumption is the main component of the embodied water intensity, with an average proportion of 52.21%. However, differences among provinces are significant, ranging from 14.82 to 80.11%. The embodied energy intensity is mainly reflected in domestic imports, with a national average of 61.01%. Domestic exports (3.69 × 1011 m3), urban household consumption (2.01 × 1011 m3), and gross fixed capital formation (1.49 × 1011 m3) share the largest proportion of final consumption, and they are also the main components in the final consumption of energy. Provincial water and energy transfers do not play major roles in relieving water stress in the net inflow areas but increase water stress in the net outflow areas. Provinces with high embodied water intensity and energy-induced water intensity tend to transfer more water to other provinces, while provinces with low intensity receive more supplies from other areas. Therefore, it is important to focus on improving the water use efficiency in provinces with active trade and high water and energy intensities, pay more attention to the demand side and avoid the continuous expansion of indirect consumption due to excessive restrictions on direct consumption.

Stochastic inverse modeling and global sensitivity analysis to assist interpretation of drilling mud losses in fractured formations Abstract This study is keyed to enhancing our ability to characterize naturally fractured reservoirs through quantification of uncertainties associated with fracture permeability estimation. These uncertainties underpin the accurate design of well drilling completion in heterogeneous fractured systems. We rely on monitored temporal evolution of drilling mud losses to propose a non-invasive and quite inexpensive method to provide estimates of fracture aperture and fracture mud invasion together with the associated uncertainty. Drilling mud is modeled as a yield power law fluid, open fractures being treated as horizontal planes intersecting perpendicularly the wellbore. Quantities such as drilling fluid rheological properties, flow rates, pore and dynamic drilling fluid pressure, or wellbore geometry, are often measured and available for modeling purposes. Due to uncertainty associated with measurement accuracy and the marked space–time variability of the investigated phenomena, we ground our study within a stochastic framework. We discuss (a) advantages and drawbacks of diverse stochastic calibration strategies and (b) the way the posterior probability densities (conditional on data) of model parameters are affected by the choice of the inverse modeling approach employed. We propose to assist stochastic model calibration through results of a moment-based global sensitivity analysis (GSA). The latter enables us to investigate the way parameter uncertainty influences key statistical moments of model outputs and can contribute to alleviate computational costs. Our results suggest that combining moment-based GSA with stochastic model calibration can lead to significant improvements of fractured reservoir characterization and uncertainty quantification.

Prediction of air pollutants PM 10 by ARBX(1) processes Abstract This work adopts a Banach-valued time series framework for component-wise estimation and prediction, from temporal correlated functional data, in presence of exogenous variables. The strong-consistency of the proposed functional estimator and associated plug-in predictor is formulated. The simulation study undertaken illustrates their large-sample size properties. Air pollutants PM10 curve forecasting, in the Haute-Normandie region (France), is addressed by implementation of the functional time series approach presented.