Proper orthogonal decomposition reduced model for mass transport in heterogenous media

Numerical models with fine discretization normally demand large computational time and space, which lead to computational burden for state estimations or model parameter inversion calculation. This article presented a reduced implicit finite difference scheme that based on proper orthogonal decomposition (POD) for two-dimensional transient mass transport in heterogeneous media. The reduction of the original full model was achieved by projecting the high-dimension full model to a low-dimension space created by POD bases, and the bases are derived from the snapshots generated from the model solutions of the forward simulations. The POD bases were extracted from the ensemble of snapshots by singular value decomposition. The dimension of the Jacobian matrix was then reduced after Galerkin projection. Thus, the reduced model can accurately reproduce and predict the original model’s transport process with significantly decreased computational time. This scheme is practicable with easy implementation of the partial differential equations. The POD method is illustrated and validated through synthetic cases with various heterogeneous permeability field scenarios. The accuracy and efficiency of the reduced model are determined by the optimal selection of the snapshots and POD bases.     

Identification of hydraulic conductivity distributions in density dependent flow fields of submarine groundwater discharge modeling using adjoint-state sensitivities

A mathematical optimal control method is developed to identify a hydraulic conductivity distribution in a density dependent flow field. Using a variational method, the adjoint partial differential equations are obtained for the density- dependent state equations used for the saline aquifer water flow. The adjoint equations are numerically solved in through a finite difference method. The developed method is applied to identify the hydraulic conductivity distribution through the numerical solution of an optimal control problem. To demonstrate the effectiveness of the optimal control method, three numerical experiments are conducted with artificial observation data. The results indicate that the developed method has the potential to accurately identify the hydraulic conductivity distribution in a saline water aquifer flow system.     

Experimental study and mathematical modelling of soluble chemical transfer from unsaturated/saturated soil to surface runoff

A one‐dimensional, two‐layer solute transport model is developed to simulate chemical transport process in an initially unsaturated soil with ponding water on the soil surface before surface runoff starts. The developed mathematical model is tested against a laboratory experiment. The infiltration and diffusion processes are mathematically lumped together and described by incomplete mixing parameters. Based on mass conservation and water balance equations, the model is developed to describe solute transport in a two‐zone layer, a ponding runoff zone and a soil mixing zone. The two‐zone layer is treated as one system to avoid describing the complicated chemical transport processes near the soil surface in the mixing zone. The proposed model was analytically solved, and the solutions agreed well with the experimental data. The developed experimental method and mathematical model were used to study the effect of the soil initial moisture saturation on chemical concentration in surface runoff. The study results indicated that, when the soil was initially saturated, chemical concentration in surface runoff was significantly (two orders of magnitude) higher than that with initially unsaturated soil, while the initial chemical concentrations at the two cases were of the same magnitude. The soil mixing depth for the initially unsaturated soil was much larger than that for the initially saturated soil, and the incomplete runoff mixing parameter was larger for the initially unsaturated soil. The higher the infiltration rate of the soil, the greater the infiltration‐related incomplete mixing parameter. According to the quantitative analysis, the soil mixing depth was found to be sensitive for both initially unsaturated and saturated soils, and the incomplete runoff mixing parameter was sensitive for initially saturated soil but not for the initially unsaturated soil; the incomplete infiltration mixing parameter behaved just the opposite. Some suggestions are made for reducing chemical loss from runoff. Copyright © 2010 John Wiley & Sons, Ltd.     

Lapse Rate Adjustments of Gridded Surface Temperature Normals in an Area of Complex Terrain: Atmospheric Reanalysis versus Statistical Up-Sampling

The applicability of elevation-regression based interpolation methods for long-term temperature normals, for example the Parameter-elevation Regressions on Independent Slopes Model (PRISM), becomes increasingly limited in data sparse, complex terrain such as that found in mountainous British Columbia (BC), Canada. Recent methods to improve both the resolution and accuracy of interpolation models have focused on the development of “up-sampling” algorithms based on local lapse rate adjustments to the original interpolated surfaces. Lapse rates can be derived from statistical models (e.g., elevation-based polynomial regression equations) or dynamical models (e.g., vertical temperature profiles from numerical weather prediction (NWP) models). This study compares a widely used statistical up-sampling algorithm, ClimateBC, with two NWP reanalysis products, the National Centers for Environmental Prediction/National Corporation for Atmospheric Research, Reanalysis 1 (NCEP1) and the more modern European Centre for Medium-range Weather Forecasts (ECMWF) Reanalysis Interim (ERA-Interim). Thirty-year climate normals for maximum and minimum temperatures were calculated using statistical up-sampling and NWP lapse rate adjustments to existing PRISM-based climate normals at a subset of stations in BC. Specifically, up-sampling model evaluation was performed using 1951–80 climate normals from an independent set of 54 surface stations (1 m to 2347 m) which were not included in the PRISM interpolation or assimilated into the NWP reanalysis products. All models performed similarly for minimum temperature, which showed only a slight improvement over PRISM. For maximum temperature, ClimateBC, NCEP1 and ERA-Interim all performed significantly better than PRISM, in particular during spring and summer. The ERA-Interim reanalysis outperformed NCEP1 in almost all months. The results suggest that lapse rate adjustment algorithms based on reanalysis products will have greater potential as progress continues on developing NWP components.

R ésumé ?[Traduit par la rédaction] L'application des techniques d'interpolation par régression en fonction de l'altitude pour les normales de température à long terme, comme le Parameter-elevation Regressions on Independent Slopes Model (PRISM), devient très difficile dans les régions accidentées pour lesquelles on dispose de données insuffisantes, par exemple les secteurs montagneux de la Colombie-Britannique (C.-B.) au Canada. Les toutes dernières méthodes destinées à augmenter le degré de résolution des modèles d'interpolation et leur précision reposent sur la conception d'algorithmes d’échantillonnage vertical fondés sur l'ajustement des surfaces interpolées originales au moyen du gradient vertical local. Nous pouvons établir les gradients verticaux à partir de modèles statistiques (p. ex., des équations de régression polynomiales en fonction de l'altitude) ou de modèles dynamiques (p. ex., des profils verticaux de température à partir de modèles de prévision numérique du temps (PNT)). Dans la présente étude, nous comparons un algorithme d’échantillonnage vertical statistique communément utilisé, le programme ClimateBC, à deux produits de réanalyse de PNT, celle des National Centres for Environmental Prediction/National Corporation for Atmospheric Research Reanalysis 1 (NCEP1), et la réanalyse provisoire (ERA-Interim) du Centre européen pour les prévisions météorologiques à moyen terme (ECMWF). Les normales climatiques de trente ans pour les températures maximums et minimums ont été calculées en appliquant la méthode d’échantillonnage vertical statistique et l'ajustement du gradient obtenu par PNT aux normales climatiques établies à partir du PRISM pour un sous-ensemble de stations en Colombie-Britannique. Plus particulièrement, nous avons procédé à l’évaluation du modèle d’échantillonnage vertical en nous servant des normales climatiques (1951–1980), pour un ensemble de 54 stations d'observation en surface indépendantes (1?m à 2347?m), exclues du modèle d'interpolation PRISM et des produits de réanalyse de PNT. Pour tous les modèles, nous avons obtenu des résultats comparables pour la température minimum, soit une légère amélioration seulement par rapport au PRISM. Pour la température maximum, nous avons obtenu avec ClimateBC, NCEP1 et ERA-Interim, des résultats nettement plus probants qu'avec PRISM, notamment au printemps et en été. Les réanalyses ERA-Interim ont donné de meilleurs résultats que NCEP1 pour pratiquement tous les mois. D'après ces résultats, le potentiel des algorithmes d'ajustements des gradients verticaux de température, établis à partir de produits de réanalyse se renforcera à mesure que les composantes de PNT se développeront.     

藏北多格错仁红层及孢粉组合特征

青藏高原北部羌塘地块广泛出露第三纪陆相红层 ,确定这些红层及其变形的时代对认识青藏高原的形成演化过程具有非常重要的意义。 1998～ 1999年 ,INDEPTH III项目地质课题组人员 2次深入西藏可可西里地区进行科学考察 ,新发现藏北多格错仁红层 ,并在其中发现较多种属的孢粉化石。该孢粉组合反映以温带旱生草原为主体的古植被面貌。通过对青藏高原北部及邻区主要新生代盆地孢粉组合与古环境演化的对比分析 ,结合多格错仁红层上覆弱变形玄武岩 2 5～ 3 2Ma的40 Ar- 3 9Ar高精度测年资料 ,推断多格错仁红层的形成时代为晚中新世 ,多格错仁红层挤压变形所致的约 5 0 %的地壳缩短量发生在中新世末—上新世初。这些资料为建立青藏高原动力学模式提供了新的年代依据     

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.