ALBERT

Description: Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream–aquifer exchanges, and (H3) the biases result from slow paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream–aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW (Modular Three-dimensional Finite-difference Groundwater Flow Model) simulation environment, and the PEST (parameter estimation) tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop lognormally distributed conductivity (K) fields on local grid scales. Stream–aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce coherent slow paths in groundwater fluxes that in turn reduce aquifer–stream exchanges. Since surface water–groundwater exchanges are critical hydrologic processes in basin-scale water budgets, these results also have implications for water resources management.

Description: Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River Basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream–aquifer exchanges, and (H3) the biases result from slow-paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream–aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW simulation environment, and the PEST tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop log-normally distributed conductivity (K) fields on local grid scales. Stream-aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce coherent slow-paths in groundwater fluxes that in turn reduce aquifer–stream exchanges. Since surface water–groundwater exchanges are critical hydrologic processes in basin-scale water budgets, these results also have implications for water resources management.

Description: Spatial statistics of earth and environmental (as well as many other) data tend to vary with scale. Common manifestations of scale-dependent statistics include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale-mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over thresholds or POTs. In this paper we explore for the first time the statistical behavior of POTs associated with samples from scale-mixtures of tfBm or tfGn. We are fortunate to have at our disposal thousands of neutron porosity values from six deep boreholes, in three diverse depositional environments, which we show possess the properties of such samples thus following the theory we proposed. The porosity data are of additional value in revealing a remarkable transition from one scaling regime to another at certain lags. The phenomena we uncover are of fundamental importance for the analysis of fluid flow and solute as well as particulate transport in complex hydrogeologic environments.

Description: The environment of ebb-tidal deltas between barrier island systems is characterized by a complex morphology with ebb- and flood-dominated channels, shoals and swash bars connecting the ebb-tidal delta platform to the adjacent island. These morphological features reveal characteristic surface sediment grain-size distributions and are subject to a continuous adaptation to the prevailing hydrodynamic forces. The mixed-energy tidal inlet Otzumer Balje between the East Frisian barrier islands Langeoog and Spiekeroog in the southern North Sea has been chosen here as an exemplary study area for the identification of relevant hydrodynamic drivers of morphology and sedimentology. We compare the effect of high-energy wave-dominated storm conditions to mid-term tide-dominated fair-weather conditions on tidal inlet morphology and sedimentology with a process-based numerical model. A multi-fractional approach with five graduated grain-size fractions between 150 and 450 microns allows the simulation of corresponding surface sediment grain-size distributions. Net sediment fluxes for distinct conditions are identified: during storm conditions, bed load sediment transport is generally onshore directed on the shallower ebb-tidal delta shoals whereas fine-grained suspended sediment bypasses the tidal inlet by wave-driven currents. During fair-weather the sediment transport mainly focuses on the inlet throat and the marginal flood channels. We show how the observed sediment grain-size distribution and the morphological response at mixed-energy tidal inlets are the result of both, wave-dominant less frequent storm conditions and mid-term tide-dominant fair-weather conditions.

Description: The environment of ebb-tidal deltas between barrier island systems is characterized by a complex morphology with ebb- and flood-dominated channels, shoals and swash bars connecting the ebb-tidal delta platform to the adjacent island. These morphological features reveal characteristic surface sediment grain-size distributions and are subject to a continuous adaptation to the prevailing hydrodynamic forces. The mixed-energy tidal inlet Otzumer Balje between the East Frisian barrier islands of Langeoog and Spiekeroog in the southern North Sea has been chosen here as a model study area for the identification of relevant hydrodynamic drivers of morphology and sedimentology. We compare the effect of high-energy, wave-dominated storm conditions to mid-term, tide-dominated fair-weather conditions on tidal inlet morphology and sedimentology with a process-based numerical model. A multi-fractional approach with five grain-size fractions between 150 and 450 μm allows for the simulation of corresponding surface sediment grain-size distributions. Net sediment fluxes for distinct conditions are identified: during storm conditions, bed load sediment transport is generally onshore directed on the shallower ebb-tidal delta shoals, whereas fine-grained suspended sediment bypasses the tidal inlet by wave-driven currents. During fair weather the sediment transport mainly focuses on the inlet throat and the marginal flood channels. We show how the observed sediment grain-size distribution and the morphological response at mixed-energy tidal inlets are the result of both wave-dominated less frequent storm conditions and mid-term, tide-dominant fair-weather conditions.

Description: We analyze scale-dependent statistics of correlated random hydrogeological variables and their extremes using neutron porosity data from six deep boreholes, in three diverse depositional environments, as example. We show that key statistics of porosity increments behave and scale in manners typical of many earth and environmental (as well as other) variables. These scaling behaviors include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over threshold or POTs. In this paper we explore the statistical scaling of data and, for the first time, corresponding POTs associated with samples from scale mixtures of tfBm or tfGn. We demonstrate that porosity data we analyze possess properties of such samples and thus follow the theory we proposed. The porosity data are of additional value in revealing a remarkable cross-over from one scaling regime to another at certain lags. The phenomena we uncover are of key importance for the analysis of fluid flow and solute as well as particulate transport in complex hydrogeologic environments.