Erratum: Revisiting the Geometry of a Ternary Diagram with the Half-Taxi Metric

Mathematical Geosciences -     

Incorporating Spatial Dependence in Predictive Vegetation Models: Residual Interpolation Methods*

Predictive vegetation modeling can be used statistically to relate the distribution of vegetation across a landscape as a function of important environmental variables. Often these models are developed without considering the spatial pattern that is inherent in biogeographical data, resulting from either biotic processes or missing or misspecified environmental variables. Including spatial dependence explicitly in a predictive model can be an efficient way to improve model accuracy with the available data. In this study, model residuals were interpolated and added to model predictions, and the resulting prediction accuracies were assessed. Adding kriged residuals improved model accuracy more often than adding simulated residuals, although some alliances showed no improvement or worse accuracy when residuals were added. In general, the prediction accuracies that were not increased by adding kriged residuals were either rare in the sample or had high nonspatial model accuracy. Regression interpolation methods can be an important addition to current tools used in predictive vegetation models as they allow observations that are predicted well by environmental variables to be left alone, while adjusting over‐ and underpredicted observations based on local factors.     

Numerical modeling of toxic nonaqueous phase liquid removal from contaminated groundwater systems: mesh effect and discretization error estimation

Numerical modeling has now become an indispensable tool for investigating the fundamental mechanisms of toxic nonaqueous phase liquid (NAPL) removal from contaminated groundwater systems. Because the domain of a contaminated groundwater system may involve irregular shapes in geometry, it is necessary to use general quadrilateral elements, in which two neighbor sides are no longer perpendicular to each other. This can cause numerical errors on the computational simulation results due to mesh discretization effect. After the dimensionless governing equations of NAPL dissolution problems are briefly described, the propagation theory of the mesh discretization error associated with a NAPL dissolution system is first presented for a rectangular domain and then extended to a trapezoidal domain. This leads to the establishment of the finger‐amplitude growing theory that is associated with both the corner effect that takes place just at the entrance of the flow in a trapezoidal domain and the mesh discretization effect that occurs in the whole NAPL dissolution system of the trapezoidal domain. This theory can be used to make the approximate error estimation of the corresponding computational simulation results. The related theoretical analysis and numerical results have demonstrated the following: (1) both the corner effect and the mesh discretization effect can be quantitatively viewed as a kind of small perturbation, which can grow in unstable NAPL dissolution systems, so that they can have some considerable effects on the computational results of such systems; (2) the proposed finger‐amplitude growing theory associated with the corner effect at the entrance of a trapezoidal domain is useful for correctly explaining why the finger at either the top or bottom boundary grows much faster than that within the interior of the trapezoidal domain; (3) the proposed finger‐amplitude growing theory associated with the mesh discretization error in the NAPL dissolution system of a trapezoidal domain can be used for quantitatively assessing the correctness of computational simulations of NAPL dissolution front instability problems in trapezoidal domains, so that we can ensure that the computational simulation results are controlled by the physics of the NAPL dissolution system, rather than by the numerical artifacts. Copyright © 2014 John Wiley & Sons, Ltd.     

The role of baseflow in dissolved solids delivery to streams in the Upper Colorado River Basin

Salinity has a major effect on water users in the Colorado River Basin, estimated to cause almost $300 million per year in economic damages. The Colorado River Basin Salinity Control Program implements and manages projects to reduce salinity loads, investing millions of dollars per year in irrigation upgrades, canal projects, and other mitigation strategies. To inform and improve mitigation efforts, there is a need to better understand sources of salinity to streams and how salinity has changed over time. This study explores salinity in the baseflow fraction of streamflow, assessing whether groundwater is a significant contributor of dissolved solids to streams in the Upper Colorado River Basin (UCRB). Chemical hydrograph separation was used to estimate baseflow discharge and baseflow dissolved solids loads at stream gages (n = 69) across the UCRB. On average, it is estimated that 89% of dissolved solids loads originate from the baseflow fraction of streamflow, indicating that subsurface transport processes play a dominant role in delivering dissolved solids to streams in the UCRB. A statistical trend analysis using weighted regressions on time, discharge, and season was used to evaluate changes in baseflow dissolved solids loads in streams (n = 27) from 1986 to 2011. Decreasing trends in baseflow dissolved solids loads were observed at 63% of streams. At the three most downstream sites, Green River at Green River, UT, Colorado River at Cisco, UT, and the San Juan River near Bluff, UT, baseflow dissolved solids loads decreased by a combined 823,000 metric tons (mT), which is approximately 69% of projected basin‐scale decreases in total dissolved solids loads as a result of salinity control efforts. Decreasing trends in baseflow dissolved solids loads suggest that salinity mitigation projects, landscape changes, and/or climate are reducing dissolved solids transported to streams through the subsurface. Notably, the pace and extent of decreases in baseflow dissolved solids loads declined during the most recent decade; average decreasing loads during the 2000s (28,200 mT) were only 54% of average decreasing loads in the 1990s (51,700 mT).     

Divergence and flow direction as indicators of subsurface heterogeneity and stage‐dependent storage in alluvial floodplains

Assuming homogeneity in alluvial aquifers is convenient, but limits our ability to accurately predict stream‐aquifer interactions. Research is needed on (i) identifying the presence of focused, as opposed to diffuse, groundwater discharge/recharge to streams and (ii) the magnitude and role of large‐scale bank and transient storage in alluvial floodplains relative to changes in stream stage. The objective of this research was to document and quantify the effect of stage‐dependent aquifer heterogeneity and bank storage relative to changes in stream stage using groundwater flow divergence and direction. Monitoring was performed in alluvial floodplains adjacent to the Barren Fork Creek and Honey Creek in northeastern Oklahoma. Based on results from subsurface electrical resistivity mapping, observation wells were installed in high and low electrical resistivity subsoils. Water levels in the wells were recorded real time using pressure transducers (August to October 2009). Divergence was used to quantify heterogeneity (i.e. variation in hydraulic conductivity, porosity, and/or aquifer thickness), and flow direction was used to assess the potential for large‐scale (100 m) bank or transient storage. Areas of localized heterogeneity appeared to act as divergence zones allowing stream water to quickly enter the groundwater system, or as flow convergence zones draining a large groundwater area. Maximum divergence or convergence occurred with maximum rates of change in flow rates or stream stage. Flow directions in the groundwater changed considerably between base and high flows, suggesting that the floodplains acted as large‐scale bank storage zones, rapidly storing and releasing water during passage of a storm hydrograph. During storm events at both sites, the average groundwater direction changed by at least 90° from the average groundwater direction during baseflow. Aquifer heterogeneity in floodplains yields hyporheic flows that are more responsive and spatially and temporally complex than would be expected compared to more common assumptions of homogeneity. Copyright © 2012 John Wiley & Sons, Ltd.     

Cenozoic landscape evolution of the Kruger National Park as derived from cosmogenic nuclide analyses

In contrast to active tectonic settings, little is known about the potential feedback between surface processes and climate change in tectonically inactive cratonic regions. Here, we studied the driving forces of erosion and landscape evolution in the Kruger National Park in South Africa using cosmogenic nuclide dating. ¹⁰Be‐derived catchment‐wide erosion rates (~2 and ~10 mm ka^?1) are similar in magnitude to erosion and rock uplift elsewhere in South Africa, suggesting that (1) rock uplift is solely the isostatic response to erosion and (2) the first‐order topography is likely of Cretaceous age. The topographic maturity is promoted by widespread exposure of rocks resistant to erosion. Our data, however, suggest that local variations in rock resistance lead to transient landscape changes, with local increases in relief and erosion rates.