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Multiyear periods (≥4 years) of extreme rainfall are increasing in frequency as climate continues to change, yet there is little understanding of how rainfall amount and heterogeneity in biophysical properties affect state changes in a sequence of wet and dry periods. Our objective was to examine the importance of rainfall periods, their legacies, and vegetation and soil properties to either the persistence of woody plants or a shift toward perennial grass dominance and a state reversal. We examined a 28‐year record of rainfall consisting of a sequence of multiyear periods (average, dry, wet, dry, average) for four ecosystem types in the Jornada Basin. We analyzed relationships between above ground net primary production (ANPP) and rainfall for three plant functional groups that characterize alternative states (perennial grasses, other herbaceous plants, dominant shrubs). A multimodel comparison was used to determine the relative importance of rainfall, soil, and vegetation properties. For perennial grasses, the greatest mean ANPP in mesquite‐ and tarbush‐dominated shrublands occurred in the wet period and in the dry period following the wet period in grasslands. Legacy effects in grasslands were asymmetric, where the lowest production was found in a dry period following an average period, and the greatest production occurred in a dry period following a wet period. For other herbaceous plants, in contrast, the greatest ANPP occurred in the wet period. Mesquite was the only dominant shrub species with a significant positive response in the wet period. Rainfall amount was a poor predictor of ANPP for each functional group when data from all periods were combined. Initial herbaceous biomass at the plant scale, patch‐scale biomass, and soil texture at the landscape scale improved the predictive relationships of ANPP compared with rainfall alone. Under future climate, perennial grass production is expected to benefit the most from wet periods compared with other functional groups with continued high grass production in subsequent dry periods that can shift (desertified) shrublands toward grasslands. The continued dominance by shrubs will depend on the effects that rainfall has on perennial grasses and the sequence of high‐ and low‐rainfall periods rather than the direct effects of rainfall on shrub production. [ABSTRACT FROM AUTHOR]

This study explores methods with which multidimensional data, e.g. time series, can be effectively incorporated into a Bayesian framework for inferring geostatistical parameters. Such series are difficult to use directly in the likelihood estimation procedure due to their high dimensionality; thus, a dimension reduction approach is taken to utilize these measurements in the inference. Two synthetic scenarios from hydrology are explored in which pumping drawdown and concentration breakthrough curves are used to infer the global mean of a log-normally distributed hydraulic conductivity field. Both cases pursue the use of a parametric model to represent the shape of the observed time series with physically-interpretable parameters (e.g. the time and magnitude of a concentration peak), which is compared to subsets of the observations with similar dimensionality. The results from both scenarios highlight the effectiveness for the shape-matching models to reduce dimensionality from 100+ dimensions down to less than five. The models outperform the alternative subset method, especially when the observations are noisy. This approach to incorporating time series observations in the Bayesian framework for inferring geostatistical parameters allows for high-dimensional observations to be faithfully represented in lower-dimensional space for the non-parametric likelihood estimation procedure, which increases the applicability of the framework to more observation types. Although the scenarios are both from hydrogeology, the methodology is general in that no assumptions are made about the subject domain. Any application that requires the inference of geostatistical parameters using series in either time of space can use the approach described in this paper. [ABSTRACT FROM AUTHOR]

The Method of Anchored Distributions (MAD) is a method for Bayesian inversion designed for inferring both local (e.g. point values) and global properties (e.g. mean and variogram parameters) of spatially heterogenous fields using multi-type and multi-scale data. Software implementations of MAD exist in C++ and C# to import data, execute an ensemble of forward model simulations, and perform basic post-processing of calculating likelihood and posterior distributions for a given application. This article describes the R package anchoredDistr that has been built to provide an Rbased environment for this method. In particular, anchoredDistr provides a range of post-processing capabilities for MAD software by taking advantage of the statistical capabilities and wide use of the R language. Two examples from stochastic hydrogeology are provided to highlight the features of the package for MAD applications in inferring anchored distributions of local parameters (e.g. point values of transmissivity) as well as global parameters (e.g. the mean of the spatial random function for hydraulic conductivity). [ABSTRACT FROM AUTHOR]

Geological heterogeneity, i.e. the spatial variability of discrete hydrogeological units, is investigated in an aquifer analog of glacio-fluvial sediments to determine how such a geological structure can be simplified for characterization needs. The aquifer analog consists of ten hydrofacies whereas the scarcity of measurements in typical field studies precludes such detailed spatial models of hydraulic properties. Of particular interest is the role of connectivity of the hydrofacies structure, along with its effect on the connectivity of mass transport, in site characterization for predicting early arrival times. Transport through three realizations of the aquifer analog is modeled with numerical particle tracking to ascertain the fast flow channel through which early arriving particles travel. Three simplification schemes of two-facies models are considered to represent the aquifer analogs, and the velocity within the fast flow channel is used to estimate the apparent hydraulic conductivity of the new facies. The facies models in which the discontinuous patches of high hydraulic conductivity are separated from the rest of the domain yield the closest match in early arrival times compared to the aquifer analog, but assuming a continuous high hydraulic conductivity channel connecting these patches yields underestimated early arrivals times within the range of variability between the realizations, which implies that the three simplification schemes could be advised but pose different implications for field measurement campaigns. Overall, the results suggest that the result of transport connectivity, i.e. early arrival times, within realistic geological heterogeneity can be conserved even when the underlying structural connectivity is modified. [ABSTRACT FROM AUTHOR]

Summary The conductivity of an aquifer is usually difficult to represent in a precise manner due to having both a high degree of spatial variability combined with a scarcity of information. As a result, the conductivity is commonly modeled as a spatial random field, defined by its expected value and a covariance function. This covariance is usually parameterized by fitting a model function to experimental data derived from point measurements of the conductivity. In this study, we investigated the two features that are often difficult to discern when using such classic characterization schemes: roughness and connectivity. These two features both share the fact that, based on point measurements of the conductivity alone, they are difficult to discern. It therefore stands to reason that the use of additional data could alleviate this problem. To that end, we used the Method of Anchored Distributions (MAD), which is a novel Bayesian tool for the inverse characterization of spatial random fields. MAD is versatile with respect to the used data, it has a modular structure and it does not assume any formal relationship between the target variable, i.e. the log hydraulic conductivity, and the data used for the inversion process, e.g. head measurements, draw-down from pumping tests or breakthrough curves. With respect to the characterization of the aforementioned features, we investigated the impact of several factors, such as different data types on the characterization process. Our findings suggest that both roughness and connectivity have only a limited impact on flow predictions, suggesting that the choice of such features is of lesser relevance if one is mainly interested in flow simulations. In case of roughness, this limited sensitivity was also seen for transport predictions if the solute had already travelled some distance. Connectivity however, can be a decisive factor for such simulations. [ABSTRACT FROM AUTHOR]

Estimation of spatial random fields (SRFs) is required for predicting groundwater flow, subsurface contaminant movement, and other areas of environmental and earth sciences modeling. This paper presents an inverse modeling framework called MAD# for characterizing SRFs, which is an implementation of the Bayesian inverse modeling technique Method of Anchored Distributions (MAD). MAD# allows modelers to “wrap” simulation models using an extensible driver architecture that exposes model parameters to the inversion engine. MAD# is implemented in an open source software package with the goal of lowering the barrier to using inverse modeling in education, research, and resource management. MAD# includes an intentionally simple user interface for simulation configuration, external software integration, spatial domain and model output visualization, and evaluation of model convergence. Four test cases are presented demonstrating the novel functionality of this framework to apply inversion in order to calibrate the model parameters characterizing a groundwater aquifer. [ABSTRACT FROM AUTHOR]

Alternative states maintained by feedbacks are notoriously difficult, if not impossible, to reverse. Although positive interactions that modify soil conditions may have the greatest potential to alter self‐reinforcing feedbacks, the conditions leading to these state change reversals have not been resolved. In a 9‐yr study, we modified horizontal connectivity of resources by wind or water on different geomorphic surfaces in an attempt to alter plant–soil feedbacks and shift woody‐plant‐dominated states back toward perennial grass dominance. Modifying connectivity resulted in an increase in litter cover regardless of the vector of transport (wind, water) followed by an increase in perennial grass cover 2 yr later. Modifying connectivity was most effective on sandy soils where wind is the dominant vector, and least effective on gravelly soils on stable surfaces with low sediment movement by water. We found that grass cover was related to precipitation in the first 5 yr of our study, and plant–soil feedbacks developed following 6 yr of modified connectivity to overwhelm effects of precipitation on sandy, wind‐blown soils. These feedbacks persisted through time under variable annual rainfall. On alluvial soils, either plant–soil feedbacks developed after 7 yr that were not persistent (active soils) or did not develop (stable soils). This novel approach has application to drylands globally where desertified lands have suffered losses in ecosystem services, and to other ecosystems where connectivity‐mediated feedbacks modified at fine scales can be expected to impact plant recovery and state change reversals at larger scales, in particular for wind‐impacted sites. [ABSTRACT FROM AUTHOR]

Dryland vegetation is influenced by biotic and abiotic land surface template (LST) conditions and precipitation (PPT), such that enhanced vegetation responses to periods of high PPT may be shaped by multiple factors. High PPT stochasticity in the Chihuahuan Desert suggests that enhanced responses across broad geographic areas are improbable. Yet, multiyear wet periods may homogenize PPT patterns, interact with favorable LST conditions, and in this way produce enhanced responses. In contrast, periods containing multiple extreme high PPT pulse events could overwhelm LST influences, suggesting a divergence in how climate change could influence vegetation by altering PPT periods. Using a suite of stacked remote sensing and LST datasets from the 1980s to the present, we evaluated PPT‐LST‐Vegetation relationships across this region and tested the hypothesis that enhanced vegetation responses would be initiated by high PPT, but that LST favorability would underlie response magnitude, producing geographic differences between wet periods. We focused on two multiyear wet periods; one of above average, regionally distributed PPT (1990–1993) and a second with locally distributed PPT that contained two extreme wet pulses (2006–2008). 1990–1993 had regional vegetation responses that were correlated with soil properties. 2006–2008 had higher vegetation responses over a smaller area that were correlated primarily with PPT and secondarily to soil properties. Within the overlapping PPT area of both periods, enhanced vegetation responses occurred in similar locations. Thus, LST favorability underlied the geographic pattern of vegetation responses, whereas PPT initiated the response and controlled response area and maximum response magnitude. Multiyear periods provide foresight on the differing impacts that directional changes in mean climate and changes in extreme PPT pulses could have in drylands. Our study shows that future vegetation responses during wet periods will be tied to LST favorability, yet will be shaped by the pattern and magnitude of multiyear PPT events. [ABSTRACT FROM AUTHOR]