We develop a multiscale zonation approach to characterize the spatial variability of Arctic polygonal ground geomorphology and to assess the relative controls of these elements on land surface and subsurface properties and carbon fluxes. Working within an ice wedge polygonal region near Barrow, Alaska, we consider two scales of zonation: polygon features (troughs, centers, and rims of polygons) that are nested within different polygon types (high, flat, and low centered). In this study, we first delineated polygons using a digital elevation map and clustered the polygons into four types along two transects, using geophysical and kite-based landscape-imaging data sets. We extrapolated those data-defined polygon types to all the polygons over the study site, using the polygon statistics extracted from the digital elevation map. Based on the point measurements, we characterized the distribution of vegetation, hydrological, thermal, and geochemical properties, as well as carbon fluxes, all as a function of polygon types and polygon features. Results show that nested polygon geomorphic zonation-polygon types and polygon features-can be used to represent distinct distributions of carbon fluxes and associated properties, as well as covariability among those properties. Importantly, the results indicate that polygon types have more power to explain the variations in those properties than polygon features. The approach is expected to be useful for improved system understanding, site characterization, and parameterization of numerical models aimed at predicting ecosystem feedbacks to the climate.
[1] This paper addresses the inverse problem in spatially variable fields such as hydraulic conductivity in groundwater aquifers or rainfall intensity in hydrology. Common to all these problems is the existence of a complex pattern of spatial variability of the target variables and observations, the multiple sources of data available for characterizing the fields, the complex relations between the observed and target variables and the multiple scales and frequencies of the observations. The method of anchored distributions (MAD) that we propose here is a general Bayesian method of inverse modeling of spatial random fields that addresses this complexity. The central elements of MAD are a modular classification of all relevant data and a new concept called "anchors." Data types are classified by the way they relate to the target variable, as either local or nonlocal and as either direct or indirect. Anchors are devices for localization of data: they are used to convert nonlocal, indirect data into local distributions of the target variables. The target of the inversion is the derivation of the joint distribution of the anchors and structural parameters, conditional to all measurements, regardless of scale or frequency of measurement. The structural parameters describe large-scale trends of the target variable fields, whereas the anchors capture local inhomogeneities. Following inversion, the joint distribution of anchors and structural parameters is used for generating random fields of the target variable(s) that are conditioned on the nonlocal, indirect data through their anchor representation. We demonstrate MAD through a detailed case study that assimilates point measurements of the conductivity with head measurements from natural gradient flow. The resulting statistical distributions of the parameters are non-Gaussian. Similarly, the moments of the estimates of the hydraulic head are non-Gaussian. We provide an extended discussion of MAD vis à vis other inversion methods, including maximum likelihood and maximum a posteriori with an emphasis on the differences between MAD and the pilot points method.Citation: Rubin, Y., X. Chen, H. Murakami, and M. Hahn (2010), A Bayesian approach for inverse modeling, data assimilation, and conditional simulation of spatial random fields, Water Resour. Res., 46, W10523,
1] Tracer tests performed under natural or forced gradient flow conditions can provide useful information for characterizing subsurface properties, through monitoring, modeling, and interpretation of the tracer plume migration in an aquifer. Nonreactive tracer experiments were conducted at the Hanford 300 Area, along with constant-rate injection tests and electromagnetic borehole flowmeter tests. A Bayesian data assimilation technique, the method of anchored distributions (MAD) , was applied to assimilate the experimental tracer test data with the other types of data and to infer the threedimensional heterogeneous structure of the hydraulic conductivity in the saturated zone of the Hanford formation.In this study, the Bayesian prior information on the underlying random hydraulic conductivity field was obtained from previous field characterization efforts using constant-rate injection and borehole flowmeter test data. The posterior distribution of the conductivity field was obtained by further conditioning the field on the temporal moments of tracer breakthrough curves at various observation wells. MAD was implemented with the massively parallel three-dimensional flow and transport code PFLOTRAN to cope with the highly transient flow boundary conditions at the site and to meet the computational demands of MAD. A synthetic study proved that the proposed method could effectively invert tracer test data to capture the essential spatial heterogeneity of the three-dimensional hydraulic conductivity field. Application of MAD to actual field tracer data at the Hanford 300 Area demonstrates that inverting for spatial heterogeneity of hydraulic conductivity under transient flow conditions is challenging and more work is needed.Citation: Chen, X., H. Murakami, M. S. Hahn, G. E. Hammond, M. L. Rockhold, J. M. Zachara, and Y. Rubin (2012), Threedimensional Bayesian geostatistical aquifer characterization at the Hanford 300 Area using tracer test data, Water Resour. Res., 48, W06501,
This study presents a stochastic, three-dimensional characterization of a heterogeneous hydraulic conductivity field within DOE's Hanford 300 Area site, Washington, by assimilating large-scale, constant-rate injection test data with small-scale, three-dimensional electromagnetic borehole flowmeter (EBF) measurement data. We first inverted the injection test data to estimate the transmissivity field, using zeroth-order temporal moments of pressure buildup curves. We applied a newly developed Bayesian geostatistical inversion framework, the method of anchored distributions (MAD), to obtain a joint posterior distribution of geostatistical parameters and local log-transmissivities at multiple locations. The unique aspects of MAD that make it suitable for this purpose are its ability to integrate multi-scale, multi-type data within a Bayesian framework and to compute a nonparametric posterior distribution. After we combined the distribution of transmissivities with depth-discrete relative-conductivity profile from the EBF data, we inferred the three-dimensional geostatistical parameters of the log-conductivity field, using the Bayesian model-based geostatistics. Such consistent use of the Bayesian approach throughout the procedure enabled us to systematically incorporate data uncertainty into the final posterior distribution. The method was tested in a synthetic study and validated using the actual data that was not part of the estimation. Results showed broader and skewed posterior distributions of geostatistical parameters except for the mean, which suggests the importance of inferring the entire distribution to quantify the parameter uncertainty
Spatial heterogeneities in soil hydrology have been confirmed as a key control on CO 2 and CH 4 fluxes in the Arctic tundra ecosystem. In this study, we applied a mechanistic ecosystem model, CLM-Microbe, to examine the microtopographic impacts on CO 2 and CH 4 fluxes across seven landscape types in Utqiaġvik, Alaska: trough, low-centered polygon (LCP) center, LCP transition, LCP rim, high-centered polygon (HCP) center, HCP transition, and HCP rim. We first validated the CLM-Microbe model against static-chamber measured CO 2 and CH 4 fluxes in 2013 for three landscape types: trough, LCP center, and LCP rim. Model application showed that low-elevation and thus wetter landscape types (i.e., trough, transitions, and LCP center) had larger CH 4 emissions rates with greater seasonal variations than highelevation and drier landscape types (rims and HCP center). Sensitivity analysis indicated that substrate availability for methanogenesis (acetate, CO 2 + H 2 ) is the most important factor determining CH 4 emission, and vegetation physiological properties largely affect the net ecosystem carbon exchange and ecosystem respiration in Arctic tundra ecosystems. Modeled CH 4 emissions for different microtopographic features were upscaled to the eddy covariance (EC) domain with an area-weighted approach before validation against EC-measured CH 4 fluxes. The model underestimated the EC-measured CH 4 flux by 20% and 25% at daily and hourly time steps, suggesting the importance of the time step in reporting CH 4 flux. The strong microtopographic impacts on CO 2 and CH 4 fluxes call for a model-data integration framework for better understanding and predicting carbon flux in the highly heterogeneous Arctic landscape.
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