Gene Hua Crystal Ng

An Ensemble Multiscale Filter for Large Nonlinear Data Assimilation Problems

Abstract Operational data assimilation problems tend to be very large, both in terms of the number of unknowns to be estimated and the number of measurements to be processed. This poses significant computational challenges, especially for ensemble methods, which are critically dependent on the number of replicates used to derive sample covariances and other statistics. Most efforts to deal with the related problems of computational effort and sampling error in ensemble estimation have focused on spatial localization. The ensemble multiscale Kalman filter described here offers an alternative approach that effectively replaces, at each update time, the prior (or background) sample covariance with a multiscale tree. The tree is composed of nodes distributed over a relatively small number of discrete scales. Global correlations between variables at different locations are described in terms of local relationships between nodes at adjacent scales (parents and children). The Kalman updating process can be carri...

Reactive transport modeling of geochemical controls on secondary water quality impacts at a crude oil spill site near Bemidji, MN

Anaerobic biodegradation of organic amendments and contaminants in aquifers can trigger secondary water quality impacts that impair groundwater resources. Reactive transport models help elucidate how diverse geochemical reactions control the spatiotemporal evolution of these impacts. Using extensive monitoring data from a crude oil spill site near Bemidji, Minnesota (USA), we implemented a comprehensive model that simulates secondary plumes of depleted dissolved O2 and elevated concentrations of Mn2+, Fe2+, CH4, and Ca2+ over a two-dimensional cross section for 30 years following the spill. The model produces observed changes by representing multiple oil constituents and coupled carbonate and hydroxide chemistry. The model includes reactions with carbonates and Fe and Mn mineral phases, outgassing of CH4 and CO2 gas phases, and sorption of Fe, Mn, and H+. Model results demonstrate that most of the carbon loss from the oil (70%) occurs through direct outgassing from the oil source zone, greatly limiting the amount of CH4 cycled down-gradient. The vast majority of reduced Fe is strongly attenuated on sediments, with most (91%) in the sorbed form in the model. Ferrous carbonates constitute a small fraction of the reduced Fe in simulations, but may be important for furthering the reduction of ferric oxides. The combined effect of concomitant redox reactions, sorption, and dissolved CO2 inputs from source-zone degradation successfully reproduced observed pH. The model demonstrates that secondary water quality impacts may depend strongly on organic carbon properties, and impacts may decrease due to sorption and direct outgassing from the source zone.

The role of model dynamics in ensemble Kalman filter performance for chaotic systems

The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or ‘diverging’, when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter’s update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as nonlinearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics.

Identifying multiple time scale rainfall controls on Mojave Desert ecohydrology using an integrated data and modeling approach for Larrea tridentata

The perennial shrub Larrea tridentata is widely successful in North American warm deserts but is also susceptible to climatic perturbations. Understanding its response to rainfall variability requires consideration of multiple time scales. We examine intra-annual to multiyear relationships using model simulations of soil moisture and vegetation growth over 50 years in the Mojave National Preserve in southeastern California (USA). Ecohydrological model parameters are conditioned on field and remote sensing data using an ensemble Kalman filter. Although no specific periodicities were detected in the rainfall record, simulated leaf-area-index exhibits multiyear dynamics that are driven by multiyear (∼3 years) rains, but with up to a 1 year delay in peak response. Within a multiyear period, Larrea tridentata is more sensitive to winter rains than summer. In the most active part of the root zone (above ∼80 cm), >1 year average soil moisture drives vegetation growth, but monthly average soil moisture is controlled by root uptake. Moisture inputs reach the lower part of the root zone (below ∼80 cm) infrequently, but once there they can persist over a year to help sustain plant growth. Parameter estimates highlight efficient plant physiological properties facilitating persistent growth and high soil hydraulic conductivity allowing deep soil moisture stores. We show that soil moisture as an ecological indicator is complicated by bidirectional interactions with vegetation that depend on time scale and depth. Under changing climate, Larrea tridentata will likely be relatively resilient to shorter-term moisture variability but will exhibit higher sensitivity to shifts in seasonal to multiyear moisture inputs.

A mechanistic modeling and data assimilation framework for Mojave Desert ecohydrology

This study demonstrates and addresses challenges in coupled ecohydrological modeling in deserts, which arise due to unique plant adaptations, marginal growing conditions, slow net primary production rates, and highly variable rainfall. We consider model uncertainty from both structural and parameter errors and present a mechanistic model for the shrub Larrea tridentata (creosote bush) under conditions found in the Mojave National Preserve in southeastern California (USA). Desert-specific plant and soil features are incorporated into the CLM-CN model by Oleson et al. (2010). We then develop a data assimilation framework using the ensemble Kalman filter (EnKF) to estimate model parameters based on soil moisture and leaf-area index observations. A new implementation procedure, the “multisite loop EnKF,” tackles parameter estimation difficulties found to affect desert ecohydrological applications. Specifically, the procedure iterates through data from various observation sites to alleviate adverse filter impacts from non-Gaussianity in small desert vegetation state values. It also readjusts inconsistent parameters and states through a model spin-up step that accounts for longer dynamical time scales due to infrequent rainfall in deserts. Observation error variance inflation may also be needed to help prevent divergence of estimates from true values. Synthetic test results highlight the importance of adequate observations for reducing model uncertainty, which can be achieved through data quality or quantity.