Regularization techniques for ill-posed inverse problems in data assimilation

Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L2, regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the presence of model error, this approach does not capture the initial state of the system accurately, as the initial state estimate is derived by minimizing the average error between the model predictions and the observations over a time window. Here we examine an alternative L1 regularization technique that has proved valuable in image processing. We show that for examples of flow with sharp fronts and shocks, the L1 regularization technique performs more accurately than standard L2 regularization.

An inverse method for determining source characteristics for emergency response applications

Following a malicious or accidental atmospheric release in an outdoor environment it is essential for first responders to ensure safety by identifying areas where human life may be in danger. For this to happen quickly, reliable information is needed on the source strength and location, and the type of chemical agent released. We present here an inverse modelling technique that estimates the source strength and location of such a release, together with the uncertainty in those estimates, using a limited number of measurements of concentration from a network of chemical sensors considering a single, steady, ground-level source. The technique is evaluated using data from a set of dispersion experiments conducted in a meteorological wind tunnel, where simultaneous measurements of concentration time series were obtained in the plume from a ground-level point-source emission of a passive tracer. In particular, we analyze the response to the number of sensors deployed and their arrangement, and to sampling and model errors. We find that the inverse algorithm can generate acceptable estimates of the source characteristics with as few as four sensors, providing these are well-placed and that the sampling error is controlled. Configurations with at least three sensors in a profile across the plume were found to be superior to other arrangements examined. Analysis of the influence of sampling error due to the use of short averaging times showed that the uncertainty in the source estimates grew as the sampling time decreased. This demonstrated that averaging times greater than about 5min (full scale time) lead to acceptable accuracy.

Retrieval of mesospheric electron densities using an optimal estimation inverse method

We present a new method to determine mesospheric electron densities from partially reflected medium frequency radar pulses. The technique uses an optimal estimation inverse method and retrieves both an electron density profile and a gradient electron density profile. As well as accounting for the absorption of the two magnetoionic modes formed by ionospheric birefringence of each radar pulse, the forward model of the retrieval parameterises possible Fresnel scatter of each mode by fine electronic structure, phase changes of each mode due to Faraday rotation and the dependence of the amplitudes of the backscattered modes upon pulse width. Validation results indicate that known profiles can be retrieved and that χ2 tests upon retrieval parameters satisfy validity criteria. Application to measurements shows that retrieved electron density profiles are consistent with accepted ideas about seasonal variability of electron densities and their dependence upon nitric oxide production and transport.

Strengthening the link between climate, hydrological and species distribution modeling to assess the impacts of climate change on freshwater biodiversity

To understand the resilience of aquatic ecosystems to environmental change, it is important to determine how multiple, related environmental factors, such as near-surface air temperature and river flow, will change during the next century. This study develops a novel methodology that combines statistical downscaling and fish species distribution modeling, to enhance the understanding of how global climate changes (modeled by global climate models at coarse-resolution) may affect local riverine fish diversity. The novelty of this work is the downscaling framework developed to provide suitable future projections of fish habitat descriptors, focusing particularly on the hydrology which has been rarely considered in previous studies. The proposed modeling framework was developed and tested in a major European system, the Adour-Garonne river basin (SW France, 116,000 km(2)), which covers distinct hydrological and thermal regions from the Pyrenees to the Atlantic coast. The simulations suggest that, by 2100, the mean annual stream flow is projected to decrease by approximately 15% and temperature to increase by approximately 1.2 °C, on average. As consequence, the majority of cool- and warm-water fish species is projected to expand their geographical range within the basin while the few cold-water species will experience a reduction in their distribution. The limitations and potential benefits of the proposed modeling approach are discussed. Copyright © 2012 Elsevier B.V. All rights reserved.

Coupled atmosphere-biophysics-hydrology models for environmental modeling

The formulation and implementation of LEAF-2, the Land Ecosystem–Atmosphere Feedback model, which comprises the representation of land–surface processes in the Regional Atmospheric Modeling System (RAMS), is described. LEAF-2 is a prognostic model for the temperature and water content of soil, snow cover, vegetation, and canopy air, and includes turbulent and radiative exchanges between these components and with the atmosphere. Subdivision of a RAMS surface grid cell into multiple areas of distinct land-use types is allowed, with each subgrid area, or patch, containing its own LEAF-2 model, and each patch interacts with the overlying atmospheric column with a weight proportional to its fractional area in the grid cell. A description is also given of TOPMODEL, a land hydrology model that represents surface and subsurface downslope lateral transport of groundwater. Details of the incorporation of a modified form of TOPMODEL into LEAF-2 are presented. Sensitivity tests of the coupled system are presented that demonstrate the potential importance of the patch representation and of lateral water transport in idealized model simulations. Independent studies that have applied LEAF-2 and verified its performance against observational data are cited. Linkage of RAMS and TOPMODEL through LEAF-2 creates a modeling system that can be used to explore the coupled atmosphere–biophysical–hydrologic response to altered climate forcing at local watershed and regional basin scales.