Mitigating the impacts of global warming on wildlife entails four practical steps. First, we need to study how processes of interest vary with temperature. Second, we need to build good temperature ...scenarios. Third, processes can be forecast accordingly. Only then can we perform the fourth step, testing mitigating measures. While having good temperature data is essential, this is not straightforward for stream ecologists and managers. Water temperature (WT) data are often short and incomplete and future projections are currently not routinely available. There is a need for generic models which address this data gap with good resolution and current models are partly lacking. Here, we expand a previously published hierarchical Bayesian model that was driven by air temperature (AT) and flow (Q) as a second covariate. The new model can hindcast and forecast WT time series at a daily time step. It also allows a better appraisal of real uncertainties in the warming of water temperatures in rivers compared to the previous version, stemming from its hybrid structure between time series decomposition and regression. This model decomposes all-time series using seasonal sinusoidal periodic signals and time varying means and amplitudes. It then links the contrasted frequency signals of WT (daily and six month) through regressions to that of AT and optionally Q for better resolution. We apply this model to two contrasting case study rivers. For one case study, AT only is available as a covariate. This expanded model further improves the already good fitting and predictive capabilities of its earlier version while additionally highlighting warming uncertainties. The code is available online and can easily be run for other temperate rivers.
We consider the perturbation of elliptic pseudodifferential operators $P(\mathbf{x},\mathbf{D})$ with more than square integrable Green's functions by random, rapidly varying, sufficiently mixing, ...potentials of the form $q(\frac{\mathbf{x}}{\varepsilon},\omega)$. We analyze the source and spectral problems associated with such operators and show that the rescaled difference between the perturbed and unperturbed solutions may be written asymptotically as $\varepsilon \to 0$ as explicit Gaussian processes. Such results may be seen as central limit corrections to homogenization (law of large numbers). Similar results are derived for more general elliptic equations with random coefficients in one dimension of space. The results are based on the availability of a rapidly converging integral formulation for the perturbed solutions and on the use of classical central limit results for random processes with appropriate mixing conditions.
This article concerns topologically non-trivial interface Hamiltonians that find many applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the ...existence of topologically protected, asymmetric edge states at the interface between two two-dimensional half spaces. The asymmetric transport is characterized by a quantized interface conductivity. The objective of this article is to compute such a conductivity and show its stability under perturbations. We present two methods. The first one computes the conductivity using the winding number of branches of absolutely continuous spectrum of the interface Hamiltonian. This calculation is independent of any bulk properties but requires a sufficient understanding of the spectral decomposition of the Hamiltonian. In the fluid flow setting, it also applies in cases where the so-called bulk-interface correspondence fails. The second method establishes a bulk-interface correspondence between the interface conductivity and a so-called bulk-difference invariant. We introduce the bulk-difference invariants characterizing pairs of half spaces. We then relate the interface conductivity to the bulk-difference invariant by means of a Fedosov-Hörmander formula, which computes the index of a related Fredholm operator and is obtained using semiclassical calculus. The two methods are used to compute invariants for representative 2 × 2 and 3 × 3 systems of equations that appear in the applications.
This letter announces and summarizes results obtained in Bal and Uhlmann (2011) 1 and considers several natural extensions. The aforementioned paper proposes a procedure for reconstructing ...coefficients in a second-order, scalar, elliptic equation from knowledge of a sufficiently large number of its solutions. We present this derivation and extend it to show which parameters may or may not be reconstructed for several hybrid (also called coupled-physics) imaging modalities including photo-acoustic tomography, thermo-acoustic tomography, transient elastography, and magnetic resonance elastography. Stability estimates are also proposed.
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from full knowledge of the albedo operator at the boundary of a ...bounded domain of interest. We present optimal stability results on the reconstruction of the absorption and scattering parameters for a given error in the measured albedo operator. PUBLICATION ABSTRACT
Providing generic and cost effective modelling approaches to reconstruct and forecast freshwater temperature using predictors as air temperature and water discharge is a prerequisite to understanding ...ecological processes underlying the impact of water temperature and of global warming on continental aquatic ecosystems. Using air temperature as a simple linear predictor of water temperature can lead to significant bias in forecasts as it does not disentangle seasonality and long term trends in the signal. Here, we develop an alternative approach based on hierarchical Bayesian statistical time series modelling of water temperature, air temperature and water discharge using seasonal sinusoidal periodic signals and time varying means and amplitudes. Fitting and forecasting performances of this approach are compared with that of simple linear regression between water and air temperatures using i) an emotive simulated example, ii) application to three French coastal streams with contrasting bio-geographical conditions and sizes. The time series modelling approach better fit data and does not exhibit forecasting bias in long term trends contrary to the linear regression. This new model also allows for more accurate forecasts of water temperature than linear regression together with a fair assessment of the uncertainty around forecasting. Warming of water temperature forecast by our hierarchical Bayesian model was slower and more uncertain than that expected with the classical regression approach. These new forecasts are in a form that is readily usable in further ecological analyses and will allow weighting of outcomes from different scenarios to manage climate change impacts on freshwater wildlife.
PDF
