Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Estimating correlated observation error statistics using an ensemble transform Kalman filter

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz ’96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Application of two-dimensional wavelet transform in near-shore X-band radar images

Among existing remote sensing applications, land-based X-band radar is an effective technique to monitor the wave fields, and spatial wave information could be obtained from the radar images. Two-dimensional Fourier Transform (2-D FT) is the common algorithm to derive the spectra of radar images. However, the wave field in the nearshore area is highly non-homogeneous due to wave refraction, shoaling, and other coastal mechanisms. When applied in nearshore radar images, 2-D FT would lead to ambiguity of wave characteristics in wave number domain. In this article, we introduce two-dimensional Wavelet Transform (2-D WT) to capture the non-homogeneity of wave fields from nearshore radar images. The results show that wave number spectra by 2-D WT at six parallel space locations in the given image clearly present the shoaling of nearshore waves. Wave number of the peak wave energy is increasing along the inshore direction, and dominant direction of the spectra changes from South South West (SSW) to West South West (WSW). To verify the results of 2-D WT, wave shoaling in radar images is calculated based on dispersion relation. The theoretical calculation results agree with the results of 2-D WT on the whole. The encouraging performance of 2-D WT indicates its strong capability of revealing the non-homogeneity of wave fields in nearshore X-band radar images.

Methane cross-validation between three Fourier Transform Spectrometers: SCISAT ACE-FTS, GOSAT TANSO-FTS, and ground-based FTS measurements in the Canadian high Arctic

We present cross-validation of remote sensing measurements of methane profiles in the Canadian high Arctic. Accurate and precise measurements of methane are essential to understand quantitatively its role in the climate system and in global change. Here, we show a cross-validation between three datasets: two from spaceborne instruments and one from a ground-based instrument. All are Fourier Transform Spectrometers (FTSs). We consider the Canadian SCISAT Atmospheric Chemistry Experiment (ACE)-FTS, a solar occultation infrared spectrometer operating since 2004, and the thermal infrared band of the Japanese Greenhouse Gases Observing Satellite (GOSAT) Thermal And Near infrared Sensor for carbon Observation (TANSO)-FTS, a nadir/off-nadir scanning FTS instrument operating at solar and terrestrial infrared wavelengths, since 2009. The ground-based instrument is a Bruker 125HR Fourier Transform Infrared (FTIR) spectrometer, measuring mid-infrared solar absorption spectra at the Polar Environment Atmospheric Research Laboratory (PEARL) Ridge Lab at Eureka, Nunavut (80° N, 86° W) since 2006. For each pair of instruments, measurements are collocated within 500 km and 24 h. An additional criterion based on potential vorticity values was found not to significantly affect differences between measurements. Profiles are regridded to a common vertical grid for each comparison set. To account for differing vertical resolutions, ACE-FTS measurements are smoothed to the resolution of either PEARL-FTS or TANSO-FTS, and PEARL-FTS measurements are smoothed to the TANSO-FTS resolution. Differences for each pair are examined in terms of profile and partial columns. During the period considered, the number of collocations for each pair is large enough to obtain a good sample size (from several hundred to tens of thousands depending on pair and configuration). Considering full profiles, the degrees of freedom for signal (DOFS) are between 0.2 and 0.7 for TANSO-FTS and between 1.5 and 3 for PEARL-FTS, while ACE-FTS has considerably more information (roughly 1° of freedom per altitude level). We take partial columns between roughly 5 and 30 km for the ACE-FTS–PEARL-FTS comparison, and between 5 and 10 km for the other pairs. The DOFS for the partial columns are between 1.2 and 2 for PEARL-FTS collocated with ACE-FTS, between 0.1 and 0.5 for PEARL-FTS collocated with TANSO-FTS or for TANSO-FTS collocated with either other instrument, while ACE-FTS has much higher information content. For all pairs, the partial column differences are within ± 3 × 1022 molecules cm−2. Expressed as median ± median absolute deviation (expressed in absolute or relative terms), these differences are 0.11 ± 9.60 × 10^20 molecules cm−2 (0.012 ± 1.018 %) for TANSO-FTS–PEARL-FTS, −2.6 ± 2.6 × 10^21 molecules cm−2 (−1.6 ± 1.6 %) for ACE-FTS–PEARL-FTS, and 7.4 ± 6.0 × 10^20 molecules cm−2 (0.78 ± 0.64 %) for TANSO-FTS–ACE-FTS. The differences for ACE-FTS–PEARL-FTS and TANSO-FTS–PEARL-FTS partial columns decrease significantly as a function of PEARL partial columns, whereas the range of partial column values for TANSO-FTS–ACE-FTS collocations is too small to draw any conclusion on its dependence on ACE-FTS partial columns.

The Impact of Land Use Patterns and Watershed Characteristics on China Lake, Kennebec County, Maine

China Lake is located in Kennebec County, Maine. Since 1983 the lake has suffered from yearly algal blooms as a result of the addition of excess nutrients. The nutrient load was amplified by erosion within the watershed. Erosion varies widely depending on a number of factors, including the slope of the land, the type of soil, and the way the land is being used. Certain land use types have a high potential to add nutrients to the environment, while others may help absorb excess nutrients and prevent erosion and runoff into the lake. A comprehensive examination of the China Lake watershed was completed using GIS to calculate the erosion potential for the entire area, taking into account past and present land use patterns. This information will help the towns around the lake to make informed decisions about future development and land management.

The Relationship Between Watershed Boundaries and Elevation in Maine

http://digitalcommons.colby.edu/atlasofmaine2005/1000/thumbnail.jpg

Hydrosedimentological dynamic on Água Fria Watershed

Este estudo objetivou estimar a quantidade de sedimento que foi carreada da microbacia do Ribeirão Água Fria (Palmas, TO) entre fevereiro de 1998 e janeiro de 1999. Almejou-se ainda investigar as relações entre a produção de sedimento e alguns fatores antrópicos e ambientais. O método de Colby foi a técnica empregada no estudo. A produção específica de sedimento e o coeficiente de remoção de sedimentos foram parâmetros também investigados neste trabalho. Foi estimada uma quantidade de 138.619 toneladas de sedimento produzido e a produção específica de sedimentos foi estimada como sendo 827 t km-2 ano-1, enquanto que o coeficiente de remoção de sedimentos foi 6,2%. A fração suspensa foi a predominante durante quase todo o período de estudo.

Topographical characteristics and evaluating water quality in watershed management

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

IFTrace: Video segmentation of deformable objects using the Image Foresting Transform

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The definition of potential infiltration areas in Guaratingueta watershed, Paraiba do Sul Basin, Southeastern Brazil: an integrated approach using physical and land-use elements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Systematic analysis of the Fourier transform spectrum of (CH3OH)-C-13 between 400 and 950 cm(-1)

We have investigated a high-resolution Fourier transform (FT) absorption spectrum of the (CH3OH)-C-13 isotopomer of methanol from 400 to 950 cm(-1) with the Ritz program. We present the assignments of 7160 transitions, 3021 of which belong to Asymmetry, and 4139 to E-symmetry. These transitions occur between states labeled by K quantum numbers up to 14, and by torsional quantum numbers n up to 4. The Ritz program evaluated the energies of the 4684 involved levels with an accuracy of the order of 10(-4) cm(-1). All of the assigned lines correspond to transitions involving torsionally excited levels within the ground small-amplitude vibrational state. (c) 2005 Elsevier B.V. All rights reserved.

Dinâmica da paisagem na Microbacia do Riacho Cajazeiras no semiárido potiguar

The semi-arid Northeast region are coming through changes since its formation causing changes in the landscape and increased degradation. The economic dynamics which was established at the Potiguar semiarid had for a long time settled in livestock, subsistence agriculture and cotton, however, these economies decline from the year 1970. Thus, the Potiguar spaces are undergoing by a process of space reordering marked by the growth of agricultural activities and the process of urbanization. In the Potiguar western region these changes weaken significantly transform the landscape. In these areas, the process of urbanization and agricultural activities have caused changes in the hinterland landscape changing the natural dynamics of the caatinga biome that has been subject to negative interference with the indiscriminate removal of vegetation. In this case, the specific study area of the watershed of Cajazeiras Creek located in the cities of Pau dos Ferros, Água Nova, Encanto and Rafael Fernandes, changes in the landscape has led to degradation and environmental fragility. From this perspective, the research objective is to assess the dynamics of the landscape of the watershed of Cajazeiras Creek, semiarid region of the state of Rio Grande do Norte, identifying the degrading factors, the most degraded areas and/or susceptible to degradation and environmental fragility. The research investigated the phenomena of light geosystems theory that emphasizes the integration of elements in shaping the landscape. During this reporting period, it was carried out exploratory and bibliographical research, and geoprocessing techniques to assess the social and environmental conditions of the researched area and its environmental fragility. To do so, first, it was made an multitemporal analisis on the basis of the years 1984, 1996 and 2009 demonstrating that the dynamics of use and land cover in the watershed of Cajazeiras Creek showed a significant change in the landscape, especially in the caatinga vegetation. This has been recovering in various areas of the watershed, especially in its upper course in the mountains of Bom Sera, in Encanto city. The analysis showed the need to develop policies and programs for the maintenance, restoration and preservation of the caatinga vegetation of the river network and of water bodies. In addition, it was identified the most degraded areas of the watershed, environmental fragility and potential emerging that take into account the landscape components such as climate, topography, geology, pedology, geomorphology and the use and occupation of the soil in an integrated manner. The results show that the landscape of the watershed has medium and high environmental fragility throughout its area, especially on the banks of the river network provided by the use and occupation of the soil in an inadequate way with the environmental conditions of the watershed

Lacustrine records of Holocene flood pulse dynamics in the Upper Paraguay River watershed (Pantanal wetlands, Brazil)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)