Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

Estimation of wind storm impacts over Western Germany under future climate conditions using a statistical-dynamical downscaling approach

A statistical–dynamical regionalization approach is developed to assess possible changes in wind storm impacts. The method is applied to North Rhine-Westphalia (Western Germany) using the FOOT3DK mesoscale model for dynamical downscaling and ECHAM5/OM1 global circulation model climate projections. The method first classifies typical weather developments within the reanalysis period using K-means cluster algorithm. Most historical wind storms are associated with four weather developments (primary storm-clusters). Mesoscale simulations are performed for representative elements for all clusters to derive regional wind climatology. Additionally, 28 historical storms affecting Western Germany are simulated. Empirical functions are estimated to relate wind gust fields and insured losses. Transient ECHAM5/OM1 simulations show an enhanced frequency of primary storm-clusters and storms for 2060–2100 compared to 1960–2000. Accordingly, wind gusts increase over Western Germany, reaching locally +5% for 98th wind gust percentiles (A2-scenario). Consequently, storm losses are expected to increase substantially (+8% for A1B-scenario, +19% for A2-scenario). Regional patterns show larger changes over north-eastern parts of North Rhine-Westphalia than for western parts. For storms with return periods above 20 yr, loss expectations for Germany may increase by a factor of 2. These results document the method's functionality to assess future changes in loss potentials in regional terms.

Model estimation of cerebral hemodynamics between blood flow and volume changes: A data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

Estimation of sea surface temperature from the Spinning Enhanced Visible and Infra Red Imager, improved using numerical weather prediction

Most of the operational Sea Surface Temperature (SST) products derived from satellite infrared radiometry use multi-spectral algorithms. They show, in general, reasonable performances with root mean square (RMS) residuals around 0.5 K when validated against buoy measurements, but have limitations, particularly a component of the retrieval error that relates to such algorithms' limited ability to cope with the full variability of atmospheric absorption and emission. We propose to use forecast atmospheric profiles and a radiative transfer model to simulate the algorithmic errors of multi-spectral algorithms. In the practical case of SST derived from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard Meteosat Second Generation (MSG), we demonstrate that simulated algorithmic errors do explain a significant component of the actual errors observed for the non linear (NL) split window algorithm in operational use at the Centre de Météorologie Spatiale (CMS). The simulated errors, used as correction terms, reduce significantly the regional biases of the NL algorithm as well as the standard deviation of the differences with drifting buoy measurements. The availability of atmospheric profiles associated with observed satellite-buoy differences allows us to analyze the origins of the main algorithmic errors observed in the SEVIRI field of view: a negative bias in the inter-tropical zone, and a mid-latitude positive bias. We demonstrate how these errors are explained by the sensitivity of observed brightness temperatures to the vertical distribution of water vapour, propagated through the SST retrieval algorithm.

Optimal estimation of sea surface temperature from split-window observations

Optimal estimation (OE) improves sea surface temperature (SST) estimated from satellite infrared imagery in the “split-window”, in comparison to SST retrieved using the usual multi-channel (MCSST) or non-linear (NLSST) estimators. This is demonstrated using three months of observations of the Advanced Very High Resolution Radiometer (AVHRR) on the first Meteorological Operational satellite (Metop-A), matched in time and space to drifter SSTs collected on the global telecommunications system. There are 32,175 matches. The prior for the OE is forecast atmospheric fields from the Météo-France global numerical weather prediction system (ARPEGE), the forward model is RTTOV8.7, and a reduced state vector comprising SST and total column water vapour (TCWV) is used. Operational NLSST coefficients give mean and standard deviation (SD) of the difference between satellite and drifter SSTs of 0.00 and 0.72 K. The “best possible” NLSST and MCSST coefficients, empirically regressed on the data themselves, give zero mean difference and SDs of 0.66 K and 0.73 K respectively. Significant contributions to the global SD arise from regional systematic errors (biases) of several tenths of kelvin in the NLSST. With no bias corrections to either prior fields or forward model, the SSTs retrieved by OE minus drifter SSTs have mean and SD of − 0.16 and 0.49 K respectively. The reduction in SD below the “best possible” regression results shows that OE deals with structural limitations of the NLSST and MCSST algorithms. Using simple empirical bias corrections to improve the OE, retrieved minus drifter SSTs are obtained with mean and SD of − 0.06 and 0.44 K respectively. Regional biases are greatly reduced, such that the absolute bias is less than 0.1 K in 61% of 10°-latitude by 30°-longitude cells. OE also allows a statistic of the agreement between modelled and measured brightness temperatures to be calculated. We show that this measure is more efficient than the current system of confidence levels at identifying reliable retrievals, and that the best 75% of satellite SSTs by this measure have negligible bias and retrieval error of order 0.25 K.

A critical revision of the estimation of the latent heat flux from two-wavelength scintillometry

Simultaneous scintillometer measurements at multiple wavelengths (pairing visible or infrared with millimetre or radio waves) have the potential to provide estimates of path-averaged surface fluxes of sensible and latent heat. Traditionally, the equations to deduce fluxes from measurements of the refractive index structure parameter at the two wavelengths have been formulated in terms of absolute humidity. Here, it is shown that formulation in terms of specific humidity has several advantages. Specific humidity satisfies the requirement for a conserved variable in similarity theory and inherently accounts for density effects misapportioned through the use of absolute humidity. The validity and interpretation of both formulations are assessed and the analogy with open-path infrared gas analyser density corrections is discussed. Original derivations using absolute humidity to represent the influence of water vapour are shown to misrepresent the latent heat flux. The errors in the flux, which depend on the Bowen ratio (larger for drier conditions), may be of the order of 10%. The sensible heat flux is shown to remain unchanged. It is also verified that use of a single scintillometer at optical wavelengths is essentially unaffected by these new formulations. Where it may not be possible to reprocess two-wavelength results, a density correction to the latent heat flux is proposed for scintillometry, which can be applied retrospectively to reduce the error.

Estimation of visual motion parameters used for bio-inspired navigation

Visual motion cues play an important role in animal and humans locomotion without the need to extract actual ego-motion information. This paper demonstrates a method for estimating the visual motion parameters, namely the Time-To-Contact (TTC), Focus of Expansion (FOE), and image angular velocities, from a sparse optical flow estimation registered from a downward looking camera. The presented method is capable of estimating the visual motion parameters in a complicated 6 degrees of freedom motion and in real time with suitable accuracy for mobile robots visual navigation.

Estimation of magnet separation for magnetic suspension applications

This thesis describes a form of non-contact measurement using two dimensional hall effect sensing to resolve the location of a moving magnet which is part of a ‘magnetic spring’ type suspension system. This work was inspired by the field of Space Robotics, which currently relies on solid link suspension techniques for rover stability. This thesis details the design, development and testing of a novel magnetic suspension system with a possible application in space and terrestrial based robotics, especially when the robot needs to traverse rough terrain. A number of algorithms were developed, to utilize experimental data from testing, that can approximate the separation between magnets in the suspension module through observation of the magnetic fields. Experimental hardware was also developed to demonstrate how two dimensional hall effect sensor arrays could provide accurate feedback, with respects to the magnetic suspension modules operation, so that future work can include the sensor array in a real-time control system to produce dynamic ride control for space robots. The research performed has proven that two dimensional hall effect sensing with respects to magnetic suspension is accurate, effective and suitable for future testing.

Synergistic angular and spectral estimation of aerosol properties using CHRIS/PROBA-1 and simulated Sentinel-3~data

A method has been developed to estimate Aerosol Optical Depth (AOD), Fine Mode Fraction (FMF) and Single Scattering Albedo (SSA) over land surfaces using simulated Sentinel-3 data. The method uses inversion of a coupled surface/atmosphere radiative transfer model, and includes a general physical model of angular surface reflectance. An iterative process is used to determine the optimum value of the aerosol properties providing the best fit of the corrected reflectance values for a number of view angles and wavelengths with those provided by the physical model. A method of estimating AOD using only angular retrieval has previously been demonstrated on data from the ENVISAT and PROBA-1 satellite instruments, and is extended here to the synergistic spectral and angular sampling of Sentinel-3 and the additional aerosol properties. The method is tested using hyperspectral, multi-angle Compact High Resolution Imaging Spectrometer (CHRIS) images. The values obtained from these CHRIS observations are validated using ground based sun-photometer measurements. Results from 22 image sets using the synergistic retrieval and improved aerosol models show an RMSE of 0.06 in AOD, reduced to 0.03 over vegetated targets.

Simplified estimation of ray-path mirroring height for HF radiowaves reflected from the ionospheric F-region

From Milsom's equations, which describe the geometry of ray-path hops reflected from the ionospheric F-layer, algorithms for the simplified estimation of mirror-reflection height are developed. These allow for hop length and the effects of variations in underlying ionisation (via the ratio of the F2- and E-layer critical frequencies) and F2-layer peak height (via the M(3000)F2-factor). Separate algorithms are presented which are applicable to a range of signal frequencies about the FOT and to propagation at the MUF. The accuracies and complexities of the algorithms are compared with those inherent in the use of a procedure based on an equation developed by Shimazaki.

Simple M-factor algorithm for improved estimation of the basic maximum usable frequency of radio waves reflected from the ionospheric F-region

The equations of Milsom are evaluated, giving the ground range and group delay of radio waves propagated via the horizontally stratified model ionosphere proposed by Bradley and Dudeney. Expressions for the ground range which allow for the effects of the underlying E- and F1-regions are used to evaluate the basic maximum usable frequency or M-factors for single F-layer hops. An algorithm for the rapid calculation of the M-factor at a given range is developed, and shown to be accurate to within 5%. The results reveal that the M(3000)F2-factor scaled from vertical-incidence ionograms using the standard URSI procedure can be up to 7.5% in error. A simple addition to the algorithm effects a correction to ionogram values to make these accurate to 0.5%.

Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.