On mathematical and physical principles of transformations of the coherent radar backscatter matrix

The congruential rule advanced by Graves for polarization basis transformation of the radar backscatter matrix is now often misinterpreted as an example of consimilarity transformation. However, consimilarity transformations imply a physically unrealistic antilinear time-reversal operation. This is just one of the approaches found in literature to the description of transformations where the role of conjugation has been misunderstood. In this paper, the different approaches are examined in particular in respect to the role of conjugation. In order to justify and correctly derive the congruential rule for polarization basis transformation and properly place the role of conjugation, the origin of the problem is traced back to the derivation of the antenna height from the transmitted field. In fact, careful consideration of the role played by the Green’s dyadic operator relating the antenna height to the transmitted field shows that, under general unitary basis transformation, it is not justified to assume a scalar relationship between them. Invariance of the voltage equation shows that antenna states and wave states must in fact lie in dual spaces, a distinction not captured in conventional Jones vector formalism. Introducing spinor formalism, and with the use of an alternate spin frame for the transmitted field a mathematically consistent implementation of the directional wave formalism is obtained. Examples are given comparing the wider generality of the congruential rule in both active and passive transformations with the consimilarity rule.

A general-method for tracking analysis and its application to meteorological data

Recent interest in the validation of general circulation models (GCMs) has been devoted to objective methods. A small number of authors have used the direct synoptic identification of phenomena together with a statistical analysis to perform the objective comparison between various datasets. This paper describes a general method for performing the synoptic identification of phenomena that can be used for an objective analysis of atmospheric, or oceanographic, datasets obtained from numerical models and remote sensing. Methods usually associated with image processing have been used to segment the scene and to identify suitable feature points to represent the phenomena of interest. This is performed for each time level. A technique from dynamic scene analysis is then used to link the feature points to form trajectories. The method is fully automatic and should be applicable to a wide range of geophysical fields. An example will be shown of results obtained from this method using data obtained from a run of the Universities Global Atmospheric Modelling Project GCM.

Using airborne laser altimetry to improve river flood extents delineated from SAR data

Flood extent maps derived from SAR images are a useful source of data for validating hydraulic models of river flood flow. The accuracy of such maps is reduced by a number of factors, including changes in returns from the water surface caused by different meteorological conditions and the presence of emergent vegetation. The paper describes how improved accuracy can be achieved by modifying an existing flood extent delineation algorithm to use airborne laser altimetry (LiDAR) as well as SAR data. The LiDAR data provide an additional constraint that waterline (land-water boundary) heights should vary smoothly along the flooded reach. The method was tested on a SAR image of a flood for which contemporaneous aerial photography existed, together with LiDAR data of the un-flooded reach. Waterline heights of the SAR flood extent conditioned on both SAR and LiDAR data matched the corresponding heights from the aerial photo waterline significantly more closely than those from the SAR flood extent conditioned only on SAR data.

Data assimilation: From photon counts to Earth System forecasts

Data assimilation – the set of techniques whereby information from observing systems and models is combined optimally – is rapidly becoming prominent in endeavours to exploit Earth Observation for Earth sciences, including climate prediction. This paper explains the broad principles of data assimilation, outlining different approaches (optimal interpolation, three-dimensional and four-dimensional variational methods, the Kalman Filter), together with the approximations that are often necessary to make them practicable. After pointing out a variety of benefits of data assimilation, the paper then outlines some practical applications of the exploitation of Earth Observation by data assimilation in the areas of operational oceanography, chemical weather forecasting and carbon cycle modelling. Finally, some challenges for the future are noted.

Flood detection in urban areas using TerraSAR-X

Flooding is a major hazard in both rural and urban areas worldwide, but it is in urban areas that the impacts are most severe. An investigation of the ability of high resolution TerraSAR-X Synthetic Aperture Radar (SAR) data to detect flooded regions in urban areas is described. The study uses a TerraSAR-X image of a 1 in 150 year flood near Tewkesbury, UK, in 2007, for which contemporaneous aerial photography exists for validation. The DLR SAR End-To-End simulator (SETES) was used in conjunction with airborne scanning laser altimetry (LiDAR) data to estimate regions of the image in which water would not be visible due to shadow or layover caused by buildings and taller vegetation. A semi-automatic algorithm for the detection of floodwater in urban areas is described, together with its validation using the aerial photographs. 76% of the urban water pixels visible to TerraSAR-X were correctly detected, with an associated false positive rate of 25%. If all urban water pixels were considered, including those in shadow and layover regions, these figures fell to 58% and 19% respectively. The algorithm is aimed at producing urban flood extents with which to calibrate and validate urban flood inundation models, and these findings indicate that TerraSAR-X is capable of providing useful data for this purpose.

Can desert dust explain the outgoing longwave radiation anomaly over the Sahara during July 2003?

Measurements of the top‐of‐the‐atmosphere outgoing longwave radiation (OLR) for July 2003 from Meteosat‐7 are used to assess the performance of the numerical weather prediction version of the Met Office Unified Model. A significant difference is found over desert regions of northern Africa where the model emits too much OLR by up to 35 Wm−2 in the monthly mean. By cloud‐screening the data we find an error of up to 50 Wm−2 associated with cloud‐free areas, which suggests an error in the model surface temperature, surface emissivity, or atmospheric transmission. By building up a physical model of the radiative properties of mineral dust based on in situ, and surface‐based and satellite remote sensing observations we show that the most plausible explanation for the discrepancy in OLR is due to the neglect of mineral dust in the model. The calculations suggest that mineral dust can exert a longwave radiative forcing by as much as 50 Wm−2 in the monthly mean for 1200 UTC in cloud‐free regions, which accounts for the discrepancy between the model and the Meteosat‐7 observations. This suggests that inclusion of the radiative effects of mineral dust will lead to a significant improvement in the radiation balance of numerical weather prediction models with subsequent improvements in performance.

Sensitivity of radar backscatter to desert surface roughness

Synthetic aperture radar (SAR) data have proved useful in remote sensing studies of deserts, enabling different surfaces to be discriminated by differences in roughness properties. Roughness is characterized in SAR backscatter models using the standard deviation of surface heights (sigma), correlation length (L) and autocorrelation function (rho(xi)). Previous research has suggested that these parameters are of limited use for characterizing surface roughness, and are often unreliable due to the collection of too few roughness profiles, or under-sampling in terms of resolution or profile length (L-p). This paper reports on work aimed at establishing the effects of L-p and sampling resolution on SAR backscatter estimations and site discrimination. Results indicate significant relationships between the average roughness parameters and L-p, but large variability in roughness parameters prevents any clear understanding of these relationships. Integral equation model simulations demonstrate limited change with L-p and under-estimate backscatter relative to SAR observations. However, modelled and observed backscatter conform in pattern and magnitude for C-band systems but not for L-band data. Variation in surface roughness alone does not explain variability in site discrimination. Other factors (possibly sub-surface scattering) appear to play a significant role in controlling backscatter characteristics at lower frequencies.

The use of earth observation techniques to improve catchment-scale pollution predictions

Remote sensing can potentially provide information useful in improving pollution transport modelling in agricultural catchments. Realisation of this potential will depend on the availability of the raw data, development of information extraction techniques, and the impact of the assimilation of the derived information into models. High spatial resolution hyperspectral imagery of a farm near Hereford, UK is analysed. A technique is described to automatically identify the soil and vegetation endmembers within a field, enabling vegetation fractional cover estimation. The aerially-acquired laser altimetry is used to produce digital elevation models of the site. At the subfield scale the hypothesis that higher resolution topography will make a substantial difference to contaminant transport is tested using the AGricultural Non-Point Source (AGNPS) model. Slope aspect and direction information are extracted from the topography at different resolutions to study the effects on soil erosion, deposition, runoff and nutrient losses. Field-scale models are often used to model drainage water, nitrate and runoff/sediment loss, but the demanding input data requirements make scaling up to catchment level difficult. By determining the input range of spatial variables gathered from EO data, and comparing the response of models to the range of variation measured, the critical model inputs can be identified. Response surfaces to variation in these inputs constrain uncertainty in model predictions and are presented. Although optical earth observation analysis can provide fractional vegetation cover, cloud cover and semi-random weather patterns can hinder data acquisition in Northern Europe. A Spring and Autumn cloud cover analysis is carried out over seven UK sites close to agricultural districts, using historic satellite image metadata, climate modelling and historic ground weather observations. Results are assessed in terms of probability of acquisition probability and implications for future earth observation missions. (C) 2003 Elsevier Ltd. All rights reserved.

A review and classification of the existing models of cyanobacteria

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting bloom occurrence in lakes and rivers. In this paper existing key models of cyanobacteria are reviewed, evaluated and classified. Two major groups emerge: deterministic mathematical and artificial neural network models. Mathematical models can be further subcategorized into those models concerned with impounded water bodies and those concerned with rivers. Most existing models focus on a single aspect such as the growth of transport mechanisms, but there are a few models which couple both.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - II. Diurnal shape of soil heat flux

For vegetated surfaces, calculation of soil heat flux, G, with the Exact or Analytical method requires a harmonic analysis of below-canopy soil surface temperature, to obtain the shape of the diurnal course of G. When determining G with remote sensing methods, only composite (vegetation plus soil) radiometric brightness temperature is available. This paper presents a simple equation that relates the sum of the harmonic terms derived for the composite radiometric surface temperature to that of belowcanopy soil surface temperature. The thermal inertia, Gamma(,) for which a simple equation has been presented in a companion paper, paper I, is used to set the magnitude of G. To assess the success of the method proposed in this paper for the estimation of the diurnal shape of G, a comparison was made between 'remote' and in situ calculated values from described field sites. This indicated that the proposed method was suitable for the estimation of the shape of G for a variety of vegetation types and densities. The approach outlined in paper I, to obtain Gamma, was then combined with the estimated harmonic terms to predict estimates of G, which were compared to values predicted by empirical remote methods found in the literature. This indicated that the method proposed in the combination of papers I and II gave reliable estimates of G, which, in comparison to the other methods, resulted in more realistic predictions for vegetated surfaces. This set of equations can also be used for bare and sparsely vegetated soils, making it a universally applicable method. (C) 2007 Elsevier B.V. All rights reserved.

Remote estimation of thermal inertia and soil heat flux for bare soil

A method is presented which allows thermal inertia (the soil heat capacity times the square root of the soil thermal diffusivity, C(h)rootD(h)), to be estimated remotely from micrometeorological observations. The method uses the drop in surface temperature, T-s, between sunset and sunrise, and the average night-time net radiation during that period, for clear, still nights. A Fourier series analysis was applied to analyse the time series of T-s . The Fourier series constants, together with the remote estimate of thermal inertia, were used in an analytical expression to calculate diurnal estimates of the soil heat flux, G. These remote estimates of C(h)rootD(h) and G compared well with values derived from in situ sensors. The remote and in situ estimates of C(h)rootD(h) both correlated well with topsoil moisture content. This method potentially allows area-average estimates of thermal inertia and soil heat flux to be derived from remote sensing, e.g. METEOSAT Second Generation, where the area is determined by the sensor's height and viewing angle. (C) 2003 Elsevier B.V. All rights reserved.

Probing the large-scale topology of the heliospheric magnetic field using Jovian electrons

Jupiter’s magnetosphere acts as a point source of near-relativistic electrons within the heliosphere. In this study, three solar cycles of Jovian electron data in near-Earth space are examined. Jovian electron intensity is found to peak for an ideal Parker spiral connection, but with considerable spread about this point. Assuming the peak in Jovian electron counts indicates the best magnetic connection to Jupiter, we find a clear trend for fast and slow solar wind to be over- and under-wound with respect to the ideal Parker spiral, respectively. This is shown to be well explained in terms of solar wind stream interactions. Thus, modulation of Jovian electrons by corotating interaction regions (CIRs) may primarily be the result of changing magnetic connection, rather than CIRs acting as barriers to cross-field diffusion. By using Jovian electrons to remote sensing magnetic connectivity with Jupiter’s magnetosphere, we suggest that they provide a means to validate solar wind models between 1 and 5 AU, even when suitable in situ solar wind observations are not available. Furthermore, using Jovian electron observations as probes of heliospheric magnetic topology could provide insight into heliospheric magnetic field braiding and turbulence, as well as any systematic under-winding of the heliospheric magnetic field relative to the Parker spiral from footpoint motion of the magnetic field.

LiDAR mapping of tidal marshes for ecogeomorphological modelling in the TIDE project

The European research project TIDE (Tidal Inlets Dynamics and Environment) is developing and validating coupled models describing the morphological, biological and ecological evolution of tidal environments. The interactions between the physical and biological processes occurring in these regions requires that the system be studied as a whole rather than as separate parts. Extensive use of remote sensing including LiDAR is being made to provide validation data for the modelling. This paper describes the different uses of LiDAR within the project and their relevance to the TIDE science objectives. LiDAR data have been acquired from three different environments, the Venice Lagoon in Italy, Morecambe Bay in England, and the Eden estuary in Scotland. LiDAR accuracy at each site has been evaluated using ground reference data acquired with differential GPS. A semi-automatic technique has been developed to extract tidal channel networks from LiDAR data either used alone or fused with aerial photography. While the resulting networks may require some correction, the procedure does allow network extraction over large areas using objective criteria and reduces fieldwork requirements. The networks extracted may subsequently be used in geomorphological analyses, for example to describe the drainage patterns induced by networks and to examine the rate of change of networks. Estimation of the heights of the low and sparse vegetation on marshes is being investigated by analysis of the statistical distribution of the measured LiDAR heights. Species having different mean heights may be separated using the first-order moments of the height distribution.

Uses of airborne scanning laser altimetry for river flood modelling and coastal geomorphology

Two ongoing projects at ESSC that involve the development of new techniques for extracting information from airborne LiDAR data and combining this information with environmental models will be discussed. The first project in conjunction with Bristol University is aiming to improve 2-D river flood flow models by using remote sensing to provide distributed data for model calibration and validation. Airborne LiDAR can provide such models with a dense and accurate floodplain topography together with vegetation heights for parameterisation of model friction. The vegetation height data can be used to specify a friction factor at each node of a model’s finite element mesh. A LiDAR range image segmenter has been developed which converts a LiDAR image into separate raster maps of surface topography and vegetation height for use in the model. Satellite and airborne SAR data have been used to measure flood extent remotely in order to validate the modelled flood extent. Methods have also been developed for improving the models by decomposing the model’s finite element mesh to reflect floodplain features such as hedges and trees having different frictional properties to their surroundings. Originally developed for rural floodplains, the segmenter is currently being extended to provide DEMs and friction parameter maps for urban floods, by fusing the LiDAR data with digital map data. The second project is concerned with the extraction of tidal channel networks from LiDAR. These networks are important features of the inter-tidal zone, and play a key role in tidal propagation and in the evolution of salt-marshes and tidal flats. The study of their morphology is currently an active area of research, and a number of theories related to networks have been developed which require validation using dense and extensive observations of network forms and cross-sections. The conventional method of measuring networks is cumbersome and subjective, involving manual digitisation of aerial photographs in conjunction with field measurement of channel depths and widths for selected parts of the network. A semi-automatic technique has been developed to extract networks from LiDAR data of the inter-tidal zone. A multi-level knowledge-based approach has been implemented, whereby low level algorithms first extract channel fragments based mainly on image properties then a high level processing stage improves the network using domain knowledge. The approach adopted at low level uses multi-scale edge detection to detect channel edges, then associates adjacent anti-parallel edges together to form channels. The higher level processing includes a channel repair mechanism.

Global estimates of snow water equivalent from passive microwave instruments: history, challenges and future developments

Snow properties have been retrieved from satellite data for many decades. While snow extent is generally felt to be obtained reliably from visible-band data, there is less confidence in the measurements of snow mass or water equivalent derived from passive microwave instruments. This paper briefly reviews historical passive microwave instruments and products, and compares the large-scale patterns from these sources to those of general circulation models and leading reanalysis products. Differences are seen to be large between the datasets, particularly over Siberia. A better understanding of the errors in both the model-based and measurement-based datasets is required to exploit both fully. Techniques to apply to the satellite measurements for improved large-scale snow data are suggested.