On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

The 2010-2011 drought in the Horn of Africa in ECMWF reanalysis and seasonal forecast products

This study evaluates the use of European Centre for Medium-Range Weather Forecasts (ECMWF) products in monitoring and forecasting drought conditions during the recent 2010–2011 drought in the Horn of Africa (HoA). The region was affected by a precipitation deficit in both the October–December 2010 and March–May 2011 rainy seasons. These anomalies were captured by the ERA-Interim reanalysis (ERAI), despite its limitations in representing the March–May interannual variability. Soil moisture anomalies of ERAI also identified the onset of the drought condition early in October 2010 with a persistent drought still present in September 2011. This signal was also evident in normalized difference vegetation index (NDVI) remote sensing data. The precipitation deficit in October–December 2010 was associated with a strong La Niña event. The ECMWF seasonal forecasts for the October–December 2010 season predicted the La Niña event from June 2010 onwards. The forecasts also predicted a below-average October–December rainfall, from July 2010 onwards. The subsequent March–May rainfall anomaly was only captured by the new ECWMF seasonal forecast system in the forecasts starting in March 2011. Our analysis shows that a recent (since 1999) drying in the region during the March–May season is captured by the new ECMWF seasonal forecast system and is consistent with recently published results. The HoA region and its population are highly vulnerable to future droughts, thus global monitoring and forecasting of drought, such as that presented here, will become increasingly important in the future. Copyright © 2012 Royal Meteorological Society

Topographic and thermal mapping of volcanic terrain using AVTIS ground-based 94-GHz dual-mode radar/radiometric imager

The All-Weather Volcano Topography Imaging Sensor remote sensing instrument is a custom-built millimeter-wave (MMW) sensor that has been developed as a practical field tool for remote sensing of volcanic terrain at active lava domes. The portable instrument combines active and passive MMW measurements to record topographic and thermal data in almost all weather conditions from ground-based survey points. We describe how the instrument is deployed in the field, the quality of the primary ranging and radiometric measurements, and the postprocessing techniques used to derive the geophysical products of the target terrain, surface temperature, and reflectivity. By comparison of changing topography, we estimate the volume change and the lava extrusion rate. Validation of the MMW radiometry is also presented by quantitative comparison with coincident infrared thermal imagery.

Using the significant dust deposition event on the glaciers of Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009 to develop a method for dating and "provenancing" of desert dust events recorded in snow pack

A significant desert dust deposition event occurred on Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009, where the deposited dust later appeared as a brown layer in the snow pack. An examination of dust transportation history and analysis of chemical and physical properties of the deposited dust were used to develop a new approach for high-resolution “provenancing” of dust deposition events recorded in snow pack using multiple independent techniques. A combination of SEVIRI red-green-blue composite imagery, MODIS atmospheric optical depth fields derived using the Deep Blue algorithm, air mass trajectories derived with HYSPLIT model and analysis of meteorological data enabled identification of dust source regions with high temporal (hours) and spatial (ca. 100 km) resolution. Dust, deposited on 5 May 2009, originated in the foothills of the Djebel Akhdar in eastern Libya where dust sources were activated by the intrusion of cold air from the Mediterranean Sea and Saharan low pressure system and transported to the Caucasus along the eastern Mediterranean coast, Syria and Turkey. Particles with an average diameter below 8 μm accounted for 90% of the measured particles in the sample with a mean of 3.58 μm, median 2.48 μm. The chemical signature of this long-travelled dust was significantly different from the locally-produced dust and close to that of soils collected in a palaeolake in the source region, in concentrations of hematite. Potential addition of dust from a secondary source in northern Mesopotamia introduced uncertainty in the “provenancing” of dust from this event. Nevertheless, the approach adopted here enables other dust horizons in the snowpack to be linked to specific dust transport events recorded in remote sensing and meteorological data archives.

Accelerated loss of alpine glaciers in the Kodar Mountains, south-eastern Siberia

The recession of mountain glaciers around the world has been linked to anthropogenic climate change and small glaciers (e.g. < 2 km2) are thought to be particularly vulnerable, with reports of their disappearance from several regions. However, the response of small glaciers to climate change can be modulated by non-climatic factors such as topography and debris cover and there remain a number of regions where their recent change has evaded scrutiny. This paper presents results of the first multi-year remote sensing survey of glaciers in the Kodar Mountains, the only glaciers in SE Siberia, which we compare to previous glacier inventories from this continental setting that reported total glacier areas of 18.8 km2 in ca. 1963 (12.6 km2 of exposed ice) and 15.5 km2 in 1974 (12 km2 of exposed ice). Mapping their debris-covered termini is difficult but delineation of debris-free ice on Landsat imagery reveals 34 glaciers with a total area of 11.72 ± 0.72 km2 in 1995, followed by a reduction to 9.53 ± 0.29 km2 in 2001 and 7.01 ± 0.23 km2 in 2010. This represents a ~ 44% decrease in exposed glacier ice between ca. 1963 and 2010, but with 40% lost since 1995 and with individual glaciers losing as much as 93% of their exposed ice. Thus, although continental glaciers are generally thought to be less sensitive than their maritime counterparts, a recent acceleration in shrinkage of exposed ice has taken place and we note its coincidence with a strong summer warming trend in the region initiated at the start of the 1980s. Whilst smaller and shorter glaciers have, proportionally, tended to shrink more rapidly, we find no statistically significant relationship between shrinkage and elevation characteristics, aspect or solar radiation. This is probably due to the small sample size, limited elevation range, and topographic setting of the glaciers in deep valleys-heads. Furthermore, many of the glaciers possess debris-covered termini and it is likely that the ablation of buried ice is lagging the shrinkage of exposed ice, such that a growth in the proportion of debris cover is occurring, as observed elsewhere. If recent trends continue, we hypothesise that glaciers could evolve into a type of rock glacier within the next few decades, introducing additional complexity in their response and delaying their potential demise.

Predictability of biomass burning in response to climate changes

Climate is an important control on biomass burning, but the sensitivity of fire to changes in temperature and moisture balance has not been quantified. We analyze sedimentary charcoal records to show that the changes in fire regime over the past 21,000 yrs are predictable from changes in regional climates. Analyses of paleo- fire data show that fire increases monotonically with changes in temperature and peaks at intermediate moisture levels, and that temperature is quantitatively the most important driver of changes in biomass burning over the past 21,000 yrs. Given that a similar relationship between climate drivers and fire emerges from analyses of the interannual variability in biomass burning shown by remote-sensing observations of month-by-month burnt area between 1996 and 2008, our results signal a serious cause for concern in the face of continuing global warming.

Using the significant dust deposition event on the glaciers of Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009 to develop a method for dating and provenancing of desert dust events recorded in snow pack.

A significant desert dust deposition event occurred on Mt. Elbrus, Caucasus Mountains, Russia on 5 May 2009, where the deposited dust later appeared as a brown layer in the snow pack. An examination of dust transportation history and analysis of chemical and physical properties of the deposited dust were used to develop a new approach for high-resolution provenancing of dust deposition events recorded in snow pack using multiple independent techniques. A combination of SEVIRI red-green-blue composite imagery, MODIS atmospheric optical depth fields derived using the Deep Blue algorithm, air mass trajectories derived with HYSPLIT model and analysis of meteorological data enabled identification of dust source regions with high temporal (hours) and spatial (ca. 100 km) resolution. Dust, deposited on 5 May 2009, originated in the foothills of the Djebel Akhdar in eastern Libya where dust sources were activated by the intrusion of cold air from the Mediterranean Sea and Saharan low pressure system and transported to the Caucasus along the eastern Mediterranean coast, Syria and Turkey. Particles with an average diameter below 8 μm accounted for 90% of the measured particles in the sample with a mean of 3.58 μm, median 2.48 μm and the dominant mode of 0.60 μm. The chemical signature of this long-travelled dust was significantly different from the locally-produced dust and close to that of soils collected in a palaeolake in the source region, in concentrations of hematite and oxides of aluminium, manganese, and magnesium. Potential addition of dust from a secondary source in northern Mesopotamia introduced uncertainty in the provenancing of dust from this event. Nevertheless, the approach adopted here enables other dust horizons in the snowpack to be linked to specific dust transport events recorded in remote sensing and meteorological data archives.

Modeling image motion in airborne Three-Line-Array (TLA) push-broom cameras

This paper presents an image motion model for airborne three-line-array (TLA) push-broom cameras. Both aircraft velocity and attitude instability are taken into account in modeling image motion. Effects of aircraft pitch, roll, and yaw on image motion are analyzed based on geometric relations in designated coordinate systems. The image motion is mathematically modeled by image motion velocity multiplied by exposure time. Quantitative analysis to image motion velocity is then conducted in simulation experiments. The results have shown that image motion caused by aircraft velocity is space invariant while image motion caused by aircraft attitude instability is more complicated. Pitch,roll and yaw all contribute to image motion to different extents. Pitch dominates the along-track image motion and both roll and yaw greatly contribute to the cross-track image motion. These results provide a valuable base for image motion compensation to ensure high accuracy imagery in aerial photogrammetry.

An effective approach for land-cover classification from airborne lidar fused with co-registered data

Airborne lidar provides accurate height information of objects on the earth and has been recognized as a reliable and accurate surveying tool in many applications. In particular, lidar data offer vital and significant features for urban land-cover classification, which is an important task in urban land-use studies. In this article, we present an effective approach in which lidar data fused with its co-registered images (i.e. aerial colour images containing red, green and blue (RGB) bands and near-infrared (NIR) images) and other derived features are used effectively for accurate urban land-cover classification. The proposed approach begins with an initial classification performed by the Dempster–Shafer theory of evidence with a specifically designed basic probability assignment function. It outputs two results, i.e. the initial classification and pseudo-training samples, which are selected automatically according to the combined probability masses. Second, a support vector machine (SVM)-based probability estimator is adopted to compute the class conditional probability (CCP) for each pixel from the pseudo-training samples. Finally, a Markov random field (MRF) model is established to combine spatial contextual information into the classification. In this stage, the initial classification result and the CCP are exploited. An efficient belief propagation (EBP) algorithm is developed to search for the global minimum-energy solution for the maximum a posteriori (MAP)-MRF framework in which three techniques are developed to speed up the standard belief propagation (BP) algorithm. Lidar and its co-registered data acquired by Toposys Falcon II are used in performance tests. The experimental results prove that fusing the height data and optical images is particularly suited for urban land-cover classification. There is no training sample needed in the proposed approach, and the computational cost is relatively low. An average classification accuracy of 93.63% is achieved.

An effective approach for selection of terrain modelling method

This letter presents an effective approach for selection of appropriate terrain modeling methods in forming a digital elevation model (DEM). This approach achieves a balance between modeling accuracy and modeling speed. A terrain complexity index is defined to represent a terrain's complexity. A support vector machine (SVM) classifies terrain surfaces into either complex or moderate based on this index associated with the terrain elevation range. The classification result recommends a terrain modeling method for a given data set in accordance with its required modeling accuracy. Sample terrain data from the lunar surface are used in constructing an experimental data set. The results have shown that the terrain complexity index properly reflects the terrain complexity, and the SVM classifier derived from both the terrain complexity index and the terrain elevation range is more effective and generic than that designed from either the terrain complexity index or the terrain elevation range only. The statistical results have shown that the average classification accuracy of SVMs is about 84.3% ± 0.9% for terrain types (complex or moderate). For various ratios of complex and moderate terrain types in a selected data set, the DEM modeling speed increases up to 19.5% with given DEM accuracy.

Scheduling satellite-based SAR acquisition for sequential assimilation of water level observations into flood modelling

Satellite-based Synthetic Aperture Radar (SAR) has proved useful for obtaining information on flood extent, which, when intersected with a Digital Elevation Model (DEM) of the floodplain, provides water level observations that can be assimilated into a hydrodynamic model to decrease forecast uncertainty. With an increasing number of operational satellites with SAR capability, information on the relationship between satellite first visit and revisit times and forecast performance is required to optimise the operational scheduling of satellite imagery. By using an Ensemble Transform Kalman Filter (ETKF) and a synthetic analysis with the 2D hydrodynamic model LISFLOOD-FP based on a real flooding case affecting an urban area (summer 2007,Tewkesbury, Southwest UK), we evaluate the sensitivity of the forecast performance to visit parameters. We emulate a generic hydrologic-hydrodynamic modelling cascade by imposing a bias and spatiotemporal correlations to the inflow error ensemble into the hydrodynamic domain. First, in agreement with previous research, estimation and correction for this bias leads to a clear improvement in keeping the forecast on track. Second, imagery obtained early in the flood is shown to have a large influence on forecast statistics. Revisit interval is most influential for early observations. The results are promising for the future of remote sensing-based water level observations for real-time flood forecasting in complex scenarios.

Volatile isoprenoid emissions from plastid to planet

Approximately 1–2% of net primary production by land plants is re-emitted to the atmosphere as isoprene and monoterpenes. These emissions play major roles in atmospheric chemistry and air pollution–climate interactions. Phenomenological models have been developed to predict their emission rates, but limited understanding of the function and regulation of these emissions has led to large uncertainties in model projections of air quality and greenhouse gas concentrations. We synthesize recent advances in diverse fields, from cell physiology to atmospheric remote sensing, and use this information to propose a simple conceptual model of volatile isoprenoid emission based on regulation of metabolism in the chloroplast. This may provide a robust foundation for scaling up emissions from the cellular to the global scale.

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or ‘truth’ trajectory, as well as with analyses using the ‘true’ observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

Analysis of full-waveform LiDAR data for classification of an orange orchard scene

Full-waveform laser scanning data acquired with a Riegl LMS-Q560 instrument were used to classify an orange orchard into orange trees, grass and ground using waveform parameters alone. Gaussian decomposition was performed on this data capture from the National Airborne Field Experiment in November 2006 using a custom peak-detection procedure and a trust-region-reflective algorithm for fitting Gauss functions. Calibration was carried out using waveforms returned from a road surface, and the backscattering coefficient c was derived for every waveform peak. The processed data were then analysed according to the number of returns detected within each waveform and classified into three classes based on pulse width and c. For single-peak waveforms the scatterplot of c versus pulse width was used to distinguish between ground, grass and orange trees. In the case of multiple returns, the relationship between first (or first plus middle) and last return c values was used to separate ground from other targets. Refinement of this classification, and further sub-classification into grass and orange trees was performed using the c versus pulse width scatterplots of last returns. In all cases the separation was carried out using a decision tree with empirical relationships between the waveform parameters. Ground points were successfully separated from orange tree points. The most difficult class to separate and verify was grass, but those points in general corresponded well with the grass areas identified in the aerial photography. The overall accuracy reached 91%, using photography and relative elevation as ground truth. The overall accuracy for two classes, orange tree and combined class of grass and ground, yielded 95%. Finally, the backscattering coefficient c of single-peak waveforms was also used to derive reflectance values of the three classes. The reflectance of the orange tree class (0.31) and ground class (0.60) are consistent with published values at the wavelength of the Riegl scanner (1550 nm). The grass class reflectance (0.46) falls in between the other two classes as might be expected, as this class has a mixture of the contributions of both vegetation and ground reflectance properties.