We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-Hölder smooth functions defined on sets with low Minkowski dimension using fully connected networks with flexible width and depth, improving existing results by logarithmic factors even in classical full-dimensional settings. A key technical ingredient is a new memorization result for deep ReLU networks that enables efficient point fitting with dense architectures. We further introduce a class of compositional models in which each component function is smooth and acts on a domain of low intrinsic dimension. This framework unifies two common assumptions in the statistical learning literature, structural constraints on the target function and low dimensionality of the covariates, within a single model. We show that deep networks can approximate such functions at rates determined by the most difficult function in the composition. As an application, we derive improved convergence rates for empirical risk minimization in nonparametric regression that adapt to smoothness, compositional structure, and intrinsic dimensionality.

There is growing interest in extending average treatment effect (ATE) estimation to incorporate non-tabular data, such as images and text, which may act as sources of confounding. Neglecting these effects risks biased results and flawed scientific conclusions. However, incorporating non-tabular data necessitates sophisticated feature extractors, often in combination with ideas of transfer learning. In this work, we investigate how latent features from pre-trained neural networks can be leveraged to adjust for sources of confounding. We formalize conditions under which these latent features enable valid adjustment and statistical inference in ATE estimation, demonstrating results along the example of double machine learning. We discuss critical challenges inherent to latent feature learning and downstream parameter estimation arising from the high dimensionality and non-identifiability of representations. Common structural assumptions for obtaining fast convergence rates with additive or sparse linear models are shown to be unrealistic for latent features. We argue, however, that neural networks are largely insensitive to these issues. In particular, we show that neural networks can achieve fast convergence rates by adapting to intrinsic notions of sparsity and dimension of the learning problem.

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NFs) work particularly well in multiple dimensions, interpreting the input-output relationship of such models is often difficult, due to the black-box character of deep learning models. In contrast, existing statistical methods for multivariate outcomes such as multivariate conditional transformation models (MCTMs) are restricted in flexibility and are often not expressive enough to represent complex multivariate probability distributions. In this paper, we combine MCTMs with state-of-the-art and autoregressive NFs to leverage the transparency of MCTMs for modeling interpretable feature effects on the marginal distributions in the first step and the flexibility of neural-network-based NFs techniques to account for complex and non-linear relationships in the joint data distribution. We demonstrate our method’s versatility in various numerical experiments and compare it with MCTMs and other NF models on both simulated and real-world data.

Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series or spatially correlated observations. In this paper, we propose a novel bootstrap method that is designed to account for data dependencies and can be executed online, making it particularly suitable for real-time applications. This method is based on an autoregressive sequence of increasingly dependent resampling weights. We prove the theoretical validity of the proposed bootstrap scheme under general conditions. We demonstrate the effectiveness of our approach through extensive simulations and show that it provides reliable uncertainty quantification even in the presence of complex data dependencies. Our work bridges the gap between classical resampling techniques and the demands of modern data analysis, providing a valuable tool for researchers and practitioners in dynamic, data-rich environments.

The complexity of black-box algorithms can lead to various challenges, including the introduction of biases. These biases present immediate risks in the algorithms’ application. It was, for instance, shown that neural networks can deduce racial information solely from a patient's X-ray scan, a task beyond the capability of medical experts. If this fact is not known to the medical expert, automatic decision-making based on this algorithm could lead to prescribing a treatment (purely) based on racial information. While current methodologies allow for the "orthogonalization" or "normalization" of neural networks with respect to such information, existing approaches are grounded in linear models. Our paper advances the discourse by introducing corrections for non-linearities such as ReLU activations. Our approach also encompasses scalar and tensor-valued predictions, facilitating its integration into neural network architectures. Through extensive experiments, we validate our method's effectiveness in safeguarding sensitive data in generalized linear models, normalizing convolutional neural networks for metadata, and rectifying pre-existing embeddings for undesired attributes.

The seasonal snow cover is an important resource in mountain regions such as the Alps, the monitoring of which is crucial for hydrology and water management. We present a portfolio of homogenized products of physical snow properties including snow extent, melt extent and state, and snow mass. The algorithm for monitoring snow extent exploits the available spectral bands of optical sensors and accounts for variations of illumination in mountains. It generates consistent snow products from different optical sensors supporting the combined use of the products. SAR data are used for monitoring the melt extent and state of the snowpack. We intercompared three algorithms in Alpine areas that are based on change detection and assessed the performance. For retrieving snow accumulation SAR interferometry is a promising tool. The procedure has been tested in the Alps using C- and L-Band SAR airborne and satellite data. Performance and critical issues have been checked in the context of field campaigns. These activities support preparations for snow mass monitoring by means of future interferometric missions.

The time-varying areal extent and duration of surface melt on ice sheets are important parameters for climate and cryosphere research and key indicators of climate change in polar regions. To evaluate snowmelt dynamics and melting/refreezing processes in Greenland and Antarctica, we developed and implemented an algorithm for generating time-series of surface melt extent and melt phases (dry, wet refreezing) based on the analysis of continuous time series of C-band active microwave satellite data. Our results, based on METOP ASCAT scatterometer and Sentinel-1 SAR data, demonstrate the excellent capability of these missions for operational monitoring of snowmelt areas, providing a consistent climate data record on the presence of liquid water in snow and firn areas of Greenland and Antarctica for studying surface melt processes and ice sheet mass loss.

This work presents the results of an algorithm for the retrieval of snow surface albedo and grain size by exploiting Sentinel-3 OLCI data. The algorithm is a hybrid approach based on spectral indices and radiative transfer theory and it was tested and intercompared with ground data from 6 field stations and other sensors in the European Alps for the period 2017-2023. The results indicate that for albedo the algorithm agrees well with ground measurements showing an unbiased Root Mean Square Error (ubRMSE) between 0.05 and 0.13 and a correlation coefficient ranging from 0.63 to 0.78 depending on the locations. For grain size, even though a general underestimation is found, the estimates reflect well the typical grain size metamorphosis from winter to spring. To further test the algorithm, these results from Sentinel-3 data were also confronted with ECOSTRESS thermal data specifically useful to show the metamorphosis of the grain size. For albedo, the algorithm was further applied to PRISMA hyperspectral images, showing consistent results with the values obtained by multispectral Sentinel-3 imagery.

Single-pass SAR interferometry (InSAR) has demonstrated a great potential for the monitoring of ice and snow melt dynamics. In particular, digital elevation models (DEM) derived from the TanDEM-X bistatic SAR mission are widely used for measuring elevation changes over glaciers through time-tagged DEM differencing. A critical aspect of this approach is represented by the mutual calibration of the input DEMs, which are normally affected by residual offsets and tilts, caused by uncertainties on the baseline estimation. Moreover, a further crucial aspect which needs to be addressed is the penetration of radar waves into the snow pack, which is closely linked to both the properties of snow and the radar parameters, such as frequency and acquisition geometry. This in turn jeopardizes the retrieval of the topographic height of the surface and adds a significant amount of uncertainty when performing DEM differencing over snow-covered areas. In this paper, we present an overview of the activities which are currently being carried out at DLR, together with partner institutions and companies, aimed at providing more reliable estimations of snow depth and glaciers topographic height changes using TanDEM-X bistatic InSAR data. We present a novel technique for performing an automatic selection of reliable calibration points, based on the use of natural targets, together with the mutual calibration procedure. Moreover, we rely on a data-driven machine learning approach for the estimation and compensation of the surface penetration bias. Preliminary results are extremely promising, also in view of future bistatic SAR missions, such as the ESA Harmony Earth Explorer mission.

Hyperparameter optimization is crucial for obtaining peak performance of machine learning models. The standard protocol evaluates various hyperparameter configurations using a resampling estimate of the generalization error to guide optimization and select a final hyperparameter configuration. Without much evidence, paired resampling splits, i.e., either a fixed train-validation split or a fixed cross-validation scheme, are often recommended. We show that, surprisingly, reshuffling the splits for every configuration often improves the final model's generalization performance on unseen data. Our theoretical analysis explains how reshuffling affects the asymptotic behavior of the validation loss surface and provides a bound on the expected regret in the limiting regime. This bound connects the potential benefits of reshuffling to the signal and noise characteristics of the underlying optimization problem. We confirm our theoretical results in a controlled simulation study and demonstrate the practical usefulness of reshuffling in a large-scale, realistic hyperparameter optimization experiment. While reshuffling leads to test performances that are competitive with using fixed splits, it drastically improves results for a single train-validation holdout protocol and can often make holdout become competitive with standard CV while being computationally cheaper.

We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level, thereby improving cost-sensitive decision-making and helping understand the sources of uncertainty. Furthermore, it allows to define total, aleatoric, and epistemic uncertainty on the basis of non-categorical measures such as variance, going beyond common entropy-based measures. In particular, variance-based measures address some of the limitations associated with established methods that have recently been discussed in the literature. We show that our proposed measures adhere to a number of desirable properties. Through empirical evaluation on a variety of benchmark data sets – including applications in the medical domain where accurate uncertainty quantification is crucial – we establish the effectiveness of label-wise uncertainty quantification.

Global feature effect methods, such as partial dependence plots, provide an intelligible visualization of the expected marginal feature effect. However, such global feature effect methods can be misleading, as they do not represent local feature effects of single observations well when feature interactions are present. We formally introduce generalized additive decomposition of global effects (GADGET), which is a new framework based on recursive partitioning to find interpretable regions in the feature space such that the interaction-related heterogeneity of local feature effects is minimized. We provide a mathematical foundation of the framework and show that it is applicable to the most popular methods to visualize marginal feature effects, namely partial dependence, accumulated local effects, and Shapley additive explanations (SHAP) dependence. Furthermore, we introduce and validate a new permutation-based interaction detection procedure that is applicable to any feature effect method that fits into our proposed framework. We empirically evaluate the theoretical characteristics of the proposed methods based on various feature effect methods in different experimental settings. Moreover, we apply our introduced methodology to three real-world examples to showcase their usefulness.

Interferometric SAR (InSAR) is a promising tool for monitoring seasonal snow and for retrieving of Snow Water Equivalent (SWE) as the interferometric phase can be related to changes in SWE (ΔSWE). The boreal forest is a challenging landscape for the InSAR retrieval of SWE since it contributes to the signal by adding an undesired component originating from the vegetation. Although the technique has been validated extensively, most of these works are limited to discrete points. For comparison, we used snowpack simulations from the SnowModel, a high-resolution spatially distributed snow evolution model. This enables a better understanding of the limitations of L-band InSAR for SWE retrieval since it allows to evaluate its performance under different conditions. We analyzed the impact on coherence of snow melt between acquisitions and analyzed pairs with wet snow presence. The interferometric phase was inverted and compared to the simulated ΔSWEfrom the SnowModel distributions for three interferometric pairs. The results indicate a good spatial match between SnowModel and InSAR estimations. However, an increased difference was observed over densely forested areas when the air temperature was close to zero in at least one of the interferometric pairs. We hypothesize that the increase in permittivity of the forest for close to zero temperatures also increases the contribution from the canopy, consequently inducing errors in the retrieval. Both ALOS2 and SnowModel ΔSWEestimates were compared with in-situ data including a snow scale, snow depth from an Automatic Weather Station (AWS), a snow pit, and manual courses.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor’s variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). This selection often depends on the initial model fit on labeled data. Early overfitting might thus be propagated to the final model by selecting instances with overconfident but erroneous predictions, often referred to as confirmation bias. This paper introduces BPLS, a Bayesian framework for PLS that aims to mitigate this issue. At its core lies a criterion for selecting instances to label: an analytical approximation of the posterior predictive of pseudo-samples. We derive this selection criterion by proving Bayes-optimality of the posterior predictive of pseudo-samples. We further overcome computational hurdles by approximating the criterion analytically. Its relation to the marginal likelihood allows us to come up with an approximation based on Laplace’s method and the Gaussian integral. We empirically assess BPLS on simulated and real-world data. When faced with high-dimensional data prone to overfitting, BPLS outperforms traditional PLS methods.

The Snow Water Equivalent (SWE) describes the amount of liquid water stored in a snow pack and is an important parameter for runoff predictions and flood forecasts. Differential Interferometric Synthetic Aperture Radar (DInSAR) can be used to estimate the SWE change between two temporally separated repeat pass SAR acquisitions utilizing the interferometric phase. However, only a limited range of SWE changes can be retrieved unambiguously due to phase wraps of the interferometric phase. In this study, the aim is to include information on snow depth obtained from the Co-polar Phase Difference (CPD) between the polarimetric channels to detect phase wraps and improve the SWE retrieval results. The investigations are performed using airborne SAR acquisitions over the Alps.

Comprehensive Ice velocity observations are essential for estimating ice sheet discharge and mass balance and are key input for modelling ice dynamic processes in response to climate warming. Based on Sentinel-1 SAR imagery we generate high-resolution ice velocity maps at 50 m posting over the ice sheets by combining SAR interferometry (InSAR) and offset-tracking (OT). The InSAR method provides improved accuracy particularly in the slow-moving interior of the ice sheets at higher resolution but requires crossing satellite acquisitions as well as image pairs with adequate coherence. On zones without crossing orbits our processing line uses the velocity vector derived from INSAR and flow direction from OT to optimally fill in gaps. Fast moving areas where coherence is not preserved are filled with OT velocity observations. The added value of the new ice velocity maps is assessed by intercomparison with operational ice velocity products and in-situ GPS data. Significant improvement compared to current products are achieved in interior parts of the ice sheets, for example helping to better constrain boundaries between ice drainage basins.

In March 2021 a field campaign was conducted in the Austrian Alps exploring the application potential and performance of snow mass (snow water equivalent, SWE) retrievals by means of repeat-pass radar interferometry (RP-InSAR). Multiple repeat-pass acquisitions were obtained with an airborne polarimetric C-band and L-band SAR, covering days without snowfall, as well as two snowfall events of different intensity. SWE maps, deduced from the observed change of the RP-InSAR phase delay in the snowpack, show good agreement with field measurements. Whereas L-band data are well applicable for SWE mapping of both snowfall events, the 2 π phase ambiguity and low coherence prevent the use of C-band data for the snowfall event of high intensity. The analysis of the campaign data is going on, addressing among other topics the application of RP-InSAR for SWE monitoring within the planned L-band SAR mission ROSE-L of the European Copernicus program and by means of geostationary C-band SAR as proposed for the Hydroterra mission.

In this work, we tested two algorithms for the retrieval of snow surface albedo and grain size by exploiting Sentinel-3 OLCI data. The first algorithm is semi-empirical based on spectral indices and radiative transfer theory adapted from Painter et al. (2009, 2012) and the second is based on an approximation of the radiative transfer theory proposed by Kokhanovsky et al. (2019). Being interested mainly in mountain areas, we introduced adaptations to account for topography and heterogeneity of the area of interest. The algorithms were tested and intercompared in the European Alps for the period 2018–2021. The results indicate that for albedo both algorithms can follow the snow dynamics from winter to springtime. Both algorithms agree well with ground measurements showing a Root Mean Square Error (RMSE) between 0.05 and 0.15 and a correlation coefficient ranging from 0.71 to 0.81. As for grain size, a general underestimation is found for both methods, even though the semiempirical method follows better the typical grain size metamorphosis from winter to spring.

This paper introduces the extended timing annotation dataset (ETAD) product for Sentinel-1 (S-1) which was developed in a joint effort of German Aerospace Center (DLR) and the European Space Agency (ESA). It allows to correct range and azimuth timing of S-1 images for geophysical effects as well as for inaccuracies in synthetic aperture radar (SAR) image focusing. In combination with the precise orbit solution, these effects determine the absolute geolocation accuracy of S-1 SAR images and the relative collocation accuracy of repeat pass image stacks. ETAD contains the gridded timing corrections for the tropospheric and ionospheric path delays, the tidal-based surface displacements, and the SAR processing effects, all of which are computed for each data take using standard models from geodesy and auxiliary atmospheric data. The ETAD product helps S-1 users to significantly improve the geolocation accuracy of the S-1 SAR products to better than 0.2 m and offers a potential solution for correcting large scale interferometric phase variations. The product layout and the product generation are described schematically. The paper also reports first results for different SAR techniques: first, the improvement in geolocation accuracy down to a few centimeters by verification of accurately surveyed corner reflector positions in the range-azimuth plane; second, the well-established offset-tracking technique, that is used for systematic ice velocity monitoring of ice sheets and glaciers, where ETAD can reduce velocity biases down to sub-centimetric values; and third, the correction of atmospheric phase contributions in wide-area interferograms used for national and European ground motion services. These early results proof the added value of the ETAD corrections and that the product design is well suited to be integrated into the processing flows of established SAR applications such as absolute ranging of targets, speckle/feature tracking and interferometry.

Within the framework of European Space Agency (ESA) activities, several campaigns were carried out in the last decade with the purpose of exploiting the capabilities of multifrequency synthetic aperture radar (SAR) data to retrieve snow information. This article presents the results obtained from the ESA SnowSAR airborne campaigns, carried out between 2011 and 2013 on boreal forest, tundra and alpine environments, selected as representative of different snow regimes. The aim of this study was to assess the capability of X- and Ku-bands SAR in retrieving the snow parameters, namely snow depth (SD) and snow water equivalent (SWE). The retrieval was based on machine learning (ML) techniques and, in particular, of artificial neural networks (ANNs). ANNs have been selected among other ML approaches since they are capable to offer a good compromise between retrieval accuracy and computational cost. Two approaches were evaluated, the first based on the experimental data (data driven) and the second based on data simulated by the dense medium radiative transfer (DMRT). The data driven algorithm was trained on half of the SnowSAR dataset and validated on the remaining half. The validation resulted in a correlation coefficient$R \simeq 0.77$between estimated and target SD, a root-mean-square error (RMSE)$\simeq 13$cm, and bias = 0.03 cm. ANN algorithms specific for each test site were also implemented, obtaining more accurate results, and the robustness of the data driven approach was evaluated over time and space. The algorithm trained with DMRT simulations and tested on the experimental dataset was able to estimate the target parameter (SWE in this case) with$R =0.74$, RMSE = 34.8 mm, and bias = 1.8 mm. The model driven approach had the twofold advantage of reducing the amount ofin situdata required for training the algorithm and of extending the algorithm exportability to other test sites.

The Sentinel-1 acquisition planning for polar regions provides almost uninterrupted observations of the Greenland Ice Sheet margin, key regions in Antarctica and other polar ice masses. The satellite constellation has thereby changed the landscape for satellite Earth observation (EO) in the polar regions, providing excellent opportunities for operational monitoring of key climate variables including ice velocity and glacier discharge. Based on Sentinel-1 SAR imagery, an archive of ice velocity maps covering the polar regions has been generated, encompassing the entire mission duration. The ice velocity maps, complemented with ice thickness and other EO datasets, form the basis for deriving ice flow, discharge fluctuations and trends at sub-monthly to multi-annual time scales, providing key input for ice dynamic and climate modelling. Our results underscore the value of long-term comprehensive monitoring of the polar ice masses, which is vital to gain insight for predicting their response to ongoing climate and ocean warming.

Reliable information on snow cover across the Northern Hemisphere and Arctic and sub-Arctic regions is needed for climate monitoring, for understanding the Arctic climate system, and for the evaluation of the role of snow cover and its feedback in climate models. In addition to being of significant interest for climatological investigations, reliable information on snow cover is of high value for the purpose of hydrological forecasting and numerical weather prediction. Terrestrial snow covers up to 50 million km2of the Northern Hemisphere in winter and is characterized by high spatial and temporal variability, making satellite observations the only means for providing timely and complete observations of the global snow cover.

Reliable information on snow cover across the Northern Hemisphere and Arctic and sub-Arctic regions is needed for climate monitoring, for understanding the Arctic climate system, and for the evaluation of the role of snow cover and its feedback in climate models. In addition to being of significant interest for climatological investigations, reliable information on snow cover is of high value for the purpose of hydrological forecasting and numerical weather prediction. Terrestrial snow covers up to 50 million km2of the Northern Hemisphere in winter and is characterized by high spatial and temporal variability. Making satellite observations the only means for providing timely and complete observations of the global snow cover.

The Sentinel satellite missions of the European Copernicus programme provide comprehensive data for long-term routine observations of the global environment. A key parameter for climate monitoring, hydrology and water management is the seasonal snow cover. We developed, implemented and tested a novel approach for monitoring snow extent and snowmelt area, exploiting the synergy of imaging radar of the Sentinel-1 mission and multispectral optical imagery of the SLSTR sensor on Sentinel-3. We describe the processing steps and algorithms for generating the synergistic snow cover product and show examples for snow cover maps over Europe based on single mission data as well as the final synergistic product.

Part of Information Retrieval evaluation research is limited by the fact that we do not know the distributions of system effectiveness over the populations of topics and, by extension, their true mean scores. The workaround usually consists in resampling topics from an existing collection and approximating the statistics of interest with the observations made between random subsamples, as if one represented the population and the other a random sample. However, this methodology is clearly limited by the availability of data, the impossibility to control the properties of these data, and the fact that we do not really measure what we intend to. To overcome these limitations, we propose a method based on vine copulas for stochastic simulation of evaluation results where the true system distributions are known upfront. In the basic use case, it takes the scores from an existing collection to build a semi-parametric model representing the set of systems and the population of topics, which can then be used to make realistic simulations of the scores by the same systems but on random new topics. Our ability to simulate this kind of data not only eliminates the current limitations, but also offers new opportunities for research. As an example, we show the benefits of this approach in two sample applications replicating typical experiments found in the literature. We provide a full R package to simulate new data following the proposed method, which can also be used to fully reproduce the results in this paper.

There is a long-stranding need of reliable space-borne observations on snow mass. Current satellite sensors and data products are largely unable to meet requirements presented in particular by numerical prediction and watershed management. Consequently, several concept studies have been initiated to address these specific needs, outlining possibilities for future space sensors focusing on retrieval of snow mass and other characteristics of the terrestrial cryosphere. The results of these of-going mission concept studies are presented and discussed. Several possible sensor options are presented, which would address diverse needs on either hemispheric or regional scales.

Reliable information on snow cover across the Northern Hemisphere and Arctic and sub-Arctic regions is needed for climate monitoring, for understanding the Arctic climate system, and for the evaluation of the role of snow cover and its feedback in climate models. In addition to being of significant interest for climatological investigations, reliable information on snow cover is of high value for the purpose of hydrological forecasting and numerical weather prediction. Terrestrial snow covers up to 50 million km2of the Northern Hemisphere in winter and is characterized by high spatial and temporal variability. Making satellite observations the only means for providing timely and complete observations of the global snow cover.

The major results and findings made during the ESA SnowPEx project concerning the evaluation of the Earth Observation-based moderate resolution snow products is presented. Both the Northern Hemisphere (NH) Snow Extent (SE) daily products as well a few regionally available products by different data providers are addressed. Comparison against daily at-ground observed Snow Depth is made, after first converting all the snow products and the in-situ observations to binary `snow/no-snow' information. We first introduce the datasets employed in the analyses, then describe the applied methodology and finally present the major findings obtained.

SESAME (SEntinel-1 SAR companion Multistatic Explorer) is a passive SAR satellite mission proposed for the ESA Earth Explorer Program. SESAME comprises two receive-only C-band SAR satellites flying in close formation to build a single-pass SAR interferometer (SP-InSAR) using the active signal of the European Sentinel-1 satellite. The SESAME mission addresses applications in geoscience and climate research that require repeat measurements of high precision elevation data over land surfaces including ice covered areas and forests, exploiting the SP-InSAR and multistatic observation geometry of the satellite formation. The objectives, the measurement approach and geo-biophysical products of the mission are described.

There is a significant difference in SWE retrieval performance between the different satellite-based products. The assessment using the Russian and Finnish snow transect data covers an extremely large and varied geographical region and spans a total of ten years (2002–2011). Additionally, the reference data are well suited for assessing coarse resolution data, as they are not point-wise measurements but distributed measurements from the snow transects or snow courses.

Results from the ESA SnowPEx project concerning the evaluation of the Earth Observation-based snow products is presented, the focus being on the Northern Hemisphere (NH) Snow Extent (SE) daily products by different data providers. Comparison against daily at-ground observed Snow Depth is made, after first converting all the snow products and the in-situ observations to binary `snow/no-snow' information. We first introduce the datasets employed in the analyses, then describe the applied methodology and finally present the major findings obtained so far. The results presented here do not cover all the investigations carried out within SnowPEx and thus can be considered as an overview of preliminary results of the validation with in-situ data which will be complemented later when the comprehensive analysis of the results is completed.

In this paper, we report results from the analysis of 3-D L-band airborne synthetic aperture radar (SAR) acquisitions acquired in March 2014 over the Mittelbergferner glacier, Austrian Alps, during the European Space Agency (ESA) campaign AlpTomoSAR. The campaign included coincident in situ measurements of snow and ice properties and ground-penetrating radar (GPR) data acquired at 600 and 200 MHz over a total length of 18 km. Radar data were acquired by repeatedly flying an L-band SAR along an oval racetrack at an altitude of about 1300 m over the glacier, such that two data stacks from opposite views are obtained. Data from all passes were coherently combined to achieve 3-D resolution capabilities, resulting in the generation of 3-D tomographic SAR (TomoSAR) cubes, where each voxel represents L-band radar reflectivity from a particular location in the 3-D space at a spatial resolution on the order of meters. TomoSAR cubes were finally corrected to account for wave propagation velocity into the ice, which was a necessary step to associate the observed features with their geometrical location, hence enabling a direct comparison to GPR data. The TomoSAR cubes show the complexity of the glacier subsurface scattering. Most areas are characterized by surface scattering in proximity of the ice surface, plus a complex pattern of in-depth volumetric scattering beneath and scattering at the ice/bedrock interface. Various subsurface features observed in GPR transects at 200 MHz clearly showed up in TomoSAR sections as well, particularly firn bodies, crevasses, layer transitions, and bedrock reflection down to 50 m below the ice surface.

The TanDEM-X/TerraSAR-X satellite formation, applying bistatic radar interferometry, delivers precise, spatially detailed topographic data, an excellent basis for mapping glacier volume change. Repeat pass data of these satellites are used for mapping glacier motion, key information for investigating the dynamic response of glaciers to changing boundary conditions. The synergistic analysis of these data sets provides main glacier parameters: the total net mass balance at annual and multi-annual intervals, the surface mass balance providing the link to atmospheric forcing, and ice export due to calving which is sensitive to changes in ice dynamics and ocean properties. The methods and capabilities of the TanDEM-X mission for delivering these parameters are described. The application is demonstrated for outlet glaciers of the Antarctic Peninsula that have been subject to major dynamic instability in recent years after collapse of buttressing ice shelves.

In this paper we present results from the tomographic analysis of L-Band SAR data acquired in February/March 2014 over the Mittelbergferner glacier, Austrian Alps, during the ESA campaign AlpTomoSAR. The campaign includes coincident in-situ measurements of snow and ice properties, as well as high-frequency Ground Penetrating Radar (GPR) data acquired over a total length of 18 km. The analyses of three-dimensional TomoSAR data cubes shows the complexity of the glacier sub-surface scattering. Most areas are characterized by surface scattering in proximity of the Lidar surface, plus a complex pattern of in-depth volumetric scattering beneath. Various subsurface features observed in GPR transects at 600 MHz and 200 MHz clearly showed up in TomoSAR sections as well. In particular: firn bodies, crevasses, and even the bedrock down to 50 m below the ice surface.

Spatial and temporal characteristics of Ku- and X-band backscatter signatures of Alpine snow are discussed and related to in situ snow observations. The radar data have been acquired with the airborne SnowSAR sensor over three test sites in the Austrian Alps during the AlpSAR campaign in winter 2012/13. An example for inversion of backscatter images in terms of snow water equivalent (SWE) is presented. The backscatter signatures of three test sites in different elevation zones show significant differences in terms of mean values and temporal trends during the winter season. These variations can be attributed to snow structure and to properties of the medium below the snow pack.

Observations of the 3D ice velocity field are important for studies of glacier hydraulics and for modeling the dynamic response of glaciers to changing boundary conditions. A method for 3D ice velocity retrieval from repeat pass SAR data of crossing orbits applying offset tracking in amplitude images is presented. In contrast to the conventional technique for ice motion mapping which assumes surface-parallel flow, this method delivers the true velocity vector. The procedure is validated using in-situ GPS data on an outlet glacier of the Vatnajökull ice cap in Iceland.

Well established techniques with partly automated processing workflows are in place to extract most relevant information about glaciers (area, elevation change, velocity) from a large variety of spaceborne sensors types (optical, microwave, altimeters). They generally provide complimentary information and are thus particularly useful when combined. With the recently launched (Cryosat-2, TanDEM-X) or planned (Sentinels 1 and 2, LDCM) satellite missions and the commitment to free data distribution by space agencies, the contribution of space-borne sensors to glacier monitoring will play an increasing role in the future.

Snow extent and water equivalent (SWE) on land and snow accumulation on glaciers are the main parameters to be delivered by the Cold Regions Hydrology High-resolution Observatory (CoReH2O) satellite. Detailed scientific and technical studies for the mission are going on within the Earth Explorer Programme of ESA. The CoReH2O sensor is a dual frequency SAR, operating at 17.2 and 9.6 GHz, VV and VH polarizations. A main task for mission preparation is the development and validation of algorithms for retrieval of snow parameters. A constrained minimization approach is proposed for SWE retrieval, matching backscatter computed with a radiative transfer model and measurements in the four SAR channels by iterating for SWE and snow grain size. The algorithm was validated with simulated and measured backscatter data. The tests confirm the feasibility of the retrieval approach and help to quantify the requirements for statistical background information which is needed for constraining the solution.

In this paper, how typical snowpack parameters with layering processes affect to the sensitivity of X- and Ku-band backscatter to the increase of SWE (Snow Water Equivalent) was analyzed. A particular motivation of this work was to contribute to the development of the geophysical algorithm of CoReH2O, a proposed ESA SAR mission currently in Phase A [1][2]. DSLDMRT forward backscatter model for microwave backscatter from snow covered terrain was used in analysis. The software is based on a second order radiative transfer model using the dense medium approach [3]. The analyses showed that the layering of snowpack changes the sensitivity of backscatter to SWE. A layer of refrozen at the bottom of snow pack (resulting from thaw-refreeze cycles at early winter) can cause a negative correlation of backscatter with the increase SWE for the beginning of the dry snow accumulation period. The positive correlation between snow grain size and SWE, typical for the temporal metamorphosis, increases the correlation between SWE and backscattering coefficient.

The acquisition of Snow Water Equivalent (SWE) at spatial resolutions higher than those of the present methods relying on inversion of coarse-scale passive microwave observations is a possible application for space-borne SAR imagery. The presented experimental campaign NoSREx (Nordic Snow Radar Experiment) was initiated to contribute to the knowledge of snowpack backscattering and emission properties, in particular, to help develop methods to retrieve SWE from high-resolution two-frequency SAR observations (at X and Ku band). Another objective was to provide data for studies exploring the synergistic use of active and passive microwave observations for monitoring of snow properties. The NoSREx campaign began in November 2009, and has recently concluded a second winter period of observations.

Ice velocities mapped by means of TerraSAR-X images in combination with surface elevation profiles measured by the altimeter system of ICESat are used to estimate glacier thinning and the increased calving flux after collapse of northern Larsen Ice Shelf on the Antarctic Peninsula in 1995 and 2002. InSAR analysis of one-day repeat pass SAR images from the ERS-l/ERS-2 tandem mission of 1995 and 1999 are these basis for retrieving the mass fluxes in the pre- collapse state. Applications of the various satellite data are shown for analysing the mass deficit and ice flow properties of Crane Glacier after disintegration of Larsen-B Ice Shelf. The ice flow acceleration shows a similar pattern for all calving glaciers on Larsen_B. The highest acceleration is observed at the front, decreasing upstream. Due to dynamic thinning at the frontal sections all main glaciers are now floating. This condition and the ongoing mass depletion will cause further frontal retreat in the coming years.

The main aim of this work is to adapt the ratio-technique for snow cover mapping developed for C-band to the X-band and high resolution COSMO-SkyMed images. This algorithm, aimed at detecting wet snow, is based on the difference in backscattering coefficients between snow- covered areas in winter images and snow-free summer images. For these purposes, a series of COSMO-SkyMed acquisitions (Stripmap PingPong mode, dual polarizations VV-VH) has been planned and acquired over the test site located in South Tyrol (Northern Italy) in correspondence of the melting and winter season. Contemporary to radar passes field campaigns have been performed. The objective is to test the sensitivity of X-band data to different snow conditions. An analysis has been carried out to find the most suitable filtering technique which allows a clearer distinction of distributions of backscattering coefficients of snow-covered and snow-free areas. Based on this analysis a first map of snow from the images acquired on 26-27 April 2010 (wet snow) was derived and compared with snow cover area derived from LANDSAT ETM+ of 20-04-2010 based on NDSI. Further statistical analysis will be carried out also considering the new acquisitions.

SIGNAL is an innovative earth exploration mission proposal with the main objective to estimate accurately and repeatedly topography and topographic changes associated with mass change or other dynamic effects on glaciers, ice caps and polar ice sheets. Elevation measurements are complemented with glacier velocity measurements, providing valuable additional information for a better understanding of the hydrology of glacierized basins and of the Arctic and Antarctic water cycle. SIGNAL is capable of monitoring all critical regions with a high spatial resolution and an adequate revisit time. This paper gives an overview about the actual mission design status and provides a brief description of the topography (DEM - digital elevation map) self-calibration strategy and the estimated global interferometric performance.

We present initial results from an experimental campaign aiming to acquire a comprehensive, full-snow season dataset of simultaneous backscatter and brightness temperature measurements of snow covered ground. The campaign is a part of Phase A activities in support of the proposed CoReH2O mission, aiming both to contribute to investigations on interpreting snow properties from active microwave observations, and to explore the possibilities for synergistic use of active measurements with existing passive microwave instruments. The campaign period covers the winter season of 2009-2010. Microwave observations are complemented by detailed in situ data of snow cover properties.

The ESA project GlobSnow develops products and services for snow extent and snow water equivalent. The time series of Snow Extent (SE) products will cover the whole seasonally snow-covered Earth for the years 1995-2010 based on the optical sensors ERS-2 ATSR-2 and Envisat AATSR data. A laboratory processing chain has been developed for testing and improving algorithms in an iterative process. The final version of the laboratory processing chain will function as a reference system for the implementation of an operational system for production of the full time series of products as well as near-real-time products produced on a daily basis. The first version of the SE product set spanning 15 years of the Northern Hemisphere is expected to be ready by the end of 2010 and will be made freely available.

Snow is a critical component of the global water cycle and climate system, and a major source of water supply in many parts of the world. There is a lack of spatially distributed information on the accumulation of snow on land surfaces, glaciers, lake ice, and sea ice. Satellite missions for systematic and global snow observations will be essential to improve the representation of the cryosphere in climate models and to advance the knowledge and prediction of the water cycle variability and changes that depend on snow and ice resources. This paper describes the scientific drivers and technical approach of the proposed Cold Regions Hydrology High-Resolution Observatory (CoReH2O) satellite mission for snow and cold land processes. The sensor is a synthetic aperture radar operating at 17.2 and 9.6 GHz, VV and VH polarizations. The dual-frequency and dual-polarization design enables the decomposition of the scattering signal for retrieving snow mass and other physical properties of snow and ice.

An incoherent amplitude correlation approach is used to derive ice motion fields of three major outlet glaciers of the Patagonia Icefields. High resolution repeat pass TerraSAR-X data of 2008 and 2009 were analyzed. The strong gradients in ice velocity of the terminus of San Rafael glacier, ranging from 2 to 16 m d-1, were captured well. Significant acceleration of the ice flow and losses in mass were observed for Upsala glacier.

Techniques for the retrieval of snow properties from Ku- and X-band radar backscatter measurements were investigated. The work contributes to feasibility studies for the CoReH2O satellite mission of ESA for which a dual frequency SAR, operating at Ku-band (17.2 GHz) and X-band (9.6 GHz), VV and VH polarizations, is proposed. A main parameter to be measured is the snow water equivalent (SWE). For the retrieval of SWE it is necessary to separate the backscatter contributions of the snow volume and the background target and to account for effects of snow grain size. The current version of the SWE retrieval algorithm applies the maximum likelihood approach matching radiative transfer forward computations with measured backscatter data. An application example for SWE retrieval is shown for the Cold Land Processes Experiment (CLPX-II) in Alaska, using Ku-band data of the NASA-JPL PolScat and X-band data of the TerraSAR-X satellite as input.

The Aerosol Land Mission (AERL) has been investigated within a study on concepts for advanced techniques that are compatible with implementation on a small satellite in the 150–200 kg range of total mass. AERL addresses the need for improved observations of atmospheric aerosol over land surfaces for air pollution control and climate research. The mission employs two instruments for multidirectional and multispectral measurements of reflected solar radiance. For measuring the columnar aerosol optical depth and properties a triple-view spectral imager with narrow band-pass filters in the 420 nm–910 nm spectral range is applied. Information on vertical layering of aerosol is obtained by dual view measurements of a grating spectrometer in the 757 nm–775 nm spectral range (oxygen A band).

In this paper, we report on an experimental activity aimed at investigating the potential of two terrestrial remote-sensing techniques, namely, ground-based SAR (GB SAR) interferometry and terrestrial laser scanning, in order to retrieve snow-depth (SD) measurements in mountainous regions. Terrestrial laser scanning is a more consolidated technique based on the measurement of the optical (near infrared) reflectivity, and it is affected by the surface of the snow layer: a temporal data sequence allows us to estimate the absolute SD variation. Recent use of SAR interferometry to evaluate snow-mass characteristics is based on relating the measured interferometric phase shift to a change in the snow mass. Interferometric GB SAR measurements and terrestrial laser scanner scans were collected together with pointwise conventional measurements of physical snow parameters during the winters of 2005/2006 and 2006/2007. The experiment was carried out in the Wattener Lizum, a high Alpine area at about 2000-m elevation north of the main ridge of the Austrian Alps in Tyrol. Notwithstanding the difficulty of providing both lengthy data record in dry snow conditions and detailed knowledge of the observed snow characteristics, the obtained results confirmed the presence of a clearly measurable interferometric phase variation in relation to the growing height of the snow layer. A comparison of the SD maps obtained through the two techniques shows differences partly due to the different nature of the two observations.

The capabilities of TerraSAR-X data for feature tracking by amplitude correlation over glacier surfaces are investigated. Methodical aspects of the amplitude correlation approach are described. The TerraSAR-X based velocity fields are compared with former InSAR derived velocities and field measurements on three outlet glaciers on the South Patagonia ice field.

The retrieval of snow parameters, and snow water equivalent in particular, are key parameters in hydrology and climate research. Theory, ground-based signature research and analysis of spaceborne scatterometry suggests that the high- frequency combination of Ku- and X-band active microwave sensors is an excellent tool for the retrieval of snow physical properties. In order to validate this, a snow measurement campaign was carried out with the University of Cranfield's portable Ground-Based Synthetic Aperture Radar (GB-SAR) System during the winter of 2006/7 at two test-sites in the Austrian Alps close to Innsbruck. Fully polarimetric X-and Ku-band backscatter signatures were acquired over a range of incidence angles (~20deg-70deg), with the active sensor operating predominately in SAR mode, but occasionally also in InSAR mode. Microwave signatures and snow properties were measured on seven different dates. Detailed complementary meteorological and snow metamorphic conditions were also recorded.

Taking into account the needs for improved, spatially detailed observations of snow and ice in climate research, hydrology, and glaciology, the satellite mission COld REgions Hydrology High-resolution Observatory, CoRe-H2O, was proposed to ESA. As payload a co- and cross-polarized Ku-band (17.2 GHz) and X-band (9.6 GHz) SAR was selected, because of its sensitivity to dry snow, thin sea ice, and the metamorphic state of snow, firn and ice on glaciers and ice caps. A cost-effective ScanSAR scheme with parabolic reflectors (each with multiple beams) is proposed fulfilling the requirements for swath width, spatial resolution and radiometry. The mission has been selected by ESA for further scientific and technical studies in the frame of the Earth Explorer Satellite Programme.

Time series of satellite radar image data of Envisat ASAR were used to study the retreat of ice shelves and glaciers at northern Larsen Ice Shelf,Antarctic Peninsula, up to March 2007. After the disintegration event in March 2002, the small remaining ice shelf section of Larsen B decreased further in area. The retreat of grounded glacier ice continued also. The glacier velocities above previous Larsen B increased further since 2004, but the acceleration has been smaller than in the first two years after the collapse in 2002. Ice export increased rapidly after the glaciers started to calve directly into the ocean. The sea level contribution due to discharge of grounded ice above the disintegrated ice shelf sections amounts to about 6% of the present glacier and ice sheet contribution to sea level rise.

Methods and applications of differential SAR interferometry (DINSAR) for detecting and monitoring slow movements of mountain slopes on the order of centimeters per year were investigated in the Austrian and Swiss Alps, using SAR images from the European ERS-1 and ERS-2 satellites. The DINSAR analysis methods and criteria for selecting SAR image pairs suitable for landslide monitoring are briefly described. Most of the detected landslides are above the tree line, because on surfaces with sparse vegetation and bare soil or rock the coherence is preserved over long periods. The investigations confirm the operational potential of DINSAR for detecting and monitoring mass movements in high Alpine areas.

An algorithm has been developed for mapping wet snow in mountainous terrain using repeat pass synthetic aperture radar (SAR) images. As a basis for algorithm development, backscattering properties of snow-free and snow-covered alpine surfaces were investigated using ERS SAR data and field measurements at test sites in the Austrian Alps. The incidence angle dependence of backscattering derived from SAR data is compared with simulations for snow-free surfaces and for surfaces covered by dry snow and wet snow. Significant seasonal changes of backscattering are observed, which are mainly caused by variations of the snow liquid water content and of the surface roughness. The importance of surface roughness for backscattering of wet snow is demonstrated by a surface roughness experiment. The algorithm for mapping wet snow applies change detection using ratios of wet snow versus snow-free or dry snow surfaces. The main steps include coregistration, speckle reduction, thresholding of ratio images, geocoding, and, optionally, combination of crossing passes to reduce the loss of information due to layover. A threshold of -3 dB was found to be appropriate for both Radarsat and ERS SAR to separate wet snow from other surfaces. Postprocessing steps, based on historic snow maps or topographic information, are used to correct for dry snow areas at high elevations. Effects of imaging geometry are investigated by comparing ERS SAR images with a look angle of 19/spl deg/ and Radarsat SAR Beam Mode S7 images with a look angle of 40/spl deg/. The comparison of snow maps from SAR and Landsat-5 Thematic Mapper images shows good agreement in areas of closed snow cover, whereas near the snow line/SAR tends to slightly underestimate the snow extent.