Kristoffer Aalstad

• Alonso-Gonzalez, Esteban; Gutmann, Ethan; Aalstad, Kristoffer; Fayad, Abbas; Bouchet, Marine & Gascoin, Simon (2021). Snowpack dynamics in the Lebanese mountains from quasi-dynamically downscaled ERA5 reanalysis updated by assimilating remotely sensed fractional snow-covered area. Hydrology and Earth System Sciences. ISSN 1027-5606. 25, s. 4455–4471. doi: 10.5194/hess-25-4455-2021. Vis sammendrag

  The snowpack over the Mediterranean mountains constitutes a key water resource for the downstream populations. However, its dynamics have not been studied in detail yet in many areas, mostly because of the scarcity of snowpack observations. In this work, we present a characterization of the snowpack over the two mountain ranges of Lebanon. To obtain the necessary snowpack information, we have developed a 1 km regional-scale snow reanalysis (ICAR_assim) covering the period 2010–2017. ICAR_assim was developed by means of an ensemble-based data assimilation of Moderate Resolution Imaging Spectroradiometer (MODIS) fractional snow-covered area (fSCA) through an energy and mass snow balance model, the Flexible Snow Model (FSM2), using the particle batch smoother (PBS). The meteorological forcing data were obtained by a regional atmospheric simulation from the Intermediate Complexity Atmospheric Research model (ICAR) nested inside a coarser regional simulation from the Weather Research and Forecasting model (WRF). The boundary and initial conditions of WRF were provided by the ERA5 atmospheric reanalysis. ICAR_assim showed very good agreement with MODIS gap-filled snow products, with a spatial correlation of R=0.98 in the snow probability (P(snow)) and a temporal correlation of R=0.88 on the day of peak snow water equivalent (SWE). Similarly, ICAR_assim has shown a correlation with the seasonal mean SWE of R=0.75 compared with in situ observations from automatic weather stations (AWSs). The results highlight the high temporal variability in the snowpack in the Lebanese mountain ranges, with the differences between Mount Lebanon and the Anti-Lebanon Mountains that cannot only be explained by hypsography as the Anti-Lebanon Mountains are in the rain shadow of Mount Lebanon. The maximum fresh water stored in the snowpack is in the middle elevations, approximately between 2200 and 2500 m a.s.l. (above sea level). Thus, the resilience to further warming is low for the snow water resources of Lebanon due to the proximity of the snowpack to the zero isotherm.

• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2020). Evaluating satellite retrieved fractional snow-covered area at a high-Arctic site using terrestrial photography. Remote Sensing of Environment. ISSN 0034-4257. 239. doi: 10.1016/j.rse.2019.111618. Fulltekst i vitenarkiv
• Fiddes, Joel; Aalstad, Kristoffer & Westermann, Sebastian (2019). Hyper-resolution ensemble-based snow reanalysis in mountain regions using clustering. Hydrology and Earth System Sciences. ISSN 1027-5606. 23(11), s. 4717–4736. doi: 10.5194/hess-23-4717-2019. Fulltekst i vitenarkiv
• Yilmaz, Yeliz; Aalstad, Kristoffer & Sen, Omer L. (2019). Multiple remotely sensed lines of evidence for a depleting seasonal snowpack in the near east. Remote Sensing. ISSN 2072-4292. 11(5). doi: 10.3390/rs11050483. Fulltekst i vitenarkiv
• Aalstad, Kristoffer; Westermann, Sebastian; Schuler, Thomas; Boike, Julia & Bertino, Laurent (2018). Ensemble-based assimilation of fractional snow-covered area satellite retrievals to estimate the snow distribution at Arctic sites. The Cryosphere. ISSN 1994-0416. 12(1), s. 247–270. doi: 10.5194/tc-12-247-2018. Fulltekst i vitenarkiv Vis sammendrag

  With its high albedo, low thermal conductivity and large water storing capacity, snow strongly modulates the surface energy and water balance, which makes it a critical factor in mid- to high-latitude and mountain en- vironments. However, estimating the snow water equiva- lent (SWE) is challenging in remote-sensing applications al- ready at medium spatial resolutions of 1km. We present an ensemble-based data assimilation framework that estimates the peak subgrid SWE distribution (SSD) at the 1km scale by assimilating fractional snow-covered area (fSCA) satel- lite retrievals in a simple snow model forced by downscaled reanalysis data. The basic idea is to relate the timing of the snow cover depletion (accessible from satellite products) to the peak SSD. Peak subgrid SWE is assumed to be log- normally distributed, which can be translated to a modeled time series of fSCA through the snow model. Assimilation of satellite-derived fSCA facilitates the estimation of the peak SSD, while taking into account uncertainties in both the model and the assimilated data sets. As an extension to previ- ous studies, our method makes use of the novel (to snow data assimilation) ensemble smoother with multiple data assimi- lation (ES-MDA) scheme combined with analytical Gaussian anamorphosis to assimilate time series of Moderate Reso- lution Imaging Spectroradiometer (MODIS) and Sentinel-2 fSCA retrievals. The scheme is applied to Arctic sites near Ny-Ålesund (79◦ N, Svalbard, Norway) where field measure- ments of fSCA and SWE distributions are available. The method is able to successfully recover accurate estimates of peak SSD on most of the occasions considered. Through the ES-MDA assimilation, the root-mean-square error (RMSE) for the fSCA, peak mean SWE and peak subgrid coefficient of variation is improved by around 75, 60 and 20%, re- spectively, when compared to the prior, yielding RMSEs of 0.01, 0.09m water equivalent (w.e.) and 0.13, respectively. The ES-MDA either outperforms or at least nearly matches the performance of other ensemble-based batch smoother schemes with regards to various evaluation metrics. Given the modularity of the method, it could prove valuable for a range of satellite-era hydrometeorological reanalyses.

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• Salzano, Roberto; Aalstad, Kristoffer; Boldrini, Enrico; Gallet, Jean-Charles; Kepski, Daniel & Luks, Bartlomiej [Vis alle 9 forfattere av denne artikkelen] (2021). Terrestrial photography applications on snow cover in Svalbard (PASSES), The State of Environmental Science in Svalbard. Svalbard Integrated Arctic Earth Observing System. ISSN 978-82-93871-00-2. s. 236–251. doi: 10.5281/zenodo.4294084.
• Salzano, Roberto; Aalstad, Kristoffer; Boldrini, Enrico; Gallet, Jean-Charles; Kȩpski, Daniel & Luks, Bartlomiej [Vis alle 9 forfattere av denne artikkelen] (2021). Terrestrial photography applications on snow cover in Svalbard (PASSES), The State of Environmental Science in Svalbard. Svalbard Integrated Arctic Earth Observing System. ISSN 978-82-93871-00-2. s. 236–251. doi: 10.5281/zenodo.4294084.
• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Bazilova, Varvara; Bertino, Laurent; Fiddes, Joel & Filhol, Simon [Vis alle 9 forfattere av denne artikkelen] (2021). Unmixing satellite imagery using data assimilation to map snow and albedo.
• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Bertino, Laurent; Fiddes, Joel; van Hove, Alouette & Pirk, Norbert [Vis alle 8 forfattere av denne artikkelen] (2021). Learning from Earth observations using data assimilation.
• Aalstad, Kristoffer; Westermann, Sebastian; Pirk, Norbert; Fiddes, Joel & Bertino, Laurent (2021). Retrieving fractional snow-covered area from optical satellites using data assimilation. Vis sammendrag

  Mapping from noisy observations to the latent states that may have generated them falls under the umbrella of inverse problems. These problems are abundant in Earth system science since our uncertain mechanistic models need to be fully specified while the system is only partially and imperfectly observed. Combined with a steadily growing observing system, this abundance has fueled the development of probabilistic Data Assimilation (DA) schemes that use Bayesian inference to fuse uncertain information from models and observations. Widely used applications of DA include the production of global atmospheric reanalyses and initializing numerical weather predictions. At the same time, the added value that DA can bring to remote sensing as a generalized framework for building retrieval algorithms remains largely untapped. In our contribution, we demonstrate the potential of data assimilation in the task of retrieving fractional snow-covered area (fSCA) from multispectral satellite imagery from moderate (MODIS) and higher (Sentinel-2 MSI, Landsat 8 OLI) optical sensors. In this analysis, we build on our previous work by focusing on the Bayelva catchment near Ny-Ålesund we have access to independent high-quality validation data obtained from terrestrial photography. We show how the general problem of linear spectral unmixing that is widely used for land cover classification can be recast as a Bayesian inverse problem. This can then be readily solved using ensemble-based data assimilation schemes, where we test both vanilla and sophisticated flavors of the particle filter and the ensemble Kalman filter, as well as Markov chain Monte Carlo benchmarks. By solving the problem in a transformed parameter space, the physical constraints of spectral unmixing are satisfied while reducing the need for ad hocery. The Bayesian data assimilation fSCA retrieval approach lets us deal with ill-posedness, incorporate physical knowledge, and account for uncertainty in the observed reflectances. It performs favorably compared to widely used techniques for fSCA retrieval such as thresholding of the NDSI, regression on the NDSI, and classical (non-negative least squares) spectral unmixing. This method is also much more scalable than classical unmixing since iterations are pre-determined and can fully exploit vectorization. Furthermore, it does not require any tuning on in-situ observations and it can also be used to solve the endmember selection problem using the concept of model evidence. Crucially, the retrieved fSCA includes dynamic uncertainty estimates that are required for satellite retrievals to be of any use in dynamic data assimilation frameworks. We envisage further validation by leveraging the network of terrestrial cameras operated by our partners in the PASSES consortium (Salzano et al., 2021; SESS Report 2021, Ch. 10). Our aim is to exploit these satellite retrievals in our ongoing efforts to produce tailored high resolution permafrost and snow reanalyses in cold regions, including Svalbard. At the same time, the approach outlined here could also be modified to retrieve surface albedo and (sub-pixel) land cover globally with even broader implications to Earth system science.

• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Bazilova, Varvara; Bertino, Laurent; Fiddes, Joel & Pirk, Norbert [Vis alle 7 forfattere av denne artikkelen] (2021). Leveraging emerging Earth observations using data assimilation. Vis sammendrag

  The task of mapping from noisy observations to the states that (given a forward model) may have generated them falls under the umbrella of inverse problems. These problems are abundant in Earth system science since our uncertain mechanistic models need to be fully specified while the system is only partially and imperfectly observed. This abundance has, combined with a steadily growing observing system, fueled the development of probabilistic Data Assimilation (DA) schemes that use Bayesian inference to fuse uncertain information from models and observations. Notable operational applications of DA include the production of global atmospheric reanalyses and initializing numerical weather predictions. Perhaps less appreciated is the added value that DA can bring to Earth Observations (EO) as a generalized framework for building retrieval algorithms. In our work we present two completely different inverse problems that show how DA can help us to make the most out of emerging EO. The first problem is snowpack reconstruction where we constrain snow models using highly informative observations of the dynamics of snow cover depletion retrieved using satellite remote sensing. We provide examples assimilating retrievals from moderate (MODIS) and higher resolution (Landsat, Sentinel-2, PlanetScope cubesats) optical sensors as well as from all-weather radar data (Sentinel-1) in the Californian Sierra Nevada, Svalbard, Finse, the Pyrenees, the Swiss Alps, and Lebanon. This method is being developed to build tailored snow and permafrost reanalysis frameworks that lead to improved global cryospheric mapping capabilities and provide new benchmarks for Earth system models. The second problem is flux inversion where we seek to infer surface fluxes of carbon, water, and heat using a drone swarm that provides distributed measurements of temperature, gas concentrations, and wind in the atmospheric boundary layer. To achieve this, we assimilate drone data into various boundary layer models, building up complexity from analytical flux-profile relationships based on the widely used Monin-Obukhov Similarity Theory to turbulence resolving large eddy simulations. Through flux inversion with the latter the hope is that we will be able to map fluxes in highly heterogeneous landscapes at the scale of Earth system models (10 km). This is not possible with existing methods like eddy covariance and can thereby shed new light on the role of flux heterogeneities in land-atmosphere coupling. When solving these problems we test various probabilistic DA schemes including variants of the ensemble Kalman filter, the particle filter, and Markov chain Monte Carlo. These schemes have been adapted to our problems by casting them as smoothers that condition the model on future observations, rather than as sequential filters, which crucially allows information to propagate backwards in time. We also emphasize how we can use DA to move beyond the usual first level of inference where we “fit” our model to data, up to the second level of inference where we can compare different competing model structures and parametrizations using the model evidence framework.

• Aalstad, Kristoffer; Fiddes, Joel; Martin, Leo Celestin Paul; Alonso-Gonzalez, Esteban; Yilmaz, Yeliz A. & Pirk, Norbert [Vis alle 7 forfattere av denne artikkelen] (2021). Workshop on downscaling with TopoSCALE for cryospheric applications. Vis sammendrag

  Meteorological forcing data is a crucial ingredient when modeling the past, present, and future state of the cryosphere. At the same time, cold regions (i.e. the high elevations and/or latitudes of our planet) where most of the cryosphere is found are typically remote with a very low density of in-situ observations. The few meteorological stations that do exist are typically quite unrepresentative due to the often extreme surface heterogeneity and complex terrain in these regions. This makes empirical-statistical and geostatistical downscaling techniques that rely heavily on station data somewhat impractical for cryospheric applications. On the other side of the scale, we have dynamical downscaling techniques that rely on using sophisticated regional climate models to downscale historical global reanalysis data or projections from global climate models. Although these are not as dependent on local observations in that they are able to mechanistically model the state of the atmosphere, they are prohibitively expensive to run at the decadal timescales and hillslope (1 km - 100 m) spatial scale that is often sought in cryospheric applications. In this workshop, we will provide an overview of various downscaling techniques and introduce the topography-based downscaling routine TopoSCALE as well as its many applications and downstream methods listed below. TopoSCALE was developed to provide a computationally feasible technique for generating hourly hillslope scale atmospheric forcing for cryospheric modeling from global reanalysis data or other atmospheric model outputs, without the need for in-situ data. It relies heavily on topographic parameters derived from digital elevation models to be able to scale the input atmospheric forcing to the local topography. It has been tested quite extensively in a variety of environments, including: the Swiss Alps, Svalbard, the California Sierra Nevada, and High Mountain Asia. TopoSCALE is also being used as part of ongoing permafrost reanalysis efforts in the ESA Permafrost_CCI project. The scheme can be coupled to a clustering framework (TopoSUB) which can speed up distributed simulations by orders of magnitude compared to the more traditional gridded approach to land surface modeling. TopoSCALE can also be used together with bias-correction techniques to help downscale future regional climate projections to the hillslope scale with applications to cryospheric climate impact studies. Recent and ongoing applications of TopoSCALE together with snow data assimilation have been particularly fruitful in being able to handle biases in solid precipitation, which has been one of the most challenging problems for downscaling in cryospheric applications. Importantly, TopoSCALE lets modellers shift limited computational resources away from the downscaling exercise to probing uncertainties through ensemble simulations and constraining these with Earth observations.

• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon; Gascoin, Simon; Stordal, Frode & Tallaksen, Lena M. (2021). Probing Fennoscandian Snow Cover Dynamics in the Community Land Model and Climate Reanalyses during the Satellite Era.
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon; Gascoin, Simon; Stordal, Frode & Tallaksen, Lena M. (2021). Benchmarking CLM5 snow cover dynamics with MODIS and reanalyses over Fennoscandia .
• Aalstad, Kristoffer & Westermann, Sebastian (2020). ACS_Bayelva_class: 302 high-resolution snow cover maps covering the 2012-2017 snowmelt seasons in the Bayelva catchment (Svalbard, Norway). Vis sammendrag

  The ACS_Bayelva_class dataset contains 302 high-resolution binary snow cover images that were obtained by classifying orthrorectified photographs of a 1.77 km^2 area of interest in the Bayelva catchment. This catchment is close to Ny-Ålesund, the northernmost permanent civilian settlement in the world and a major hub for polar research, in the Norwegian high-Arctic Svalbard archipelago. The imagery has a (roughly) daily temporal resolution and a ground sampling distance (pixel spacing) of 0.5 m. The dataset spans 6 snowmelt seasons, covering the months May-August for the period 2012-2017. The orthophotos were obtained by processing oblique time-lapse photographs taken by a terrestiral automatic camera system (ACS) mounted at 562 m a.s.l. near the summit of Scheteligfjellet (719 m a.s.l.) a few kilometers west of Ny-Ålesund. The orthophotos were manually classified into binary snow cover images (0=no snow, 1=snow) by iteratively selecting a (visually) optimal threshold on the intensity in the blue band for each image. More details are provided in the study of Aalstad et al. (2020) [a copy is available in this repository] where this dataset was created. The ACS was maintained by scientists from the group of Sebastian Westermann at the Section for Physical Geography and Hydrology in the Department of Geosciences at the University of Oslo, Oslo, Norway.

• Aalstad, Kristoffer; Westermann, Sebastian; Fiddes, Joel; Karsten, Logan; McCreight, James & Bertino, Laurent (2020). Testing ensemble-based snow reanalysis in the Lakes basin using the ASO.
• Aalstad, Kristoffer; Westermann, Sebastian; Pirk, Norbert; Fiddes, Joel; Karsten, Logan & McCreight, James [Vis alle 8 forfattere av denne artikkelen] (2020). Constraining land surface models with emerging observations.
• Aalstad, Kristoffer; Westermann, Sebastian; Fiddes, Joel; McCreight, James & Bertino, Laurent (2020). Retrieving, validating, and assimilating fractional snow-covered area from emerging optical satellites for snow reanalysis. Vis sammendrag

  Accurately estimating the snow water equivalent (SWE) that is stored in the worlds mountains remains a challenging and important unsolved problem. The SWE reconstruction approach, where the remotely sensed seasonal depletion of fractional snow-covered area (fSCA) is used with a snow model to build up the snowpack in reverse, has been used for decades to help tackle this problem retrospectively. Despite some success, this deterministic approach ignores uncertainties in the snow model, the meteorological forcing, and the remotely sensed fSCA. A trade-off has also existed between the desired temporal and spatial resolution of the satellite-retrieved fSCA depletion. Recently, ensemble-based data assimilation techniques that can account for the uncertainties inherent in the reconstruction exercise have allowed for probabilistic snow reanalyses. In addition, new higher resolution optical satellite constellations such as Sentinel-2 and the PlanetScope cubesats have been launched into polar orbit, potentially eliminating the aforementioned trade-off. We combine these two developments, namely ensemble-based data assimilation and the emerging remotely sensed data streams, to see if snow reanalyses can be improved at the hillslope (100 m) scale in complex terrain. As a first step, we develop accurate high-resolution binary snow-cover maps using a terrestrial automatic camera system installed on a mountaintop near Ny-Ålesund (Svalbard, Norway). These maps are used to validate fSCA retrieved from various satellite sensors (MODIS, Sentinel-2 MSI, and Landsat 8 OLI) using algorithms ranging from simple thresholding of the normalized difference snow index to spectral unmixing. Through the validation, we demonstrate that the spectral unmixing technique can obtain unbiased fSCA retrievals at the hillslope scale. Next, we move to the Mammoth Lakes basin in the Californian Sierra Nevada, USA, where we have access to independent validation data retrieved from several Airborne Snow Observatory (ASO) and Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) flights. Using these airborne retrievals as a reference, we show that fSCA can be retrieved at the hillslope scale with reasonable accuracy at an unprecedented near daily revisit period using a combination of the Landsat, Sentinel-2 MSI, RapidEye, and PlanetScope satellite constellations. In a series of data assimilation experiments we show how the combination of these constellations can lead to significant improvements in hillslope scale snow reanalyses as gauged by various evaluation metrics. Furthermore, it is suggested that an iterative ensemble smoother data assimilation scheme can provide more robust SWE estimates than other smoothers that have previously been proposed for snow reanalysis. We briefly conclude with thoughts as to the current impediments to conducting a global hillslope scale snow reanalysis and propose avenues for further research, such as how snow reanalyses can help in the prediction exercise.

• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon Vincent P; Stordal, Frode & Tallaksen, Lena M. (2020). The Representation of the Fennoscandian Snow Cover Phenology in Reanalyses and CLM5 during the MODIS-era. Vis sammendrag

  Snow plays an important role in cold regions through its effect on the terrestrial exchange of energy, water, and carbon. Accurately simulating snow processes is therefore important in capturing various climate feedbacks in Earth system models. The representation of the subgrid heterogeneity of snow properties (e.g. coverage, depth, density, albedo) are, in addition to accumulation and snowmelt, major sources of uncertainty in the snow modules of land surface schemes. Using multiple data sources is essential to address these uncertainties and to evaluate overall model performance. Unlike in-situ observations, satellite remote sensing products provide unique representative information at the scale of Earth system models. The Moderate Resolution Imaging Spectroradiometer (MODIS) sensor onboard the Aqua and Terra satellites provide a continuous long-term climate record for the last two decades. In this study, two daily snow cover data sets from MODIS (MOD10A1 and MYD10A1) were used to retrieve fractional snow-covered area (fSCA) and several snow cover metrics (e.g. snow cover duration, first and last day of snow) over Fennoscandia for the 2001-2020 water years. We use these retrievals to evaluate the fSCA outputs from multiple reanalyses (ERA5-Land, ERA5, and MERRA-2) and the latest version of the Community Land Model (CLM5) which is the land component of the Community Earth System Model (CESM) and the Norwegian Earth System Model (NorESM). In order to test the accuracy of the MODIS data, we employed Sentinel-2 and Landsat 8 satellite retrievals as well as local‐scale measurements around the Finse Eco-Hydrological Observatory (Finse EcHO), a low-alpine site in central Norway. Lastly, we compared the trends in snow cover metrics with terrestrial water storage anomalies obtained from the Gravity Recovery and Climate Experiment (GRACE) to better understand the regional water cycle dynamics over this region. This study provides a useful starting point for integrating Earth observations into Earth system modeling in cold regions to help identify and constrain sources of uncertainty. Acknowledgement : This study is conducted under the LATICE strategic research initiative funded by the Faculty of Mathematics and Natural Sciences at the University of Oslo, and the EMERALD (project #294948) funded by the Research Council of Norway.

• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon Vincent P; Stordal, Frode & Tallaksen, Lena M. (2020). Fennoscandian snow cover phenology from MODIS, CLM5, and climate reanalyses.
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon Vincent P; Stordal, Frode & Tallaksen, Lena M. (2020). Scandinavian snow cover phenology from MODIS, CLM, and reanalyses.
• Aalstad, Kristoffer; Westermann, Sebastian; Fiddes, Joel & Bertino, Laurent (2019). Retrieving the depletion of snow-covered area from multiple optical satellite sensors with applications for SWE reanalysis.
• Aalstad, Kristoffer; Westermann, Sebastian; Karsten, Logan; Gutmann, Ethan; McCreight, James & Fiddes, Joel [Vis alle 7 forfattere av denne artikkelen] (2018). Ensemble-based reanalysis of the seasonal montane snowpack: Lessons from the ASO.
• Aalstad, Kristoffer; Westermann, Sebastian; Karsten, Logan; Fiddes, Joel & Bertino, Laurent (2018). Snow history matching in mountainous terrain.
• Aalstad, Kristoffer; Westermann, Sebastian; Bertino, Laurent; Schuler, Thomas; Boike, Julia & Karsten, Logan (2018). Towards high-resolution Bayesian snow reconstruction in permafrost regions.
• Aalstad, Kristoffer; Westermann, Sebastian; Schuler, Thomas; Boike, Julia & Bertino, Laurent (2017). Ensemble-based subgrid snow data assimilation.
• Aalstad, Kristoffer; Westermann, Sebastian; Schuler, Thomas; Boike, Julia & Bertino, Laurent (2017). Towards High-Resolution SWE Mapping in Permafrost Regions.
• Aalstad, Kristoffer; Westermann, Sebastian; Schuler, Thomas; Boike, Julia & Bertino, Laurent (2017). Towards High-Resolution SWE Mapping in Permafrost Regions.
• Leclercq, Paul Willem; Aalstad, Kristoffer; Altena, Bas & Elvehøy, Hallgeir (2017). Modelling of glacier surface mass balance with assimilation of glacier mass balance and snow cover observations from remote sensing.
• Christakos, Konstantinos; Varlas, George; Cheliotis, Ioannis; Aalstad, Kristoffer; Papadopoulos, Anastasios & Katsafados, Petros [Vis alle 7 forfattere av denne artikkelen] (2017). Quantitative variability of renewable energy resources in Norway.
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2016). An ensemble-based subgrid snow data assimilation framework applied to the southern Swiss alps.
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2016). An ensemble-based subgrid snow data assimilation framework.
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2016). An ensemble-based snow data assimilation framework.
• Aalstad, Kristoffer; Westermann, Sebastian; Boike, Julia; Bertino, Laurent & Aas, Kjetil Schanke (2016). An ensemble-based snow data assimilation framework with applications to permafrost modeling.
• Schuler, Thomas; Aalstad, Kristoffer; Aas, Kjetil Schanke; Burkhart, John; Dunse, Thorben & Filhol, Simon [Vis alle 9 forfattere av denne artikkelen] (2016). Towards real-time snow products for Svalbard.
• Aalstad, Kristoffer; Bertino, Laurent & Westermann, Sebastian (2016). An ensemble-based subgrid snow data assimilation framework.
• Leclercq, Paul Willem; Aalstad, Kristoffer; Elvehøy, Hallgeir & Altena, Bas (2016). Assimilation of glacier mass balance and snow cover fraction observations in a glacier surface mass balance model.
• Leclercq, Paul Willem; Aalstad, Kristoffer; Elvehøy, Hallgeir & Altena, Bas (2016). Assimilation of glacier mass balance and snow cover fraction observations in a glacier surface mass balance model.
• Westermann, Sebastian; Langer, Moritz; Østby, Torbjørn Ims; Peter, Maria; Boike, Julia & Gisnås, Kjersti [Vis alle 12 forfattere av denne artikkelen] (2016). Mapping the thermal state of permafrost through modeling and remote sensing .
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2019). Ensemble-based retrospective analysis of the seasonal snowpack. University of Oslo. ISSN 1501-7710.
• Aalstad, Kristoffer & Berntsen, Terje Koren (2015). Applying the Eddy Covariance Method Under Difficult Conditions. University of Oslo.

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