Kristoffer Aalstad

• Virkkala, Anna-Maria; Wargowsky, Isabel; Vogt, Judith; Kuhn, McKenzie A.; Madaan, Simran & Windholz, Tiffany [Show all 269 contributors for this article] (2026). ABCFlux v2: Arctic–boreal CO2 and CH4 monthly flux observations and ancillary information across terrestrial and freshwater ecosystems. Earth System Science Data. ISSN 1866-3508. 18(9), p. 6357–6409. doi: 10.5194/essd-18-6357-2026. Full text in Research Archive Show summary

  Measurements of surface-atmosphere carbon dioxide (CO 2 ) and methane (CH 4 ) fluxes have been relatively sparse across the Arctic tundra and boreal biomes, causing significant uncertainties in carbon budget estimates from the region. While the availability of Arctic-boreal carbon flux data has increased substantially over the past decade, the data have remained spread across different repositories, scientific articles, and unpublished sources, making it difficult to leverage. Here we present a new dataset of monthly Arctic-boreal carbon fluxes (ABCFlux v2) across terrestrial (wetlands and uplands) and freshwater (lakes and rivers) ecosystems compiled from previous syntheses including the Arctic-boreal CO 2 flux database (ABCFlux v1), the Boreal-Arctic Wetland and Lake Methane Dataset (BAWLD-CH4), and the Global River Methane Database (GRiMeDB). In addition, we consider data from general-purpose (e.g., Zenodo) and flux network repositories, literature, and site principal investigators. The dataset includes surface-atmosphere CO 2 fluxes of gross primary production (GPP), ecosystem respiration (Reco), and net ecosystem exchange (NEE), alongside CH 4 fluxes. For aquatic ecosystems, we split CH 4 fluxes into diffusive and ebullitive flux pathways, and included potential emissions from transient storage in the water column (“storage fluxes”), alongside CO 2 and CH 4 concentrations dissolved in the surface water. Fluxes are measured through a variety of methods including chamber and eddy covariance techniques alongside bubble traps, ice-surveys, and concentration-based turbulence-driven modelling in aquatic ecosystems. The monthly flux data are reported together with supporting methodological and environmental metadata. The resulting ABCFlux v2 has 23 847 flux site-months, 8182 concentration site-months, and 199 seasonal observations from 1024 sites, and includes 56 139 reported fluxes (i.e. sum of GPP, Reco, NEE, and CH 4 fluxes) from the years 1984 to 2024. The majority of monthly observations occurred after 1999. Wetlands had the highest number of site-month observations (8758), followed by boreal forest (6981), lotic ecosystems (6275), lentic ecosystems (3799) and upland tundra (3308). Measurements of CO 2 dominated the dataset across most ecosystem types (25 222) except for lentic ecosystems, where CH 4 flux site-months (3098) were more frequent than CO 2 flux site-months (2915). Overall, ABCFlux v2 includes 160 % more site-months for terrestrial CO 2 flux data compared to ABCFlux v1. Integrating and updating BAWLD-CH4 flux data from growing season averages to monthly fluxes resulted in 5671 site-months of chamber CH 4 data compared to 762 site-years. This collaborative initiative, involving contributions from over 260 researchers, provides a comprehensive overview of the current state of the Arctic-boreal carbon flux network and its data, and serves as an important step in reducing uncertainties in Arctic-boreal carbon budgets and in enhancing our understanding of climate feedbacks. The data can be accessed at ORNL DAAC at https://doi.org/10.3334/ORNLDAAC/2448 (Virkkala et al., 2026).

• Aalstad, Kristoffer; Alonso-González, Esteban; Pirk, Norbert; Westermann, Sebastian; Willmes, Clarissa & Yang, Ruitang (2026). Evolving beyond collapse: an adaptive particle batch smoother for cryospheric data assimilation. Geoscientific Model Development. ISSN 1991-959X. 19(18), p. 8565–8596. doi: 10.5194/gmd-19-8565-2026. Full text in Research Archive Show summary

  We present a new adaptive particle-based data assimilation scheme for cryospheric applications that leverages promising developments in importance sampling. The proposed approach seeks to combine some of the advantages of two widely used classes of schemes: particle methods and iterative ensemble Kalman methods. Specifically, it extends the Particle Batch Smoother (PBS) that is commonly used in cryospheric data assimilation, with the Adaptive Multiple Importance Sampling algorithm. This adaptive formulation transforms the PBS into an iterative scheme with improved resilience against ensemble collapse and the ability to implement early-stopping strategies. As such, computational cost is automatically adapted to the complexity of the problem at hand, even down to the grid-cell and water year level in distributed multiyear simulations. In homage to the schemes that it builds on, we coin this new algorithm the Adaptive Particle Batch Smoother (AdaPBS) and we test it across a range of scenarios. First, we conducted an intercomparison of some of the most commonly used cryospheric data assimilation algorithms using Markov Chain Monte Carlo (MCMC) simulation as a costly gold-standard benchmark in a simplified temperature index model assimilating snow depth observations. We further evaluated AdaPBS by assimilating snow depth observations from the ESMSnowMIP project at 6 different sites spanning 3 continents, using an ensemble of simulations generated with the more complex Flexible Snow Model (FSM2). Our results demonstrate that AdaPBS is a robust and reliable tool, outperforming or at least matching the performance of other commonly used algorithms and successfully handling complex cases with dense observational datasets. All experiments were carried out using the open-source Multiple Snow Data Assimilation System (MuSA) toolbox, which now includes AdaPBS and MCMC among the growing list of available cryospheric data assimilation methods. Beyond our cryospheric focus, the scheme has the potential to be applied directly to the closely related fields of land surface and hydrological data assimilation as well as more general geoscientific Bayesian inference problems.

• Hove, Alouette van; Aalstad, Kristoffer & Pirk, Norbert (2026). Actively inferring methane sources with drones. Environmental Data Science (EDS). 5. doi: 10.1017/eds.2026.10029. Full text in Research Archive Show summary

  This study presents a framework that combines Bayesian inference with reinforcement learning to guide drone-based sampling for methane source estimation. Synthetic gas concentration and wind observations are generated using a calibrated model derived from real-world drone measurements, providing a more representative testbed that captures atmospheric boundary layer variability. We compare three path planning strategies—preplanned, myopic (short-sighted), and non-myopic (long-term)—and find that non-myopic policies trained via deep reinforcement learning consistently yield more precise and accurate estimates of both source location and emission rate. We further investigate centralized multi-agent collaboration and observe comparable performance to independent agents in the tested single-source scenario. Our results suggest that effective source term estimation depends on correctly identifying the plume and obtaining low-noise concentration measurements within it. Precise localization further requires sampling in close proximity to the source, including slightly upwind. In more complex environments with multiple emission sources, multi-agent systems may offer advantages by enabling individual drones to specialize in tracking distinct plumes. These findings support the development of intelligent, data-driven sampling strategies for drone-based environmental monitoring, with potential applications in climate monitoring, emission inventories, and regulatory compliance.

• Alonso-González, Esteban; Harpold, Adrian; Lundquist, Jessica D.; Piske, Cara; Sourp, Laura & Aalstad, Kristoffer [Show all 7 contributors for this article] (2026). Ensemble-based data assimilation improves hyperresolution snowpack simulations in forests. The Cryosphere. ISSN 1994-0416. 20, p. 209–225. doi: 10.5194/tc-20-209-2026. Full text in Research Archive Show summary

  Snowpack dynamics play a key role in controlling hydrological and ecological processes at various scales, but snow monitoring remains challenging. Data assimilation techniques are emerging as promising tools to improve uncertain snowpack simulations by fusing state-of-the-art numerical models with information rich, but noisy observations. However, the occlusion of the ground below the forest canopy limits the retrieval of snowpack information from remote sensing tools. Remote sensing observations in these environments are spatially incomplete, impeding the implementation of fully distributed data assimilation techniques. Here we propose different experiments to propagate the information obtained in forest clearings, where it is possible to retrieve observations, towards the sub-canopy, where the point of view of remote sensors is occluded. The experiments were conducted in forests within Sagehen Creek watershed (California, USA), by updating simulations conducted with the Flexible Snow Model (FSM2) using airborne lidar snow data using the Multiple Snow data Assimilation system (MuSA). The successful experiments improved the reference simulations significantly both in terms of validation metrics (correlation coefficient from R=0.1 to R=0.8 on average) and spatial patterns. Data assimilation configurations using geographical distances and space of topographical dimensions, improved the reference run. However, those creating a space of synthetic coordinates by combining the spatiotemporal data assimilation with a principal components analysis did not show any improvement, even degrading some validation metrics. Future data assimilation initiatives would benefit from building specific localization functions that are able to model the spatial snowpack relationships at different resolutions.

• Bekken, Michael Andrew; Vatne, Astrid; Larsen, Poul; Ibrom, Andreas; Larsen, Klaus Steenberg & Elberling, Bo [Show all 14 contributors for this article] (2025). Carbon dynamics of a controlled peatland rewetting experiment in the Norwegian boreal zone. Scientific Reports. 16(1). doi: 10.1038/s41598-025-30836-2. Full text in Research Archive Show summary

  A controlled peatland rewetting experiment was conducted on two adjacent drained peatland sites in southeastern Norway. Eddy covariance monitoring of CO 2 and CH 4 fluxes at both sites began in 2019. In 2021, the Treatment Site was rewetted while the Control Site remained drained. Using nine environmental variables and the processed flux data as training data, Bayesian Additive Regression Tree (BART) models were used to generate annual flux balances for CO 2 and CH 4 . The 4-year mean annual flux at the Control Site was 17.3 ± 10 g CO 2 -C m − 2 yr − 1 and 4.6 ± 0.1 g CH 4 -C m − 2 yr − 1 . At the Treatment Site, the 2-year mean annual flux before the rewetting was 12.2  ±  3.8 g CO 2 -C m − 2 yr − 1 and 1.8  ±  0.04 g CH 4 -C m − 2 yr − 1 . In the first year after rewetting the annual flux was 53.3  ±  13 g CO 2 -C m − 2 yr − 1 and 3.8  ±  0.3 g CH 4 -C m − 2 yr − 1 , and in the second year after rewetting the annual flux was 41.2  ±  18 g CO 2 -C m − 2 yr − 1 and 3.4  ±  0.4 g CH 4 -C m − 2 yr − 1 . BART counterfactual modeling was able to estimate the effect of the rewetting on CO 2 and CH 4 fluxes. Two years after the rewetting, the BART counterfactual modeling estimated that the cumulative fluxes had increased by 80.3 ± 49 g CO 2 -C m − 2 and 3.4 ± 0.47 g CH 4 -C m − 2 because of the rewetting. Carbon flux monitoring of both sites is ongoing as the Control Site remains drained and the soil and vegetation at the Treatment Site continues to adjust to the altered hydrological regime after rewetting.

• Cao, Wenxue; Aalstad, Kristoffer; Schmidt, Louise Steffensen; Westermann, Sebastian & Schuler, Thomas (2025). Bayesian data assimilation on an Arctic glacier: learning from large ensemble twin experiments. Journal of Glaciology. ISSN 0022-1430. 71, p. 1–17. doi: 10.1017/jog.2025.10101. Full text in Research Archive Show summary

  Numerical modeling is crucial for quantifying the evolution of cryospheric processes. At the same time, uncertainties hamper process understanding and predictive accuracy. Here, we suggest improving glacier surface mass balance simulations for the Kongsvegen glacier in Svalbard through the application of Bayesian data assimilation techniques in a set of large ensemble twin experiments. Noisy synthetic observations of albedo and snow depth, generated using the multilayer CryoGrid community model with a full energy balance, are assimilated using two ensemble-based data assimilation schemes: the particle batch smoother and the ensemble smoother. A comprehensive evaluation exercise demonstrates that the joint assimilation of albedo and snow depth improves the simulation skill by up to 86% relative to the prior in specific glacier regions. The particle batch smoother excels in representing albedo dynamics, while the ensemble smoother is marginally more effective for snow depth under low snowfall conditions in the ablation area. By combining the strengths of both observations, the joint assimilation achieves improved surface mass balance simulations across different glacier zones using either assimilation scheme. This work underscores the potential of ensemble-based data assimilation methods for refining glacier models by offering a robust framework to enhance predictive accuracy and reduce uncertainties in cryospheric simulations. Further advances in glacier data assimilation research with both synthetic and real observations will be critical to better understanding the fate and role of Arctic glaciers in a changing climate.

• Hove, Alouette van; Aalstad, Kristoffer; Lind, Vibeke; Arndt, Claudia; Odongo, Vincent & Ceriani, Rodolfo [Show all 9 contributors for this article] (2025). Inferring methane emissions from African livestock by fusing drone, tower, and satellite data. Biogeosciences. ISSN 1726-4170. 22(16), p. 4163–4186. doi: 10.5194/bg-22-4163-2025. Full text in Research Archive Show summary

  Considerable uncertainties and unknowns remain in the regional mapping of methane sources, especially in the extensive agricultural areas of Africa. To address this issue, we developed an observing system that estimates methane emission rates by assimilating drone and flux tower observations into an atmospheric dispersion model. We used our novel Bayesian inference approach to estimate emissions from various ruminant livestock species in Kenya, including diverse herds of cattle, goats, and sheep, as well as camels, for which methane emission estimates are particularly sparse. Our Bayesian estimates aligned with Tier 2 emission values of the Intergovernmental Panel on Climate Change. In addition, we observed the hypothesized increase in methane emissions after feeding. Our findings suggest that the Bayesian inference method is more robust under non-stationary wind conditions compared to a conventional mass balance approach using drone observations. Furthermore, the Bayesian inference method performed better in quantifying emissions from weaker sources, estimating methane emission rates as low as 100 g h−1. We found a ± 50 % uncertainty in emission rate estimates for these weaker sources, such as sheep and goat herds, which reduced to ± 12 % for stronger sources, like cattle herds emitting 1000–1500 g h−1. Finally, we showed that radiance anomalies identified in hyperspectral satellite data can inform the planning of flight paths for targeted drone missions in areas where source locations are unknown, as these anomalies may serve as indicators of potential methane sources. These promising results demonstrate the efficacy of the Bayesian inference method for source term estimation. Future applications of drone-based Bayesian inference could extend to estimating methane emissions in Africa and other regions from various sources with complex spatiotemporal emission patterns, such as wetlands, landfills, and wastewater disposal sites. The Bayesian observing system could thereby contribute to the improvement of emission inventories and verification of other emission estimation methods.

• Blandini, Giulia; Avanzi, Francesco; Campo, Lorenzo; Gabellani, Simone; Aalstad, Kristoffer & Girotto, Manuela [Show all 9 contributors for this article] (2025). Learning to filter: snow data assimilation using a Long Short-Term Memory network. The Cryosphere. ISSN 1994-0416. 19, p. 4759–4783. doi: 10.5194/tc-19-4759-2025. Full text in Research Archive Show summary

  Trustworthy estimates of snow water equivalent and snow depth are essential for water resource management in snow-dominated regions. While ensemble-based data assimilation techniques, such as the Ensemble Kalman Filter (EnKF), are commonly used in this context to combine model predictions with observations therefore to improve model performance, these ensemble methods are computationally demanding and thus face significant challenges when integrated into time-sensitive operational workflows. To address this challenge, we present a novel approach for data assimilation in snow hydrology by utilizing Long Short-Term Memory (LSTM) networks. By leveraging data from 7 diverse study sites across the world to train the algorithm on the output of an EnKF, the proposed framework aims to further unlock the use of data assimilation in snow hydrology by balancing computational efficiency and complexity. We found that a LSTM-based data assimilation framework achieves comparable performance to state estimation based on an EnKF in improving open-loop estimates with only a small performance drop in terms of RMSE for snow water equivalent (+6 mm on average) and snow depth (+6 cm), respectively. All but 2 out of 14 site-specific-LSTM configurations improved on the Open Loop estimates. The inclusion of a memory component further enhanced LSTM stability and performance, particularly in situations of data sparsity. When trained on long datasets (25 years), this LSTM data assimilation approach also showed promising spatial transferability, with less than a 20 % reduction in accuracy for snow water equivalent and snow depth estimation. Once trained, the framework is computationally efficient, achieving a 70 % reduction in computational time compared to a parallelized EnKF. Training this new data assimilation approach on data from multiple sites showed that its performance is robust across various climate regimes, during dry and average water-year types, with only a limited drop in performance compared to the EnKF (+6 mm RMSE for SWE and +18 cm RMSE for snow depth). This work paves the way for the use of deep learning for data assimilation in snow hydrology and provides novel insights into efficient, scalable, and less computationally demanding modeling framework for operational applications.

• Mazzolini, Marco; Aalstad, Kristoffer; Esteban, Alonso-González,; Westermann, Sebastian & Treichler, Désirée (2025). Spatio-temporal snow data assimilation with the ICESat-2 laser altimeter. The Cryosphere. ISSN 1994-0416. 19(9), p. 3831–3848. doi: 10.5194/tc-19-3831-2025. Full text in Research Archive Show summary

  The satellite laser altimeter ICESat-2 provides accurate surface elevation observations across the globe. With a high-resolution digital elevation model (DEM), we can use such measurements to retrieve snow depth profiles even in remote areas where snow amounts are poorly constrained. However, the adoption of these retrievals remains low since they are very sparse in space, as the satellite measures along profiles, and in time, as the revisit is 3 months. Data assimilation (DA) methods can exploit snow observations to constrain snow models and provide gap-free distributed simulations. The assimilation of observations related to snow cover is well-established, but there are currently no methods to assimilate sparse ICESat-2 snow depth profiles. We propose an approach that spatially propagates information using – instead of the classic geographical distance – an abstract distance measured in a feature space defined by a topographical index and the melt-out date climatology. We demonstrate this framework for a small experimental catchment in the Spanish Pyrenees through three experiments. We assimilate different snow observations in an intermediate-complexity snow model: fractional snow-covered area (fSCA) retrievals from Sentinel-2, snow depth profiles from ICESat-2 located in proximity of the catchment or both fSCA and depth in a joint assimilation experiment. Results show that assimilating ICESat-2 snow depth profiles successfully updates the neighbouring unobserved catchment, improving the simulated average snow depth compared to the prior run. Another encouraging finding is that adding the snow depth profiles to fSCA observations leads to an accurate reconstruction of the snow depth spatial distribution. Evaluating the simulations with a set of independent drone-based snow depth maps using a probabilistic skill score, we find that for the accumulation season the joint assimilation's score improves by 19 % the established approach of only assimilating fSCA. The direct but incomplete snow depth information from ICESat-2 is a key constraint on simulated basin-average snow depth. This study makes use of globally available datasets and shows the promise of adopting ICESat-2's snow depth retrievals in seasonal snow modelling, especially when also assimilating complementary observations. In light of our encouraging results, more research with different experimental designs in varying snow conditions combined with continued methodological development is desirable to further catalyse the use of these retrievals in cryospheric and hydrologic applications.

• Keetz, Lasse Torben; Aalstad, Kristoffer; Fisher, Rosie; Terán, Christian Poppe; Naz, Bibi S. & Pirk, Norbert [Show all 8 contributors for this article] (2025). Inferring Parameters in a Complex Land Surface Model by Combining Data Assimilation and Machine Learning. Journal of Advances in Modeling Earth Systems. 17(6). doi: 10.1029/2024MS004542. Full text in Research Archive Show summary

  Complex Land Surface Models (LSMs) rely on a plethora of parameters. These parameters and the associated process formulations are often poorly constrained, which hampers reliable predictions of ecosystem dynamics and climate feedbacks. Robust and uncertainty-aware parameter estimation with observations is complicated by, for example, the high dimensionality of the model parameter space and the computational cost of LSM simulations. Herein, we adapt a novel Bayesian data assimilation (DA) and machine learning framework termed “calibrate, emulate, sample” (CES) to infer parameters in a widely-used LSM coupled with a demographic vegetation model (CLM-FATES). First, an iterative ensemble Kalman smoother provides an initial estimate of the posterior distribution (“calibrate”). Subsequently, a machine-learning-based emulator is trained on the resulting model-observation mismatches to predict outcomes for unseen parameter combinations (“emulate”). Finally, this emulator replaces CLM-FATES simulations in an adaptive Markov Chain Monte Carlo approach enabling computationally feasible posterior sampling with enhanced uncertainty quantification (“sample”). We test our implementation with synthetic and real observations representing a boreal forest site in southern Finland. We estimate a total of six plant-functional-type-specific photosynthetic parameters by assimilating evapotranspiration (ET) and gross primary production (GPP) flux data. CES provided the best estimates of the synthetic truth parameters when compared to data-blind emulator sampling designs while all approaches reduced model-observation errors compared to a default parameter simulation (GPP: - 10% to - 30%, ET: -4% to -6%). Although errors were also consistently reduced with real data, comparing the emulator designs was less conclusive, which we mainly attribute to equifinality, structural uncertainty within CLM-FATES, and/or unknown errors in the data that are not accounted for.

• Hove, Alouette van; Aalstad, Kristoffer & Pirk, Norbert (2024). Guiding drones by information gain. Proceedings of Machine Learning Research (PMLR). 233(89-96). Full text in Research Archive Show summary

  The accurate estimation of locations and emission rates of gas sources is crucial across various domains, including environmental monitoring and greenhouse gas emission analysis. This study investigates two drone sampling strategies for inferring source term parameters of gas plumes from atmospheric measurements. Both strategies are guided by the goal of maximizing information gain attained from observations at sequential locations. Our research compares the myopic approach of infotaxis to a far-sighted navigation strategy trained through deep reinforcement learning. We demonstrate the superior performance of deep reinforcement learning over infotaxis in environments with non-isotropic gas plumes.

• Aga, Juditha; Piermattei, Livia; Girod, Luc; Aalstad, Kristoffer; Eiken, Trond & Kääb, Andreas [Show all 7 contributors for this article] (2024). Acceleration of coastal-retreat rates for high-Arctic rock cliffs on Brøggerhalvøya, Svalbard, over the past decade. Earth Surface Dynamics. ISSN 2196-6311. 12(5), p. 1049–1070. doi: 10.5194/esurf-12-1049-2024. Full text in Research Archive Show summary

  In many Arctic regions, marine coastlines change rapidly in our currently warming climate. In contrast, coastal rock cliffs on Svalbard are considered to be relatively stable. Long-term trends of coastal-retreat rates for rock cliffs on Svalbard remain unknown, but quantifying them could improve our understanding of coastal dynamics in the Canadian Arctic Archipelago. This study presents coastal-retreat rates for rock cliffs along several kilometres of Brøggerhalvøya, Svalbard. The analysis relies on high-resolution orthoimages from 1970, 1990, 2010, and 2021. The data are corroborated by high-precision dGNSS (differential Global Navigation Satellite System) measurements obtained along selected segments of the coastline. Our analysis reveals statistically significant acceleration in coastal-retreat rates across Brøggerhalvøya between 2010 and 2021. The northeast-facing coastline features fairly stable conditions, with retreat rates of 0.04 ± 0.06 m a−1 (1970–1990; calculated retreat rate ± the corresponding measurement uncertainty), 0.04 ± 0.04 m a−1 (1990–2010), and 0.06 ± 0.08 m a−1 (2010–2021). Along the southwest-facing coastline, higher retreat rates of 0.26 ± 0.06 m a−1 (1970–1990), 0.24 ± 0.04 m a−1 (1990–2010), and 0.30 ± 0.08 m a−1 (2010–2021) were calculated. For the most recent decade, this corresponds to an increase of 50 % for the northeast-facing coastline and an increase of 25 % for the southwest-facing coastline. Furthermore, for the northeast-facing coastline, the proportion of the coastline affected by erosion increased from 47 % (1970–1990) to 65 % (2010–2021), while it stayed consistently above 90 % for the southwest-facing coastline. The recent acceleration in retreat rates coincides with increasing storminess and retreating sea ice, factors that can enhance coastal erosion.

• Guidicelli, Matteo; Aalstad, Kristoffer; Treichler, Désirée & Salzmann, Nadine (2024). A combined data assimilation and deep learning approach for continuous spatio-temporal SWE reconstruction from sparse ground tracks. Journal of Hydrology X. 25. doi: 10.1016/j.hydroa.2024.100190. Full text in Research Archive Show summary

  Our understanding of the impact of climate change on water availability and natural hazards in high-mountain regions is limited due to the spatial and temporal scarcity of ground observations of precipitation and snow. Freely available, satellite-based information about the snowpack is currently mainly limited to indirect measurements of snow-covered area or very coarse-scale snow water equivalent (SWE), but only for flat areas in lowlands without vegetation cover. Novel space-based laser altimeters, such as ICESat-2, have the potential to provide high-resolution snow depth data in worldwide mountain regions where no ground observations exist. However, these space-based laser altimeters come with spatial gaps between ground tracks, obtained without repetition at a give location. To overcome these drawbacks, here, we present a combined probabilistic data assimilation and deep learning approach to reconstruct spatio-temporal SWE from observations of snow depth along ground tracks, imitating ICESat-2 tracks in view of a potential future global application. Our approach is based on assimilating SWE and snow cover information in a degree-day model with an iterative ensemble smoother (IES) which allows temporally reconstructing SWE along hypothetical ground tracks separated by 3 km. As input, the degree-day model uses daily precipitation and downscaled air temperature from the ERA5 reanalysis. A feedforward neural network (FNN) is then used for spatial propagation of the daily mean and standard deviation of the updated SWE ensemble members obtained from the IES. The combined IES-FNN approach provides uncertainty-aware spatio-temporally continuous estimates of SWE. We tested our approach in the alpine Dischma valley (Switzerland) using high-resolution snow depth maps obtained from photogrammetric techniques mounted on airplanes and unmanned aerial system observations. Our results show that the IES-FNN model provides reliable estimates at a resolution of approximately 100 m. Even assimilating only one SWE observation during the year (combined with satellite-based melt-out date estimates) produces satisfying results when evaluating the IES-FNN SWE reconstructions on independent dates and smaller (<4 km2) areas: mean absolute error of 86 mm (78 mm) at Schürlialp (Latschüelfurgga) for average SWE of 180 mm (254 mm), and average spatial linear correlation with the reference SWE of 0.51 (0.48). However, the assimilated SWE observation must not be too early in the accumulation season or too late in the melt season when the snowpack is starting or ending to accumulate or melt, respectively. Smaller distances between ground tracks (1500 m and 500 m) show improved performance of the IES-FNN approach in space, with no significant improvement in terms of temporal reconstruction. Applying the IES-FNN approach to e.g., real ICESat-2 data, remains challenging due to the higher uncertainties associated with these data. However, the approach we propose remains potentially very helpful in addressing the problem of scarcity of ground observations of precipitation and snow in high-mountain regions.

• Temuujin, Khurelbaatar; Dashtseren, Avirmed; Etzelmüller, Bernd; Undrakhtsetseg, Tsogtbaatar; Aalstad, Kristoffer & Westermann, Sebastian (2024). Spatial variability of near-surface ground temperatures in a discontinuous permafrost area in Mongolia. Frontiers in Earth Science. 12. doi: 10.3389/feart.2024.1456012. Full text in Research Archive Show summary

  In Central Asia, the ground thermal regime is strongly affected by the interplay between topographic factors and ecosystem properties. In this study, we investigate the governing factors of the ground thermal regime in an area in Central Mongolia, which features discontinuous permafrost and is characterized by grassland and forest ecosystems. Miniature temperature dataloggers were used to measure near-surface temperatures at c. 100 locations throughout the 6 km2 large study area, with the goal to obtain a sample of sites that can represent the variability of different topographic and ecosystem properties. Mean annual near-surface ground temperatures showed a strong variability, with differences of up to 8 K. The coldest sites were all located in forests on north-facing slopes, while the warmest sites are located on steep south-facing slopes with sparse steppe vegetation. Sites in forests show generally colder near-surface temperatures in spring, summer and fall compared to grassland sites, but they are warmer during the winter season. The altitude of the measurement sites did not play a significant role in determining the near-surface temperatures, while especially solar radiation was highly correlated. In addition, we investigated the suitability of different hyperspectral indices calculated from Sentinel-2 as predictors for annual average near-surface ground temperatures. We found that especially indices sensitive to vegetation properties, such as the Normalized Difference Vegetation Index (NDVI), show a strong correlation. The presented observations provide baseline data on the spatiotemporal patterns of the ground thermal regime which can be used to train or validate modelling and remote sensing approaches targeting the impacts of climate change.

• Mazzolini, Marco; Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Westermann, Sebastian & Treichler, Désirée (2024). Spatio-temporal snow data assimilation with the ICESat-2 laser altimeter. The Cryosphere Discussions. doi: 10.5194/egusphere-2024-1404. Full text in Research Archive
• Pirk, Norbert; Aalstad, Kristoffer; Mannerfelt, Erik Schytt; Clayer, Francois; Wit, Heleen de & Christiansen, Casper Tai [Show all 9 contributors for this article] (2024). Disaggregating the Carbon Exchange of Degrading Permafrost Peatlands Using Bayesian Deep Learning. Geophysical Research Letters. ISSN 0094-8276. 51(10). doi: 10.1029/2024GL109283. Full text in Research Archive Show summary

  Extensive regions in the permafrost zone are projected to become climatically unsuitable to sustain permafrost peatlands over the next century, suggesting transformations in these landscapes that can leave large amounts of permafrost carbon vulnerable to post-thaw decomposition. We present 3 years of eddy covariance measurements of CH4 and CO2 fluxes from the degrading permafrost peatland Iškoras in Northern Norway, which we disaggregate into separate fluxes of palsa, pond, and fen areas using information provided by the dynamic flux footprint in a novel ensemble-based Bayesian deep neural network framework. The 3-year mean CO2-equivalent flux is estimated to be 106 gCO2 m−2 yr−1 for palsas, 1,780 gCO2 m−2 yr−1 for ponds, and −31 gCO2 m−2 yr−1 for fens, indicating that possible palsa degradation to thermokarst ponds would strengthen the local greenhouse gas forcing by a factor of about 17, while transformation into fens would slightly reduce the current local greenhouse gas forcing.

• Zweigel, Robin Benjamin; Dashtseren, Avirmed; Temuujin, Khurelbaatar; Aalstad, Kristoffer; Webster, Clare & Stuenzi, Simone M. [Show all 9 contributors for this article] (2024). Simulating the Thermal Regime and Surface Energy Balance of a Permafrost-Underlain Forest in Mongolia. Journal of Geophysical Research (JGR): Earth Surface. ISSN 2169-9003. 129(6). doi: 10.1029/2023JF007609. Full text in Research Archive Show summary

  Forests overlap with large parts of the northern hemisphere permafrost area, and representing canopy processes is therefore crucial for simulating thermal and hydrological conditions in these regions. Forests impact permafrost through the modulation of radiative fluxes and exchange of turbulent fluxes, precipitation interception and regulation of transpiration. Forests also feature distinct soil layers of litter and organic matter, which play central roles for the infiltration and evaporation of water, while also providing thermal insulation for deeper ground layers. In this study, we present a new module within the CryoGrid community model to simulate forest ecosystems and their impact on the surface water and energy balance. The module includes a big-leaf vegetation scheme with adaptations for canopy heat storage and transpiration. Furthermore, we account for the effect of surface litter layers on water and energy transfer. We show that the model is capable of simulating radiation, snow cover and ground temperatures below a deciduous needleleaf forest on a north-facing slope in the Khentii Mountains in Central Mongolia. A sensitivity analysis of topographic aspect and ecosystem configuration confirms the important role of the litter layers for the energy and water balance of the ground. Furthermore, it suggests that the presence of permafrost is primarily linked to topographic aspect rather than the presence of forest at this site. The presented model scheme can be used to study the development of the ground thermal regime in forests, including the state of permafrost, under different climate, ecosystem, and land use scenarios.

• Alonso-Gonzalez, Esteban; Aalstad, Kristoffer; Pirk, Norbert; Mazzolini, Marco; Treichler, Désirée & Leclercq, Paul [Show all 9 contributors for this article] (2023). Spatio-temporal information propagation using sparse observations in hyper-resolution ensemble-based snow data assimilation. Hydrology and Earth System Sciences (HESS). ISSN 1027-5606. 27(24), p. 4637–4659. doi: 10.5194/hess-27-4637-2023. Full text in Research Archive Show summary

  Data assimilation techniques that integrate available observations with snow models have been proposed as a viable option to simultaneously help constrain model uncertainty and add value to observations by improving estimates of the snowpack state. However, the propagation of information from spatially sparse observations in high-resolution simulations remains an under-explored topic. To remedy this, the development of data assimilation techniques that can spread information in space is a crucial step. Herein, we examine the potential of spatio-temporal data assimilation for integrating sparse snow depth observations with hyper-resolution (5 m) snow simulations in the Izas central Pyrenean experimental catchment (Spain). Our experiments were developed using the Multiple Snow Data Assimilation System (MuSA) with new improvements to tackle the spatio-temporal data assimilation. Therein, we used a deterministic ensemble smoother with multiple data assimilation (DES-MDA) with domain localization. Three different experiments were performed to showcase the capabilities of spatio-temporal information transfer in hyper-resolution snow simulations. Experiment I employed the conventional geographical Euclidean distance to map the similarity between cells. Experiment II utilized the Mahalanobis distance in a multi-dimensional topographic space using terrain parameters extracted from a digital elevation model. Experiment III utilized a more direct mapping of snowpack similarity from a single complete snow depth map together with the easting and northing coordinates. Although all experiments showed a noticeable improvement in the snow patterns in the catchment compared with the deterministic open loop in terms of correlation (r=0.13) and root mean square error (RMSE = 1.11 m), the use of topographical dimensions (Experiment II, r=0.63 and RMSE =  0.89 m) and observations (Experiments III, r=0.92 and RMSE =  0.44 m) largely outperform the simulated patterns in Experiment I (r=0.38 and RMSE = 1.16 m). At the same time, Experiments II and III are considerably more challenging to set up. The results of these experiments can help pave the way for the creation of snow reanalysis and forecasting tools that can seamlessly integrate sparse information from national monitoring networks and high-resolution satellite information.

• Renette, Cas; Aalstad, Kristoffer; Aga, Juditha; Zweigel, Robin Benjamin; Etzelmüller, Bernd & Lilleøren, Karianne Staalesen [Show all 8 contributors for this article] (2023). Simulating the effect of subsurface drainage on the thermal regime and ground ice in blocky terrain in Norway. Earth Surface Dynamics. ISSN 2196-6311. 11(1), p. 33–50. doi: 10.5194/esurf-11-33-2023. Full text in Research Archive Show summary

  Ground temperatures in coarse, blocky deposits such as mountain blockfields and rock glaciers have long been observed to be lower in comparison with other (sub)surface material. One of the reasons for this negative temperature anomaly is the lower soil moisture content in blocky terrain, which decreases the duration of the zero curtain in autumn. Here we used the CryoGrid community model to simulate the effect of drainage on the ground thermal regime and ground ice in blocky terrain permafrost at two sites in Norway. The model set-up is based on a one-dimensional model domain and features a surface energy balance, heat conduction and advection, as well as a bucket water scheme with adjustable lateral drainage. We used three idealized subsurface stratigraphies, blocks only, blocks with sediment and sediment only, which can be either drained (i.e. with strong lateral subsurface drainage) or undrained (i.e. without drainage), resulting in six scenarios. The main difference between the three stratigraphies is their ability to retain water against drainage: while the blocks only stratigraphy can only hold small amounts of water, much more water is retained within the sediment phase of the two other stratigraphies, which critically modifies the freeze–thaw behaviour. The simulation results show markedly lower ground temperatures in the blocks only, drained scenario compared to other scenarios, with a negative thermal anomaly of up to 2.2 ∘C. For this scenario, the model can in particular simulate the time evolution of ground ice, with build-up during and after snowmelt and spring and gradual lowering of the ice table in the course of the summer season. The thermal anomaly increases with larger amounts of snowfall, showing that well-drained blocky deposits are less sensitive to insulation by snow than other soils. We simulate stable permafrost conditions at the location of a rock glacier in northern Norway with a mean annual ground surface temperature of 2.0–2.5 ∘C in the blocks only, drained simulations. Finally, transient simulations since 1951 at the rock glacier site (starting with permafrost conditions for all stratigraphies) showed a complete loss of perennial ground ice in the upper 5 m of the ground in the blocks with sediment, drained run; a 1.6 m lowering of the ground ice table in the sediment only, drained run; and only 0.1 m lowering in the blocks only, drained run. The interplay between the subsurface water–ice balance and ground freezing/thawing driven by heat conduction can at least partly explain the occurrence of permafrost in coarse blocky terrain below the elevational limit of permafrost in non-blocky sediments. It is thus important to consider the subsurface water–ice balance in blocky terrain in future efforts in permafrost distribution mapping in mountainous areas. Furthermore, an accurate prediction of the evolution of the ground ice table in a future climate can have implications for slope stability, as well as water resources in arid environments.

• Hove, Alouette van; Aalstad, Kristoffer & Pirk, Norbert (2023). Using reinforcement learning to improve drone-based inference of greenhouse gas fluxes. Nordic Machine Intelligence (NMI). 3, p. 1–6. doi: 10.5617/nmi.9897. Full text in Research Archive Show summary

  Accurate mapping of greenhouse gas fluxes at the Earth's surface is essential for the validation and calibration of climate models. In this study, we present a framework for surface flux estimation with drones. Our approach uses data assimilation (DA) to infer fluxes from drone-based observations, and reinforcement learning (RL) to optimize the drone's sampling strategy. Herein, we demonstrate that a RL-trained drone can quantify a CO_2 hotspot more accurately than a drone sampling along a predefined flight path that traverses the emission plume. We find that information-based reward functions can match the performance of an error-based reward function that quantifies the difference between the estimated surface flux and the true value. Reward functions based on information gain and information entropy can motivate actions that increase the drone's confidence in its updated belief, without requiring knowledge of the true surface flux. These findings provide valuable insights for further development of the framework for the mapping of more complex surface flux fields.

• Westermann, Sebastian; Ingeman-Nielsen, Thomas; Scheer, Johanna; Aalstad, Kristoffer; Aga, Juditha & Chaudhary, Nitin [Show all 24 contributors for this article] (2023). The CryoGrid community model (version 1.0) - a multi-physics toolbox for climate-driven simulations in the terrestrial cryosphere. Geoscientific Model Development. ISSN 1991-959X. 16(9), p. 2607–2647. doi: 10.5194/gmd-16-2607-2023. Full text in Research Archive Show summary

  The CryoGrid community model is a flexible toolbox for simulating the ground thermal regime and the ice–water balance for permafrost and glaciers, extending a well-established suite of permafrost models (CryoGrid 1, 2, and 3). The CryoGrid community model can accommodate a wide variety of application scenarios, which is achieved by fully modular structures through object-oriented programming. Different model components, characterized by their process representations and parameterizations, are realized as classes (i.e., objects) in CryoGrid. Standardized communication protocols between these classes ensure that they can be stacked vertically. For example, the CryoGrid community model features several classes with different complexity for the seasonal snow cover, which can be flexibly combined with a range of classes representing subsurface materials, each with their own set of process representations (e.g., soil with and without water balance, glacier ice). We present the CryoGrid architecture as well as the model physics and defining equations for the different model classes, focusing on one-dimensional model configurations which can also interact with external heat and water reservoirs. We illustrate the wide variety of simulation capabilities for a site on Svalbard, with point-scale permafrost simulations using, e.g., different soil freezing characteristics, drainage regimes, and snow representations, as well as simulations for glacier mass balance and a shallow water body. The CryoGrid community model is not intended as a static model framework but aims to provide developers with a flexible platform for efficient model development. In this study, we document both basic and advanced model functionalities to provide a baseline for the future development of novel cryosphere models.

• Filhol, Simon; Fiddes, Joel & Aalstad, Kristoffer (2023). TopoPyScale: A Python Package for Hillslope Climate Downscaling. Journal of Open Source Software (JOSS). 8(86), p. 1–6. doi: 10.21105/joss.05059. Full text in Research Archive Show summary

  Global climate reanalyses and projections are available worldwide for the past and coming century. However, model grids remain too coarse to be directly relevant at the hillslope-scale (Fan et al., 2019), requiring adapted downscaling tools to account for the effects of local topography. Mountain regions are experiencing accelerated warming with the cryosphere rapidly responding to climate change. To understand and study geomorphological, hydrological, and glaciological changes, we need tools to downscale meteorological timeseries for the basic atmospheric variables used to solve surface energy and mass balance in process-based models. Advanced dynamical downscaling methods exist, though they come with a high computational cost and complex technical setup (Kruyt et al., 2022). TopoPyScale uses a pragmatic approach to downscaling by minimizing complexity, reducing computational cost, simplifying interoperability with land surface models, while retaining physical coherence and allowing the primary drivers of land surface-atmosphere interaction to be considered. The toolbox is designed to be flexible in its usage and development.

• Pirk, Norbert; Aalstad, Kristoffer; Yilmaz, Yeliz A.; Vatne, Astrid; Popp, Andrea & Horvath, Peter [Show all 12 contributors for this article] (2023). Snow-vegetation-atmosphere interactions in alpine tundra. Biogeosciences. ISSN 1726-4170. 20(11), p. 2031–2047. doi: 10.5194/bg-20-2031-2023. Full text in Research Archive Show summary

  The interannual variability of snow cover in alpine areas is increasing, which may affect the tightly coupled cycles of carbon and water through snow–vegetation–atmosphere interactions across a range of spatio-temporal scales. To explore the role of snow cover for the land–atmosphere exchange of CO2 and water vapor in alpine tundra ecosystems, we combined 3 years (2019–2021) of continuous eddy covariance flux measurements of the net ecosystem exchange of CO2 (NEE) and evapotranspiration (ET) from the Finse site in alpine Norway (1210 m a.s.l.) with a ground-based ecosystem-type classification and satellite imagery from Sentinel-2, Landsat 8, and MODIS. While the snow conditions in 2019 and 2021 can be described as site typical, 2020 features an extreme snow accumulation associated with a strong negative phase of the Scandinavian pattern of the synoptic atmospheric circulation during spring. This extreme snow accumulation caused a 1-month delay in melt-out date, which falls in the 92nd percentile in the distribution of yearly melt-out dates in the period 2001–2021. The melt-out dates follow a consistent fine-scale spatial relationship with ecosystem types across years. Mountain and lichen heathlands melt out more heterogeneously than fens and flood plains, while late snowbeds melt out up to 1 month later than the other ecosystem types. While the summertime average normalized difference vegetation index (NDVI) was reduced considerably during the extreme-snow year 2020, it reached the same maximum as in the other years for all but one of the ecosystem types (late snowbeds), indicating that the delayed onset of vegetation growth is compensated to the same maximum productivity. Eddy covariance estimates of NEE and ET are gap-filled separately for two wind sectors using a random forest regression model to account for complex and nonlinear ecohydrological interactions. While the two wind sectors differ markedly in vegetation composition and flux magnitudes, their flux response is controlled by the same drivers as estimated by the predictor importance of the random forest model, as well as by the high correlation of flux magnitudes (correlation coefficient r=0.92 for NEE and r=0.89 for ET) between both areas. The 1-month delay of the start of the snow-free season in 2020 reduced the total annual ET by 50 % compared to 2019 and 2021 and reduced the growing-season carbon assimilation to turn the ecosystem from a moderate annual carbon sink (−31 to −6 gC m−2 yr−1) to a source (34 to 20 gC m−2 yr−1). These results underpin the strong dependence of ecosystem structure and functioning on snow dynamics, whose anomalies can result in important ecological extreme events for alpine ecosystems.

• Pirk, Norbert; Aalstad, Kristoffer; Westermann, Sebastian; Vatne, Astrid; Hove, Alouette van & Tallaksen, Lena Merete [Show all 8 contributors for this article] (2022). Inferring surface energy fluxes using drone data assimilation in large eddy simulations. Atmospheric Measurement Techniques. ISSN 1867-1381. 15(24), p. 7293–7314. doi: 10.5194/amt-15-7293-2022. Full text in Research Archive Show summary

  Spatially representative estimates of surface energy exchange from field measurements are required for improving and validating Earth system models and satellite remote sensing algorithms. The scarcity of flux measurements can limit understanding of ecohydrological responses to climate warming, especially in remote regions with limited infrastructure. Direct field measurements often apply the eddy covariance method on stationary towers, but recently, drone-based measurements of temperature, humidity, and wind speed have been suggested as a viable alternative to quantify the turbulent fluxes of sensible (H) and latent heat (LE). A data assimilation framework to infer uncertainty-aware surface flux estimates from sparse and noisy drone-based observations is developed and tested using a turbulence-resolving large eddy simulation (LES) as a forward model to connect surface fluxes to drone observations. The proposed framework explicitly represents the sequential collection of drone data, accounts for sensor noise, includes uncertainty in boundary and initial conditions, and jointly estimates the posterior distribution of a multivariate parameter space. Assuming typical flight times and observational errors of light-weight, multi-rotor drone systems, we first evaluate the information gain and performance of different ensemble-based data assimilation schemes in experiments with synthetically generated observations. It is shown that an iterative ensemble smoother outperforms both the non-iterative ensemble smoother and the particle batch smoother in the given problem, yielding well-calibrated posterior uncertainty with continuous ranked probability scores of 12 W m−2 for both H and LE, with standard deviations of 37 W m−2 (H) and 46 W m−2 (LE) for a 12 min vertical step profile by a single drone. Increasing flight times, using observations from multiple drones, and further narrowing the prior distributions of the initial conditions are viable for reducing the posterior spread. Sampling strategies prioritizing space–time exploration without temporal averaging, instead of hovering at fixed locations while averaging, enhance the non-linearities in the forward model and can lead to biased flux results with ensemble-based assimilation schemes. In a set of 18 real-world field experiments at two wetland sites in Norway, drone data assimilation estimates agree with independent eddy covariance estimates, with root mean square error values of 37 W m−2 (H), 52 W m−2 (LE), and 58 W m−2 (H+LE) and correlation coefficients of 0.90 (H), 0.40 (LE), and 0.83 (H+LE). While this comparison uses the simplifying assumptions of flux homogeneity, stationarity, and flat terrain, it is emphasized that the drone data assimilation framework is not confined to these assumptions and can thus readily be extended to more complex cases and other scalar fluxes, such as for trace gases in future studies.

• Alonso-Gonzalez, Esteban; Aalstad, Kristoffer; Baba, Mohamed Wassim; Revuelto, Jesus; Lopez-Moreno, Juan I & Fiddes, Joel [Show all 8 contributors for this article] (2022). The Multiple Snow Data Assimilation System (MuSA v1.0). Geoscientific Model Development. ISSN 1991-959X. 15(24), p. 9127–9155. doi: 10.5194/gmd-15-9127-2022. Full text in Research Archive Show summary

  Accurate knowledge of the seasonal snow distribution is vital in several domains including ecology, water resources management, and tourism. Current spaceborne sensors provide a useful but incomplete description of the snowpack. Many studies suggest that the assimilation of remotely sensed products in physically based snowpack models is a promising path forward to estimate the spatial distribution of snow water equivalent (SWE). However, to date there is no standalone, open-source, community-driven project dedicated to snow data assimilation, which makes it difficult to compare existing algorithms and fragments development efforts. Here we introduce a new data assimilation toolbox, the Multiple Snow Data Assimilation System (MuSA), to help fill this gap. MuSA was developed to fuse remotely sensed information that is available at different timescales with the energy and mass balance Flexible Snow Model (FSM2). MuSA was designed to be user-friendly and scalable. It enables assimilation of different state variables such as the snow depth, SWE, snow surface temperature, binary or fractional snow-covered area, and snow albedo and could be easily upgraded to assimilate other variables such as liquid water content or snow density in the future. MuSA allows the joint assimilation of an arbitrary number of these variables, through the generation of an ensemble of FSM2 simulations. The characteristics of the ensemble (i.e., the number of particles and their prior covariance) may be controlled by the user, and it is generated by perturbing the meteorological forcing of FSM2. The observational variables may be assimilated using different algorithms including particle filters and smoothers as well as ensemble Kalman filters and smoothers along with their iterative variants. We demonstrate the wide capabilities of MuSA through two snow data assimilation experiments. First, 5 m resolution snow depth maps derived from drone surveys are assimilated in a distributed fashion in the Izas catchment (central Pyrenees). Furthermore, we conducted a joint-assimilation experiment, fusing MODIS land surface temperature and fractional snow-covered area with FSM2 in a single-cell experiment. In light of these experiments, we discuss the pros and cons of the assimilation algorithms, including their computational cost.

• Fiddes, Joel; Aalstad, Kristoffer & Lehning, Michael (2022). TopoCLIM: rapid topography-based downscaling of regional climate model output in complex terrain v1.1. Geoscientific Model Development. ISSN 1991-959X. 15(4), p. 1753–1768. doi: 10.5194/gmd-15-1753-2022. Full text in Research Archive Show summary

  This study describes and evaluates a new down-scaling scheme that specifically addresses the need for hillslope-scale atmospheric-forcing time series for modelling the local impact of regional climate change projections on the land surface in complex terrain. The method has a global scope in that it does not rely directly on surface observations and is able to generate the full suite of model forcing variables required for hydrological and land surface modelling in hourly time steps. It achieves this by utilizing the previously published TopoSCALE scheme to generate synthetic observations of the current climate at the hillslope scale while accounting for a broad range of surface-atmosphere interactions. These synthetic observations are then used to debias (downscale) CORDEX climate variables using the quantile mapping method. A further temporal disaggregation step produces sub-daily fields. This approach has the advantages of other empirical-statistical methods, including speed of use, while it avoids the need for ground data, which are often limited. It is therefore a suitable method for a wide range of remote regions where ground data is absent, incomplete, or not of sufficient length. The approach is evaluated using a network of high-elevation stations across the Swiss Alps, and a test application in which the impacts of climate change on Alpine snow cover are modelled.

• 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 (HESS). ISSN 1027-5606. 25(8), p. 4455–4471. doi: 10.5194/hess-25-4455-2021. Full text in Research Archive Show summary

  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. Full text in Research Archive Show summary

  The seasonal snow-cover is one of the most rapidly varying natural surface features on Earth. It strongly modulates the terrestrial water, energy, and carbon balance. Fractional snow-covered area (fSCA) is an essential snow variable that can be retrieved from multispectral satellite imagery. In this study, we evaluate fSCA retrievals from multiple sensors that are currently in polar orbit: the operational land imager (OLI) on-board Landsat 8, the multispectral instrument (MSI) on-board the Sentinel-2 satellites, and the moderate resolution imaging spectroradiometer (MODIS) on-board Terra and Aqua. We consider several retrieval algorithms that fall into three classes: thresholding of the normalized difference snow index (NDSI), regression on the NDSI, and spectral unmixing. We conduct the evaluation at a high-Arctic site in Svalbard, Norway, by comparing satellite retrieved fSCA to coincident high-resolution snow-cover maps obtained from a terrestrial automatic camera system. For the lower resolution MODIS retrievals, the regression-based retrievals outperformed the unmixing-based retrievals for all metrics but the bias. For the higher resolution sensors (OLI and MSI), retrievals based on NDSI thresholding overestimated the fSCA due to the mixed pixel problem whereas spectral unmixing retrievals provided the most reliable estimates across the board. We therefore encourage the operationalization of spectral unmixing retrievals of fSCA from both OLI and MSI.

• Fiddes, Joel; Aalstad, Kristoffer & Westermann, Sebastian (2019). Hyper-resolution ensemble-based snow reanalysis in mountain regions using clustering. Hydrology and Earth System Sciences (HESS). ISSN 1027-5606. 23(11), p. 4717–4736. doi: 10.5194/hess-23-4717-2019. Full text in Research Archive Show summary

  Spatial variability in high-relief landscapes is immense, and grid-based models cannot be run at spatial resolutions to explicitly represent important physical processes. This hampers the assessment of the current and future evolution of important issues such as water availability or mass movement hazards. Here, we present a new processing chain that couples an efficient sub-grid method with a downscaling tool and a data assimilation method with the purpose of improving numerical simulation of surface processes at multiple spatial and temporal scales in ungauged basins. The novelty of the approach is that while we add 1–2 orders of magnitude of computational cost due to ensemble simulations, we save 4–5 orders of magnitude over explicitly simulating a high-resolution grid. This approach makes data assimilation at large spatio-temporal scales feasible. In addition, this approach utilizes only freely available global datasets and is therefore able to run globally. We demonstrate marked improvements in estimating snow height and snow water equivalent at various scales using this approach that assimilates retrievals from a MODIS snow cover product. We propose that this as a suitable method for a wide variety of operational and research applications where surface models need to be run at large scales with sparse to non-existent ground observations and with the flexibility to assimilate diverse variables retrieved by Earth observation missions.

• 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. 11(5). doi: 10.3390/rs11050483. Full text in Research Archive Show summary

  The snow-fed river basins of the Near East region are facing an urgent threat in the form of declining water resources. In this study, we analyzed several remote sensing products (optical, passive microwave, and gravimetric) and outputs of a meteorological reanalysis data set to understand the relationship between the terrestrial water storage anomalies and the mountain snowpack. The results from different satellite retrievals show a clear signal of a depletion of both water storage and the seasonal snowpack in four basins in the region. We find a strong reduction in terrestrial water storage over the Gravity Recovery and Climate Experiment (GRACE) observational period, particularly over the higher elevations. Snow-cover duration estimates from Moderate Resolution Imaging Spectroradiometer (MODIS) products point towards negative and significant trends up to one month per decade in the current era. These numbers are a clear indicator of the partial disappearance of the seasonal snow-cover in the region which has been projected to occur by the end of the century. The spatial patterns of changes in the snow-cover duration are positively correlated with both GRACE terrestrial water storage decline and peak snow water equivalent (SWE) depletion from the ERA5 reanalysis. Possible drivers of the snowpack depletion are a significant reduction in the snowfall ratio and an earlier snowmelt. A continued depletion of the montane snowpack in the Near East paints a bleak picture for future water availability in this water-stressed region.

• 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), p. 247–270. doi: 10.5194/tc-12-247-2018. Full text in Research Archive Show summary

  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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• Yılmaz, Yeliz A.; Aalstad, Kristoffer; Guillet, Gregoire; Rounce, David; Tober, Brandon & Yang, Ruitang [Show all 8 contributors for this article] (2026). Probabilistic calibration of glacier projections using data assimilation. doi: 10.5194/egusphere-egu26-14845. Full text in Research Archive Show summary

  Global glacier mass loss is accelerating, yet considerable spread in projected glacier changes remains due to model structure, forcing, and parameter uncertainty. Most global glacier projections rely on relatively simple models where calibration approaches are essential to constrain uncertainty by using scarce observations. Probabilistic calibration strategies that help with quantifying uncertainities have recently incorporated into a limited number of global glacier models. As a next step, we suggest employing Bayesian data assimilation methods with untapped potential to integrate multi source observations (in-situ, satellite, reanalysis) when calibrating global glacier model projections.Here, we present a probabilistic calibration framework for the Python Glacier Evolution Model (PyGEM) based on ensemble-based data assimilation. Two data assimilation techniques (PBS and AdaPBS) are used to calibrate mass balance parameters to constrain future projections of glacio-hydrological variables (surface mass balance and runoff) between 2015 and 2100 under four SSP climate scenarios across the Scandinavian region. In this work, we compare our calibration results with commonly used deterministic and probabilistic glacier model calibration algorithms which are already in use in PyGEM. Our probabilistic calibration framework based on data assimilation has the potential to quantify and disentangle uncertainties from climate forcing, model structure, and parameters. Better constrained and uncertainty-aware glacier models increases confidence in projections of future glacier change and their relevant impacts. This work paves the way for producing policy relevant global glacier projections and scenarios with their uncertainty estimates within the ERC-AdG GLACMASS project.

• Aalstad, Kristoffer; Alonso-González, Esteban; Mazzolini, Marco & Girotto, Manuela (2026). Multiple Snow Data Assimilation and Bayesian Muses. doi: https:/www.youtube.com/watch?v=rYR7kqAvgCk. Full text in Research Archive Show summary

  Accurate estimation of essential snow variables at desired spatial and temporal scales is challenged by process complexity and the large extent yet mostly remote location of snow-covered regions. A method to jointly overcome model and observational shortcomings is data assimilation, which leverages the information content in both observations and models while accounting for uncertainty. In the first half of this seminar, we introduce the primary methodologies used in the broad snow-hydrology field, along with their benefits and challenges. We also cover applications of recent snow data assimilation research efforts targeted at improving SWE and/or snow-related states such as snowfall and streamflow.  In the second half, we introduce the Multiple Snow Data Assimilation (MuSA) system which seeks to facilitate the use of these methods across the broader snow science community. Therein, we provide several recent examples of how ideas from Bayesian computation can be used as muses for solving practical snow data assimilation problems. Our talks reflect key ideas from a recent cryospheric data assimilation workshop that are being synthesized in a review article.

• Aalstad, Kristoffer; Alonso-González, Esteban; Fiddes, Joel; Kääb, Andreas; Pirk, Norbert & Treichler, Désirée [Show all 9 contributors for this article] (2026). Global ensemble-based mountain snow reanalysis. doi: https:/snowhydro.unirioja.es/public/files/Snowhydro_abstracts.pdf. Full text in Research Archive Show summary

  Snow is an essential climate variable that regulates the global cycles of energy, carbon, and water. However, the state of the snowpack is only partially observable by satellites due to gaps, noise, and indirect retrieval algorithms. The fusion of uncertain snow models and noisy observations through data assimilation presents a natural solution to this problem. Nonetheless, data assimilation has received relatively little attention from the snow remote sensing community despite its potential to serve as a generalized retrieval method that adds value by inferring gap-free hidden snow state variables with uncertainty quantification. We present ongoing research on applying ensemble-based data assimilation techniques to produce a global mountain snow reanalysis constrained by satellite data. These efforts are motivated by the challenge of estimating seasonal snow mass in mountainous terrain which remains a major unsolved problem in snow hydrology. Taking a step towards solving this problem, we aim to generate the first global, consistent, ensemble-based, daily, kilometer-scale reanalysis of seasonal snow mass (i.e. snow water equivalent) and fractional snow-covered area dynamics for all mountains outside Antarctica. To produce our reanalysis, we assimilate fractional snow-covered area satellite retrievals from ESA Snow_cci into a simple snow model run at a relatively high spatio-temporal resolution. Given the efficiency of our model, we are able to leverage promising iterative ensemble-based schemes while ensuring that the problem remains computationally feasible. Specifically, we build on developments hybridizing ensemble Kalman and particle methods for robust and tractable Bayesian inference. We also demonstrate how to hierarchically infer hyperparameters related to snow climatology. The new reanalysis approach is evaluated using independent spaceborne, airborne, and in-situ validation data. Finally, we benchmark the performance of our reanalysis by comparing it to other global mountain snow products. Unlike existing global snow mass products, our product is uncertainty-aware and is tailored to address a key knowledge gap concerning mountain snow mass. We highlight that, by combining observations with models, data assimilation can transform largely untapped climate data into actionable climate information on essential climate variables. The uncertainty quantification in this probabilistic climate information enables informed decision making in response to climate change and its impacts.

• Hove, Alouette van; Aalstad, Kristoffer; Lind, Vibeke; Arndt, Claudia; Odongo, Vincent & Ceriani, Rodolfo [Show all 9 contributors for this article] (2025). Inferring methane emissions from African livestock by fusing drone, tower, and satellite data. 9th International Greenhouse Gas and Animal Agriculture (GGAA2025) conference. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Mazzolini, Marco; Guillet, Gregoire; Yang, Ruitang & Hock, Regine (2025). Data assimilation for snow and glacier modeling in climate applications. Full text in Research Archive
• Yilmaz, Yeliz A.; Jansen, Arnaud; Aalstad, Kristoffer; Mazzolini, Marco & Alonso-González, Esteban (2025). Snow data assimilation for understanding snowpack and streamflow shifts in Hardangervidda. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Guillet, Gregoire; Rounce, David; Tober, Brandon & Yang, Ruitang [Show all 7 contributors for this article] (2025). Calibrating future glacier projections using data assimilation. doi: https:/imc2025.info/imc25/abstract/calibrating-future-glacier-projections-using-data-assimilation/. Full text in Research Archive Show summary

  Global glacier mass is changing rapidly, and projections of global glacier mass balance under changing climatic conditions are crucial for informed decision-making. Existing glacier projections use relatively simple glacier models constrained by sparse observations. In these projections, model calibration plays a key role in constraining uncertainty. The use of Bayesian data assimilation methods for calibration by integrating multiple emerging observational data sets (in-situ mass balance measurements, climate reanalyses, and satellite remote sensing) to constrain model parameters and their dynamics remains relatively unexplored. Such a probabilistic calibration strategy could enable us to quantify and disentangle uncertainties related to the glacier model, the selected climate model forcing, and internal climate variability. The Python Glacier Evolution Model (PyGEM) is one of a handful of global glacier models that allow us to simulate the evolution of the mass balance of all glaciers in the world. In this work, we adopt ensemble-based data assimilation methods to calibrate PyGEM model parameters and thus constrain future projections of glacier mass balance across Scandinavia. We compare our results with traditional glacier model calibration algorithms and the Bayesian gold standard Markov Chain Monte Carlo (MCMC) method in PyGEM for glacio-hydrological indicators (surface mass balance and runoff projections) between 2015 and 2100 with four SSP scenarios. This work serves as the kernel for a scalable glacier data assimilation framework to produce policy relevant global glacier projections and scenarios within the recently funded ERC-AdG GLACMASS project. The probabilistic calibration framework developed in this study can in principle be adapted for a wide range of cryospheric applications.

• Yilmaz, Yeliz A.; Jansen, Arnaud; Aalstad, Kristoffer; Mazzolini, Marco & Alonso-González, Esteban (2025). Investigating Snowpack and Streamflow Changes with Snow Data Assimilation in Hardangervidda. Full text in Research Archive Show summary

  Snowmelt rates have a direct influence on downstream water availability and are changing significantly in response to shifting climatic conditions. However, the specific drivers and direction of these changes require further investigation across different regions and timescales. In this study, we investigated the impact of climate change on snowmelt rates and streamflow in the Hardangervidda region of Norway. The Multiple Snow Data Assimilation System (MuSA) was used to simulate historical (2001–2020) and future (mid- and end-century) snowpack conditions by assimilating a long-term satellite-based record of fractional snow-covered area from MODIS. Using MuSA outputs under the RCP8.5 scenario, we applied the Simple Dynamical Systems approach to simulate future streamflow in the Kvenna catchment. Our results show that while meltwater volumes increase at mid-century due to higher snowmelt rates, they decline by the end of the century. Annual peak flow decreases in both future periods (by 26% and 36%, respectively) with a seasonal shift in its timing from spring/summer to autumn/winter. Seasonal total discharge increases during winter/spring, but decreases during summer. Our findings highlight substantial changes in snowmelt dynamics and streamflow patterns on the Hardangervidda plateau under future climate scenarios. The anticipated earlier and more variable melt events along with altered peak flow timing may complicate for future reservoir and water resource management.

• Mazzolini, Marco; Cowherd, Marianne; Aalstad, Kristoffer; Girotto, Manuela; Alonso-González, Esteban & Treichler, Désirée (2025). Modelling snow spatial covariances to improve the assimilation of sparse observations. Full text in Research Archive
• Mazzolini, Marco; Cowherd, Marianne; Aalstad, Kristoffer; Girotto, Manuela; Alonso-González, Esteban & Treichler, Désirée (2025). Data assimilation of sparse snow depth observation with optimized spatial transfer of information. doi: https:/lps25.esa.int/programme/programme-session/?id=F04A2D11-A598-4F96-92B0-4652E462A8DD&presentationId=DE10A404-4AA5-40EF-B5CA-0FBDBEE68EE2. Full text in Research Archive Show summary

  The satellite laser altimeter ICESat-2 provides accurate surface elevation observations across our living planet. With a high-resolution digital elevation model (DEM), we can use such measurements to retrieve snow depth profiles. Such observations are of great societal relevance because water managers could potentially use them to infer snow amounts even in remote montane areas, where the role of snow as water tower is not actively monitored. However, these retrievals are not currently used operationally because they are very sparse in space and time: ICESat-2 measures along profiles with a three-month repeat interval. The high spatio-temporal variability of the seasonal snowpack limits the observations’ value. Data Assimilation (DA) methods allow to use information from snow observations to constrain snow models and provide gap-free distributed simulations. The assimilation of observations like snow cover is considered the state-of-the-art for generating retrospective reanalysis, but the use of sparse snow depth observations in DA is an active research area as those could be used in an operational manner. Covariance localization has been adopted to spatially transfer information from observed locations to similar unobserved locations. Traditionally, the geographical distance has been used to define the similarity between locations. In previous studies, we showed that topographical indices and the climatology of the melt-out date are also relevant parameters for determining the similarity. However, this measure was considered as a fixed hyperparameter. In this work, we exploit airborne lidar snow depth maps acquired by the Airborne Snow Observatory (ASO) to optimize the similarity measure between simulated cells. Gaussian Processes (GP) offer a probabilistic approach to infer the relative relevance of geographic, topographic and snow-climatology variables through a method called Automatic Relevance Determination (ARD). Preliminary results from the East River basin in Colorado, USA, indicate that ARD can successfully learn repeated snow depth patterns from a water year and improve the spatial transfer of information for successive water years when only a profile is measured. The learned relative relevance is used in a set of full spatio-temporal DA experiments designed to quantify the potential contribution of snow depth observations from the satellite altimeter ICESat-2 for seasonal snow operational forecasts.

• Treichler, Désirée; Mazzolini, Marco & Aalstad, Kristoffer (2025). Cryo-DA workshop. doi: https:/www.mn.uio.no/geo/english/research/projects/snowdepth/events/cryodaworkshop-oslo.html. Full text in Research Archive Show summary

  Discussion lead for four discussion sessions at the cryo-DA workshop

• Mazzolini, Marco; Aalstad, Kristoffer; Alonso-González, Esteban; Westermann, Sebastian & Treichler, Désirée (2025). Spatio-temporal snow data assimilation with the ICESat-2 laser altimeter. Full text in Research Archive Show summary

  Presentation: methods for spatio-temporal propagation of sparse snow data

• Aalstad, Kristoffer; Guillet, Gregoire; Yang, Ruitang; Yilmaz, Yeliz & Hock, Regine (2025). Glacier reanalysis using hierarchical data assimilation. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Guillet, Gregoire & Hock, Regine (2025). Strategies for Future Projections with PyGEM. Full text in Research Archive
• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Mazzolini, Marco & Willmes, Clarissa (2025). Adventures in snow data assimilation. Full text in Research Archive Show summary

  In this talk I will provide a guided tour of some of our adventures in snow data assimilation. The role that snow reanalysis can play in filling key observational gaps from both established and emerging Earth observations will be a recurring theme. This will be highlighted through examples from some ongoing work on trying to estimate global seasonal snow water equivalent using optical satellite data. Through our adventures, I hope to showcase the still largely untapped potential that data assimilation holds for adding value to Earth observations and constraining snow model uncertainty. 

• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Fiddes, Joel; Guillet, Gregoire; Kääb, Andreas Max & Mazzolini, Marco [Show all 11 contributors for this article] (2025). Ensemble-based cryospheric reanalysis to infer global snow mass. Full text in Research Archive Show summary

  Snow, glaciers, and permafrost are essential climate variables (ECV) that regulate the global cycles of energy, carbon, and water. At the same time, these cryospheric ECVs are only partially observable by satellites due to gaps, noise, and indirect retrieval algorithms. Data assimilation (DA), namely the Bayesian fusion of uncertain models and noisy observations, presents a natural solution to the problem of partial observability. Nonetheless, unlike in numerical weather prediction, DA has received relatively little attention from the Earth observation (EO) community despite its potential as a generalized retrieval framework that adds value by filling gaps and inferring latent ECVs with uncertainty quantification. This contribution presents active research on applying ensemble-based DA techniques to carry out cryospheric reanalysis constrained by satellite data. Our future goals with these efforts are to generate consistent global high resolution reanalyses of seasonal snow mass (also known as snow water equivalent or simply SWE), glacier mass balance, and the thermal state of permafrost. In doing so, we seek to leverage a myriad of data streams including Earth observing satellites, global atmospheric reanalyses, airborne retrievals, and in-situ observations. Here we focus on seasonal snow since accurate global snow mass estimation, particularly in mountainous terrain, remains a major unsolved problem in snow hydrology. To help tackle this problem, we are developing a global scale ensemble-based snow reanalysis product by assimilating ESA Snow_cci fractional snow-covered area retrievals. Using a simple snow model we are able to devote considerable computational resources to generate a global snow reanalysis at daily temporal resolution and kilometric spatial resolution while still being able to afford using promising iterative ensemble-based DA schemes. For the latter, we explore recent developments in hybridizing iterative ensemble Kalman and particle methods to provide robust Bayesian posterior inference. In particular, we demonstrate how these schemes can be used as nested smoothers to hierarchically infer prior hyperparameters related to snow climatology. The new reanalysis approach is evaluated using independent spaceborne, airborne, and in-situ validation data by comparing its performance to state-of-the-art regional snow reanalyses and existing global snow mass products in the form of ERA5-Land reanalysis data and ESA Snow_cci SWE retrievals. Unlike existing global snow products, this new snow reanalysis product is uncertainty-aware, assimilates snow satellite data, and specifically targets a key knowledge gap concerning mountain snow mass. Concurrent efforts to adapt this DA framework towards the generation of global ensemble-based reanalyses for glaciers and permafrost will also be showcased to emphasize synergies across these terrestrial cryospheric reanalysis efforts. We highlight that, by combining EO with cryospheric models, ensemble-based DA can transform largely untapped climate data into actionable climate information on cryospheric ECVs. The baked-in uncertainty quantification in this probabilistic climate information empowers us to make decisions in response to climate change and its perilous impacts on the mountain cryosphere.

• Aalstad, Kristoffer; Blandini, Giulia; Guidicelli, Matteo; Pirk, Norbert & Hove, Alouette van (2025). Learning to assimilate and assimilating to learn. Full text in Research Archive Show summary

  https://www.hydrologiraadet.no/seminar-om-maskinlaering-innen-hydrologi-og-meteorologi-25-april/

• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Blandini, Giulia; Guidicelli, Matteo & Willmes, Clarissa (2025). Adventures in terrestrial cryospheric data assimilation. Full text in Research Archive Show summary

  In this talk I will provide a guided tour of our adventures applying data assimilation to various terrestrial cryospheric problems. While the focus will primarily be on seasonal snow, I will also present some related developments for glacier and permafrost modeling. The role that targeted terrestrial cryospheric reanalysis can play in filling key observational gaps from both established and emerging Earth observations will be a recurring theme. This will be highlighted through examples from some ongoing work on trying to estimate global seasonal snow water equivalent using optical satellite data. Throughout the talk, I will provide several examples of combining machine learning and data assimilation to both speed up and enhance inference. Moreover, I will introduce some recent forays into hybrid and adaptive particle schemes as well as some experimental work on ensemble-based hierarchical inference. Through our adventures, I hope to showcase the still largely untapped potential that data assimilation holds for adding value to observations and constraining model uncertainty across a broader range of problems.

• Aalstad, Kristoffer (2025). Fundamentals of Cryospheric Data Assimilation. Full text in Research Archive Show summary

  https://www.mn.uio.no/geo/english/research/projects/snowdepth/events/cryodaworkshop-oslo.html

• Treichler, Désirée; Mazzolini, Marco; Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Aune, Simen Dalseid & Bühler, Yves [Show all 10 contributors for this article] (2024). Snow measured with a space laser. Full text in Research Archive
• Mazzolini, Marco; Aalstad, Kristoffer; Alonso-Gonzalez, Esteban & Treichler, Désirée (2024). Spatio-temporal snow data assimilation with the ICESat-2 laser altimeter. Full text in Research Archive
• Mazzolini, Marco; Aalstad, Kristoffer; Treichler, Désirée & Alonso-Gonzalez, Esteban (2024). Spatio-temporal snow data assimilation with the ICESat-2 laser altimeter. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon; Gascoin, Simon; Pirk, Norbert & Remmers, Janneke [Show all 9 contributors for this article] (2024). Leveraging Earth observations to model snow cover dynamics over Scandinavia. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon; Gascoin, Simon; Pirk, Norbert & Remmers, Janneke [Show all 9 contributors for this article] (2024). Using Earth observations to model snow cover over Scandinavia. Full text in Research Archive
• Aalstad, Kristoffer; Willmes, Clarissa; Mazzolini, Marco & Kreynen, Dylan (2024). Snow data assimilation at UiO. Full text in Research Archive
• Aalstad, Kristoffer; Hock, Regine; Mazzolini, Marco; Pirk, Norbert; Treichler, Désirée & Westermann, Sebastian [Show all 9 contributors for this article] (2024). Ensemble-Based Reanalysis of the Terrestrial Cryosphere. Full text in Research Archive Show summary

  The terrestrial cryosphere in the form of glaciers, permafrost, and seasonal snow, plays a vital role in the climate system by regulating the global cycles of energy, carbon, and water. As a result, these components of the cryosphere are considered essential climate variables (ECVs) by the Global Climate Observing System. At the same time, these ECVs are only partially observable by Earth observing satellites due to gaps, noise, and indirect retrieval algorithms. The statistical fusion of uncertain models and noisy observations referred to as data assimilation in geoscience represents a natural solution to this problem of partial observability. Nonetheless, beyond the confines of weather prediction and atmospheric reanalyses, data assimilation has received relatively little attention in broader Earth system science despite its potential for adding value to observations by filling gaps and inferring latent ECVs with uncertainty quantification. In this contribution, we present ongoing efforts in several projects applying ensemble-based (probabilistic) data assimilation techniques to carry out long term and large scale reanalyses of the terrestrial cryosphere. Our lofty goals in these projects are to generate global high resolution multi-decadal ensemble-based reanalyses of glacier mass balance, the thermal state of permafrost, and seasonal snow mass. In doing so, we are leveraging a plethora of emerging data from Earth observing satellites, global atmospheric reanalyses, and in-situ observations. Herein, we will focus mainly on the general implementation of the novel ensemble-based methods that we are using to solve the reanalysis (or reconstruction) problem as opposed to the structure of the specific cryospheric models and data that they are applied to. Considerable emphasis is placed on how these methods can be deployed at unprecedented spatio-temporal scales while retaining uncertainty quantification that is crucial in guiding decisions. Looking further ahead, we will highlight the challenges that remain in pushing the boundaries of terrestrial reanalysis efforts towards the hillslope (100 m) scale and making use of the largely untapped and continuously growing stream of Earth observation data.

• Treichler, Désirée; Mazzolini, Marco; Piermattei, Livia; Webster, Clare; Girod, Luc & Aalstad, Kristoffer [Show all 7 contributors for this article] (2023). SNOWDEPTH: Spaceborne snow depth measurements from ICESat-2 laser altimetry and data assimilation. Full text in Research Archive
• Mazzolini, Marco; Treichler, Désirée; Aalstad, Kristoffer & Alonso-Gonzalez, Esteban (2023). Satellite Altimetry as a New Data Source for Snow Depth Data Assimilation. Full text in Research Archive
• Mazzolini, Marco; Aalstad, Kristoffer; Treichler, Désirée & Alonso-Gonzalez, Esteban (2023). Spatio-temporal snow data assimilation with laser altimetry. Full text in Research Archive
• Mazzolini, Marco; Aalstad, Kristoffer; Treichler, Désirée & Alonso-Gonzalez, Esteban (2023). Satellite Altimetry for Data Assimilation. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon; Gascoin, Simon; Pirk, Norbert & Remmers, Janneke [Show all 8 contributors for this article] (2022). Evaluating modeled snow cover dynamics over Fennoscandia using Earth observations and reanalyses. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon; Gascoin, Simon; Pirk, Norbert & Remmers, Janneke [Show all 8 contributors for this article] (2022). Evaluating modeled snow cover dynamics over Fennoscandia using Earth observations. Full text in Research Archive Show summary

  The snow cover is an essential part of the climate system in cold regions through its effects on the terrestrial water, energy, and carbon balance. Due to the high spatiotemporal variability of snow, it is challenging to resolve snow cover dynamics in models. Thus, our ability to improve the representation of these dynamics in Earth System Models (ESMs) leans heavily on the accuracy and representativeness of the observational data sets used for model evaluation. The big picture provided by the long-term climate data record from satellites helps us to monitor changes in land cover over large areas. At the same time, rapidly developing drone and terrestrial imaging technology provides higher resolution information over specific areas. This complimentary information from spaceborne, airborne, and terrestrial Earth observations is invaluable for better understanding the complex processes in the climate system. In our work, we are currently exploiting estimates of snow-covered area from different optical sensors onboard polar orbiting satellites that are imaging the Nordic region. Drone and terrestrial images are being explored as a source of validation and calibration data for the satellite products.  Having representative snow cover maps enables us to better evaluate the terrestrial component of the Norwegian Earth System Model (NorESM), namely the Community Land Model (CLM5). With a focus on snow processes, we are conducting an analysis using satellite-based estimates of snow-covered area (MODIS, Sentinel-2, and Landsat 8), snow simulations from CLM5, snow variables from several climate reanalyses (ERA5, ERA5-Land, and MERRA-2), and in-situ data from eddy covariance stations (LATICE flux sites). Two offline CLM5 simulations are conducted with different atmospheric forcing, namely the default data set (GSWP3) and ERA5. We are investigating trends in the snow cover phenology, which we characterize using snow cover duration, first and last days of the snow cover, and consecutive snow cover days for each snow season over the last two decades. This work illuminates a path to integrate Earth observations with Earth system modeling in cold environments to both identify and constrain sources of uncertainty. Acknowledgement: This ongoing study is supported by the LATICE (Land-ATmosphere Interactions in Cold Environments) strategic research initiative funded by the University of Oslo, and the project EMERALD (294948) funded by the Research Council of Norway.

• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon; Gascoin, Simon; Stordal, Frode & Tallaksen, Lena M. (2021). Fennoscandian snow cover dynamics in the MODIS era. Full text in Research Archive
• Salzano, Roberto; Aalstad, Kristoffer; Boldrini, Enrico; Gallet, Jean-Charles; Kepski, Daniel & Luks, Bartlomiej [Show all 9 contributors for this article] (2021). Terrestrial photography applications on snow cover in Svalbard (PASSES), The State of Environmental Science in Svalbard. Svalbard Integrated Arctic Earth Observing System. ISSN 9788293871002. p. 236–251. doi: 10.5281/zenodo.4294084. Full text in Research Archive
• Aalstad, Kristoffer; Fiddes, Joel; Martin, Leo Celestin Paul; Alonso-Gonzalez, Esteban; Yilmaz, Yeliz A. & Pirk, Norbert [Show all 7 contributors for this article] (2021). Workshop on downscaling with TopoSCALE for cryospheric applications. Full text in Research Archive Show summary

  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.

• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Bazilova, Varvara; Bertino, Laurent; Fiddes, Joel & Pirk, Norbert [Show all 7 contributors for this article] (2021). Leveraging emerging Earth observations using data assimilation. Full text in Research Archive Show summary

  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; Westermann, Sebastian; Pirk, Norbert; Fiddes, Joel & Bertino, Laurent (2021). Retrieving fractional snow-covered area from optical satellites using data assimilation. Full text in Research Archive Show summary

  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.

• Salzano, Roberto; Aalstad, Kristoffer; Boldrini, Enrico; Gallet, Jean-Charles; Kȩpski, Daniel & Luks, Bartlomiej [Show all 9 contributors for this article] (2021). Terrestrial photography applications on snow cover in Svalbard (PASSES), The State of Environmental Science in Svalbard. Svalbard Integrated Arctic Earth Observing System. ISSN 9788293871002. p. 236–251. doi: 10.5281/zenodo.4294084. Full text in Research Archive Show summary

  Ground-based observations are critical requirements for many disciplines that are trying to monitor climate change in a remote environment such as the Svalbard archipelago. This overview of cameras operating in Svalbard has been compiled by searching for specific applications that monitor the snow cover and by collecting information about images that can be accessed on the internet, including those not solely dedicated to cryospheric research. The survey identified 43 cameras operating in the region that are managed by research institutions and private companies. These cameras include facilities operated by different nationalities. The datasets vary, but the feasibility of using them to determine fractional snow cover is generally limited. Identifying the key metadata necessary to survey the available devices revealed problems and knowledge gaps that prevent using the full potential of terrestrial photography networks in Svalbard.

• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Bazilova, Varvara; Bertino, Laurent; Fiddes, Joel & Filhol, Simon [Show all 9 contributors for this article] (2021). Unmixing satellite imagery using data assimilation to map snow and albedo. Full text in Research Archive
• 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. Full text in Research Archive
• 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. Full text in Research Archive
• Aalstad, Kristoffer; Alonso-Gonzalez, Esteban; Bertino, Laurent; Fiddes, Joel; Hove, Alouette van & Pirk, Norbert [Show all 8 contributors for this article] (2021). Learning from Earth observations using data assimilation. Full text in Research Archive
• 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. Full text in Research Archive
• Yilmaz, Yeliz A.; Aalstad, Kristoffer; Filhol, Simon Vincent P; Stordal, Frode & Tallaksen, Lena M. (2020). Scandinavian snow cover phenology from MODIS, CLM, and reanalyses. Full text in Research Archive
• 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. Full text in Research Archive Show summary

  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.

• 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. Full text in Research Archive Show summary

  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.

• Aalstad, Kristoffer; Westermann, Sebastian; Pirk, Norbert; Fiddes, Joel; Karsten, Logan & McCreight, James [Show all 8 contributors for this article] (2020). Constraining land surface models with emerging observations. Full text in Research Archive
• 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. Full text in Research Archive
• 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. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian; Bertino, Laurent; Schuler, Thomas; Boike, Julia & Karsten, Logan (2018). Towards high-resolution Bayesian snow reconstruction in permafrost regions. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian; Karsten, Logan; Fiddes, Joel & Bertino, Laurent (2018). Snow history matching in mountainous terrain. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian; Karsten, Logan; Gutmann, Ethan; McCreight, James & Fiddes, Joel [Show all 7 contributors for this article] (2018). Ensemble-based reanalysis of the seasonal montane snowpack: Lessons from the ASO. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian; Schuler, Thomas; Boike, Julia & Bertino, Laurent (2017). Ensemble-based subgrid snow data assimilation. Full text in Research Archive
• 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. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian; Schuler, Thomas; Boike, Julia & Bertino, Laurent (2017). Towards High-Resolution SWE Mapping in Permafrost Regions. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian; Schuler, Thomas; Boike, Julia & Bertino, Laurent (2017). Towards High-Resolution SWE Mapping in Permafrost Regions. Full text in Research Archive
• Christakos, Konstantinos; Varlas, George; Cheliotis, Ioannis; Aalstad, Kristoffer; Papadopoulos, Anastasios & Katsafados, Petros [Show all 7 contributors for this article] (2017). Quantitative variability of renewable energy resources in Norway. Full text in Research Archive
• 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. Full text in Research Archive
• 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. Full text in Research Archive
• Schuler, Thomas; Aalstad, Kristoffer; Aas, Kjetil Schanke; Burkhart, John; Dunse, Thorben & Filhol, Simon [Show all 9 contributors for this article] (2016). Towards real-time snow products for Svalbard. Full text in Research Archive
• Aalstad, Kristoffer; Bertino, Laurent & Westermann, Sebastian (2016). An ensemble-based subgrid snow data assimilation framework. Full text in Research Archive
• Westermann, Sebastian; Langer, Moritz; Østby, Torbjørn Ims; Peter, Maria; Boike, Julia & Gisnås, Kjersti [Show all 12 contributors for this article] (2016). Mapping the thermal state of permafrost through modeling and remote sensing. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2016). An ensemble-based snow data assimilation framework. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2016). An ensemble-based subgrid snow data assimilation framework. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian; Boike, Julia; Bertino, Laurent & Aas, Kjetil Schanke (2016). An ensemble-based snow data assimilation framework with applications to permafrost modeling. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2016). An ensemble-based subgrid snow data assimilation framework applied to the southern Swiss alps. Full text in Research Archive
• Aalstad, Kristoffer; Westermann, Sebastian & Bertino, Laurent (2019). Ensemble-based retrospective analysis of the seasonal snowpack. Universitetet i Oslo. Full text in Research Archive Show summary

  This thesis presents a satellite-based modeling framework that can estimate how much snow was stored in the terrain. These estimates can help guide climate analysis and prediction. Accurate quantification of Earth’s snow mass is a long-standing problem to which a solution is direly needed with ongoing climate change. Snow plays an essential role in the climate system and snowmelt is a vital source of freshwater for a quarter of the world’s population. The framework combines satellite imagery and historic weather data to remotely estimate snow mass by leveraging enhanced ensemble-based data assimilation algorithms. The result is a retrospective analysis (reanalysis) of the snow mass that can be obtained for any location on Earth. So far, this framework has been successfully implemented in three different environments: Svalbard, the Californian Sierra Nevada, and the Swiss Alps. In the future, snow reanalyses could be used to train algorithms to predict snow mass in near real time. They may also help validate and subsequently improve climate models. Ultimately this would allow us to make even more informed future projections of the possible fate of the environment that sustains us.

• Aalstad, Kristoffer & Berntsen, Terje Koren (2015). Applying the Eddy Covariance Method Under Difficult Conditions. Universitetet i Oslo. Full text in Research Archive Show summary

  We assess how reliable the Eddy-Covariance (EC) method is in estimating surface fluxes under the difficult conditions that occur in the high Arctic. Emphasis is placed on stable stratification and the breakdown of EC assumptions that may occur in such a regime. To investigate these difficulties we developed an EC processing module from scratch, providing an extensive and transparent overview of the EC method. Raw data was obtained from an open path EC system located in the Bayelva catchment near Ny Ålesund (79&deg;N), Svalbard, Norway. Our flux estimates are in reasonable agreement with those found from the standardized EC package TK2. Strong relative non-stationarity represents the greatest hindrance to data quality at Bayelva, occurring for 11% of the data period. Overall, average relative flux uncertainties were found to be 20% for both the sensible (SH) and latent heat (LH) flux. Under stable stratification these uncertainties were considerably higher, 27% on average. Through Ogive classification we found that the traditional 30 minute SH and LH fluxes converged (resolved the turbulent cospectrum) 70% of the time. Here too the stable regime stands out, with low convergence fractions of 41% and 48% for LH and SH, respectively. To our knowledge it is the first time such an analysis has been carried out in the Arctic. Concluding, while usually successful for neutral and unstable conditions, the traditional 30 minute flux averaging period is, more often than not, poorly suited for the stable regime. We attribute this to the observed and predicted shift in cospectral peaks towards lower periods under stable stratification, along with an erosion of the cospectral gap. An apparently simple fix of reducing the averaging period is not generally a valid solution. The required reduction could introduce unacceptable levels of flux uncertainty.

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