Marco Mazzolini

• 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.

• 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
• 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.

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• 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.

• 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.; 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
• Treichler, Désirée; Mazzolini, Marco; Liu, Zhihao; Aune, Simen Dalseid; Bühler, Yves & Filhol, Simon [Show all 9 contributors for this article] (2025). Performance of high-resolution snow depth data from ICESat-2 spaceborne laser altimetry. Full text in Research Archive
• Treichler, Désirée; Mazzolini, Marco; Aune, Simen Dalseid; Bühler, Yves; Girod, Luc & Liu, Zhihao [Show all 8 contributors for this article] (2025). High-resolution snow depth profiles from ICESat-2. doi: https:/lps25.esa.int/lps25-presentations/presentations/316/_316.pdf. Full text in Research Archive Show summary

  To date, snow depth measurements require manual measurements or targeted field campaigns. The ATLAS sensor onboard the ICESat-2 satellite acquires profiles of surface elevation measurements of very high accuracy. When compared with an accurate digital elevation model (DEM) from snow-free conditions, this data directly translates into snow depth measurements. Previous studies used the spatially summarised ICESat-2 data products ATL06 and ATL08 with an along-profile resolution of 20-100 m. They found that ICESat-2 can provide average snow depth estimates at the watershed scale with decimeter-level uncertainties. Uncertainties and bias were found to strongly increase with slope and depend on the reference DEM accuracy and the quality of the co-registration of the datasets. This study uses the individual photon data product ATL03 that has an along-track resolution of 0.7 m and thus the potential to provide high-resolution snow depth profiles. Each overpass results in a profile pair separated by 90 m laterally and consisting of a weak and a strong beam with approximately four times as many return photons. We compare different photon filtering and co-registration methods for five field sites in Norway, Finland, and Switzerland including alpine terrain of different topography, sparse and dense forest. Given careful pre-processing, we find that ATL03 data can yield snow depth profiles with a few meters' spatial resolution that closely match profiles derived from reference snow depth maps from uncrewed aerial vehicles (UAVs) acquired within 5-10 days of an ICESat-2 overpass. The goodness of fit depends on the chosen filtering method which should be adjusted to the acquisition conditions and the presence of vegetation and snow on trees to yield optimal results. Dataset co-registration is crucial for steep terrain, and in some areas, the strong and weak beam have different spatial offsets that require separate co-registration for each beam. Given locally optimised pre-processing, the uncertainty (mean absolute deviation, MAD) for ICESat-2/UAV data pairs ranges from 0.05 m in a sparsely forested, flat site to 0.4 m in a very steep alpine site. Bias (median residual) ranges from a few centimetres to several decimetres. For most sites the snow depths retrieved from strong and weak beams are consistently offset, with a vertical difference of up to 25 cm between strong/weak snow depth profiles for the same filtering/co-registration method and site, suggesting inconsistencies in the geolocation of beams of the same pair in ATL03 data. Improved low-level processing on the data provider's side in future ATL03 data versions may reduce the differences between the beams. This study finds that, given accurate reference DEMs, ICESat-2 data can not only provide catchment-scale snow depth averages but also high-resolution snow depth profiles in areas where no measurements currently exist, showcasing the potential of spaceborne laser altimetry for providing high-resolution snow depth measurements globally.

• 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; 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.

• 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
• Aalstad, Kristoffer; Willmes, Clarissa; Mazzolini, Marco & Kreynen, Dylan (2024). Snow data assimilation at UiO. Full text in Research Archive
• Treichler, Désirée; Filhol, Simon; Mazzolini, Marco; Yilmaz, Yeliz A. & Silantyeva, Olga (2024). UiO’s snow field sites, measurements, remotely sensed datasets, and climate container. 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
• Liu, Zhihao; Treichler, Désirée & Mazzolini, Marco (2023). Snow depth retrieval using satellite altimetry, climate reanalysis data and machine learning: A case study in mainland Norway. Full text in Research Archive
• Treichler, Désirée; Mazzolini, Marco; Liu, Zhihao & Guidicelli, Matteo (2023). SNOWDEPTH: Global snow depths from spaceborne remote sensing for permafrost, high-elevation precipitation, and climate reanalyses. Full text in Research Archive
• Treichler, Désirée; Mazzolini, Marco; Piermattei, Livia; Webster, Clare; Girod, Luc & Bühler, Yves (2023). Spaceborne snow depth measurements from ICESat-2 laser altimetry. 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
• Treichler, Désirée; Mazzolini, Marco; Piermattei, Livia; Webster, Clare & Girod, Luc (2022). Spaceborne snow depth measurements from ICESat-2 laser altimetry. Full text in Research Archive

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