Surface mass balance (SMB) provides mass input to the surface of the Antarctic and Greenland Ice Sheets and therefore comprises an important control on ice sheet mass balance and resulting contribution to global sea level change. As ice sheet SMB varies highly across multiple scales of space (meters to hundreds of kilometers) and time (hourly to decadal), it is notoriously challenging to observe and represent in models. In addition, SMB consists of multiple components, all of which depend on complex interactions between the atmosphere and the snow/ice surface, large-scale atmospheric circulation and ocean conditions, and ice sheet topography. In this review, we present the state-of-the-art knowledge and recent advances in ice sheet SMB observations and models, highlight current shortcomings, and propose future directions. Novel observational methods allow mapping SMB across larger areas, longer time periods, and/or at very high (subdaily) temporal frequency. As a recent observational breakthrough, cosmic ray counters provide direct estimates of SMB, circumventing the need for accurate snow density observations upon which many other techniques rely. Regional atmospheric climate models have drastically improved their simulation of ice sheet SMB in the last decade, thanks to the inclusion or improved representation of essential processes (e.g., clouds, blowing snow, and snow albedo), and by enhancing horizontal resolution (5-30 km). Future modeling efforts are required in improving Earth system models to match regional atmospheric climate model performance in simulating ice sheet SMB, and in reinforcing the efforts in developing statistical and dynamic downscaling to represent smaller-scale SMB processes.

Abstract. The geodetic method is widely used for assessing changes in the mass balance of mountain glaciers. However, comparison of repeated digital elevation models only provides a glacier volume change that must be converted to a change in mass using a density assumption. This study investigates this conversion factor based on a firn compaction model applied to simplified glacier geometries with idealized climate forcing, and two glaciers with long-term mass balance series. It is shown that the "density" of geodetic volume change is not a constant factor and is systematically smaller than ice density in most cases. This is explained by the accretion/removal of low-density firn layers, and changes in the firn density profile with positive/negative mass balance. Assuming a value of 850 ± 60 kg m−3 to convert volume change to mass change is appropriate for a wide range of conditions. For short time intervals (≤3 yr), periods with limited volume change, and/or changing mass balance gradients, the conversion factor can however vary from 0–2000 kg m−3 and beyond which requires caution when interpreting glacier mass changes based on geodetic surveys.

Glaciers in the Central Asian mountain ranges Tien Shan, Pamir and Pamir Alay are important water reservoirs for the dry low lands. These mountain glaciers attracted scientific interest already early. Soviet research programs investigated several sites from the 1960s until the 1990s. The resulting historical data are unique for the region and essential to answer open questions about the glaciers’ response to climate change. Regional-scale remote sensing studies reported balanced or positivemass changes for glaciers in Western High Mountain Asia for the last decades. With glaciers losing mass globally, this is a unique phenomenon. A precipitation increase is discussed to be a potential reason of this mass balance anomaly. However, the lack of in situ data hampers strengthening these assumptions and impedes quantifying the uncertainties of studies based on remote sensing data and gridded precipitation products. The Pamir Alay is located at the edge of the anomalous regions. Soviet researchers collected unique glaciological and meteorological data for Abramov glacier, located in this data-scarce region. Of particular interest are very detailed firn studies that provide information about the past precipitation rates and allow studying accumulation processes. Thanks to the availability of further, exceptionally detailed measurements, it is possible to relate the accumulation processes to the glacier-wide mass balance. This thesis aims at investigating the historical and present firn conditions of Abramov glacier as well as the changes therein over the past five decades. The firn processes were related to the surface energy andmass balance of Abramov glacier. Thereby, the influence of firn changes on the glacier-wide mass balance was studied. The underlying work involved (i) compiling and processing of historical firn, mass balance and meteorological data; (ii) measuring current firn conditions; and (iii) applying a coupled surface energy balance – multilayer subsurface model to Abramov glacier. The comparison of historical and current in situ data showed that the firn conditions of Abramov glacier have changed little between the 1970s and 2018. The data, however, also suggested a precipitation increase. The results of the coupled firn-mass balance model indicate that the firn properties of the 1970s were the result of specific meteorological conditions with low precipitation and high incoming solar radiation. These conditions were also reflected in very negative glacier mass balances. Precipitation increased during the following decades and allowed the firn to recover in the upper areas of the accumulation zone. Therefore, the internal accumulation (refreezing of melt water in the firn) increased. It is also shown that internal accumulation substantially contributed to the glacier-wide mass balance of Abramov. For the most recent years, firn conditions become again icier and mass losses increased. The presented thesis found in situ evidence of increased precipitation rates and their positive impact on themass balance for a glacier located in the data scarce western High Mountain Asia. The work highlights the importance of firn processes for understanding the response of mountain glaciers to climate change. Moreover, it demonstrates the importance of historic (Soviet) research and the suitability of the Russian terminology for analysing firn processes. Die Gletscher imZentralasiatischen Pamir-, Pamir Alay- und Tien Shan-Gebirge sind wichtige Wasserspeicher für das tiefer gelegene trockene Vorland. Schon früh haben diese Gletscher wissenschaftliches Interesse geweckt. Sowjetische Forschungsprogramme haben mehrere Standorte von den 1960er bis in die 1990er Jahre intensiv untersucht. Diese historischen Daten sind für die Region einmalig und könnten helfen, offene Fragen bezüglich der dortigen Gletscherveränderungen als Folge des Klimawandels zu beantworten. Mehrere regionale fernerkundungsbasierte Studien haben gezeigt,

Accurate firn density estimation is essential for assessing glacier mass balance. However, the accuracy of existing firn densification models (FDMs) is limited by an incomplete understanding of firn compaction dynamics, particularly as firn structure alters in warming conditions. This study proposes the firn density prediction transformer (FDTransformer), a deep learning framework that combines firn densification physics to improve density estimation. By employing the transformer network with sequential self-attention mechanisms, the FDTransformer learns a nonlinear mapping between physical firn parameters input and observed firn density, enabling physics-to-density sequence transformation. These physically constrained parameters are estimated by applying physics-based FDMs. Evaluated using <i>in situ</i> measurements from three Greenland sites (Dye-2, KAN_U, and Summit) with varying firn evolution patterns, the FDTransformer reduces mean absolute error by 30%, 42%, and 24%, respectively, compared to the physics-based FDMs. This study demonstrates that combining deep learning techniques with firn densification physics can improve firn density assessment.

&amp;lt;p&amp;gt;The potential of surface altimetry and photogrammetry for assessing the volume change of glaciers is tremendous and the scope of available data sets is increasing at a rapid pace. Surface elevation changes are now available for all glaciers globally and the time periods that can be resolved by these data are becoming shorter. However, most glaciological and hydrological studies rely on glacier mass change instead of volume change, thus necessitating a conversion accounting for the density of the gained or lost ice, firn or snow. While glaciers gain or lose volume, their firn coverage simultaneously changes, both in terms of extent, thickness and density, complicating the estimation of the conversion factor. Often, geodetic studies use a density of volume change equal to 850 kg m&amp;lt;sup&amp;gt;-3&amp;lt;/sup&amp;gt;&amp;amp;#160;which has been found to be valid for a wide range of cases. Nevertheless, particular situations, e.g. changes in mass balance gradients related to abrupt accelerations or decelerations of local atmospheric warming might result in significant departures of the conversion factor from this reference value. This probably represents the most important uncertainty factor in regional to global-scale assessments of geodetic glacier mass change.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Here, we substantially update the assessment of the optimal conversion between volume and mass change by Huss (2013) and apply the same firn densification model to all roughly 200'000 glaciers globally. Local annual surface mass balance over the period 2000-2019 is prescribed by the global glacier model GloGEM. The model is driven by ERA5 climate re-analysis data, and cumulative modelled mass balance is constrained to match observations of geodetic elevation change for each individual glacier for 2000-2019. By comparing mass balance and computed glacier volume changes resulting from the firn density model, a volume-to-mass change conversion factor is derived for each glacier and any period over the last two decades. Our assessment thus accounts for local changes in climate and, hence, shifts in the properties of the firn coverage, as well as the observed changes of each individual glacier.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;A considerable variance in the factors necessary to convert geodetic ice volume change to mass change is found, both at the regional scale but also for different time periods of the same region. For many regions, the estimate of 850&amp;amp;#177;60 kg m&amp;lt;sup&amp;gt;-3&amp;lt;/sup&amp;gt; for the density of ice volume change is valid, encompassing most of the investigated periods within 2000-2019. However, for some - mostly high-latitude - regions significantly lower and higher conversion factors have been found, related to particular long-term changes in firn density and thickness. Various assumptions and simplifications are involved in this global-scale assessment. Nevertheless, we consider our results as a helpful guideline for estimating volume-to-mass conversion factors in geodetic studies around the world over arbitrary time periods.&amp;lt;/p&amp;gt;