Distributed Mass Balance Model Research Articles

Applying a distributed mass-balance model to identify uncertainties in glaciological mass balance on Brewster Glacier, New Zealand

AbstractA distributed mass-balance model is used over a 10-year period for the re-analysis of a glaciological mass-balance time series obtained from Brewster Glacier, New Zealand. Mass-balance modelling reveals glaciological mass balance has been overestimated, with an average mass loss of −516 mm w.e. a−1 not captured by observations at the end of the ablation season, which represents 35% of the annual mass balance. While the average length of the accumulation season (199 days) remains longer than the ablation season (166 days), melting is not uncommon in the core part of the accumulation season, with 2–32% of total snowfall being melted. Refreezing of meltwater is also important, with 10% of surface and subsurface melt being refrozen in the present climate. Net radiation, driven primarily by net shortwave radiation, is the main contributor to melt energy, with melt variability mainly influenced by the turbulent heat fluxes, net longwave radiation and the heat flux from precipitation in the ablation season. Snowfalls in summer are an important moderator of melt, highlighting the critical role of the ice-albedo feedback and phase of precipitation on seasonal mass balance. A complete homogenisation of the long-term glaciological mass balance for Brewster Glacier is still required.

An imbalancing act: the delayed dynamic response of the Kaskawulsh Glacier to sustained mass loss

AbstractThe Kaskawulsh Glacier is an iconic outlet draining the icefields of the St. Elias Mountains in Yukon, Canada. We determine and attempt to interpret its catchment-wide mass budget since 2007. Using SPOT5/6/7 data we estimate a 2007–18 geodetic balance of −0.46 ± 0.17 m w.e. a−1. We then compute balance fluxes and observed ice fluxes at nine flux gates to examine the discrepancy between the climatic mass balance and internal mass redistribution by glacier flow. Balance fluxes are computed using a fully distributed mass-balance model driven by downscaled and bias-corrected climate-reanalysis data. Observed fluxes are calculated using NASA ITS_LIVE surface velocities and glacier cross-sectional areas derived from ice-penetrating radar data. We find the glacier is still in the early stages of dynamic adjustment to its mass imbalance. We estimate a committed terminus retreat of ~23 km under the 2007–18 climate and a lower bound of 46 km3of committed ice loss, equivalent to ~15% of the total glacier volume.

Implementing an object-based multi-index protocol for mapping surface glacier facies from Chandra-Bhaga basin, Himalaya

Surface glacier facies are superficial expressions of a glacier that are distinguishable based on differing spectral and structural characteristics according to their age and inter-mixed impurities. Increasing bodies of literature suggest that the varying properties of surface glacier facies differentially influence the melt of the glacier, thus affecting the mass balance. Incorporating these variations into distributed mass balance modelling can improve the perceived accuracy of these models. However, detecting and subsequently mapping these facies with a high degree of accuracy is a necessary precursor to such complex modelling. The variations in the reflectance spectra of various glacier facies permit multiband imagery to exploit band ratios for their effective extraction. However, coarse and medium spatial resolution multispectral imagery can delimit the efficacy of band ratioing by muddling the minor spatial and spectral variations of a glacier. Very high-resolution imagery, on the other hand, creates distortions in the conventionally obtained information extracted through pixel-based classification. Therefore, robust and adaptable methods coupled with higher resolution data products are necessary to effectively map glacier facies. This study endeavours to identify and isolate glacier facies on two unnamed glaciers in the Chandra-Bhaga basin, Himalayas, using an established object-based multi-index protocol. Exploiting the very high resolution offered by WorldView-2 and its eight spectral bands, this study implements customized spectral index ratios via an object-based environment. Pixel-based supervised classification is also performed using three popular classifiers to comparatively gauge the classification accuracies. The object-based multi-index protocol delivered the highest overall accuracy of 86.67%. The Minimum Distance classifier yielded the lowest overall accuracy of 62.50%, whereas, the Mahalanobis Distance and Maximum Likelihood classifiers yielded overall accuracies of 77.50% and 70.84% respectively. The results outline the superiority of the object-based method for extraction of glacier facies. Forthcoming studies must refine the indices and test their applicability in wide ranging scenarios.

COMPARISON OF PIXEL AND OBJECT-BASED CLASSIFICATION TECHNIQUES FOR GLACIER FACIES EXTRACTION

Abstract. Glacier facies are zones of snow on a glacier that have certain specific spectral characteristics that enable their characterization. The accuracy of their extraction will determine the end accuracy of the distributed mass balance model calibrated by this information. Therefore, coarse to medium resolution satellites are not preferable for this particular function as the data derived from such sensors will potentially blur out the minute spatial variations on the surface of a glacier. Very high resolution (VHR) sensors (such as, WorldView (WV)-1, 2, 3) are thus much more suited for this particular task. Hence, this study aims to extract the available glacier facies on the Sutri Dhaka glacier, Himalayas, using very high-resolution WorldView-2 (WV-2) imagery. Extensive pre-processing of the imagery was performed to prepare the data for this purpose. The steps incorporated for this purpose consist of 1) Data Calibration, 2) Mosaicking, 3) Pan Sharpening, 4) Generation of 3D surface, and 5) Digitization. Using image classification as the primary method of information extraction, this study tests the ever-popular pixel-based classification technique against the uprising object-based classification technique. In doing so, this study aims to determine the most accurate technique of information extraction for the WV-2 imagery in the given scenario. The presence of unique bands (Coastal (0.40–0.45 μm), Red Edge (0.705–0.745 μm), NIR-1 (0.770–0.895 μm) and NIR-2 (0.86–1.04 μm) in the multispectral range of WV-2, allows this study to perform facies classification through the development of customized spectral index ratios (SIRs) in the object-based domain. Establishment of thresholds was hence necessitated for information extraction through the developed SIRs. Three supervised classifiers, namely, a) Mahalanobis distance, b) Maximum likelihood, and c) Minimum distance to mean, were then used to perform classification, thereby allowing a comparative analysis between the classification schemes. Accuracy assessment for each classification scheme was performed using error matrices. The object-based approach achieved an overall accuracy of 90% (κ = 0.88) and the highest overall accuracy among the pixel-based classification methods is 78.57% (κ = 0.75). The results clearly portray that the object-based method delivered much higher accuracy than the pixel-based methods. The carry home message is that future studies must examine the transferability and accuracy of the customized SIRs in varying scenarios, as different scenarios will require varying threshold adjustments. Forthcoming studies can also develop sensor specific and unique indices for other sensors that are suitable for such applications.

Sensitivity of mountain glacier mass balance to changes in bare-ice albedo

ABSTRACTAlbedo is an important parameter in the energy balance of bare-ice surfaces and modulates glacier melt rates. The prolongation of the ablation period enforces the albedo feedback and highlights the need for profound knowledge on impacts of bare-ice albedo on glacier mass balance. In this study, we assess the mass balance sensitivity of 12 Swiss glaciers with abundant long-term in-situ data on changes in bare-ice albedo. We use pixel-based bare-ice albedo derived from Landsat 8. A distributed mass-balance model is applied to the period 1997–2016 and experiments are performed to assess the impact of albedo changes on glacier mass balance. Our results indicate that glacier-wide mass-balance sensitivities to changes in bare-ice albedo correlate strongly with mean annual mass balances (r2= 0.81). Large alpine glaciers react more sensitively to bare-ice albedo changes due to their ablation areas being situated at lower elevations. We find average sensitivities of glacier-wide mass balance of −0.14 m w.e. a−1per 0.1 albedo decrease. Although this value is considerably smaller than sensitivity to air temperature change, we stress the importance of the enhanced albedo feedback that will be amplified due to atmospheric warming and a suspected darkening of glacier surface in the near future.

Effects of local advection on the spatial sensible heat flux variation on a mountain glacier

Abstract. Distributed mass balance models, which translate micrometeorological conditions into local melt rates, have proven deficient to reflect the energy flux variability on mountain glaciers. This deficiency is predominantly related to shortcomings in the representation of local processes in the forcing data. We found by means of idealized large-eddy simulations that heat advection, associated with local wind systems, causes small-scale sensible heat flux variations by up to 100 Wm−2 during clear sky conditions. Here we show that process understanding at a few observation sites is insufficient to infer the wind and temperature distributions across the glacier. The glacier-wide hourly averaged sensible heat fluxes are both over- and underestimated by up to 16 Wm−2 when using extrapolated temperature and wind fields. The sign and magnitude of the differences depend on the site selection, which is used for extrapolation as well as on the large-scale flow direction. Our results demonstrate how the shortcomings in the local sensible heat flux estimates are related to topographic effects and the insufficient characterization of the temperature advection process.

Mass Balance Re-analysis of Findelengletscher, Switzerland; Benefits of Extensive Snow Accumulation Measurements

A re-analysis is presented here of a 10-year mass balance series at Findelengletscher, a temperate mountain glacier in Switzerland. Calculating glacier-wide mass balance from the set of glaciological point balance observations using conventional approaches, such as the profile or contour method, resulted in significant deviations from the reference value given by the geodetic mass change over a five-year period. This is attributed to the sparsity of observations at high elevations and to the inability of the evaluation schemes to adequately estimate accumulation in unmeasured areas. However, measurements of winter mass balance were available for large parts of the study period from snow probings and density pits. Complementary surveys by helicopter-borne ground-penetrating radar (GPR) were conducted in three consecutive years. The complete set of seasonal observations was assimilated using a distributed mass balance model. This model-based extrapolation revealed a substantial mass loss at Findelengletscher of -0.43m w.e. a^-1 between 2004 and 2014, while the loss was less pronounced for its former tributary, Adlergletscher (-0.30m w.e. a^-1). For both glaciers, the resulting time series were within the uncertainty bounds of the geodetic mass change. We show that the model benefited strongly from the ability to integrate seasonal observations. If no winter mass balance measurements were available and snow cover was represented by a linear precipitation gradient, the geodetic mass balance was not matched. If winter balance measurements by snow probings and snow density pits were taken into account, the model performance was substantially improved but still showed a significant bias relative to the geodetic mass change. Thus the excellent agreement of the model-based extrapolation with the geodetic mass change was owed to an adequate representation of winter accumulation distribution by means of extensive GPR measurements.

Re-analysis of seasonal mass balance at Abramov glacier 1968–2014

AbstractAbramov glacier, located in the Pamir Alay, Kyrgyzstan, is a reference glacier within the Global Terrestrial Network for Glaciers. Long-term glaciological measurements exist from 1968 to 1998 and a mass-balance monitoring programme was re-established in 2011. In this study we re-analyse existing mass-balance data and use a spatially distributed mass-balance model to provide continuous seasonal time series of glacier mass balance covering the period 1968–2014. The model is calibrated to seasonal mass-balance surveys and then applied to the period with no measurements. Validation and recalibration is carried out using snowline observations derived from satellite imagery and, after 2011, also from automatic terrestrial camera images. We combine direct measurements, remote observations and modelling. The results are compared to geodetic glacier volume change over the past decade and to a ground-penetrating radar survey in the accumulation zone resolving several layers of accumulation. Previously published geodetic mass budget estimates for Abramov glacier suggest a close-to-zero mass balance for the past decade, which contradicts our results. We find a low plausibility for equilibrium conditions over the past 15 years. Instead, we suggest that the glacier’s sensitivity to increased summer air temperature is decisive for the substantial mass loss during the past decade.

The footprint of Asian monsoon dynamics in the mass and energy balance of a Tibetan glacier

Abstract. Determinations of glacier-wide mass and energy balance are still scarce for the remote mountains of the Tibetan Plateau, where field measurements are challenging. Here we run and evaluate a physical, distributed mass balance model for Zhadang Glacier (central Tibet, 30° N) based on in-situ measurements over 2009–2011 and an uncertainty estimate by Monte Carlo and ensemble strategies. The model application aims to provide the first quantification of how the Indian Summer Monsoon (ISM) impacts an entire glacier over the various stages of the monsoon's annual cycle. We find a strong and systematic ISM footprint on the interannual scale. Early (late) monsoon onset causes higher (lower) accumulation, and reduces (increases) the available energy for ablation primarily through changes in absorbed shortwave radiation. By contrast, only a weak footprint exists in the ISM cessation phase. Most striking though is the core monsoon season: local mass and energy balance variability is fully decoupled from the active/break cycle that defines large-scale atmospheric variability during the ISM. Our results demonstrate quantitatively that monsoon onset strongly affects the ablation season of glaciers in Tibet. However, we find no direct ISM impact on the glacier in the main monsoon season, which has not been acknowledged so far. This result also adds cryospheric evidence that, once the monsoon is in full swing, regional atmospheric variability prevails on the Tibetan Plateau in summer.

Distributed mass-balance modelling on two neighbouring glaciers in Ortles-Cevedale, Italy, from 2004 to 2009

AbstractA 6 year application of an enhanced temperature-index mass-balance model to Careser and La Mare glaciers, Eastern Italian Alps, is presented. The two glaciers exhibit very different characteristics, and a comprehensive dataset of distributed mass-balance measurements was used to test the model performance. The model was run using meteorological data acquired outside the glaciers. The work was focused on two main aspects: (1) the development of a morphological redistribution procedure for snow, and (2) the comparison of three different melt algorithms proposed in the literature. The results show that the simple method proposed for snow redistribution can greatly improve simulation of winter balance, and further improvements would be achievable by collecting data on inaccessible and high-altitude areas. All three melt formulations displayed a good skill level and very similar results in modelling the mass-balance distribution over glacier areas, with slightly better results from a multiplicative algorithm in capturing the vertical balance gradient. The simulation errors are related to aspect and elevation, and tend to be spatially aggregated. Some assumptions concerning the spatial and temporal distribution of air temperature and incoming solar radiation, although reasonable and widely used in the literature, may be responsible for this aggregation. Hence, there is a need to further investigate the processes that regulate the distribution of melt energy, and that appear to control the current deglaciation phase in this area.

Mass balance of Pizolgletscher

Abstract. Half of the glaciers in the Swiss Alps are smaller than 0.1 km2. Despite this, the mass budget of small glaciers and their response to ongoing climate change is rarely studied. A new mass balance monitoring programme on Pizolgletscher (0.08 km2) in north-eastern Switzerland was started in 2006. This paper presents first results and describes a new approach to determining the mass balance of glaciers. Seasonal field observations are interpreted using a distributed mass balance model in daily resolution that allows spatial inter- and extrapolation of sparse data points and the calculation of mass balance over arbitrary time periods. Evaluation of aerial photographs acquired in subdecadal intervals since 1968 allows inclusion of data on changes in glacier area and ice volume, contributing towards a long-term reconstruction of Pizolgletscher's mass balance. The analysis revealed fast mass loss over the last three years with annual balances of -1.61 m w.e. in 2006/2007, -0.71 m w.e. in 2007/2008, and -1.46 m w.e. in 2008/2009 and high spatial variability of mass balance on Pizolgletscher.

Response of the ice cap Hardangerjøkulen in southern Norway to the 20th and 21st century climates

Abstract. Glaciers respond to mass balance changes by adjusting their surface elevation and area. These properties in their turn affect the local and area-averaged mass balance. To incorporate this interdependence in the response of glaciers to climate change, models should include an interactive scheme coupling mass balance and ice dynamics. In this study, a spatially distributed mass balance model, comprising surface energy balance calculations, was coupled to a vertically integrated ice-flow model based on the shallow ice approximation. The coupled model was applied to the ice cap Hardangerjøkulen in southern Norway. The available glacio-meteorological records, mass balance and glacier length change measurements were utilized for model calibration and validation. Forced with meteorological data from nearby synoptic weather stations, the coupled model realistically simulated the observed mass balance and glacier length changes during the 20th century. The mean climate for the period 1961–1990, computed from local meteorological data, was used as a basis to prescribe climate projections for the 21st century at Hardangerjøkulen. For a linear temperature increase of 3 °C from 1961–1990 to 2071–2100, the modelled net mass balance soon becomes negative at all altitudes and Hardangerjøkulen disappears around the year 2100. The projected changes in the other meteorological variables could at most partly compensate for the effect of the projected warming.

Homogenization of long-term mass-balance time series

AbstractThe re-analysis of long-term mass-balance time series is important to provide bias-corrected mass-balance data for climate-change impact studies. A method to homogenize time series of comprehensive mass-balance monitoring programmes is presented and applied to the nearly 50 year mass-balance records of Griesgletscher and Silvrettagletscher, Switzerland. Using a distributed mass-balance model in daily resolution we correct the mass-balance data for varying observation dates. Direct point measurements are combined with independent geodetic mass changes, a prerequisite for a thorough homogenization of mass-balance records. Differences between mass balance evaluated in the hydrological year or according to the measurement period and the stratigraphic system are analysed and may be up to ±0.5mw.e. a−1. Cumulative mass balance of both glaciers based on the glaciological method generally agrees well with geodetic mass change on the investigated glaciers. However, for Silvretta-gletscher a significant bias of +0.37mw.e. a−1 has been detected and corrected for since 1994.

Solar radiation, cloudiness and longwave radiation over low-latitude glaciers: implications for mass-balance modelling

AbstractBroadband radiation schemes (parameterizations) are commonly used tools in glacier mass-balance modelling, but their performance at high altitude in the tropics has not been evaluated in detail. Here we take advantage of a high-quality 2 year record of global radiation (G ) and incoming longwave radiation (L ↓) measured on Kersten Glacier, Kilimanjaro, East Africa, at 5873 m a.s.l., to optimize parameterizations of G and L ↓. We show that the two radiation terms can be related by an effective cloud-cover fraction neff , so G or L ↓ can be modelled based on neff derived from measured L ↓ or G, respectively. At neff = 1, G is reduced to 35% of clear-sky G, and L ↓ increases by 45–65% (depending on altitude) relative to clear-sky L ↓. Validation for a 1 year dataset of G and L ↓ obtained at 4850 m on Glaciar Artesonraju, Peruvian Andes, yields a satisfactory performance of the radiation scheme. Whether this performance is acceptable for mass-balance studies of tropical glaciers is explored by applying the data from Glaciar Artesonraju to a physically based mass-balance model, which requires, among others, G and L ↓ as forcing variables. Uncertainties in modelled mass balance introduced by the radiation parameterizations do not exceed those that can be caused by errors in the radiation measurements. Hence, this paper provides a tool for inclusion in spatially distributed mass-balance modelling of tropical glaciers and/or extension of radiation data when only G or L ↓ is measured.

A calibrated mass balance model for Vatnajökull, Iceland

Vatnajokull (Iceland) is the largest ice cap in the world where the energy and mass balance have been studied with good spatial and temporal resolution. In this paper we use these data to analyze the energy balance and to construct a calibrated and spatially distributed mass balance model. The incoming longwave radiation is best modeled as a function of meteorological variables in the free atmosphere just above the rel- atively thin katabatic layer, instead of those at the 2 m level. The ratio of changes in the 2 m temperature to changes in the free atmospheric temperature (the climate sensitivity) is smaller than 1. Therefore, when the bulk method is used to compute the turbulent fluxes, the 2 m temperature must be explicitly calculated. Otherwise the sensitivity of Vatnajokull to climatic change would be overestimated. When the model is forced with data from a permanent weather station not on the ice cap, it reproduces the observed mass balance reasonably well. Horizontal precipitation gradients over Vatnajokull are large, which results in a strongly varying sensitivity to external temperature changes over the ice cap. The mass balance and its sensitivity is thus highly dependent on local climatic conditions. For a temperature increase of 1 K and a simultaneous precipitation increase of 5.3%, the mean specific mass balance of Vatnajokull decreases by 0.56 m w.e.

A control scheme for packed bed reactors having a changing catalyst activity profile. I: On-line parameter estimation and feedback control

The efficient control of an exothermic packed bed reactor is demonstrated in concert with the distributed parameter state estimation of temperature and concentration profiles and on-line estimation of the catalyst activity profile. The position-dependent catalyst activity is estimated using recursive least squares with a variable forgetting factor, a distributed mass balance model and the current estimated temperature profile. The temperature level in the reactor is regulated through control of the maximum estimated reactor temperature using the reactor coolant temperature as the manipulated variable. These methods are demonstrated both through closed-loop simulation and experiments with a laboratory-scale reactor for the partial oxidation of methanol. The experiments included both setpoint changes and disturbance rejection. The estimation and control system effectively overcomes errors in initial conditions, heat transfer parameters and kinetic parameters.