Temperature-index Melt Research Articles

Automated ablation stakes to constrain temperature-index melt models

Abstract We developed automated ablation stakes to measure colocated in situ changes in relative glacier-surface elevation and climatological drivers of ablation. The designs, refined over 10 years of development and deployments, implement open-source hardware and common building materials. The ablation stakes record distance to the snow/ice surface, air temperature and relative humidity every 1–15 min. Using these high-frequency data, we demonstrate that melt factors calculated using standard melt-rate vs temperature regressions converge over averaging windows of approximately 12 h or greater. Furthermore, we evaluate an integral approach to estimating temperature-index melt factors for ablation. In a test case on Glaciar Perito Moreno, Argentina, this integral approach reveals an overall positive-degree-day melt factor of 7.5 mm w.e. $^\circ$ C−1 d−1. We describe four deployments with iteratively improved designs and provide a list of materials required to construct an automated ablation stake.

Asynchronous glacial dynamics of Last Glacial Maximum mountain glaciers in the Ikh Bogd Massif, Gobi Altai mountain range, southwestern Mongolia: aspect control on glacier mass balance

Abstract. Mountain glacier mass balance is affected by factors other than climate, such as topography, slope, and aspect. In midlatitude high-mountain regions, the north–south aspect contrast can cause significant changes in insolation and melt, resulting in local asynchrony in glacial dynamics. This study documents the asynchronous response of two paleoglaciers in southwestern Mongolia to the local topoclimatic factors using 10Be exposure age dating and 2D ice surface modeling. 10Be surface exposure age dating revealed that the Ikh Artsan south-facing valley glacier culminated (MIA1) at 20.1 ± 0.7 ka, coinciding with the global Last Glacial Maximum (gLGM). In contrast, the north-facing Jargalant paleoglacier (MJ1) culminated at 17.2 ± 1.5 ka, around Heinrich Stadial 1 and during the post-gLGM Northern Hemisphere warming. Our temperature-index melt model predicts that ablation will be substantially lower on the north-facing slope, as it is exposed to less solar radiation and cooler temperatures than the south-facing slope. The 2D ice surface modeling also revealed that the south-facing Ikh Artsan Glacier abruptly retreated from its maximum extent at 20 ka, but the Jargalant Glacier on the shaded slope consistently advanced and thickened due to reduced melt until 17 ka. The timing of the modeled glacier culmination is consistent within ± 1σ of the 10Be exposure age results. Extremely old ages ranging from 636.2 to 35.9 ka were measured for the inner moraines in the Jargalant cirque (MJ2–MJ4), suggesting a problem with inheritance from boulders eroded from the summit plateau.

Snowmelt estimation using an empirical radiation model

This study developed a novel approach for estimating snowmelt using an empirical radiation model, referred to as the Empirical Radiation Snowmelt Model, or ERSM. ERSM assumes that energy available to melt snow is equivalent to the sum of the shortwave radiation absorbed by the snowpack and the net longwave radiation at the snow surface. ERSM has two components. The first component is an empirically determined relationship between the observed daily snowmelt and the daily potential shortwave radiation. The longwave radiation component is implicitly estimated through its influence on the observed snowmelt. The daily potential shortwave radiation was found using two calculated parameters: the top-of-the-atmosphere shortwave radiation and the albedo of the snow surface. This first component simulates the average snowmelt that will occur for a given level of the potential shortwave radiation. The second component of ERSM estimates the difference between the average snowmelt simulated from the potential shortwave radiation (first component) and the actual snowmelt that occurred on any day. Observations from 20 SNOTEL11SNOTEL-U.S. Department of Agriculture, Natural Resources Conservation Service Snow Telemetry site. sites in the Truckee River Watershed were used to develop separate ERSM parameters for each site. ERSM was able to robustly predict snowmelt for all sites considered in this study. The error statistics vary with the magnitude of the observed daily snowmelt and the best results were found for magnitudes at which the majority of snowmelt occurs. A particularly valuable application of ERSM is its use to estimate the melt factor required by temperature index snowmelt models. ERSM can explain a large degree of the observed variance of the temperature index melt factor.

Response of glacier modelling parameters to time, space, and model complexity: Examples from eastern slopes of Canadian Rocky Mountains

Mountain glaciers are at risk of rapid retreat and require an accurate prediction of their melt and evolution. However, there is a great deal of hassle with mountain glacier melt modelling at a regional scale. Most advanced physical process-based models require an ample amount of high-resolution measurements, while widely-used empirical models suffer from parameter transferability. We developed a glacier melt, mass balance, and evolution modelling framework using three temperature index melt modelling approaches. We performed 24 model scenarios to examine the response of 19 empirical parameters to the effects of: (1) two time periods, for understanding how parameter response can vary with time period considered for the simulation; (2) two glaciers located at the eastern slopes of the Canadian Rocky Mountains, for understanding the effects of glaciers hydro-climate and geographic setting; and (3) two levels of complexity in the model structure including melt and mass balance models coupled with (complex) and without (simple) glacier evolution modules. The results showed that the best optimal melt parameter sets vary temporally and spatially for both simple and complex models, indicating that they are not transferable from one period to another and across glaciers. The variations of ice melt parameters are greater than the snowmelt parameters. The spatiotemporal variations of parameters are resulted from the geographical and local climatic settings and energy balance components, including albedo parameterization on the glacier surface, the altitudinal variations of the glaciers, and the slope and aspects to which glaciers are exposed. For all models, the most sensitive parameter is temperature Lapse rate (LR), but with increasing model complexity, the parameter responses vary depending on the melt model structure and input data. Our study provides important information for modelling glacier melt and evolution at a regional scale.

Estimation and analysis of the Antecedent Temperature Index–Melt Rate (ATIMR) function using observed data from the Kırkgöze-Çipak Basin, Turkey

The ability to manipulate multiple variable temporal and spatial atmospheric and earth-born parameters with a single air temperature value affecting the melting and accumulation processes of the snowpack is a convenient approach for the design of water policies and the effective use of water resources. Some of the temperature index models require snowpack’s melt rate as a function of the accumulated number of heating degree-days determined using a model with the Antecedent Temperature Index–Melt Rate (ATIMR) function, in which the modeler can adjust the melt rates during the season. The use of ATIMR function provides a reasonable method; however, the literature on the nature of the default ATIMR function (developed in 1991 and currently in use) is largely unclear and not understandable or practicable. For that reason, in this study, the point-specific and domain-based ATIMR functions specific to the region were determined physically in a logical manner using error propagation analysis. Thus, it was found that R-square values up to 0.99 precision can be obtained. The Hydrologic Engineering Center’s hydrologic modeling system (HEC-HMS) was used and the results were found to be characteristically and statistically effective and valid for various Snow Water Equivalent (SWE) simulations. In addition, it was revealed that the unexpected behavior of a rapid decreasing-increasing trend observed in the tail part of the modeled ATIMR function resulted from the metamorphic processes in the wet snowpack. Therefore, it is crucial to analyze snow metamorphism without simplistic assumptions of dry snow due to the interception of water in the snowpack, particularly in case of having ice and crust layers for the subject region (i.e., Radar Station at 2891 m. asl). Within this study, three-year data sets were obtained from three different meteorology and snow observation stations that have been specially constructed and operated at different elevations and aspects in Kırkgöze-Çipak Basin. The snowmelt-dominated basin is considered to be the source of the headwaters of the Euphrates River.

Snowmelt modeling using two melt-rate models in the Urumqi River watershed, Xinjiang Uyghur Autonomous Region, China

In this paper, the performance of the classic snowmelt runoff model (SRM) is evaluated in a daily discharge simulation with two different melt models, the empirical temperature-index melt model and the energy-based radiation melt model, through a case study from the data-sparse mountainous watershed of the Urumqi River basin in Xinjiang Uyghur Autonomous Region of China. Theclassic SRM, which uses the empirical temperature-index method, and a radiation-based SRM, incorporating shortwave solar radiation and snow albedo, were developed to simulate daily runoff for the spring and summer snowmelt seasons from 2005 to 2012, respectively. Dailymeteorological and hydrological data were collected from three stations located in the watershed. Snowcover area (SCA) was extracted from satellite images. Solarradiation inputs were estimated based on a digital elevation model (DEM). Theresults showed that the overall accuracy of the classic SRM and radiation-based SRM for simulating snowmelt discharge was relatively high. Theclassic SRM outperformed the radiation-based SRM due to the robust performance of the temperature-index model in the watershed snowmelt computation. Nosignificant improvement was achieved by employing solar radiation and snow albedo in the snowmelt runoff simulation due to the inclusion of solar radiation as a temperature-dependent energy source and the local pattern of snowmelt behavior throughout the melting season. Ourresults suggest that the classic SRM simulates daily runoff with favorable accuracy and that the performance of the radiation-based SRM needs to be further improved by more ground-measured data for snowmelt energy input.

Current Practice and Recommendations for Modelling Global Change Impacts on Water Resource in the Himalayas

Global change is expected to have a strong impact in the Himalayan region. The climatic and orographic conditions result in unique modelling challenges and requirements. This paper critically appraises recent hydrological modelling applications in Himalayan river basins, focusing on their utility to analyse the impacts of future climate and socio-economic changes on water resource availability in the region. Results show that the latter are only represented by land use change. Distributed, process-based hydrological models coupled with temperature-index melt models are predominant. The choice of spatial discretisation is critical for model performance due to the strong influence of elevation on meteorological variables and snow/ice accumulation and melt. However, the sparsity and limited reliability of point weather data, and the biases and low resolution of gridded datasets, hinder the representation of the meteorological complexity. These data limitations often limit the selection of models and the quality of the outputs by forcing the exclusion of processes that are significant to the local hydrology. The absence of observations for water stores and fluxes other than river flows prevents multi-variable calibration and increases the risk of equifinality. The uncertainties arising from these limitations are amplified in climate change analyses and, thus, systematic assessment of uncertainty propagation is required. Based on these insights, transferable recommendations are made on directions for future data collection and model applications that may enhance realism within models and advance the ability of global change impact assessments to inform adaptation planning in this globally important region.

The Open Global Glacier Model (OGGM) v1.1

Abstract. Despite their importance for sea-level rise, seasonal water availability, and as a source of geohazards, mountain glaciers are one of the few remaining subsystems of the global climate system for which no globally applicable, open source, community-driven model exists. Here we present the Open Global Glacier Model (OGGM), developed to provide a modular and open-source numerical model framework for simulating past and future change of any glacier in the world. The modeling chain comprises data downloading tools (glacier outlines, topography, climate, validation data), a preprocessing module, a mass-balance model, a distributed ice thickness estimation model, and an ice-flow model. The monthly mass balance is obtained from gridded climate data and a temperature index melt model. To our knowledge, OGGM is the first global model to explicitly simulate glacier dynamics: the model relies on the shallow-ice approximation to compute the depth-integrated flux of ice along multiple connected flow lines. In this paper, we describe and illustrate each processing step by applying the model to a selection of glaciers before running global simulations under idealized climate forcings. Even without an in-depth calibration, the model shows very realistic behavior. We are able to reproduce earlier estimates of global glacier volume by varying the ice dynamical parameters within a range of plausible values. At the same time, the increased complexity of OGGM compared to other prevalent global glacier models comes at a reasonable computational cost: several dozen glaciers can be simulated on a personal computer, whereas global simulations realized in a supercomputing environment take up to a few hours per century. Thanks to the modular framework, modules of various complexity can be added to the code base, which allows for new kinds of model intercomparison studies in a controlled environment. Future developments will add new physical processes to the model as well as automated calibration tools. Extensions or alternative parameterizations can be easily added by the community thanks to comprehensive documentation. OGGM spans a wide range of applications, from ice–climate interaction studies at millennial timescales to estimates of the contribution of glaciers to past and future sea-level change. It has the potential to become a self-sustained community-driven model for global and regional glacier evolution.

Hydrological response of two high altitude Swiss catchments to energy balance and temperature index melt schemes

Comparison of energy Balance (EB) and temperature Index (TI) snow/ice melt methods for glacio-hydrological modeling in the Alps has been the subject of numerous studies; however, the debate on which method is preferable under which conditions and for which application is still ongoing. In this study, both melting routines were tested within the complex numerical framework of the fully distributed model (Alpine3D) to analyze the differences. We included two high-altitude Swiss alpine glaciered catchments, which represent two distinct types of glaciers, namely cirque and valley glaciers, with different weather conditions, topography, and data type. In this experiment, hydrological discharge in the Damma catchment was overestimated by the model with EB approach, which demonstrated Nash-Sutcliffe efficiency (NSE) of 0.61 mainly due to the overestimation of wind speed and longwave radiation. On the other hand, model with TI approach obtained a high NSE of 0.93, as this simple conceptual model does not rely on the abovementioned variables. For the Arolla catchment, better results were observed for both EB and TI melt schemes, with slight underestimation in modeled runoff as shown by NSEs of 0.89 and 0.77, respectively. The very satisfactory performance of EB model at the Arolla catchment is due to the use of input data sets from local weather stations that are more representative of the real catchment conditions. It was observed that the EB melt model performs better if driven with correct meteorological data sets from catchment-representative stations and that the calibration procedure of TI-melt model significantly affects its accuracy.

An estimate of glacier mass balance for the Chandra basin, western Himalaya, for the period 1984–2012

ABSTRACTAn improved understanding of fresh water stored in the Himalaya is crucial for water resource management in South Asia and can be inferred from glacier mass-balance estimates. However, field investigations in the rugged Himalaya are limited to a few individual glaciers and short duration. Therefore, we have recently developed an approach that combines satellite-derived snowlines, a temperature-index melt model and the accumulation-area ratio method to estimate annual mass balance of glaciers at basin scale and for a long period. In this investigation, the mass balance of 146 glaciers in the Chandra basin, western Himalaya, is estimated from 1984 to 2012. We estimate the trend in equilibrium line altitude of the basin as +113 m decade−1and the mean mass balance as −0.61 ± 0.46 m w.e. a−1. Our basin-wide mass-balance estimates are in agreement with the geodetic method during 1999–2012. Sensitivity analysis suggests that a 20% increase in precipitation can offset changes in mass balance for a 1 °C temperature rise. A water loss of 18% of the total basin volume is estimated, and 67% for small and low-altitude glaciers during 1984–2012, indicating a looming water scarcity crisis for villages in this valley.

Climate change drives expansion of Antarctic ice-free habitat.

Antarctic terrestrial biodiversity occurs almost exclusively in ice-free areas that cover less than 1% of the continent. Climate change will alter the extent and configuration of ice-free areas, yet the distribution and severity of these effects remain unclear. Here we quantify the impact of twenty-first century climate change on ice-free areas under two Intergovernmental Panel on Climate Change (IPCC) climate forcing scenarios using temperature-index melt modelling. Under the strongest forcing scenario, ice-free areas could expand by over 17,000 km2 by the end of the century, close to a 25% increase. Most of this expansion will occur in the Antarctic Peninsula, where a threefold increase in ice-free area could drastically change the availability and connectivity of biodiversity habitat. Isolated ice-free areas will coalesce, and while the effects on biodiversity are uncertain, we hypothesize that they could eventually lead to increasing regional-scale biotic homogenization, the extinction of less-competitive species and the spread of invasive species.

Mass balance observations and reconstruction for Batysh Sook Glacier, Tien Shan, from 2004 to 2016

In this study we present an analysis of measured annual mass balances for the period 2011 to 2016 and a reconstruction of seasonal mass balances from 2004 to 2010 for Batysh Sook Glacier located in the Kyrgyz Tien Shan. Conventional methods and a model-based extrapolation of the point measurements were used to obtain glacier-wide mass balances and to analyze glaciological measurements. Especially at the beginning of the re-established glacier mass balance monitoring program, deviations between the different methods were significant, having a range of 0.40m w.e. a−1. With the improvement of the measurement network in later years, the results of the different extrapolation methods showed better agreement (range of 0.10 to 0.22m w.e. a−1). For 2011 to 2016, the profile method revealed a mass loss of −0.41±28m w.e. a−1. The contour line method yielded a negative mean mass balance of −0.34±20m w.e a−1, whereas the model-based extrapolation clearly resulted in the most negative value of −0.43±16m w.e. a−1 for the same period.The same distributed accumulation and temperature index melt model used to extrapolate point measurements from 2011 to 2016 was applied in order to reconstruct the mass balance from 2004 to 2010. The model was driven by daily air temperature and precipitation data from a nearby meteorological station and the model parameters were calibrated with in-situ measurements of annual mass balances collected from 2011 to 2016. Winter accumulation measurements taken in May 2014 were used for calibration purposes and to deduce snow distribution patterns. Subseasonal model performance was validated based on the snow cover depletion pattern observed on satellite images during the summer months from 2004 to 2016. For Batysh Sook Glacier an average annual mass balance of −0.39±0.26m w.e. a−1 was found for the period 2003/04 to 2015/16.

Glacier mass balance simulation using SWAT distributed snow algorithm

ABSTRACTApplication of a temperature-index melt model incorporated into the Soil and Water Assessment Tool (SWAT) is presented to simulate mass balance (MB) and equilibrium line altitude (ELA) of three glaciers. The snow accumulation/melt parameters were adjusted to glacierized and free glacier areas, respectively. The SWAT snow algorithm enabled us to consider spatial variation of snow parameters by elevation bands across the sub-basins, while in the previous studies using SWAT, the related parameters were constant for an entire basin. The results show slight improvement in runoff simulation and significant improvement in simulated MB when considering ELA in model calibration. The results showed that SWAT can be applied to simulate MB, vertical MB distribution and annual ELA, with light calibration efforts for data-scarce catchments. The accuracy of the results depends on the modelled area of ablation zone from which most of the meltwater is released.

Mass-balance reconstruction for Glacier No. 354, Tien Shan, from 2003 to 2014

AbstractThis study presents a reconstruction of the seasonal mass balance of Glacier No. 354, located in the Akshiirak range, Kyrgyzstan, from 2003 to 2014. We use a distributed accumulation and temperature-index melt model driven by daily air temperature and precipitation from a nearby meteorological station. The model is calibrated with in situ measurements of the annual mass balance collected from 2011 to 2014. The snow-cover depletion pattern observed using satellite imagery provides additional information on the dynamics of mass change throughout the melting season. Two digital elevation models derived from high-resolution satellite stereo images acquired in 2003 and 2012 are used to calculate glacier volume change for the corresponding period. The geodetic mass change thus derived is used to validate the modelled cumulative glacier-wide balance. For the period 2003–12 we find a cumulative mass balance of –0.40±10mw.e.a-1. This result agrees well with the geodetic balance of –0.48±0.07mw.e.a-1over the same period.

Sensitivity of glacier runoff projections to baseline climate data in the Indus River basin

Quantifying the contribution of glacier runoff to water resources is particularly important in regions such High Mountain Asia, where glaciers provide a large percentage of seasonal river discharge and support large populations downstream. In remote areas, direct field measurements of glacier melt rates are difficult to acquire and rarely observed, so hydro-glaciological modeling and remote sensing approaches are needed. Here we present estimates of glacier melt contribution to the Upper Indus watershed over the last 40 years using a suite of seven reanalysis climate datasets that have previously been used in hydrological models for this region, a temperature-index melt model and > 29,000 km2 of ice cover. In particular, we address the uncertainty in estimates of meltwater flux that is introduced by the baseline climate dataset chosen, by comparing the results derived from each. Mean annual glacier melt contribution varies from 8 km3 yr-1 and 169 km3 yr-1, or between 4-78% of the total annual runoff in the Indus, depending on temperature dataset applied. Under projected scenarios of an additional 2-4°C of regional warming by 2100 AD, we find annual meltwater fluxes vary by >200% depending on the baseline climate dataset used and, importantly, span a range of positive and negative trends. Despite significant differences between climate datasets and the resulting spread in meltwater fluxes, the spatial pattern of melt is highly correlated and statistically robust across all datasets. This allows us to conclude with confidence that fewer than 10% of the >20,000 glaciers in the watershed contribute more than 80% of the total glacier runoff to the Indus. These are primarily large, low elevation glaciers in the Karakoram and Hindu Kush. Additional field observations to ground-truth modeled climate data will go far to reduce the uncertainty highlighted here and we suggest that efforts be focused on those glaciers identified to be most significant to water resources.

Surface ablation model evaluation on a drifting ice island in the Canadian Arctic

A 4-week micro-meteorological dataset was collected by an automatic weather station on a small ice island (0.13km2) adrift off Bylot Island (Lancaster Sound, Nunavut, Canada) during the 2011 melt season. This dataset provided an opportunity to identify the environmental variables and energy fluxes that contribute most to surface ablation during the melt season, as well as test previously developed surface melt (ablation) models. Surface ablation was estimated using energy fluxes calculated using the bulk aerodynamic approach (EBAWS) and three existing surface ablation models. These models included a simple solar radiation model developed for iceberg use (CIS-IB), a more sophisticated energy-balance model developed for ice island use (CIS-II), and a temperature index melt (TIM) model based on an assumed relationship between air temperature, time, and surface ablation. The models were driven by our measured micro-meteorological data (optimal forcing) or regional environmental forecast data from the Global Environmental Multiscale (GEM) Model, which is used for operational iceberg modeling. The sensible heat flux contributed most to the ice surface's available melt energy (47%), followed by net radiation (38%) and the latent heat flux (30%), while the subsurface heat flux removed 15% of available energy. When cumulative surface ablation was predicted with these calculated energy fluxes (EBAWS), observed surface ablation was under-predicted by 38%. Results illustrate the decreased performance of the melt models when run with GEM data versus in-situ micro-meteorological data, which is optimal for model input but not available for operational modeling. The CIS-II model under-predicted cumulative surface ablation by 5.7% (RMSE=1.2cm) with observed micro-meteorological data and over-predicted cumulative surface ablation by 35% when run with GEM model data. This is likely a result of the GEM model wind speed being 57% greater than that recorded on the ice island. Since surface ablation plays a greater relative role in overall deterioration of ice islands than traditional icebergs due to morphological differences (size, surface structure), it must be accurately represented in operational ice island deterioration models. The costs and benefits between parsimonious TIM models and skilled energy-balance models are weighed here for operational modelers to consider, along with the complications caused by the use of the regional environmental data input provided by the GEM model for operational modeling efforts.

Sensitivity of Icelandic river basins to recent climate variations

Variations in 22 hydrological variables were considered for 8 watersheds in Iceland to analyse the quantitative impact of variations in climate on hydrology during the period 1971–2006. Observed streamflow characteristics were examined together with information about rain/snow fraction, snow storage, snow and glacier melting derived from gridded precipitation and temperature data using a simple temperature-index melt model. The effect of the observed temperature and precipitation variations was examined by comparing subsets of the data containing the 25\% coldest and warmest and the 25\% wettest and driest years of each series. The seasonality of streamflow of all catchments and timing of hydrological events were found to be sensitive to differences of 1.1–1.4 °C in the annual temperature between the warm and cold data subsets. Snow storage was smaller and depleted earlier and the onset of spring snowmelt was shifted several weeks earlier in warm years, while glacial melt volumes increased by 20–40\%. These changes caused greater discharge in winter and spring and less discharge in summer, except for glacierized catchments where summer flow was maintained by glacier melt. Annual precipitation was 40–58\% greater in the wet compared with the dry data subsets, resulting in substantial seasonal and annual increases of rain, snow storage and snowmelt, streamflow volumes and flood occurrence rate. The seasonal distribution and timing of hydrological events were, however, usually not systematically different. Snow storage and glaciers are found to exert a strong influence on streamflow in Icelandic river catchments, making them sensitive to climate variations. The nature of the hydrological response is not spatially uniform but depends on location, altitude distribution and catchment type.

Assessment of the Melt Rate Function in a Temperature Index Snow Model Using Observed Data

AbstractTemperature index snowmelt models often require representation of a snowpack’s melt rate. Defining the melt rate as a function of an accumulated number of warming degree-days is achieved in some temperature index models through the antecedent temperature index–melt rate (ATIMR) function, and provides a reasonable method for adjusting the melt rate during the season. Modelers have typically relied on a default ATIMR function developed two decades ago. However, literature concerning the nature of this default function and how it was developed is largely nonexistent. This paper presents results of a comparison between the default ATIMR function and ATIMR functions computed from field data from two headwater stations within the American River watershed upstream of Folsom Lake, California. An error analysis was also performed using the site-specific data. Using the Hydrologic Engineering Center’s hydrologic modeling system (HEC-HMS), it was found that modeled results often varied dramatically between t...

Parameter sensitivity of a distributed enhanced temperature-index melt model

AbstractWe investigate the sensitivity of a distributed enhanced temperature-index (ETI) melt model, in order to understand which parameters have the largest influence on model outputs and thus need to be accurately known. We use melt and meteorological data from two Alpine glaciers and one glacier in the Andes of Chile. Sensitivity analysis is conducted in a systematic way in terms of parameters and the different conditions (day, night, clear-sky, overcast), melt seasons and glaciers examined. The sensitivity of total melt to changes in individual parameters is calculated using a local method around the optimal value of the parameters. We verify that the parameters are optimal at the distributed scale and assess the model uncertainty induced by uncertainty in the parameters using a Monte Carlo technique. Model sensitivity to parameters is consistent across melt seasons, glaciers, different conditions and the daily statistics examined. The parameters to which the model is most sensitive are the shortwave-radiation factor, the temperature lapse rate for extrapolation of air temperature, the albedo parameters, the temperature threshold and the cloud transmittance factor parameters. A parameter uncertainty of 5% results in a model uncertainty of 5.6% of mean melt on Haut Glacier d’Arolla, Switzerland.

MODELS FOR CLIMATIC RECONSTRUCTION UPON GLACIER EQUILIBRIUM-LINE ALTITUDE VARIATION

The glacier ELA(equilibrium-line altitude) is one of the important parameters responding to climate change.Glacier behaviors such as advancing or retreating are controlled by the variations in ELA.In contrast to variations in glacier length or area,variations in ELA respond almost simultaneously to climate change;therefore,it could be used to analyze the characteristics of climate change in different regions.The statistical models of climatic reconstruction based on variations in ELA(e.g.,the model based on the relationship between temperature and precipitation at ELA,Lapse-rate model and Temperature index melt model) have simple structure,and can get better simulation results.However,all of them could not be derived from physical causes influencing the ELA variation(e.g.,climatic factors).Furthermore,they became limited in use and unconvincing in theory when lacking sufficient data.The physical methods(e.g.,Energy and mass balance model) are based on the energy factor influencing glacier change and related to the mechanism of ELA variation.Although this model has many parameters and is very complicated in algorithm,it could get more accurate results.Due to the effect of glacier types and the limitation of each model,the applicability and accuracy of the different models are variable.