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Ice and Ice Forces in Small Steep Rivers
No full textEnglish summary
Given the right circumstances ice can wreak havoc on riverine infrastructure. Ice runs pushing ice floes against bridge piers is frequently the governing design condition for bridges in cold regions. The physics of these interactions are complex and forces are hard to predict. Current standards and calculation methods for calculating these quasi-static ice forces disagree both on order of magnitude and underlying mechanics. While there reigns general agreement that ice thickness and ice strength are critical parameters, great difficulties remain for the accurate and reliable estimation of these parameters (Paper I). In small-steep rivers in particular these estimates are difficult. Anchor ice dams complicate things by encouraging the growth of highly complex and variable ice structures. Paper III provides a novel approach for quickly and accurately estimating ice thicknesses in generally inaccessible steep rivers using an unmanned aerial vehicle (UAV), structure for motion and automated GIS processing. Paper II provides new insights into how ice strength varies in steep rivers. Through statistical analysis it shows a novel and effective way of predicting anchor ice dam locations, proportion of river impacted by anchor ice dams as well as providing new data on how anchor ice dam strengths are distributed. As a whole, this thesis provides the river ice engineer with new and balanced guidance on how to go about predicting ice forces in small steep river.Norsk sammendrag
Is kan under visse omstendigheter påføre store skader på infrastruktur i elver. Istrykk på bropilarer er ofte dimensjonerende for bruer i kalde strøk. Fysikken bak disse interaksjonene er komplekse og kreftene vanskelige å forutsi. Nåværende design-koder og kalkulasjons metoder for disse kvasi-statiske iskreftene er uengie om både størrelses orden og underliggende mekanikk. Det regjerer en generel konsensus at is-tykkelse og is-styrke er kritiske parametre, men store vanskeligheter gjenstår før nøyaktige og påligelige estimater av disse er mulig (Paper I). Spesielt i små bratte elver så er disse estimatene vanskelige. Bunn-is dammer kompliserer ting ved å oppmuntre vekst av høyst komplekse og variable is strukturer. Paper III beskriver en ny tilnærming for raskt og effektiv estimering av is-tykkelse i generelt utilgjengelige bratte elver ved bruk av fjernstyrt drone, structure from motion (SfM) og automatisert GIS prosessering. Paper II gir ny innsikt i hvordan is-styrke varierer i bratte elver. Gjennomstatistisk analyse så viser den en ny og effektiv måte å forutsi bunn-is dam lokasjoner, brøk av elven påvirket av bunn-is dam formasjon, i tillegg til å gi nye data om hvordan bunn-is dam styrke er distribuert i disse elvene. Somen helhet så tilbyr denne avhandlingen elve-is ingeniøren med en ny og balansert veiledning på hvordan man best kan forutsi is-krefter i små bratte elver
Predicting flows in ungauged small rural catchments using hydrological modelling
Full text linkFlow data are important information for water resources management such as flood risk management, water utilization, and environmental impact assessment in a changing environment. However, most of the catchments that we are interested in are ungauged which makes a method to predict flow in ungauged catchments an important prerequisite. Reliable estimation of continuous streamflow in ungauged catchments has remained a fundamental challenge in hydrology, although significant insights have been gained in recent years. Flood is the most typical example of natural risk and causes significant economic damage worldwide. Flood risk will become more frequent in the future because of climate and land use changes and may cause increased impacts on human health and economic losses. Growing economic losses are evidence of the increasing intensity of floods draining from small catchments to small watercourses which are usually not sufficiently considered by the flood risk management approaches. Knowledge of hydrological impacts of climate change is essential to aid infrastructure owners in managing the impacts on existing and planned water infrastructures. To provide a meaningful climate impact results at ungauged small rural catchments, it is necessary to use high spatial and temporal resolutions of climate data that can be used to force high resolution hydrological models; however, rainfall-runoff modelling in such catchments is hampered by a lack of both observed discharge and precipitation data and high resolution climate data. To address the challenges of flood risk management, a parsimonious continuous rainfall-runoff model (Distance Distribution Dynamics) with high resolution climate data has been used as the main tool to predict flow and to study impact of climate change; however, the parameters of the model cannot be obtained by calibration on the flow data and hence need to be obtained by regionalization.
The Distance Distribution Dynamics (DDD) model has been regionalized for 41 gauged small rural catchments in Norway (area ≤ 50km2). Three regionalization methods: multiple regression, physical similarity (single-donor and pooling-group based methods) and a combination of the two methods, are used in this study. Seven independent catchments, which are not used in the regionalisation process, are used for validation of the regionalization methods. The combined method (multiple regression and pooling-group type of physical similarity) performs the best of all methods. The DDD model like many other rainfall-runoff models, underestimates floods in many cases in the continuous simulations. To improve the prediction of flood peaks in a continuous simulation, a dynamic river network method is conceptualized and implemented in the DDD model. The method is applied for 15 catchments in Norway and tested on 91 flood peaks. The performance of the method is evaluated using relative errors and mean absolute relative errors and the simulated flood peaks are improved significantly with the method. The mean absolute relative error of the simulated peaks is reduced from 32.9% (without dynamic river networks) to 15.7% (with dynamic river network method). The 0.75 and 0.25 quantiles of the relative errors of the simulated flood peaks are reduced from 41% to 23% and from 22% to 1% respectively. The regionalized DDD model with dynamic river network has been used to study the hydrological impacts of climate change on six ungauged small rural catchments in Bergen area of Norway using a new high-resolution regional climate projection with improved performance with regards to the precipitation distribution. The results show that in the future period (2070-2100), there will be an increase in the mean annual flow compared to the reference period (1981-2011). The maximum increase is 33.3%, and the minimum increase is 16.5%. The mean autumn, winter and spring flows show an increase for the study catchments and contributed significantly for the increase in mean annual flows, but there will be a decrease in the mean summer flows from the study catchments. The maximum decrease in the mean summer flow is 35.2% and the minimum decrease is 7.2%. The results also show that the mean annual maximum flows (floods) increases by 28.9% to 38.3% in the future period. The results of the flood frequency analysis show that there will be an increase of floods (16.1% to 42.7%) with a return periods of 2, 5, 10, 20, 25, 50, 100 and 200 years in small rural catchments at Bergen area of Norway
Remotely sensed data for bathymetric mapping and ecohydraulics modelling in rivers
Full text linkRiver management decisions must be based on the best knowledge available. But acquiring information on river conditions and translating it into sufficient mitigation measures can be both time- and resource demanding. Remote sensing data can be an important source of information on the current state of rivers, and may also be used in scenario assessments of future river conditions. This PhD-study has focused on the use of remote sensing data as a source of information on bathymetry, seasonal mesohabitats for fish, scenarios of mitigation measures, and strategies on environmental eDNA sampling. Each of these four information elements are often central parts in river assessments. The results from the PhD-study are presented in four scientific papers and include remote sensing data from green and red LIDAR, multispectral satellite imagery and aerial photos collected and applied in four Norwegian rivers.
For the assessment of seasonal mesohabitats for fish, two remote sensing technologies were used: LIDAR and aerial photos. The LIDAR data enabled a 10x10 cm resolution bathymetry used as input to a 2D hydraulic model for the simulation of hydraulic heterogeneity. The aerial photos were used as both a source of calibration data and for assessing spatial heterogeneity along the river banks. The results show that both spatial heterogeneity and hydraulic heterogeneity are significant mesoscale habitat characteristics for European Grayling during its spawning period. No significant relationships were found on spatial and hydraulic heterogeneity for brown trout, emphasising the need for species-specific assessments in terms of mesoscale habitat characteristics.
While LIDAR data may be a source of high-resolution bathymetry, collecting and processing LIDAR data can be costly and time consuming. An alternative remote sensing data source for river assessments is multispectral imagery or (the previously mentioned) aerial photos. The application of multispectral imagery from two satellite platforms and aerial photos for mapping of bathymetry by linear models was tested in four rivers within the same geographical region. LIDAR and SONAR data was used in the study for establishing linear image-to-depth models and for verifying the modelled bathymetry. Platform-specific regional models were then established and tested by combining intercept and slope coefficients from the linear models in the four rivers.
The results showed that while the final quality of platform-specific regional model bathymetry did not fully match the quality of LIDAR-based bathymetry, overall model performance was adequate for depth calculations. For Worldview-2 images and aerial photos, coefficients of determination (R2) were in the 0.52-0.82 and 0.73-0.91 range, respectively. By adjusting the regional models with estimated local depth and a brightness factor, results on depth calculations improved slightly when compared to the LIDAR-based bathymetry, with coefficients of determination in the 0.47-0.84 and 0.71- 0.91 range, respectively.
Point cloud format LIDAR data can easily be modified e.g., for use in assessment of different mitigation measure scenarios. Modified LIDAR data was tested in a public preference study on scenarios for mitigation measures related to weir adjustments and changes in flow-dependent water covered areas in weir basins. The study was conducted in a bypass section (i.e., a river section with water withdrawal) with a 65-70% reduction in yearly discharge due to hydropower production. Findings from the study show that LIDAR data are highly useful for scenario-based adjustments and modelling of weirs. As the potential dry/wet interface at or around the weirs can be hydraulically complex, these locations may require high-density mapping using a combination of red and green LIDAR. Results from the study also include a structured and standardized framework for public preference assessments in rivers which includes the potential use of remote sensing data as input to mitigation measure scenarios.
A successful green LIDAR scan depends on a range of factors e.g., the technology applied in the scan process, signal pathway length and disturbances, river conditions and post-processing capabilities. Failure to address each of these factors when applying LIDAR may result in inadequate point cloud classification or coverage. In a study of strategic environmental eDNA sampling for biomonitoring in a river dominated by weirs and flow alteration, a regional adjusted image-to-depth model was applied on remote sensing imagery for river sections where two consecutive LIDAR scans returned inadequate coverage of bathymetry. Results on simulated depths and velocities adequately matched corresponding in-situ measurements of the same variables. Results from generalized mixed models testing the effect of spatial and abiotic variables on sample eDNA concentrations showed that sample location habitat type and season significantly affected eDNA concentrations of brown trout and minnow. Furthermore, weirs were found to be barriers for the dispersion of eDNA during autumn, while no significant effects of weirs were found during spring
Hydrodynamic rainfall-runoff modelling for flash floods in small and steep catchments
No full textGlobal warming and climate change lead to more frequent and extreme weather events. These include sudden and intense rainfall and rising temperatures which cause flash floods. In steep terrains, flash floods with high-flow velocities lead to erosion and sedimentation with potential disastrous changes of flood path. Flash floods caused by heavy rainfall with snowmelt contribution due to sudden rise in temperature (rain-on-snow events) have become common in autumn and winter in snow-covered Nordic catchments. These events have caused widespread damage, closure of roads and bridges and landslides leading to evacuations in affected areas. Therefore, the analysis of such flood types becomes more important in terms of inundation area, water depths and flow-velocities to identify critical locations in a catchment.
Hydrological and hydraulic models are usually used to simulate flash floods. But most of the traditional hydrological models only give output as a hydrograph but do not represent the consequences such as velocity, water depth, sheer stress etc. at any point or region in the catchment. So, the flood hydrograph from a traditional hydrologic model must be combined with a hydraulic model for downstream consequences. In the traditional method of manual coupling, the output from the hydrologic model is used as input and set as input boundary condition in the hydraulic models. This method of manual coupling requires the separate calibration of two models which makes it a time-consuming process. Sometimes due to many tributaries, more than one boundary condition is required and it is difficult to decide where to set the input boundary conditions in the hydraulic model. In addition to this, there is always some residual flow along the river from the catchment or the water from small tributaries, which is difficult to estimate and add in the hydraulicmodel calculations. In small and steep catchments, the inflow contribution from every section of the water course can be important to determine where critical conditions may arise.
To overcome these challenges and the hassle of manual coupling of the two models, the direct rainfall method (DRM) also known as rain-on-grid (RoG) technique was tested in this research work. Primarily, TELEMAC-2D, a Hydrodynamic Rainfall-Runoff (HDRR) model, with Curve Number (CN) infiltration method, was used for this purpose in a study site of 10.5 km2 steep catchment located in western Norway. Spatially distributed precipitation data with a resolution of 1km by 1km was used as input instead of point precipitation data to reduce the uncertainties related to precipitation distribution over the catchment.
Since TELEMAC-2D is an open source toolbox, it was possible to make changes in the source code ourselves and implement spatially distributed precipitation as input. Since TELEMAC-2D doesn’t have a snow routine, initially only those peak flow events were simulated which were induced by rainfall without any contribution from snowmelt. Seven such events were simulated and a sensitivity analysis was conducted for the parameters such as the CN values, size of mesh elements, roughness and antecedent moisture conditions (AMC) in the catchment. In addition, a 200-year design flood was simulated to show the potential damages in the catchment. The study explored the benefits and limitations of the approach through a comprehensive description of model construction, calibration, and sensitivity analysis. The results showed that calibrated models can satisfactorily reproduce peak flows and produce relevant information about water velocities and inundation. Since, floods can reach even more extreme levels when snowmelt combines with the surface runoff generated by rainfall events. When rain falls on an existing snowpack in addition to the sudden increase in temperature, it is known as a rainon-snow (RoS) event. These events can result into destructive flash floods due to the sudden melting of snow combined with the extreme rainfall.
Hence, in the next part of the thesis work, the contribution and effect of snowmelt in flash floods were analysed. The hydrological model HBV was used to find out the portions of snow and rain from the raw precipitation data and to calculate the snowmelt. The sum of snowmelt and rain calculated from HBV, which eventually contributes to flash floods, was used as the input precipitation in TELEMAC-2D for HDRR modelling. The results showed the importance of including snowmelt for distributed runoff generation and how the combination of hydrological and hydraulic models allows to extract flow hydrographs anywhere in the catchment. It is also possible to extract the flow velocities and water depth at each time-step showing the critical points in the catchment in terms of flooding. The RoG technique works particularly good for single peak events, but not for floods with longduration sustained flow and which are generated by multiple rainfall storms. The results indicated a need for implementation of time-varying CN values or another infiltration model with a time-varying infiltration rate for such multi-storm floods.
Therefore, another HDRR model HEC-RAS 2D with the Green-Ampt Redistribution (GAR) infiltration method was tested and compared with TELEMAC-2D for its RoG technique. CN method was applied in both the models to simulate two single storm events up to 20 hours duration. NSE and R2 for the models ranged from 0.70 to 0.90 and from 0.93 to 0.95. Moreover, the two models were compared for the calibration process, computational time, mesh size and shape, model availability in general, as well as for the results including inundated areas, water depths and velocity of water after a flood event. In addition, The GAR method was applied in HEC-RAS 2D for a multi-peak flood event with sustained flow between the peaks, but the results showed that even this method was unable to reproduce all the peaks of the flood event. Therefore a sensitivity analysis of the GAR parameters was done to understand why GAR method could not reproduce the multi-storm flood. The sensitivity analysis showed that the results are not very sensitive to the two GAR parameters which are responsible to influence the flow of the later peaks.
Neither of the HDRR models could reproduce such multi-storm long duration floods because of the fact that both the HDRR models permanently lose the infiltrated water out of the model domain which usually contribute as the return flow to the river which is mainly the reason for the sustained flow between the multiple storms and for a gradual recession limb of a flow hydrograph. However, neither of the models incorporate a return flow algorithm. Hence, the HDRR models should only be used if it is sure that the infiltrated water goes to the deep base flow where there is no chance of subsurface return flow, or they should be used only for shortduration single storm floods.
Potential follow up to this research work can be to implement a subsurface flow module or the contribution of return flow in the fully integrated hydrologic- hydrodynamic RoG models. This enhancement would enable these models to effectively handle both short and long duration floods. Moreover, a snow routine can also be implemented in the HDRR models which eliminates the need of a separate model to calculate snow storage and snowmelt in the catchment
Prediction of Culvert Failure - A desktop study of water-driven culvert failure in Soknedal using a developed method
Full text linkThe risk connected to water-related hazards on roads and railways is becoming more acute in Norway. A significant maintenance backlog combined with climate change and land modification and -intervention has increased the probability for such events to occur, and the importance of the road- and railway infrastructure is increasing with a growing Norwegian economy. This work focuses on the hazard connected to water-driven culvert failure, and is a part of the research center Klima 2050 s endeavor to achieve better risk estimation for stormwater management in small catchments.
The main objective of this work is to develop a method to predict culvert failure. Failure is defined in the work as exceedance of the capacity given by the headwater that is considered safe. The method is based on using a constructed fault tree and estimates the failure occurrence from flood return periods. It is aimed to be practically applicable for risk assessments and feasible as a desktop study, primarily using available information from public Norwegian databanks and services. It is found that methods chosen to estimate capacity and flood has to be of low complexity to achieve the aim of practicality. Three simple methods are used to estimate capacity, the NIFS-formula is used to estimate flood return periods and the effects of climate- and land cover change is considered through using constant percentages of change in flood size.
Three scientific questions are established in order to provide a reference point in the development of the method and to explore its capabilities as a desktop study for risk assessments. They deal with how often culvert failure occurs under possible failure modes, the effects of climate- and land cover change on the occurrence, and how it can be reduced to an acceptable level. In answering the questions and testing the method which is developed, the work provides a case study of eight culverts in Soknedal which have previously failed and led to damages on a railway line. The findings show that the culverts will not fail unless they are severely blocked. This can occur due to slides, which are relatively common in Soknedal, or if the maintenance is inadequate.
The uncertainties in the risk estimation provided by the method are potentially large and need to be further investigated. Independently of whether the method is deemed useful and the uncertainties acceptable, this work provides a comprehensive overview of the risk connected to culverts and how it can possibly be modelled
The Role of Reservoirs in Drought Mitigation in Ethiopia, Awash River Basin
No full textDrought is weather related natural hazard that can affect a particular region or entire country. It affects the lives of people, livestock, and economic development of a given region or country. In Ethiopia it is becoming a recurrent phenomenon which usually is caused due to lack of precipitation for an extended period. This extended lack of precipitation causes water shortage of different demand sectors of a given community. As majority of the food production in Ethiopia is dependent on rain-fed agriculture the impact is much worse. It often turns into famine and food crisis. Hence, This thesis work aims in analysing drought and its mitigation measures in Awash river basin. Detail drought assessment is performed on a sub basin level. Standardized precipitation index and standardized stream flow index are used to characterize meteorological and hydrological droughts of the basin respectively. A good relationship is found between meteorological and hydrological droughts based on shorter time scale of drought index calculation. Drought severity maps are developed using Arc view to have an over view of drought affected areas. The lower and middle Awash are found to be hit by extreme and severe drought in a higher percentage. A drought of moderate and mild severity is common across the basin.
Impact of climate change on drought severity in the future is also analysed. The impact is analysed by downscaling historical and future climate data of three RCP scenarios of Moh hadely and MPI climate models by using Arc map and R-programming language. A total of 54 index points are downscaled with in the catchment and average values are used when more than two index points are downscaled per sub basin. It is found that drought severity due to climate change will increase in the future in the upper and middle part of the basin. In the lower part almost same type of drought is found but this is uncertain due to the fact that the correlation of downscaled climate data and observed data is found to be very weak. A WEAP model is also used to analyse the role of reservoirs and integrated water resource management to mitigate drought. A set of future scenarios are tested to identify efficient management options to minimize water deficiency
Implementation of GARTO as an infiltration routine in a full hydrological model
No full textClimate change is expected to give more intense rainfall events, while urbanisation leads to more impervious surfaces. This combined with growing cities, increase the stress on the existing storm water infrastructure, and may result in more frequent flooding in urban areas.
The land use in urban catchments affects the stormwater runoff patterns. More impervious surfaces lead to runoff hydrographs reaching the flood peaks faster, and having higher peaks. Having green spaces and water retention on the other hand, results in hydrographs with a shape more similar to natural conditions: smaller peaks reaching maxima later.
To do urban hydrology assessments, e.g. for understanding the effects of land use changes, modelling of the hydrological processes in an urban area might be beneficial. Hydrological models can simulate the runoff patters from a catchment based on input parameters such as soil properties and rainfall patterns. Spatially distributed hydrological models are hydrological models that divides a catchment into smaller cells, each with its own properties and input parameters.
Spatially distributed hydrological models used in Norway today do not consider the mechanisms of infiltration and are therefore not applicable for urban hydrology assessments. This thesis therefore suggests including infiltration by implementing an infiltration routine in a hydrological model. The infiltration model Green-Ampt with redistribution Tablot and Ogden (GARTO) was chosen to create the base of the routine. Further, the widely used hydrological model Hydrologiska Byråns Vattenbalansavdelning (HBV) model was chosen for implementation of the infiltration routine. The HBV model already exists in open source database gihub, under Statkraft Hydrological Forecasting Tools (SHyFT).
The routine was coded separately in C++ and the results were compared to results from Lai et al. (2015). The routine was also tested against infiltration and soil moisture data of a green roof in Trondheim. The code was then implemented in SHyFT.
The comparison to the results from Lai et al. (2015) gave satisfactory results. The routine also managed to match parts of the results from a green roof. A sensitivity analysis on the soil properties shows that saturated conductivity is the most sensitive soil moisture constant. Further the routine match good with expected infiltration responses
Analysis and modelling of recent large floods on the river Gaula
Full text linkIn order to study the flood from 2009, 2010 and 2011 that have been impacting the Gaula
waterway, a hydrological and operational model have been built.
A brief description of the study is given as an introduction, followed by the description of the study place which is located in Midtre Gaudal in Sør Trondelag, it comprises of four (04) unregulated catchments being Gaulfoss the biggest and the rest of them being part of Gaulfoss.
Daily and Hourly data have been collected, analyzed and formatted so they can be compatible
with ENKI platform. Once the model is set and the parameters assigned, the calibration can
be started. While processing the results it was possible to see that even though R2 was the
simulated discharge was not meeting the aforementioned floods.
An exercise has been made by using radar data and scale the precipitation value and evaluate
how much does this affects the model.
As a second part of the study, the hydropower system developed in Samla Plan (Habberstad,
1984) was used to build an operational model in nMag to see how good this system would have work with the mentioned floods.
Discussions, comments and conclusions included in the study
Analysis and modelling of recent large floods on the river Gaula
Full text linkIn order to study the flood from 2009, 2010 and 2011 that have been impacting the Gaula
waterway, a hydrological and operational model have been built.
A brief description of the study is given as an introduction, followed by the description of the study place which is located in Midtre Gaudal in Sør Trondelag, it comprises of four (04) unregulated catchments being Gaulfoss the biggest and the rest of them being part of Gaulfoss.
Daily and Hourly data have been collected, analyzed and formatted so they can be compatible
with ENKI platform. Once the model is set and the parameters assigned, the calibration can
be started. While processing the results it was possible to see that even though R2 was the
simulated discharge was not meeting the aforementioned floods.
An exercise has been made by using radar data and scale the precipitation value and evaluate
how much does this affects the model.
As a second part of the study, the hydropower system developed in Samla Plan (Habberstad,
1984) was used to build an operational model in nMag to see how good this system would have work with the mentioned floods.
Discussions, comments and conclusions included in the study
Hydrological forecasting in catchments with glaciers
Full text linkThe runoff forecast is crucial in Norway because the country bases most of its electricity from hydropower. The hydrological model has thus been improved for years in order to foresee the runoff in the best possible way. In Norway, there are many catchments with extensive water storage: glaciers. Those catchments represent a significant part of the catchments where hydropower is produced. Therefore knowing the right amount of outflow from a catchment with glaciers is essential but more challenging.
The runoff forecast has been assessed on catchments where the glacier area is decisive for the runoff regime. The catchments chosen are located in Jostedalsbreen, the biggest glacier in Europe, in south Norway. The catchments have specific characteristics in slope, land types etc. which can test the robustness of the hydrological model used, HBV-model. This simple model is not specifically built for glacier behaviour analysis and thus does not include complex calculation on the glacier part. Hence, forecasting runoff with HBV-model for a catchment with glaciers is expected to be arduous.
After several trials, two calibrations were done for the two purposes: one strictly hydrological runoff oriented and the other glaciers behaviour related. The simulations were realised in different catchments on a long period of fifty-two years. The concern about the accuracy of the HBV-model to generate a consistent runoff in the catchments selected proved to be unfounded. The first calibration gives so good results in term of runoff that an update of the model for catchments with higher portion with glaciers does not seem necessary. However, to get those results the model passes through calculations which do not fit with what happens in the physical system especially in climatological part and in the snow routine. So the second calibration was realised in order to have routines closer to the physical phenomena.
The two different simulation results were then studied for their glacier changes. It appears that both calibrations give reversely extreme glacier mass balances. Therefore, it is difficult to conclude anything for glacier mass balance values in the catchment.
After, the climate change in the region was studied to forecast the runoff in the next hundred years. Two different scenarios were evaluated. They give relatively close results in term of the runoff forecast. The glacier mass balances are also close to each other. The scenario A with the highest increase of temperature has stronger impact on the runoff and mass balance of the glaciers. However, it is difficult to conclude on the glacier state at the end of the period with the only two calibrations used, but they will eventually decrease
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