Cumulative Mass Balance Research Articles

Mass Balance of South-East Alaska and North-West British Columbia Glaciers from 1976 to 1984: Methods and Results

The annual surface mass balance for 1983 and 1984 and the 10 year cumulative mass balances for 1975–85 were calculated for 60 south-east Alaskan and north-west British Columbia glaciers. At present, the mass balance is positive on nine, at equilibrium on nine, and negative on 42 glaciers. The ratio of glaciers with positive and equilibrium mass balance to glaciers with negative mass-balance has not changed significantly since 1946; however, the magnitude of negative balances has declined on 39 of the 42 glaciers. The annual mass balance of south-east Alaska and north-west British Columbia glaciers cannot be measured on more than a few glaciers. This paper presents the methods and results for a mass-balance model using as input local weather records, Juneau Icefield field studies, and satellite imagery. The primary variable in mass balance from one glacier to another is the budget gradient. The budget gradient varies predictably according to three parameters: ocean proximity, surface slope, and valley width-valley height. The annual fluctuation of the budget gradient can be determined by examination of local weather records, determination of activity indexes, and delineation of the equilibrium-line gradient from the maritime to the continental part of each icefield. The latter two variables are determined using largely satellite imagery, keyed to topographic maps. This procedure, where applicable, yielded mass-balance errors of ±0.16–0.22 m and 10 year cumulative mass-balance errors of ±0.08–0.15 m.

Mass Balance of South-East Alaska and North-West British Columbia Glaciers from 1976 to 1984: Methods and Results

The annual surface mass balance for 1983 and 1984 and the 10 year cumulative mass balances for 1975–85 were calculated for 60 south-east Alaskan and north-west British Columbia glaciers. At present, the mass balance is positive on nine, at equilibrium on nine, and negative on 42 glaciers. The ratio of glaciers with positive and equilibrium mass balance to glaciers with negative mass-balance has not changed significantly since 1946; however, the magnitude of negative balances has declined on 39 of the 42 glaciers.The annual mass balance of south-east Alaska and north-west British Columbia glaciers cannot be measured on more than a few glaciers. This paper presents the methods and results for a mass-balance model using as input local weather records, Juneau Icefield field studies, and satellite imagery. The primary variable in mass balance from one glacier to another is the budget gradient. The budget gradient varies predictably according to three parameters: ocean proximity, surface slope, and valley width-valley height. The annual fluctuation of the budget gradient can be determined by examination of local weather records, determination of activity indexes, and delineation of the equilibrium-line gradient from the maritime to the continental part of each icefield. The latter two variables are determined using largely satellite imagery, keyed to topographic maps.This procedure, where applicable, yielded mass-balance errors of ±0.16–0.22 m and 10 year cumulative mass-balance errors of ±0.08–0.15 m.

Wave Ogives

AbstractWave ogives arise in a solution of the continuity equation by the method of characteristics. Steady ice flow is assumed. Ice velocity, channel width, and mass-balance functions combine to form a wave-excitation potential that yields the forcing function for wave ogives. This linear-systems formulation extends the ogive theory of Nye. Convolution of the temporal cumulative mass balance and spatial forcing functions gives the total wave pattern below an ice fall. Many ice falls do not generate ogives because the wave amplitude is modulated by a factor related to ice-fall length. The wave ogives at Austerdalsbreen, Norway, are due almost entirely to ice acceleration at the top of the ice-fall, i.e. the same zone that King and Lewis showed was responsible for forming Forbes bands.

Glacier Mapping to Confirm Results from Mass-Balance Measurements

Annual mass-balance measurements have been made at a number of glaciers in Norway since the beginning of the 1960s, A detailed and reliable map is necessary as a base for field work and more than twenty glacier maps have been constructed photogrammetrically at scales of 1:10 000 or 1:20 000 since 1952. For some of the glaciers more than one map has been constructed and changes in glacier volume can be calculated, provided the maps have sufficient accuracy.For the glaciers, Nigardsbreen, Hellstugubreen, and Gråsubreen, two or more good maps are available and these form a good basis for comparisons and calculations of changes in volume between the years when the air photographs were taken.Comparisons have been made for Gråsubreen between 1968 and 1984, for Hellstugubreen between 1968 and 1980, and for Nigardsbreen between 1964 and 1984.The calculations are made by placing a 100 m grid on the glacier maps and comparing the altitude for corresponding points. The changes in height are regarded as representative for the 0.01 km2 glacier areas represented by each point.Results from the investigation have been used to check the accuracy in cumulative mass balance for corresponding periods.Repeated air photography, at intervals of 5—10 years, can be used in the future to find the cumulative mass balance for a great number of glaciers at lower cost than “normal” mass-balance work.

Wave Ogives

AbstractWave ogives arise in a solution of the continuity equation by the method of characteristics. Steady ice flow is assumed. Ice velocity, channel width, and mass-balance functions combine to form a wave-excitation potential that yields the forcing function for wave ogives. This linear-systems formulation extends the ogive theory of Nye. Convolution of the temporal cumulative mass balance and spatial forcing functions gives the total wave pattern below an ice fall. Many ice falls do not generate ogives because the wave amplitude is modulated by a factor related to ice-fall length. The wave ogives at Austerdalsbreen, Norway, are due almost entirely to ice acceleration at the top of the ice-fall, i.e. the same zone that King and Lewis showed was responsible for forming Forbes bands.

Glacier Mapping to Confirm Results from Mass-Balance Measurements

Annual mass-balance measurements have been made at a number of glaciers in Norway since the beginning of the 1960s, A detailed and reliable map is necessary as a base for field work and more than twenty glacier maps have been constructed photogrammetrically at scales of 1:10 000 or 1:20 000 since 1952. For some of the glaciers more than one map has been constructed and changes in glacier volume can be calculated, provided the maps have sufficient accuracy. For the glaciers, Nigardsbreen, Hellstugubreen, and Gråsubreen, two or more good maps are available and these form a good basis for comparisons and calculations of changes in volume between the years when the air photographs were taken. Comparisons have been made for Gråsubreen between 1968 and 1984, for Hellstugubreen between 1968 and 1980, and for Nigardsbreen between 1964 and 1984. The calculations are made by placing a 100 m grid on the glacier maps and comparing the altitude for corresponding points. The changes in height are regarded as representative for the 0.01 km2 glacier areas represented by each point. Results from the investigation have been used to check the accuracy in cumulative mass balance for corresponding periods. Repeated air photography, at intervals of 5—10 years, can be used in the future to find the cumulative mass balance for a great number of glaciers at lower cost than “normal” mass-balance work.

Development and Validation of a Numerical Model Simulating Evaporation from Short Cores

AbstractA theoretically‐based assessment of the short core evaporimeter technique for measuring evaporation from the soil surface can be conducted using numerical simulation. As an initial step, a numerical model is developed that simulates evaporation from isothermal, homogeneous, finite soil columns with a specified initial water content profile. Features of this model include nonlinearized solution of the highly nonlinear surface boundary condition, automatic adjustment of time‐step size according to a mass balance criterion, remaximization of program efficiency at each time‐step, and the use of soil surface temperature as the primary forcing function. The validity of the model was established through its ability to realistically simulate the constant and falling rate stages of soil drying, including root‐time behavior, and by its good mass conservation and stability characteristics. Drying of a clay soil with an initial uniform water content of 0.40 cm3w cm‐3pm for 12 000 min under a constant evaporative demand of 4.4 × 10−4 cm3w cm‐2pm min−1 could be simulated with a time‐step size ranging from 10 to 13.7 min, a specific mass (i.e. flux) balance of < 3%, a cumulative mass balance of < 0.3%, and with generally < five iterations per time‐step. A discretization analysis revealed that for the first centimeter below the soil surface a 0.2‐cm nodal spacing was required to obtain accurate estimates of the evaporative flux and the near‐surface water content profile. Below that depth, however, nodal spacing can be greatly increased without serious reduction of accuracy. Successful validation of the model supports extension to field conditions.

Estimation of the percentage of annual groundwater recharge with bomb tritium using a cumulative mass balance method

The bomb tritium (3H) distribution patterns in the aquifer beneath an abandoned landfill at the Canadian Forces Base (CFB) Borden, Ontario, and in a sandy aquifer at Whiteshell Nuclear Research Establishments (WNRE) Pinawa, Manitoba, all in Canada, were delineated in great detail. A sampling and monitoring network of multilevel samplers and bundle piezometers were used. The directions of groundwater flow were established, and the boundary between the tritiated and non-tritiated zones of the two aquifers were closely demarcated. Using a cumulative mass balance method, the3H input mass into the aquifers was compared with the3H mass in groundwater storage to estimate the percentages of annual groundwater recharge from 1953 to 1978. Two recharge calculations for theeffective recharge zone and thetotal recharge area of the aquifers as established from the flownet analysis, and the distributions of dissolved geochemical constitutents showed that theeffective recharge zone calculations gave higher values of 30.6 cm/yr for CFB Borden and 20.1 cm/yr for WNRE while thetotal recharge areas gave lower values of 19.1 and 10.1 cm/yr for the Borden and WNRE aquifers respectively. The two recharge values provide possible minimum and maximum recharge estimates for the two study areas.