Short-term glacier variations can be important for water supplies or hydropower production, and glaciers are important indicators of climate change.
This is why the interest in near-real-time mass balance nowcasting is considerable.
Here, we address this interest and provide an evaluation of continuous observations of point mass balance based on online cameras transmitting images every 20 min. The cameras were installed on three Swiss glaciers during summer 2019, provided 352 near-real-time point mass balances in total, and revealed melt rates of up to 0.12 m water equivalent per day (
Glaciers around the world are shrinking.
For example, Switzerland has lost already more than a third of its glacier volume since the 1970s
A glacier mass balance nowcasting framework assimilating relevant observations could deliver these near-real-time mass balances whenever required.
While nowcasting frameworks exist, for example, for the mass balance of the Greenland Ice Sheet
In many cases, mass balance analyses are available twice a year and are based on seasonal in situ observations
In this study, we address the issue of low-frequency observations, ensemble modeling, and the lack of knowledge about short-term parameter variability as part of the project CRAMPON (Cryospheric Monitoring and Prediction Online).
The latter aims at delivering near-real-time glacier mass balance estimates for mountain glaciers using data assimilation.
To obtain high-frequency data at a relatively low cost, we equipped three Swiss glaciers – Glacier de la Plaine Morte, Findelgletscher, and Rhonegletscher – with seven cameras in total. The cameras were operated in summer 2019 and took images of a mass balance stake marked every 2
Ensemble stability and suitability for operational use is ensured by designing the particle filter such that, at any instance, each model has a minimum contribution to the mass balance model ensemble.
In particular, models with temporarily bad performance are not excluded from the ensemble and can thus regain weight later.
To address parameter uncertainty, we drive the mass balance model ensemble with both Monte Carlo samples of uncertain meteorological input and prior parameter distributions obtained from calibration to past, longer-term seasonal mass balance series.
By using an augmented state formulation of the particle filter, we constrain model parameters as well
As a result, we demonstrate (1) how a workflow including daily melt observations, ensemble modeling, and data assimilation works in practice, (2) to what extent the assimilated mass balances are able to reproduce cumulative observations, and (3) how the ensemble performs with respect to both reference forecasts and seasonal analyses from in situ measurements.
We use Glacier de la Plaine Morte, Rhonegletscher, and Findelgletscher in summer 2019 as test sites (Fig.
Main characteristics and installed cameras for the investigated glaciers. Glacier area and elevation range refer to the year 2019
For acquiring daily point mass balances in the field, we use off-the-shelf cameras and logger boxes from the company Holfuy Ltd.
We mount the cameras to a construction of aluminum stakes that we designed for glacier applications.
Figure
The camera setup used to obtain daily estimates of glacier point mass balance. Here, the camera has just been mounted on the snow-covered surface of Glacier de la Plaine Morte (19 June 2019).
The camera observes an ablation stake, which is marked with colored tape at 2
Figure
Overview of camera station availability during summer 2019. Cameras have been mounted and torn down at different times due to weather and staff restrictions. Station names are defined in Table
In total, we obtained 352 daily point mass balance observations between 20 June 2019 and 3 October 2019. The camera longest in the field was on Glacier de la Plaine Morte (91 d between 20 June 2019 and 18 September 2019), while those shortest in the field were two cameras at the tongue of Rhonegletscher (52 d between 13 August 2019 and 2 October 2019). Very few data gaps occurred due to failure of the mobile network over which the data were transmitted.
Once camera images are on our servers, they are read manually to obtain daily cumulative surface height change
The relationship between observations of surface height change since an initial point in time (in our case the time at which a camera is set up) and the cumulative glacier mass balance is given through the simple linear observation operator
To model glacier mass balance, we employ verified products of daily mean and maximum 2
Temperature uncertainty, given as a root-mean-square error, varies per season from 0.94
For operational reasons, the precipitation grids contain the 06:00–06:00 local time precipitation sums and thus do not conform with the 00:00–00:00 temperature values
Shortwave radiation is derived using data from the geostationary satellite series Meteosat. As an uncertainty,
Glacier outlines for the year 2019 are obtained from GLAMOS (Glacier Monitoring Switzerland), and mass balances are calculated over a fixed glacier surface area
For calibration and verification, we use mass balance data acquired in the frame of GLAMOS
Glacier surface mass balance consists of two components:
accumulation and ablation.
We model accumulation and ablation on elevation bins whose vertical extent is determined by a
Since all three glaciers we investigate are in the GLAMOS measurement program and winter mass balance observations are available, the effect of spatial variations in snow accumulation differing from a linear gradient can be incorporated.
This is done by choosing a factor
To model surface ablation, we set up an ensemble of three TI melt models and one simplified energy-balance melt model.
We choose this ensemble since the individual models differ in the degree of complexity by which they describe the surface energy balance The “BraithwaiteModel” uses only air temperature as input to calculate melt The “HockModel” uses potential incoming solar radiation as an additional predictor for melt The “PellicciottiModel” employs surface albedo and actual incoming shortwave solar radiation Albedo is approximated according to the combined decay equation for deep and shallow snow in The “OerlemansModel” calculates melt energy as the residual term of a simplified surface energy balance equation
For the data assimilation procedure described in Sect.
Calibration workflow used to obtain a prior estimate for the parameters of the model ensemble .
Following
Once the model parameters have been optimized, we determine the value of
To ensure that all mass balance model predictions stay within the observational uncertainty, we perform data assimilation.
In particular, we employ a particle filter since it does not restrict the class of state transition models and error distributions.
Especially when temperatures are around the melting point, the system becomes nonlinear since melt occurs above but not below this point.
As a consequence, the distributions we deal with are not necessarily Gaussian.
The facts that (a) the temperature chosen to parametrize the melting point is not the same for all four models, (b) the individual model prior distributions are combined to obtain the ensemble prediction, and (c) there can also be accumulation contributing to the overall mass balance add further complexity.
We do not use other data assimilation approaches, such as variational methods or ensemble Kalman filtering, because variational methods encounter difficulties when dealing with non-Gaussian priors
Some extensions of the common particle filter framework allow model parameters and model performance to be estimated over time. With this, we aim at providing optimal, daily mass balance estimates at the glacier scale.
The general framework for data assimilation consists of a system whose state
To put this general framework into practice, we use the particle filter, which is a sequential Monte Carlo data assimilation method.
Instead of handling conditional distributions of
Usually, particle filtering comprises three repeated steps:
the predict step, the update step, and the resampling step.
In our case, these steps mean the following:
during the predict step, particles holding possible mass balance states are propagated forward in time using the state transition in Eq. (
The flowchart in Fig.
Particle filter workflow during 1 mass budget year (“MB year”). We use uncertain model estimates to predict mass balance with 10 000 particles and reset the cumulative mass balance when a camera is set up. The model mass balance estimate is updated at time steps for which observations are available. To avoid overconfidence of the particle filter, we apply a partial resampling technique. The individual particle filter steps are sketched in Fig.
Illustration of the individual particle filter steps. The example refers to a case in which four models (blue, orange, red, and green) start with two particles each. The blue curve represents the observation distribution. At time step
The temporal dynamics of the glacier mass balance state can be described by the accumulation model in Eq. (
As the state has to provide all information that is needed to predict the next observation, we also include the surface albedo and the snow water equivalent on the ice in our state vector.
Hence, the state vector is defined as
During the predict step, the explicit temporal evolution of the physical state
We use a total of
Sample mean and standard deviations for the prior parameter distributions used on Glacier de la Plaine Morte, Findelgletscher, and Rhonegletscher. For a definition of the listed parameters, refer to Eqs. (
In the update step, all particles are then reweighted by multiplying the density of the observations
During the resampling step, the updated weights are used to choose a new set of
To overcome this problem, we assign a minimum contribution to each model of the ensemble, regardless of the model's performance at a certain time step.
To compensate for the potentially too high resampling rate of a poor prediction, we lower the weights of all particles of a model whose contribution has been deliberately increased to match the chosen minimum contribution.
In turn, we increase the weights of all other particles to compensate for their underrepresentation. This means that on average, the original weights per model remain unchanged.
For technical details of the resampling procedure, see Appendix
The dynamics of the augmented state is defined such that the model index does not change over time. However, parameters are evolved temporally such that after a long period without observations,
To validate the daily mass balance predictions made with the particle filter, we use the CRPS (continuous ranked probability score). The CRPS is designed to estimate the deviation of a probabilistic forecast from an observation. It takes into account both the deviation of the median forecast from the actual observation (forecast reliability) and the spread of the forecast distribution (forecast resolution). This means that a forecast close to the observation median can still receive a poor CRPS if the forecast distribution spread is high, and the other way around. Lower values of the CRPS correspond to better forecasts. The minimum value is zero, corresponding to a perfect, deterministic forecast of the observation.
The CRPS is defined as
Figure
Considering all stations, we have observed ice melt rates of up to 0.12
As shown by the pictures from station FIN 1 (Fig.
Besides the direct observations presented above (Sect.
We consider two types of reference forecasts:
first, a forecast with (i) mean glacier-wide melt parameters as obtained from past calibration (Sect.
Finally, we calculate the CRPS for the two reference forecasts by inserting two different values into the CRPS equation:
(a) the mass balance of each day separately and (b) the cumulative mass balance.
Note that for the particle filter, there is no need to make this distinction. Indeed, the daily deviation from a mass balance observation also equals the deviation from the cumulative observation.
Figure
Median CRPS values over “
For the particle filter, daily and cumulative melt observations are generally reproduced well, with an average CRPS of 0.012 [0.012]
Comparing the CRPS of the particle filter with the reference forecasts, the performance closest to the particle filter is delivered by the forecast produced with mean melt parameters and no uncertainty in the meteorological input (mean CRPS
In general and for the individual glaciers, the particle filter improves the CRPS of the reference forecasts by 95 % to 96 %. For the daily forecasts, the performance of the particle filter is only partly better, with improvements in CRPS between 8 % and 48 %. Along with the performance, a further important advantage of the particle filter is that it provides daily estimates for the results' uncertainties without need for further calculations. Indeed, this information can be essential, especially for the operational application of our framework.
A different approach for validating the particle filter is to only use subsets of the available camera observations as input and to evaluate the predicted mass balances at the remaining locations (cross-validation).
We do so by splitting the available observations into training and test subsets of cameras, i.e., by keeping the time series of a given station together (as opposed to splitting individual time series).
Our test sets always contains one time series; i.e., we perform a leave-one-out cross-validation.
Figure
Temporal evolution of the CRPS as determined in a leave-one-out cross-validation procedure on Rhonegletscher and Findelgletscher. “TRAIN” and “TEST” stand for the stations assimilated by the particle filter and the station used for the validation, respectively.
We find that, in general, the cumulative mass balance at the test locations follows the cumulative observation curve well but not as closely as when the test location's data are assimilated with the particle filter.
This shows the benefit of having several cameras per glacier mounted at different elevations.
For Findelgletscher, we find 8.8 % average deviation (median CRPS of 0.071 and 0.108
The temporal pattern evident in Fig.
The above results show the ability of the particle filter to also predict melt at locations without observations, albeit with a lower performance when compared to the situation in which all observations are assimilated. The results also show that even with an augmented particle filter, it is demanding to find a unique, glacier-wide parameter set that correctly reproduces the mass balance at all locations.
We compare our assimilated model ensemble predictions to the glacier-wide annual mass balance reported by GLAMOS at the autumn field date of the mass budget year 2019.
We do so by running the model from the field campaign date in autumn 2018.
Figure
Schematic model and parameter settings on Rhonegletscher during the mass budget year 2019. After an initial phase with parameters from past calibration, the precipitation correction factor
During the period preceding the installation of our cameras, we calculate mass balance with the parameters calibrated in Sect.
Mass balances calculated with the particle filter between the autumn field dates of 2018 and 2019 against the values reported by GLAMOS. See text for the difference of particle filtering with and without pre-selection. Uncertainty values are given as standard deviations.
For particle filtering without pre-selection of initial conditions, the difference from the GLAMOS analyses is 0.67
We analyze model performance by considering the temporal evolution of the model probabilities
Figure
Temporal evolution of model probabilities (solid lines) and model particles (stacked bars) for the three modeled glaciers. The fast switch in model probabilities occurring for Findelgletscher between 07 and 8 August 2019 is further depicted in Fig.
In general, we find that the model probabilities are sensitive to the ensemble input, such as the parameter priors, and the prescribed meteorological uncertainty.
This is an indication of the ensemble choosing the model combination that best reproduces the observations at any time.
Note that none of the models is removed from the ensemble in the resampling step even when the model performs poorly.
During the assimilation period, indeed, models can recover and can show good performances at a later stage (see, for example, the HockModel for Rhonegletscher or the PellicciottiModel for Findelgletscher). This shows the utility of the resampling procedure introduced in Sect.
During the assimilation period of an individual glacier, often one model dominates the ensemble for a given amount of time (“model dominance” being the case in which the model probability is
Violin plots with scattered particles as an example for a fast switch in assigned model probability (cf. Fig.
In terms of the temporal evolution, the model dominance for Rhonegletscher and Glacier de la Plaine Morte is determined already within the first few days and changes only a little after that.
Changes in model dominance can be observed for Rhonegletscher and Findelgletscher, instead.
In the case of Rhonegletscher, for example, the model dominance switches from the PellicciottiModel to the OerlemansModel and later to the HockModel. For Findelgletscher, however, there is a transition from the OerlemansModel to the PellicciottiModel. This transition is particularly noticeable between 7 and 8 August 2019 (Fig.
Figure
Temporal evolution of the various model parameters for Findelgletscher. Shown are the sample means (lines) and the standard deviations (bands). Note that for the OerlemansModel, parameter
Three phases of quick parameter changes can be observed. First, the parameters change rapidly on the first days of the assimilation period. This means that the prior parameter distributions do not match the exact parameter distributions needed to model the mass balance at the camera locations. This is due to both the calibration time span (seasonal calibration vs. daily application) and the low sample size of the calibrated parameters. A second rapid change can be observed after the second camera has been switched on, i.e., on 24 July 2019. Here, an adjustment in the parameters is needed in order to accommodate the mass balance at both stations equally well. The third rapid change starts when ablation at station FIN 1 is highest but when radiation and temperature are not at their maximum. Here, the change might be due to the model being forced to yield high ablation rates despite only moderate meteorological forcing. This shows the advantage of employing the model ensemble as opposed to, for example, a single model with deterministic parameters: the ensemble also reproduces system states which cannot be explained by the uncertain meteorological input.
In this study, we mounted seven cameras on three Swiss glaciers, delivering 352 point mass balance observations throughout summer 2019.
At the camera locations, we observed daily melt rates of up to 0.12
The mass balances given by the particle filter were closer to the cumulative observations (CRPS
Assume that camera
The technical details of the resampling procedure in Sect.
However, introducing a restriction on the minimum number of particles per model can lead to biased estimates as poor models with probability
Temporal evolution of the ensemble mass balance state at stations FIN 1 and FIN 2. In the top two panels, the evolution of the mean and standard deviation of the filter (black lines and yellow shaded area) around the centered observations (blue lines and blue shaded area) is shown. In the bottom panel the mean deviation of the filter from the observations at both stations is shown.
The camera observations are available under the following DOI:
Time lapse videos of all camera observations used in this study are available as videos under the following DOIs: PLM 1:
JML had the particle filter idea, implemented all models, did all figures, and wrote the paper. HRK supervised the particle filter methodology, brought in the method to prevent models from disappearing from the ensemble, and reviewed the paper. MH commented on the method, reviewed the paper, and mounted some of the stations. CO prepared and mounted most of the stations. MK commented on the particle filter and reviewed the paper. DF did the overall supervision, proposed to use data assimilation in JML's doctorate, commented on the method, reviewed the paper, and acquired the funding.
The authors declare that they have no conflict of interest.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We would like to acknowledge the funding that we got from GCOS (Global Climate Observing System) Switzerland and the extensive support that we got from the manufacturer of the cameras and transmitter boxes, Holfuy Ltd (in particular Gergely Mátyus).
We would like to thank the teachers of the Joint ECMWF and University of Reading Data Assimilation Training Course that helped to significantly improve Johannes Marian Landmann's knowledge on data assimilation, in particular Javier Amezcua.
Further, we would like to thank Anastasia Sycheva and Emmy Stigter for test-reading the methods chapter for reader friendliness.
We appreciate the help from all people that conducted the field work apart from the authors, namely Małgorzata Chmiel, Amaury Dehecq, Lea Geibel, Katja Henz, Serafine Kattus, Johanna Klahold, Claudia Kurzböck, Amandine Sergeant, and Michaela Wenner, and we thank all people that took part in the round-robin experiment apart from the authors, namely Amaury Dehecq, Eef van Dongen, Elias Hodel, Jane Walden, and Michaela Wenner.
Kudos to Dominik Gräff for helping to “TCify” Sect.
This paper was edited by Marie Dumont and reviewed by Douglas Brinkerhoff and one anonymous referee.