Predicting glacier mass balance by data assimilation from on-ice cameras
Authors: Landmann Johannes , Ogier Christophe , Huss Matthias , Farinotti Daniel 
Published: March 2020

&lt;p&gt;With the widespread retreat of glaciers, concerns emerge for the availability of water resources. These concerns are largest for future dry spells, when runoff from other sources is low. In this context, mass balance estimates for time horizons from days to weeks might help to better manage water resources in alpine regions. Here, we obtain such estimates from a combined modelling and data assimilation approach. Starting with three glaciers with detailed monitoring in Switzerland, we extrapolate our signal to other unmeasured glaciers in the country.&lt;/p&gt;&lt;p&gt;For the mass balance modeling, an ensemble of four melt models is tuned to match semi-annual in-situ observations from the Glacier Monitoring Switzerland (GLAMOS) program. With this ensemble, we then infer mass balance for the observed glaciers. Three of the glaciers (Rhonegletscher, Findelgletscher and Glacier de la Plaine Morte) were equipped with on-ice cameras between mid-June and early October 2019. The cameras transmitted 352 daily point mass balance observations which we assimilate into our model results by employing a particle filter.&lt;/p&gt;&lt;p&gt;To transfer the mass balance information of the three well-observed glaciers to other glaciers in Switzerland, we make use of the strong spatial correlation of cumulative melt. In a workflow here termed &amp;#8220;percentile extrapolation method&amp;#8221;, first, all glaciers without direct mass balance measurements are calibrated based on geodetic mass balances covering the 1980-2010 period. To reduce the large uncertainty in calibration on geodetic mass changes, we first predict average mass balance model parameters for each glacier with a random forest regressor. Then, we tune these parameters to match the geodetic mass balance in a least squares minimization. As soon as a mass balance climatology for the past has been calculated with this calibration, we determine with which percentiles of this climatology the current year&amp;#8217;s mass balance ensemble estimate overlaps at the well-observed glaciers. These percentiles are then extrapolated in space using inverse distance weighting and they are applied to the climatology of unmeasured glaciers. The procedure yields a mass balance estimate at every single day of a year for every Swiss glacier taking into account specific glacier characteristics.&lt;/p&gt;&lt;p&gt;We compare the assimilated camera mass balances with interpolated measurements from the GLAMOS program. First results indicate that for the annual mass balance, the camera data lower the mean absolute error to 0.19 m water equivalent (w.e.), from 0.36 m w.e for a model prediction without data assimilation. The standard deviation of the prediction ensemble is reduced by 0.37 m w.e. on average. A cross-validation using percentile extrapolation between the glaciers equipped with a camera shows that annual mass balance can be predicted within 0.27 m w.e.. The summer (May to September) melt of other glaciers in the GLAMOS program can be predicted with an absolute error of 0.07m w.e. (model: 0.27 m w.e). Our results indicate that the continuous monitoring of a few selected sites has the potential of strongly improving daily near real-time mass balance estimates at the regional scale.&lt;/p&gt;