## 2.13.5. Computation of the surface mass balance[¶](#computation-of-the-surface-mass-balance "Permalink to this headline")
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This section describes the computation of surface mass balance and associated runoff terms. The description here only applies to regions where glacial melt runs off and is replaced by ice, not to regions where glacial melt remains in place. Thus, by default, this only applies to Greenland and Antarctica, not to mountain glaciers elsewhere in the world. (See also section [2.13.3](#glacier-regions).)

The SMB of a glacier or ice sheet is the net annual accumulation/ablation of mass at the upper surface. Ablation is defined as the mass of water that runs off to the ocean. Not all the surface meltwater runs off; some of the melt percolates into the snow and refreezes. Accumulation is primarily by snowfall and deposition, and ablation is primarily by melting and evaporation/sublimation. CLM uses a surface-energy-balance (SEB) scheme to compute the SMB. In this scheme, the melting depends on the sum of the radiative, turbulent, and conductive fluxes reaching the surface, as described elsewhere in this document.

Note that the SMB typically is defined as the total accumulation of ice and snow, minus the total ablation. The SMB flux passed to CISM is the mass balance for ice alone, not snow. We can think of CLM as owning the snow, whereas CISM owns the underlying ice. Fluctuations in snow depth between 0 and 10 m water equivalent are not reflected in the SMB passed to CISM. In transient runs, this can lead to delays of a few decades in the onset of accumulation or ablation in a given glacier column.

SMB is computed and sent to the CESM coupler regardless of whether and where CISM is operating. However, the effect of SMB terms on runoff fluxes differs depending on whether and where CISM is evolving in two-way-coupled mode. This is described by the variable _glc\_dyn\_runoff\_routing_. (This is real-valued in the code to handle the edge case where a CLM grid cell partially overlaps with the CISM grid, but we describe it as a logical variable here for simplicity.) In typical cases where CISM is not evolving, _glc\_dyn\_runoff\_routing_ will be false everywhere; in these cases, CISM’s mass is not considered to be part of the coupled system. In cases where CISM is evolving and sending its own calving flux to the coupler, _glc\_dyn\_runoff\_routing_ will be true over the CISM domain and false elsewhere.

Any snow capping (section [2.7.6](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Hydrology/CLM50_Tech_Note_Hydrology.html#runoff-from-glaciers-and-snow-capped-surfaces)) is added to \\(q\_{ice,frz}\\). Any liquid water (i.e., melted ice) below the snow pack in the glacier column is added to \\(q\_{ice,melt}\\), then is converted back to ice to maintain a pure-ice column. Then the total SMB is given by \\(q\_{ice,tot}\\):

(2.13.1)[¶](#equation-13-1 "Permalink to this equation")\\\[q\_{ice,tot} = q\_{ice,frz} - q\_{ice,melt}\\\]

CLM is responsible for generating glacial surface melt, even when running with an evolving ice sheet. Thus, \\(q\_{ice,melt}\\) is always added to liquid runoff (\\(q\_{rgwl}\\)), regardless of _glc\_dyn\_runoff\_routing_. However, the ice runoff flux depends on _glc\_dyn\_runoff\_routing_. If _glc\_dyn\_runoff\_routing_ is true, then CISM controls the fate of the snow capping mass in \\(q\_{ice,frz}\\) (e.g., eventually transporting it to lower elevations where it can be melted or calved). Since CISM will now own this mass, the snow capping flux does _not_ contribute to any runoff fluxes generated by CLM in this case.

If _glc\_dyn\_runoff\_routing_ is false, then CLM sends the snow capping flux as runoff, as a crude representation of ice calving (see also sections [2.7.6](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Hydrology/CLM50_Tech_Note_Hydrology.html#runoff-from-glaciers-and-snow-capped-surfaces) and [2.13.3](#glacier-regions)). However, this ice runoff flux is reduced by \\(q\_{ice,melt}\\). This reduction is needed for conservation; its need is subtle, but can be understood with either of these explanations:

*   When ice melts, we let the liquid run off and replace it with new ice. That new ice needs to come from somewhere to keep the coupled system in water balance. We “request” the new ice from the ocean by generating a negative ice runoff equivalent to the amount we have melted.
    
*   Ice melt removes mass from the system, as it should. But the snow capping flux also removes mass from the system. The latter is a crude parameterization of calving, assuming steady state - i.e., all ice gain is balanced by ice loss. This removal of mass due to both accumulation and melt represents a double-counting. Each unit of melt indicates that one unit of accumulation should not have made it to the ocean as ice, but instead melted before it got there. So we need to correct for this double-counting by removing one unit of ice runoff for each unit of melt.
    

For a given point in space or time, this reduction can result in negative ice runoff. However, when integrated over space and time, for an ice sheet that is near equilibrium, this just serves to decrease the too-high positive ice runoff from snow capping. (The treatment of snow capping with _glc\_dyn\_runoff\_routing_ false is based on this near-equilibrium assumption - i.e., that ice accumulation is roughly balanced by \\(calving + melt\\), integrated across space and time. For glaciers and ice sheets that violate this assumption, either because they are far out of equilibrium with the climate or because the model is being run for hundreds of years, there are two ways to avoid the unrealistic ice runoff from snow capping: by running with an evolving, two-way-coupled ice sheet or by changing a glacier region’s ice runoff behavior as described in section [2.13.3](#glacier-regions).)

In regions where SMB is computed for glaciers, SMB is also computed for the natural vegetated land unit. Because there is no ice to melt in this land unit, it can only generate a zero or positive SMB. A positive SMB is generated once the snow pack reaches its maximum depth. When running with an evolving ice sheet, this condition triggers glacial inception.
