Glen's flow law is an empirical law derived from both field and experimental data (Glen 1955). In its original form Glen expressed the law as
$$
\dot\varepsilon = B \exp{(-Q/RT)}\sigma^n
$$
where $\dot\varepsilon$ is the deformation rate, $B$ $Q$ and $n$ are empirical constants, $R$ is the gas constant and $T$ is the absolute temperature.
This formulation introduces a temperature dependence on the deformation.
The empirical constant $n$ is commonly taken as being $=3$ but this is basically an average of various experimental results. Goldsby (2009) showed that $n$ can be both smaller and larger depending if the stresses are very low or very high, respectively. Millstein et al. (2022) show that the stress dependence may be even larger than previously thought with $n\approx 4.1$ in fast flowing areas of ice sheets.
The viscosity parameter $A$ ($B$ in Glen's notation) will vary with ice temperature as seen above. However, the viscosity parameter is also sensitive to several other parameters such as pressure, crystal size and shape, crystal orientation, impurities in the ice (Gow and Williamson 1976, Hooke 1981, Alley 1992). Hence the viscosity parameter can be seen as site specific.
Clearly the value of B may be impossible to predict unless a wealth of information is known about the glacier ice throughout its body. So one way do deal with this is to use the viscosity parameter as a tuning parameter. Usually this involves comparing model output with measured velocities. This approach has been implemented in many different ways by modellers of glaciers and ice sheets. In models with a thermodynamic component the flow law may still include a temperature dependence.
In the review by Hooke (1981) it also seems clear that laboratory and field experiments yielding the empirical constants $A$ and $n$ diverge. One reason for this is that small laboratory specimens of ice yield values that are not fully representative of natural conditions.
So, the final comment is that using a single value of A is a last resort when the complexity of the natural ice cannot be accommodated in calculations or models. The value of $A$ is still site specific and not generally transferable between glaciers or sites on glaciers. In the end the use of solution for the flow law depends on what is "good enough" for the problem to be solved.
References
Alley R, 1992. Flow-law hypotheses for ice-sheet modeling. Journal of Glaciology, 38(129), 245-256. doi:10.3189/S0022143000003658
Glen JW, 1955. The creep of polycrystalline ice. Proceedings of the
Royal Society, Series A228 519–538. https://doi.org/10.1098/rspa.1955.0066
Goldsby D, 2009. Superplastic flow of ice relevant to glacier and ice-sheet
mechanics. In Knight P, (ed.) Glacier Science and Environmental Change. Oxford: Wiley-Blackwell, 527pp. https://doi.org/10.1002/9780470750636.ch60
Gow AJ and Williamson T, 1976. Rheological implications of the internal structure and crystal fabrics of the West Antarctic ice sheet as revealed by deep core drilling at Byrd Station. Geological Society of America Bulletin, 87,
1665–1677.
Hooke RLeB, 1981. Flow law for polycrystalline ice in glaciers: comparison of theoretical predictions, laboratory data, and field measurements. Reviews of Geophysics and Space Physics, 19(4), 664–672. https://doi.org/10.1029/RG019i004p00664
Millstein JD, Minchew BM and Pegler SS, 2022. Ice viscosity is more sensitive to stress than commonly assumed. Commun Earth Environ 3, 57. https://doi.org/10.1038/s43247-022-00385-x
