  The origins of the hot solar corona and the supersonically expanding solar
wind are still the subject of debate. A key obstacle in the way of producing
realistic simulations of the Sun-heliosphere system is the lack of a physically
motivated way of specifying the coronal heating rate. Recent one-dimensional
models have been found to reproduce many observed features of the solar wind by
assuming the energy comes from Alfven waves that are partially reflected, then
dissipated by magnetohydrodynamic turbulence. However, the nonlocal physics of
wave reflection has made it difficult to apply these processes to more
sophisticated (three-dimensional) models. This paper presents a set of robust
approximations to the solutions of the linear Alfven wave reflection equations.
A key ingredient to the turbulent heating rate is the ratio of inward to
outward wave power, and the approximations developed here allow this to be
written explicitly in terms of local plasma properties at any given location.
The coronal heating also depends on the frequency spectrum of Alfven waves in
the open-field corona, which has not yet been measured directly. A model-based
assumption is used here for the spectrum, but the results of future
measurements can be incorporated easily. The resulting expression for the
coronal heating rate is self-contained, computationally efficient, and
applicable directly to global models of the corona and heliosphere. This paper
tests and validates the approximations by comparing the results to exact
solutions of the wave transport equations in several cases relevant to the fast
and slow solar wind.
