  The Richards equation is commonly used to model the flow of water and air
through soil, and it serves as a gateway equation for multiphase flows through
porous media. It is a nonlinear advection-reaction-diffusion equation that
exhibits both parabolic-hyperbolic and parabolic-elliptic kinds of
degeneracies. In this study, we provide reliable, fully computable, and locally
space-time efficient a posteriori error bounds for numerical approximations of
the fully degenerate Richards equation. For showing global reliability, a
nonlocal-in-time error estimate is derived individually for the time-integrated
$H^1(H^{-1})$, $L^2(L^2)$, and the $L^2(H^1)$ errors. A maximum principle and a
degeneracy estimator are employed for the last one. Global and local space-time
efficiency error bounds are then obtained in a standard $H^1(H^{-1})\cap
L^2(H^1)$ norm. The reliability and efficiency norms employed coincide when
there is no nonlinearity. Moreover, error contributors such as flux
nonconformity, time discretization, quadrature, linearization, and data
oscillation are identified and separated. The estimates are also valid in a
setting where iterative linearization with inexact solvers is considered.
Numerical tests are conducted for nondegenerate and degenerate cases having
exact solutions, as well as for a realistic case. It is shown that the
estimators correctly identify the errors up to a factor of the order of unity.
