  While a number of bounds are known on the zero forcing number $Z(G)$ of a
graph $G$ expressed in terms of the order of a graph and maximum or minimum
degree, we present two bounds that are related to the (upper) total domination
number $\gamma_t(G)$ (resp. $\Gamma_t(G)$) of $G$. We prove that
$Z(G)+\gamma_t(G)\le n(G)$ and $Z(G)+\frac{\Gamma_t(G)}{2}\le n(G)$ holds for
any graph $G$ with no isolated vertices of order $n(G)$. Both bounds are sharp
as demonstrated by several infinite families of graphs. In particular, we show
that every graph $H$ is an induced subgraph of a graph $G$ with
$Z(G)+\frac{\Gamma_t(G)}{2}=n(G)$. Furthermore, we prove a characterization of
graphs with power domination equal to $1$, from which we derive a
characterization of the extremal graphs attaining the trivial lower bound
$Z(G)\ge \delta(G)$. The class of graphs that appears in the corresponding
characterizations is obtained by extending an idea from [D.D.~Row, A technique
for computing the zero forcing number of a graph with a cut-vertex, Linear
Alg.\ Appl.\ 436 (2012) 4423--4432], where the graphs with zero forcing number
equal to $2$ were characterized.
