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The oxygen is calculated in mg per kg per something, so what does $h^{-1}$ stand for? hours maybe?
The formula given below is an estimation of oxygen consumption for Atlantic salmon
\begin{equation} V_{O_{2}} (mg \cdot kg^{-1} \cdot h^{-1}) = 61.6(\pm6.6) BW^{-0.33(\pm0.11)} \cdot 1.03(\pm0.10)^{T} \cdot 1.79(\pm(0.10))^{U} \label{eq:salmonoxygenconsumption} \end{equation}
Here is a link containing the scientific article describing the formula - ScienceDirect
Yeah, it's hours.
Further down in the paper, you can read,
The mass exponent was estimated to be −0.33 (b in Eq. (4)) for the specific metabolic rate \begin{equation} V_{O_{2}} (mg\space {O_{2}} \cdot kg^{-1} \cdot h^{-1}) \end{equation}
Rate by very definition implies an extent of time; since mg refers to oxygen and kg refers to water, the only variable left is h, which evidently refers to hours. Hours also jives well with the experimental design.
