The phrase "as a function of the vertical" is correct and usable in written English.
It can be used in contexts involving mathematics, physics, or any field where relationships between variables are discussed, particularly when referring to vertical dimensions or axes.
Example: "The data was analyzed as a function of the vertical to determine the impact of height on the results."
Alternatives: "in relation to the vertical" or "as it pertains to the vertical".
The accuracy of the numerical representation of atmospheric wave motion as a function of the vertical discretization was analyzed in a recent study.
The bistable beam responses to the loading are experimentally determined for the buckling force and actuating force as a function of the vertical position of the applied force (displacement control).
It is found that the solids fluxes increase strongly, practically linearly, as a function of the vertical position and depend on the excess gas velocity but not on the particle size, while the most often used phenomenological two-phase fluidized bed models assume the vertical solids fluxes to be constant.
In force spectroscopy, the cantilever deflection is recorded as a function of the vertical displacement of the piezoelectric scanner, i.e., as the sample is pushed toward the tip and retracted.
Specifically, the stress state within the models evolves from an initial equilibrium state where the horizontal effective stresses are defined as a function of the vertical effective stress using horizontal stress coefficients.
In each panel (each season), the solid line represents the linear regression of the data, an empirical formula of the ESF occurrence probability as a function of the vertical drift is derived from the linear regression, and ρ is the correlation coefficient between the vertical drift velocity and the irregularity occurrence rate.
And when you look at this, in addition to seeing Fourier himself, you should recognize that what you're looking at is basically a signal which is brightness as a function of the horizontal and vertical spatial variables.
Variation of current density versus the potential as a function of the pH for the vertical 1T-WS2 nanosheets.
Temperatures are reported as a function of the depth in km (vertical axis on the right side of the diagram) or as the number of control volumes (cvn; vertical axis at the left side of the diagram).
Regression trees (CART) are used to model the aircraft engine fuel flow rate as a function of the aircraft pressure altitude, ground speed, vertical speed and takeoff mass in the climb out and approach phases of flight.
In this talk, we use hierarchical Bayesian Multiple Linear Regression to model the fuel flow rate as a function of the aircraft pressure altitude, ground speed, vertical speed, and aircraft mass.
