# The Implementation of Precise Point Positioning (PPP): A Comprehensive Review
## 2 Error Sources in PPP
### Site Displacement Effects
#### 2.8.3 Ocean Loading  
Oceanic loading refers to the deformation of the earth's crust caused by ocean tides. Analogous to solid tides, this effect has semidiurnal and diurnal cycles but with no permanent component. Typically, the induced site displacement is on the order of centimeters, predominantly in the vertical plane. However, in coastal regions, these displacements can escalate up to 10 cm [7]. The influence of oceanic loading may often be disregarded for daily static positioning or stations significantly inland. Conversely, it becomes imperative to account for this effect during shorter processing intervals, especially when in close proximity to oceanic bodies and when precision at the centimeter level is required in kinematic processing.  
Ocean loading is characterized by the summation of eleven primary tidal harmonics; each harmonic \(j\) is characterized by its amplitude \(A_{cj}\), phase \(\phi_{cj}\), and time-varying argument \(\chi_{j}(t)\)[65]. The amplitude and phase values of each depend on site and chosen model. These values can be obtained from the ocean loading service website [67], where they are represented in the south, west, and up directions. For each direction, the displacement \(\Delta c\) due to ocean loading can be calculated as  
\[\Delta c=\sum_{j=1}^{11}A_{cj}\cos(\chi_{j}(t)-\phi_{cj}) \tag{26}\]  
The astronomical arguments \(\chi_{j}(t)\) are calculated following the FORTRAN subroutines provided by IERS ([[https://iers-conventions.obspm.fr/content/chapter7/software/](https://iers-conventions.obspm.fr/content/chapter7/software/)]([https://iers-conventions.obspm.fr/content/chapter7/software/](https://iers-conventions.obspm.fr/content/chapter7/software/)), accessed on 6 August 2023). The eleven harmonics in (26) encompass the semidiurnal \((M_{2},S_{2},N_{2},K_{2})\), diurnal \((K_{1},O_{1},P_{1},Q_{1})\), and long-period \((M_{f},M_{m},S_{sa})\) tide waves.  
The ocean loading displacement vector in the ECEF frame, denoted as \(\Delta\mathbf{r_{ocean}}\), can be determined from the calculated \(\Delta c\) components similar to (25). However, before applying the same rotation matrix, the west and south ocean components must be converted to the east and north directions through sign inversion.  
Finally, it is important to note that two key decisions should be made when downloading the amplitude and phase data from the ocean loading provider. The first choice pertains to the ocean tide model. As recommended by [65], the latest models should be used unless consistency with old models is necessary. The ocean loading service website [67] provides details on all available models. The Finite Element Solution (FES) model is an example of these models, and the latest version currently available is FES2014b. The second choice relates to whether CoM correction is required in the ocean model. While ocean tides influence the earth's CoM, this correction is not required in PPP, as the IGS products are referenced to the ITRF, which is crust-fixed and remains unaltered by the earth's CoM [7].