## 2 Materials  
### GPGP Measured Data  
There are two main necessary variables for the validation of the OF model: the towline tension and the speed through water (\(u_{\rm stw}\)) of the cleanup system. They have been continuously measured throughout the System 002 GPGP campaign, from August 2021 until December 2022, and more recently, during the GPGP campaigns of systems larger than System 002.  
To measure the towline tension, a Running Line Monitor (Figure 2) is installed on each towing line. The tension is measured every second, and it is transmitted and registered to a computer on board the vessel.  
These measurements were post-processed in the following manner:  
1. The mean tension was calculated for periods of 3 h, for each of the towing lines. The sum of the mean values for each towline provides the combined towline tension, which is the variable to be validated in the present work.
2. The error associated with the combined towline tension was calculated. Taking the mean tension for a specific time period introduces an error because the true mean value, for a specific metocean condition, can be anywhere between the extreme values of the dynamic response. Therefore, the difference between the calculated mean and the maximum tension for the 3 h period was taken as the associated error.
3. The RLM has a high accuracy, typically between 0.5% and 2.0% of the measured load. The associated error described in the previous point is typically higher than the error associated with each instant measurement. Regarding the speed through water (\(u_{\rm stw}\)) measurements, two main sources were considered:  
1. A Doppler Velocity Logger (DVL) supplies the \(u_{\rm stw}\) of the vessel, which is registered on a computer on board the vessel.
2. The Speed Over Ground (SOG) of the vessel combined with the sea surface current velocity estimation, from the X-band radar of the vessel.  
The measurements produced by both sources were compared over a specific amount of time, normally corresponding to three hours of test or normal operation. If the measurements are similar, then \(u_{\rm stw}\) is deemed consistent, and the average between the two values is calculated and used in the validation. Figure 3 is an illustration showing this consistency between the two sources.  
Figure 2: Running Line Monitor (RLM) to measure towline tension.  
The error associated with the speed through water measurement is calculated in the following manner:  
1. The DVL on the vessels has an accuracy of 1.5%.
2. Since two sources of data are considered to calculate the average value, an error of half the difference between the two measured values is introduced.
3. Finally, the maximum between the previous two errors is taken as the speed-through-water-associated error.  
Since the OF simulations to be used in the validation process are run in the no-waves condition, the GPGP measurements must correspond to low wave conditions for comparison purposes. Based on the data gathered during the GPGP expeditions, the significant wave height range was set as \(H_{\rm s}\in[1:2]\) m with periods \(T_{\rm s}>12\) s, which are considered appropriate for the validation. Further details on the comparison between the OF results and GPGP data are presented in Section 3.4.