Evaluation of Regional Tidal Model on the West Coast of North Sumatera Province

On the west coast of North Sumatra, the availability of tidal data has not been optimal, hence a tidal model is required to describe marine information. The regional tidal model (developed by Indonesia Geospatial Agency, hereafter called as BIG model) was built from multi-mission altimetry data that was assimilated with 138 tide stations (TS) data over the Indonesian ocean before 2018. The research aimed to evaluate the BIG model using TS data that was built after 2018, namely, TS.Barus, TS.Sirombu and TS.Batahan at 2019-2020. The research method is to calculate the Root Mean Square, Root Sum of Squares, Root Sum of Squares of the In-phase and Quadrature, and Discrepancy (D) of 8 harmonic constants (HC: M2, K1, S2, O1, P1, N2, K2, Q1). Also calculated the correlation between BIG model and prediction from TS data in January 2021. According to HC analysis, the smallest amplitude difference in K1 TS.Barus is - 0.0077m, while the largest is 0.0278m in M2 TS.Batahan.Q1 has the least RMS at 0.0039m, while M2 has the most at 0.035m.The Discrepancy (D) between the BIG model and TS data is 5.5609 percent, showing that the tidal model is reliable. The correlation value between BIG model and predicted observational data shows a strong positive relationship, indicated by an R value between 0.996 - 0.998.


Introduction
The dynamic condition of the Indonesian Ocean, which reaches about 108.000 kilometers of coastline, makes up-to-date ocean information considered.Meanwhile, the availability of tidal data in all Indonesian waters has not yet been optimal, so a tidal model is needed to represent marine information in areas where there are no real-time tides.Tides are the movement of rising and falling sea levels that are influenced by many things according to the theory of tides [8].Tidal theory starts from the old theory to the dynamic theory.The cycle that occurs is influenced by the gravitational attraction of celestial bodies, with the main contribution coming from the gravity of the Moon and the Sun [11].Tidal Stations (TS) provide tidal observation data accurately with high frequency, especially in the coastal area.Furthermore, tidal data had been used to determine the tidal model and ground-truth data [5].The existence of a tidal model can provide accurate tidal correction in various uses of sea level data such as the implementation of bathymetric surveys [13].The regional tidal model (BIG model) is a representation of tidal phenomenon in Indonesia's ocean which is determined by assimilation between data of tidal observation in 138 tidal stations and altimetry data (Topex, Jason-1, Jason-2, dan Jason-3) [1].Evaluation of the regional tidal model of BIG is needed to acknowledge its reliability in providing ocean information to the entire coastal area of Indonesia.The corresponding tidal stations of this research are located on the West Coast of North Sumatera Province.There are three Tidal Stations of Geospatial Information Agency that have been operated since 2019, they are TS Barus, TS Sirombu, and TS Batahan.More information appears in

Research Data
This study used two types of the dataset, namely: 1. Regional tidal model from the Geospatial Information Agency (BIG Model) with ASCII format downloaded from https://srgi.big.go.id/ on September 5 th 2022.
2. Tidal observation data from the Permanent Tidal Station (PTS) in ASCII format, recording intervals every 1 hour for over 1 year (2019)(2020).This data will be used as ground-truth data.

Tidal Harmonic Analysis
The analysis method of tides is done by using basic arithmetic of the system motion of the earth, moon, and sun as the theory of tidal equilibrium.But the tidal conditions in a location are different from the equilibrium conditions because the sea provides a complex response due to variations in sea depth.Harmonic analysis is a mathematical method that is applied to determine the height and surface currents of water by estimating the amplitude and phase of a set of tidal constants that represent astronomical tides [2].The approach taken is to describe a series of tidal observations into wave contributions that are in accordance with the tidal constituents [10].Harmonic Analysis Method of Least Squares (HAMELS) is a sea level determination model that gives the minimum square of the error to the observed sea level [2].Harmonic analysis using the least squares method, where the prediction of sea level (h) according to the time period (t) relative to the average sea level (h0) and the amplitude () and phase (ϕ  ) according to the following equation ( 1) : This tidal harmonic constant is used in the calculation of the tidal datum, tidal prediction, and the construction of tidal models [14].The amplitudes of the 4 (four) main constants namely K1, O1, M2, and S2 are then used in the calculation of the Formzhal number for determining the type of tide.The Formzhal principle is the division of the sum of 2 (two) diurnal amplitudes (K1 and O1) by the sum of 2 (two) semi-diurnal amplitudes (M2 and S2) [2] as follows equation ( 2): (2)

Tide Model Evaluation Method
Evaluation of the accuracy of the tidal model can be carried out using 2 methods, the analysis of control points in the field (coastal and pelagic tidal constants) and the analysis of the reduction of sea level time series variance from multiple altimetry satellite missions [4].The evaluation method in this research applies control point analysis in the field from bilinear interpolation of tidal constants from the model grid to available tidal reference points to allow the model tidal constants to be evaluated against control values in the field.The evaluation stages are as follows: a) Calculation of the RMS deviation value (Root Mean Square) to determine the error value between the observation data and the tidal model from the harmonic constant [5] for each j constituent of the tidal model according to the formula (3): Where, ℎ1  , ℎ1  , ℎ2  , and ℎ2  are the squares of the in-phase amplitude of the tidal model and the control points in the field at each point i and the constituent j, while N is the number of points where the square of the in-phase tidal amplitude is calculated.
b) Determining RSS (Root Sum of Square) is an indicator that represented the difference between model and ground control, it is used to point out the total effect of n main constituent and to measure the precision of every tidal modal [5] as written in the formula (4): c) Calculating RSSIQ (Root Sum of Squares of the In-phase and Quadrature Amplitudes) is to obtain the various tidal model errors which are evaluated to ground control as produced from calculating the RSS process according to the formula (5): Coefficient Correlation Analysis (R) is used to indicate the strength of the relationship between observation data (xi) and the tidal prediction (yi), where  is the average of the observation data and  is the average of the prediction [6] as shown in the formula (7):

Discrepancy (D) value between BIG model and observational data
Harmonic analysis of the BIG model and the data observation of the tide gauge shows the amplitude and phase from the eight harmonic constants which are M2, K1, S2, O1, P1, N2, K2, dan Q1.Every harmonic constant from each observation data (TS.Barus, TS.Sirombu, and TS.Batahan) is compared to the BIG model, the result is shown in Table 3.1 Table 3.1 shows that there is a difference in the smallest amplitude value, namely the K1 constant between the BIG and TS.Barus models of -0.0077 meters, while the largest amplitude difference is the M2 constant between the BIG and TS.Batahan models of 0.0278 meters.Meanwhile, the smallest phase difference is the K2 constant between the BIG and TS.Barus models of -6.8450 degrees, while the largest difference is the Q1 constant between the BIG and TS.Sirombu models of 10.9800 degrees.The results of the difference values are shown in  Each harmonic constant from the BIG model and observational data on TS.Barus, TS.Sirombu and TS.Batahan is calculated for RMS, RSS, RSSIQ, and Discrepancy (D) according to equations ( 3), ( 4), ( 5), and ( 6) resulting in the values in Table 3.3.The smallest RMS value is the Q1 constant of 0.0039 meters and the largest is the M2 constant of 0.0354 meters.The value of Discrepancy (D) between the BIG model and the three observational data gives a result of 5.5609%, this shows the good reliability of the BIG model in representing sea level height at the three tidal station observation locations.Variations in accuracy are shown from the RMS value of the BIG model and observational data for each tidal constant.The tidal height from the observation data of tidal stations, the majority of which are in coastal areas, is relative because it is affected by the effects of vertical ground movement.Meanwhile, the tidal model is generally built from the contribution of multimission altimetry satellite data that has a good level of accuracy for the ocean area and tidal observation data, so that the resolution of the tidal model affects the extraction of tidal constants [5].

The comparison between raw data and prediction from the BIG model and observational data
Eight (8) harmonic constants from the results of the harmonic analysis are used to calculate tidal predictions for each tidal station for a month in January 2021.The correlation analysis between predictions from the BIG model and predictions from observational data on raw data is shown by the scatter diagram in

Figure 1 . 1 .
Figure 1.1.Research Location: West Coast of North Sumatra Province d) The calculation of Discrepancy Percentage (D), D is directly proportional to the RSS value.A smaller D value indicates a smaller tidal model error rate, whereas a larger D value indicates a larger tidal model error rate, as the following formula (6):

Figure 3 . 1 Figure 3 . 1 .
Figure 3.1.(a) Amplitude differences from the BIG model and observational data, (b) Phase differences from the BIG model and observational data Based on the value of the harmonic constant of the BIG model and the observation data at each station, the calculation of the Formzhal number with equation (2) produces an F value of 0.3715 -0.4106 at TS. Barus, F value of 0.4529 -0.4678 at TS. Batahan and an F value of 0.3428.-0.3773 in TS.Sirombu which shows the type of mixed tide, which is double daily in all locations, as shown in Table3.2

Table 3 . 1 .
The differences in amplitude and phase between HC from the BIG model and observational data

Table 3 . 3 .
[12]Error and Discrepancy (D) values from the BIG model and observational dataEvaluation of the BIG tidal model compared to observational data has been carried out in the Java Ocean.The discrepancy (D) values of the BIG, TPXO7-Atlas, and FES2012 tidal models are 36.6972%,76.6712%,and28.6967%,respectively,indicating that FES2012 has the smallest error.The BIG model is more able to represent sea level predictions than the TPXO7-Atlas global model, but it is still not good when compared to the FES2012 global model[3].The global tidal model has the same tidal trend and is not significantly different from tidal observation data in several locations, including TS. Sabang, TS.Natuna, TS.Marina Ancol, TS.Sendang Biru, TS.Sebatik, TS.Sheet, TS.Makassar, TS.Maritaing, TS.Ternate, TS.Jayapura and TS.Merauke, which is indicated by a positive and strong correlation value close to 1[12].