The Verification Significant Wave Height Technique in Indonesian Waters and Analysis of Low Air Pressure

— A limited number of marine meteorological instruments for making observations in Indonesian waters are problems in verifying the BMKG-OFS model. The satellite altimetry was selected as a verification tool due to its wide measurement range. The verification was carried out by adjusting the coordinates, time, and grid of SWH obtained and orbit of the satellite path from the satellite altimetry to the model and overlaying the models' results as a pattern analysis in July 2018 – June 2019. The next step was a statistical analysis to determine the performance of the model. The analysis obtained 43% maximum SWH formed due to the low-pressure centers in the Pacific Ocean. The remaining spreads across the South China Sea, Indian Ocean, Andaman Sea and the Gulf of Australia. This study revealed that the SWH values from satellites were higher than the model. On every three hourly and monthly bases, the SWH of the bias, RMSE, and correlation coefficient were equivalent. The lowest bias of 0.26 occurred at 9.00 UTC, the lowest RMSE of 0.48 occurred at 21:00 UTC, and the maximum correlation coefficient of 0.82 occurred at 18:00 UTC. Whereas on a monthly scale, the lowest bias and RMSE, and the maximum correlation coefficient occurred in November. Based on these results, the BMKG-OFS model can be used to predict SWH in Indonesian waters. Besides, this verification technique can be an alternative as a new tool to verify maritime weather in the operational of BMKG.


I. INTRODUCTION
Indonesia has a two-thirds area of water and the secondlongest coastline globally, creating the potential resource and risk that change over time [1], [2]. One of the potentials and risks is the Significant Wave Height (SWH). SWH is the mean wave height of one-third of the measured waves [3]. A good SWH observation is carried out on a ship in the middle of the sea through the Voluntary Observing Ships (VOS) program, which has the longest continuity from 1888-present [4]. However, this method is considered inefficient to be done daily, covering a wide range of oceans. Thus, other approaches such as modeling and remote sensing were carried out. Remote sensing in this study refers to the utilization of Satellite altimetry.
Satellite altimetry has been used since the 2008s; the latest use until now is Jason 3, after the termination of Jason-2 on 17 January 2016 [5], [6]. Although there are other satellites such as SARAL and CryoSat-2, Jason 2 is relatively constant in measuring and providing data. Satellite altimetry works by selecting the area underneath based on cycles and passes, producing location data (longitude and latitude) that is not constant over time [7]. Therefore, further processing is required for analysis. It is a challenge to develop a technique for the data generated to be used further.
Another SWH observation method is modeling. A model tends to use a mathematical approach and assumptions in the predictions so that the results tend to be different from reality [8]. In regard to the use of the model, the Marine Meteorological Center (MMC) at the Meteorological, Climatological and Geophysical Agency (BMKG) currently has a marine weather model (OFS-models) implemented since the end of 2016, including the SWH predictions. This model refers to the Wave Watch III (WW3) model, which is a third-generation wave model developed by the National Centers for Environmental Prediction (NCEP), the part of the National Oceanic and Atmospheric Administration (NOAA).
Very few satellite altimetry is currently used as verification tools for the model [9]- [12].
Therefore, a technique is needed in verifying waves between model-derived data and satellite altimetry observations. Research conducted by Appendini et. al. [14] presents a distinctive wave model verification concept compared to the previous techniques. In the study, the modelderived data is compared to the altimetry data that corresponds to the satellite's orbital position. However, its application requires a long way in creating a physical parameters time group as observed from the coordinates of the grid used. It also requires more than one software.
Reflecting upon the two methods above, this study verifies the OFS-SWH model towards the satellite altimetry measurements. By far, there has never been a detailed verification of the OFS model for the whole year. In addition, after the verification data is collected, the time the model provides the best results is not provided. Therefore, this paper presents a recap of the OFS-SWH model's verification towards the satellite altimetry measurements for one full year (i.e., July 2018 -June 2019) and shows the model's time shows its best performance from the statistical analysis.

II. MATERIALS AND METHOD
The verification was carried out July 2018 -June 2019 in the coordinates 90 0 -145 0 east latitude, 15 0 north -15 0 south longitude. The data used are altimetry data retrieved from ftp://eftp.ifremer.fr/, and OFS-model retrieved from http://peta-maritim.bmkg.go.id/ render/. Both require login accessed. The verification is limited to the SWH parameter. The verification method was conducted by adjusting the coordinates and time of the OFS model and satellite data. In general, the adjustment was made by making intervals of coordinates from satellite data to represent the model coordinates. For satellite, time synchronization was done by adjusting to the modeling time format with intervals of 3 hours. The next step was to overlay the OFS model results to find out the similarity in value. Besides, the SWH plotting time series were performed for each satellite path. It is worth noting the altimetry data used was the along-track monomission technique, the combination of Jason 2, Cryosat, and Saral. This technique records all SWH along the satellite path.
Since the altimetry produced non-constant location data every time result from the cycle and pass trajectory, a grid structure is needed. In a grid structure, each coordinate range is given a grid index. This grid-indexing method provides two advantages: faster processing and a better contour for further analysis. In this study, the grid size used was 0.5 0 . After determining the grid values, the coordinates and time adjustment were performed in the following steps:

A. Satellite Coordinate Settings
At this stage, the longitude coordinate system setting uses the equation as follows: with a = lon max − lon min 0.5 (2) n ranges from 0 to a-1. The values of the satellite altimeter coordinate are transformed into a range of values with the equation: lon (n+1) ≤ x < lon (n+2) = n + 1 This method enables a faster and more efficient calculation, especially over large areas. The same method is performed for the latitude.

B. Satellite Data Timing Setting
As previously described, the BMKG-OFS time input is in the interval of 3 hours for all model parameters. Thus, the time adjustment was conducted by setting all satellite measurements at 1.5 hours before and after the main time. This is done to ensure that data from the satellite is following the main time section. After the grouping, each main time was given a sequence number from number 1 to finish, adjusting the full version's main time. This is crucial since the satellite altimetry only records the water's physical parameters without an observation of the land.

C. Grid Settings on the Model
The grid settings in the altimetry data is intended to group the coordinates and data into a particular grid value. The use of the grid in the model adjusts to the grid generated from the altimetry data processing. The model's grid settings are intended to produce smoother images and plot data to be overlapped with the satellite trajectories. The initial grid of BMKG-OFS was 0.0625 0 . It was then interpolated to a new grid of 0.01 0 . The selection of the 0.01 0 value is based on the ability of the computer available for a quick calculation. It is possible to reduce the value of the grid model in order to obtain accurate data ranges and smoother map contours. The interpolation equation is as: where: x and f 1 (x) is the point to be sought through interpolation.
x 0 and f(x 0 ) is the first known data point.
x 1 and f(x 1 ) is the second known data point.

D. Model Data Coordinate Setting
The main principle in this setting is similar to point II-A. However, the calculated number of coordinates adjusts to the time length of the model since the main time is multiplied by 3.

E. Model Data Timing Setting
In the BMKG-OFS system, the SWH data used was updated every 00 UTC and 12 UTC. The distinction between the two lies in the WW3 input with a time difference of 12 hours. In this study, the only data taken is at 00:00 UTC, which provides the forecast for the next 7 days. Thus, eight data observations were sufficient. Each observation was 3 hours, representing one day of observation. The remaining were ignored, for they are the predictions for the next 6 days. The time setting was not performed since the OFS system's data will be compared to the 3 hours intervals.

F. Statistical Analysis
The previous steps resulted in two main SWH data: the SWH data from the altimetry observation and that from the OFS system, which is ready to be overlapped in one map. In the overlapping process, a maximum of eight types of verification contour maps will be produced. The types represent the 3 hour-per-day observation. The results depend on observations of satellite altimetry over Indonesian waters. The next step is a validation performed by statistical analysis through the following equations: where: = BMKG-OFS model output. oi = altimetry measurements. = the mean of BMKG-OFS model output. = the mean of altimetry measurements. Fig. 1 depicts an example of overlapping satellite altimeter SWH with the OFS system in the east and west monsoon. The model-derived data and satellite altimetry data were made similar to the matrix resolution for the overlapping process. The model resolution of 881x481 was adjusted to 3001x5501. The resolution adjustment did not affect the contours produced as the interpolation used was the linear interpolation. The linear interpolation refers to the changes in resolution at one point to be adjusted to the points around it linearly up to the last point. The Indonesian waters in two monsoons were generally calm, with an average wave height below 1 meter. Meanwhile, the wave outside Indonesian waters was higher. The Pacific Ocean is relatively calmer in the east monsoon (Fig. 1a) than the west monsoon (Fig. 1b). Further studies are needed to see the effect of monsoons on the SWH values in Indonesian waters.

A. Altimetry and OFS Model
While the lower panel of Fig. 1a and 1b (graph) presents a time series plot of the model output with satellite observations. The model-derived output was higher than that measured by the altimetry satellite. The high values of the WW3 model are a separate note due to the uncertain factors that influence it. Observed in detail, the plot from satellite observations has highly fluctuated since the observations were made every time; times, the value tended to fluctuate extremely. This is due to the change in the satellite altimetry trajectory measurement (maintaining zero compared to nan).  Appendini et. al. [13] compared the mean of SWH, and standard deviation of altimetry data using the model obtained the same location. However, when the pressure center was low, the maximum SWH value obtained from the altimetry and model showed different locations. In the next subsection, the extreme value distribution of SWH due to the lowpressure center can be obtained from the OFS model and can be detected by the same altimetry trajectory. In addition, the total altimetry trajectory that passes Indonesian waters in July 2018 -June 2019 is presented in Figure 2. It delineates that the total trajectories fluctuate each month, with the most trajectories of 179 in December and the least of 73 in June. Normally altimetry data will be filled every 3 hours in one day. This means that there will be a minimum of 240 trajectories per month. However, this rarely happens since satellite altimetry never crosses at consecutive observations. The calculation results obtained that higher percentage SWH observation satellites are higher when compared to the model results for a weak category (≤ 2 m). However, for the strong category (>2 m) high percentage SWH observation of satellite is lower when compared to the model. This is the absence of territorial divisions based on the bathymetry range because, as is known generally Indonesian waters are shallow, and beyond, it is generally deep (see Fig.  1). The SWH values at the low-pressure centers around Indonesian waters. Throughout 2018, the maximum SWH value detected from the satellite altimetry was 15 meters on 23 November 2018, at 18:00 UTC. On the other hand, the maximum SWH value from OFS-model occurred in lowpressure areas. There are also moments when satellite altimetry crossed just above the low-pressure center, having different SWH observation values ( Table 1). One of the inputs from the OFS-model is the influence of the wind. If there is a cyclone (marked by a low pressure) in an area, the waters traversed by the eye (cyclone) have a much higher SWH value than the surrounding waters [15]. This can be explained by the momentum balance and enthalpy exchange from the ocean's evaporation and then transformed into energy dissipation to form a low pressure in the atmospheric boundary layer [16], [17].
Generally, low-pressure centers are characterized by high SWH in almost evenly manner in each month of 2018. 43% (10 occurrences) of high SWH occurred in the Pacific Ocean waters of the Eastern Philippines. The remaining spreads across the South China Sea, Indian Ocean, Andaman Sea, and Australia's Gulfs. An interesting incident occurred on 02 April 2019, in which a tropical cyclone named Wallace formed around the Northern Waters of Australia (10 0 south latitude) entered the Banda Sea, Indonesia, on 03 April 2019. It then turned back to the south due to the Coriolis force [18]. This cyclone reached its peak on 07 April 2019, marked by a height of 8 meters SWH, then decayed on 09 April 2019 at a southern latitude of 150 with an SWH interval of 3-4 meters. The Wallace cyclone increased the intensity of rainfall in Maluku and surrounding areas, in addition to causing high waves. Data compiled from BMKG shows that on 05 April 2019, moderate-heavy rainfall intensity occurred in Southeast Sulawesi, Nusa Tenggara Timur (NTT), Maluku, and Papua. In comparison, the wave height of 4.0-6.0 meters occurred in southern Rotte Island, Timor Sea of southern NTT, and the Indian Ocean of southern NTT. A tropical low pressure was also formed in the Southern Java Sea on 24 January 2019, at 21:00 UTC. Yet, its power decayed five days later due to insufficient energy.
The tropical cyclone Wallace was still in the safe category because most of its path occurred in the ocean. Conversely, the Cyclone Pabuk that occurred on 1 January 2019 had been affected differently. This cyclone was initially formed in the central South China Sea at southern latitudes 5 0 [19]. It then strengthened and reached the Gulf of Thailand on 2-4 January 2019, with a maximum SWH of 8 meters. In 5 January 2019, at 06:00 UTC, this cyclone crossed mainland Thailand. At 21:00 UTC, the SWH increased to 7 meters and decays on 06 January 2019 in the Andaman Sea on the same day. The tropical cyclones crossing the mainland need special attention since they impact economic losses and damage [20]. Data collected from [21] revealed that Cyclone Pabuk caused rough seas, damage to public facilities, and thousands of people displaced. Referring to research [22], the Northern Hemisphere (NH) has a higher cyclone frequency but with a much lower trend than the Southern Hemisphere (SH). This is because NH has much land as a form of heat exchange with the ocean; it was the main ingredient for cyclone formation. Reference [23] shows in more detail the heat transfer of the sea to the north through the equator contributing to the warming of the NH seas.
Referring to Table 1, the cyclone with the most tremendous damage and loss in this study was the Mangkhut that occurred in the Philippines' western waters with a total economic loss of $3.7 billion and at least 130 fatalities [24]. It affected Indonesia with an increase in rainfall in some areas crossed by the cyclone's tail, such as Sumatra, Java, Kalimantan, to Papua. This cyclone caused waves up to 4 meters in height in Indonesia's eastern and southern waters. The occurrence of tropical cyclones in the hemisphere appears with another month. In the NH is generally form in June to November with a peak in August-September (44%). The SH is from November to April with a peak in January-March (66%). However, there was no trend in the increase in the global number of tropical cyclones from 1985-2014, with around 80 tropical cyclones each year worldwide [25].
To add, Table 1 delineates a satellite altimeter trajectory recorded just above the low-pressure center on 24 November 2018 at 18:00-21:00 UTC. The obtained SWH value for satellite altimetry measurement was in accordance with the model, which was 4.5 meters. Whereas on the second occurrence on 19 January 2019, at 18:00 UTC, the SWH value of the satellite altimetry measurement was 1 meter, while in the model, it was 6 meters. The difference suggests the importance of validation using the altimetry data. The technique is often applied in validating a model [26] or validating it with other observation tools [27]. Besides, Indonesian waters have a relatively low SWH (<1m) compared to their outer waters. This has generally been in accordance with forecasts issued by the Indonesian Marine Meteorological Center, BMKG, except these waters are affected by tropical cyclones.  I  THE RECAPS OF HIGH SWH DUE TO LOW PRESSURE DETECTED BY THE BMKG-OFS MODEL. THE LIGHT GRAY COLOR SHOWS THE SWH ALTIMETER   MEASUREMENTS THAT HIGHER THAN THE MODEL, WHILE THE DARK GRAY COLOR INDICATES THE ALTIMETER MEASUREMENT THAT WAS JUST ABOVE THE LOW-PRESSURE CENTER TO THE MODEL B. Model Performance A cumulative stacked bar graph is presented to find out the performance of the SWH-derived model toward the altimetry data (Fig. 3a). The lowest to highest statistical analyses in a row are bias, RMSE, and correlation coefficient for all observations. The lowest bias of 0.26 occurred at 9:00 UTC; the lowest RMSE of 0.48 occurred at 21:00 UTC, and the highest correlation coefficient of 0.82 was obtained at 18.00 UTC. The smaller the bias value, the better the output of the model. The RMSE values indicate the distance or proximity of the distribution of the model results to satellite observations. The lower the value, the better the results of the model used. While the correlation coefficient describes the closeness of the two results: the greater the value, the closer the relationship. Thus, it can be summarized that bias, RMSE, and correlation do not occur at the same time. This is due to the fluctuation of the SWH value as presented in Table 1. The correlation coefficient of 0.69-0.82 was categorized as moderate until a strong positive relationship [28] explained the diversity of satellite data. In Indonesia, water shows similar results that during one month (January) also resulted in a correlation of 0.69 [29]. The verification recapitulation in July 2018 -June 2019 is presented in Fig. 3b. The lowest to highest statistical analysis results in a row are bias, RMSE, and correlation coefficient for the month. This pattern is exactly the same as the observation time of Fig. 3a. The lowest bias and RMSE occurred in November. In the same month, the highest correlation occurred.  The best combination of statistical analysis was in November. On the contrary, less ideal statistical results occurred in June (Fig. 3b). Compared to the total satellite trajectory (Fig. 2) in the two months, the performance of the model was not affected by the number of trajectories. Thus, the model is said to be quite reliable compared to satellite data. As a comparison, similar results were also conducted on Jason 2 satellite every month [26]. Obtained the mean bias is lower than RMSE, with the mean bias almost equal to zero and RMSE about 0.2-0.4. Furthermore, several recent studies have compared altimetry satellites with various models, such as study [30] comparing the ECMWF IFS (European Centre for Medium-Range Weatyher Forecasts Integrated Forecasting System) model with Cryosat-2 obtained SWH correlation in NE Atlantic and Pacific by 0.98 and 0.95, respectively. In Indonesia, Sulawesi (Celebes) waters especially, also conducted verification with WW3 model against Jason-2 by determining several types of Jason-2 data, namely WIW19, ALES (Adaptive Leading Edge Subwaveform), and SGDR (Gephysical Data Records Sensor) of 0.72, 0.74, and 0.55, respectively [31]. The low correlation in Sulawesi waters is due to low wind speed, which produces low waves and stronger echo intensity than the surrounding area [32].
The further processing results showed the filtering technique resulted in the least difference in coefficient values obtained. The difference was 1/100 from the initial correlation coefficient ranging from 0.68 to 0.81. Besides, the method's application, by ignoring some of the minimum values of SWH, did not show significant differences in RMSE values and correlation coefficient [33]. This means that satellite altimetry is suitable to be used as a real observation of SWH data. However, it does not cover all areas of water in one measurement.

IV. CONCLUSION
This study has successfully verified the OFS-SWH model of satellite altimetry for one the full year (i.e., July 2018 -June 2019). The technique was performed by adjusting the position and time of the altimetry data to the model. The total trajectories fluctuated every month and were obtained with the most trajectories of 179 in December and the lowest of 73 in June. From the whole set of observations, three important pieces of information was obtained: a high SWH is associated with the low-pressure center, a high SWH measurement was detected more through satellite altimetry, and in some cases, satellite altimetry that passes just above the low-pressure center has different SWH value to the model. A total of 17 low-pressure centers (July 2018-June 2019) were formed, in which the Mangkhut tropical cyclone (10 September 2018) had the greatest damage and loss.
The statistical analysis results were analyzed on a three hourly and monthly basis. On the three-hourly basis, the lowest bias 0.26 occurred at 9:00 UTC, the lowest RMSE 0.48 occurred at 21:00 UTC, and the most significant correlation of 0.82 occurs at 18:00 UTC. While on the monthly scale, the lowest bias and RMSE were found in November, and the largest correlation coefficient was in November. In general, these results are not much different from the verification stage carried out every month. In conclusion, this technique can be an alternative as a new tool to verify maritime weather in the operation of BMKG.
ACKNOWLEDGMENT A profound appreciation is addressed to MMC, Pusat Meteorologi Maritim (Pusmetmar), BMKG, Indonesia, and ifremer, France, to offer the data OFS model altimetry respectively so that this research can be completed. We are grateful to the Center for Education and Training, Pusat Pendidikan dan Pelatihan (Pusdiklat) BMKG, Indonesia to fund this research with a scholarship scheme.