Predictive Model for Northern Thailand Rainfall Using Niño Indexes and Sea Surface Height Anomalies in the South China Sea

Abstract

Northern Thailand rainfall (NTR) plays a crucial role in supplying surface water resources for downstream regions that millions of Thais rely on. The NTR has been reported to be adversely affected by the recent climate change making it impossible to accurately predict rainfall for better water management. In this work, we attempt to find an indicator that can be used to predict monthly NTR using an oceanic index based on sea surface height anomaly (SSHA) called the South China Sea Index (SCSI). First, we investigate the lead-lag relationships between NTR and several well-known indices. Relationships of NTR-Niño1+2 and NTR-Niño3 appear to be relatively strong. We then perform empirical orthogonal function (EOF) analysis on SSHA in the South China Sea and observe that the 2nd principal component (PC) time series and NTR strongly correlate. However, direct use of PC time series is computationally costly. Instead, we use SSHA information relating to the second EOF mode to create SCSI without performing EOF analysis. The correlation of SCSI-NTR is negatively strong. Lastly, we forecast NTR using SARIMAX models with Niño1+2, Niño3, and SCSI as inputs. The best model was SARIMAX (1, 0, 1)(0, 0, 2)12 using SCSI and Nino3 as inputs with AIC = 2368.705, RMSE = 51.167 mm per month and $R^2$ = 0.732. Result raises capacity for effective climate change-related planning and management in the area.

1. Introduction

Thailand is in the Southeast Asia region, located in between the Pacific and Indian Oceans. A variety of agricultural products such as rice, vegetables, fruits, and meat products are exported to other countries; thus, Thailand is known as the kitchen of the world. The ability to maintain the exportation of these products has faced risks from climate variability. Rainfall in northern Thailand plays a significant role in supplying water to agricultural areas in the northern and central regions. Reliable rainfall prediction is thus a matter of great concern because it would help plan the planting period well in advance.

In recent years, scientists have monitored oceanic and atmospheric patterns to study climate change. Drought and heavy rainfall may be influenced by major phenomena reflecting global teleconnection changes, such as the El Niño-Southern Oscillation (ENSO) and Walker circulation [1]. Many researchers have great interest in studying relationships or impacts of oceanic indices related to sea surface temperature (SST) on rainfall in various regions. Studies of rainfall influenced by Niño SST kinds such as Niño1+2, Niño3, Niño3.4, Niño4, the Oceanic Niño Index (ONI) and the Multivariate ENSO Index (MEI) were investigated in [2,3,4,5,6] for example. In [4], the impacts of El Niño on East Asian monsoon rainfall over six decades (1957–2016) have been investigated. The estimation of rainfall using lagged Niño was studied in [6]. A study by Bazo et al. [7] found that the Dipole Mode Index (DMI) has a strong influence on rainfall variability in northwest Peru. In 2009, Geethalakshmi et al. [8] discovered that the correlation between the northeast monsoon rainfall in the Indian Ocean area and the DMI was much weaker than ENSO. Different effects of El Niño and IOD on China’s rainfall were studied by [9]. Another well-known index which is an atmospheric index based on sea level pressure differences between Tahiti and Darwin called the Southern Oscillation Index (SOI). SOI is used as a key feature for monitoring ENSO events. Several researchers studied the responses of rainfall in various places due to the SOI effect [10,11,12,13]. However, studies on the relationships between these ENSO-related indices and rainfall in Thailand are few and most results are locally short [5,14,15,16,17].

According to the literature, the impacts of well-known indices on rainfall vary from time to time and from place to place. To have a better prediction of rainfall, various indices that have a high impact on local rainfall have been introduced especially near the equatorial regions. Thus, this region is one of the hottest regions and has many oceanic-atmospheric activities forming within the region including many unpredictable storms. There are several studies focused on the effect of equatorial Indian Ocean oscillation (EQUINOO) on rainfall [18,19,20,21]. The study of [20] developed new indexes by incorporating equatorial zonal wind index with Niño indices to improve rainfall prediction accuracy. In 2015, Surendran et al. [21] investigated connections between the Indian summer monsoon and a composite index of ENSO and EQUINOO, then applied the composite index to forecast the Indian summer monsoon. The study of a new index on the equatorial region by Ji et al. [22] analyzed the effect of SST anomalies in different seasons on the rainfall of coastal areas of eastern China. They found that SST indices related to Niño1+2, Niño3 and IOD are highly linked with precipitation in the coastal regions of eastern China when SST indices lead for 2 to 4 months.

It is known that anomalous winds can force Kelvin and Rossby waves, which are key mechanisms of ocean circulation and climate variability in the ocean [23]. In a normal state, sea level pressure over the western Pacific is lower than that in the east. This pressure difference causes the trade winds to blow from east to the west in the equatorial Pacific [1,24]. Note, that propagations of the Kelvin and Rossby waves can be observed in SSH variation [25,26,27]. However, patterns of SSH and SST anomalies do not replicate each other because SST anomaly is related to heat exchanges between the ocean and atmosphere, but SSHA represents the density change in the water column, which is related to both salinity and temperature changes [25].

The use of SSH variability enables researchers to understand changes in the ocean caused by Kelvin waves, and Rossby waves. These two waves carry subsurface heat content affecting changes in SST. Several studies related to sea level changes have been investigated in various aspects such as anomalous events over the Indian Ocean [24,26,28], Asian monsoons [25,29], eddy evolution [27] and heat flux globally [30]. In 1997, Chambers et al. [30] estimated ocean heat storage using TOPEX altimeter data. In 1999, Chambers et al. [24] used information on wind anomalies, SST, and SSH to study the development of major El Niño events in 1994 and 1997–1998. This study found that the wind anomalies were found to be well correlated with the sea level variations in both the Pacific and Indian Oceans. Furthermore, prior to the peak of El Niño, the Kelvin waves appear to deepen the thermocline in the eastern Pacific and help advect warm water eastward along the equator below the surface, while denser and colder water accumulates in the west Pacific. Later, Gera et al. [25] analyzed the changes in SSH and SST anomalies to understand the changes in upper ocean heat content due to the effects of Kelvin and Rossby waves during the strong/weak monsoons in the Indian Ocean. Years with strong monsoon mostly result in a high amount of rainfall in the Indian continent, while the opposite results for weak monsoon years. This study found that the SSH-SST anomalies were well correlated during the summer monsoon season over most parts of the north Indian Ocean including the west central equatorial Indian Ocean, south central Indian Ocean, and the Bay of Bengal. Additionally, they observed that there is much convection in these regions. The study inferred that both SSH and SST anomalies over these regions have strongly affected rainfall over central India. Recently, Albert et al. [26] used ocean heat content derived from oceanic-atmospheric factors to study possible causes and mechanisms of warming trends in the Arabian Sea. With SSH observations, they found a downwelling Kelvin wave leading to the warming in the eastern Arabian Sea, while the deepening of thermocline associating with the Rossby wave led to the warming in the southern Arabian Sea, while Trott and Subrahmanyam [27] used SSHA to observe the evolutions of eddies associating with the propagations of Rossby and Kelvin waves.

Not only is the South China Sea a jigsaw transporting warm water between the Pacific and Indian Oceans [31], but it is also an important passage for storms and typhoons originating in Pacific areas, contributing rainfall to the East Asia and Southeast Asia regions including the northern Thailand. This suggests that oceanic variability in the South China Sea may play an important role in affecting climate variability in Thailand. Based on the above discussion on SSH variations and their effects on air-sea interactions, SSH could be a potential candidate as a predictor for the NTR. Thus, in this study, we will investigate SSH variability within the South China Sea and its connection to the NTR from 1993 to 2021. Then, we will investigate the performance of SARIMAX models to predict the NTR with the combination of some well-known oceanic-atmospheric indices and a new time series related to SSH. Results will lead to a better understanding of rainfall variability in northern Thailand. This article describes the data sources in Section 2 and introduces important techniques in Section 3. Section 4 is devoted to the results and discussion. The summary is given in Section 5.

2. Data

To investigate the relationships between oceanic indices and rainfall in northern Thailand, the following data sets are used in this study.

1.

We acquired the monthly data of the well-known atmospheric and oceanic indices, including Niño1+2, Niño3, Niño3.4, Niño4, ONI, SOI and DMI from the period of January 1993 to December 2022. These data can be obtained from the National Oceanic and Atmospheric Administration (NOAA), Boulder, CO, USA. (https://psl.noaa.gov/data/climateindices/list/accessed on 1 March 2022).

2.

Daily rainfall from 28 stations in northern Thailand (see Figure 1) from January 1993 to December 2021 are obtained from the Thai Meteorological Department. The daily rainfall data from all stations are combined into monthly rainfall to represent the NTR.

3.

SSH data set from January 1993 to December 2022 with a horizontal resolution of 0.25° × 0.25° are available from the E.U. Copernicus Marine Service Information; (https://doi.org/10.48670/moi-00148 accessed on 31 January 2023). We acquire daily SSH data in the area covering the Gulf of Thailand and the South China Sea (97°–123° E and 1°–25.5° N) to investigate a possible link between sea surface height variability with rainfall.

Notice that the availability of rainfall data is limited, while the other data sets are easily accessed. Thus, in this study, we will use the information from SSH and other indices as inputs to forecast rainfall in the year 2022.

3. Methods

Techniques used in this study are the EOF analysis for extracting dominant information of SSH and SARIMAX for predicting the NTR. In addition, the Pearson correlation is another important tool used for determining the relationship between any couple of variables. Lastly, the Akaike information criterion (AIC) is used as a tool for choosing a suitable model. The following are brief summaries of the methods.

1.

The EOF technique is commonly used to analyze data in geophysics [24,32,33,34,35,36]. Here, we prepare the SSH data matrix, then SSHA is computed by removing the longtime mean of SSH from the SSH data matrix. Finally, we perform EOF analysis to obtain the dominant patterns of SSHA variability and their corresponding principal components (PCs) based on eigenvalue decomposition of covariance matrix using MATLAB software version 2018a.

2.

The SARIMAX model is a popular statistical model used for analyzing and forecasting time series data that combines an autoregressive integrated moving average (ARIMA) with seasonal components and the effect of exogenous variables in the model [37,38,39]. In this study, we use statsmodels library for python code which is available at: (https://www.statsmodels.org/dev/generated/statsmodels.tsa.statespace.sarimax.SARIMAX.html). The SARIMAX model is represented by SARIMAX $(p,d,q){(P,D,Q)}_s$, where p denotes the order of the autoregressive (AR) component, d denotes the order of differencing required to make stationarity in the data, and q denotes the order of the moving average (MA) components; while $P,D,Q$ are similar to $p,d,q$ but for the seasonal component and s denotes the number of time periods in a season. The general SARIMAX model can be written as [37,39]

$$\begin{array}{cc}\hfill y_t=& {\beta }_0+{\beta }_1{X}_{1,t}+{\beta }_2{X}_{2,t}+\cdots +{\beta }_k{X}_{k,t}\hfill \\ \hfill & +{\displaystyle \frac{(1-{\theta }_{1}B-{\theta }_2{B}^2-\cdots -{\theta }_q{B}^q)(1-{\Theta }_1{B}^s-{\Theta }_2{B}^{2s}-\cdots -{\Theta }_Q{B}^{Qs})}{(1-{\varphi }_{1}B-{\varphi }_2{B}^2-\cdots -{\varphi }_p{B}^p)(1-{\Phi }_1{B}^s-{\Phi }_2{B}^{2s}-\cdots -{\Phi }_P{B}^{Ps})}}{\epsilon }_t\hfill \end{array}$$

(1)

3.

The Pearson correlation coefficient is one of the common measures for detecting the degree of association between two variables. The value of the correlation coefficient sits in the range of showing the strength and direction of the relationship, which can be either negative or positive. The range division of the correlation coefficient adapted from [40] is shown in Figure 2.

4.

The AIC is asymptotically efficient and a biased estimator of the discrepancy between all candidate models and the true model [41]. Because of its ability to balance the trade-off between model fit and complexity, it is commonly used to identify the most appropriate and parsimonious model for a given set of data. Typically, the model with the lowest AIC is selected.

4. Result and Discussion

4.1. Rainfall and Oceanic Indices

Our preliminary investigation of rainfall data from 1993 to 2021 shows that the monthly average NTR over 28 rainfall stations is 112.1 mm. Figure 3 reveals that the monthly average rainfall from May to October is higher-than-average, which mainly corresponds to the wet season (JJAS) while the transition periods in the May months have more rainfall than the October months on average. As expected, the monthly average rainfall of the other months (summer and winter) is lower than average.

We next investigate the relationships between NTR and the following oceanic indices, including Niño indices, ONI, SOI and DMI during the period of 1993–2021 using Pearson correlations [42]. The correlation coefficient values are listed in

Table 1. Correlation coefficients between the NTR and oceanic/atmospheric indices.

Index Leads NTR (Month)	Niño1+2	Niño3	Niño3.4	Niño4	ONI	SOI	DMI
2	0.247 **	0.424 **	0.322 **	0.063	$-0.064$	0.045	$-0.034$
3	0.549 **	0.557 **	0.299 **	$-0.053$	$-0.077$	0.071	$-0.061$
4	0.694 **	0.524 **	0.169 **	$-0.186$ **	$-0.088$	0.091	$-0.099$

** Significant at 0.01 level.

. Results indicate that NTR and Niño1+2 have a relatively strong correlation value of 0.694 with the Niño1+2 index leading rainfall by 4 months and a moderate correlation of 0.557 when the Niño3 index leads rainfall by 3 months, which are found to be significant with p-value < 0.01. While the other correlations are weak. Figure 4 reveals relationship among the Niño1+2, Niño3 and NTR. One can notice that both Niño1+2 and Niño3 indices and the NTR show an annual cycle. The above results support our decision to perform further investigation on the effect of Niño1+2 and Niño3 on the amount of NTR in Section 4.5. Note, that these two variables were used as the main factors to study the relationships or variabilities of rainfall in China [22], Thailand [43] and India [44].

4.2. EOF of SSHA

The EOF analysis is applied to extract the dominant patterns of SSHA variability in the South China Sea. Figure 5 and Figure 6 reveal the six highest orthogonal modes and their associated PCs of SSHA. Combining these six modes, it contains 83.55% of the total variance, with modes 1–6 explaining 41.50%, 28.52%, 5.73%, 3.76%, 2.71% and 1.33% of the total variance, respectively. Each mode has distinct characteristics, as shown in Figure 5.

The first mode exhibits a monopole pattern showing one dominant region at the center of the South China Sea. The second mode reveals a significant feature in the South China Sea variability with two alternative signs of high and low SSHA pools. One pool is located near the west coast of the Philippines (115°–120.25° E and 15°–20° N) and another pool is located in the Gulf of Thailand (49°–105° E and 5°–14° N). The third mode shows three alternative dominant oscillations in the north-south direction of the South China Sea. The fourth mode shows one dominant pattern in the northeastern to southwestern direction. The fifth mode shows alternative pools in the area of eastern Vietnam and the north of Borneo Island, Celebes and Sulu Seas. The variability shown in the sixth mode shows north-south alternative characteristics. Note, that the physical characteristics of these features related to SSHA in the South China Sea are unknown and would be an interesting topic to study in the future.

PC time series associated with the EOF patterns of SSHA are plotted in Figure 6. These PCs capture the fluctuation of dominant patterns of the SSHA in the South China Sea at different locations and time periods. PC1, PC2 and PC3 are associated with annual variabilities with an increasing trend for PC1. To describe the association between these PCs and NTR, we examine Pearson’s correlation coefficients and obtain the results listed in

Table 2. Correlation coefficients between the PC time series and NTR.

	PC1	PC2	PC3	PC4	PC5	PC6
NTR	$-0.040$	$-0.820$ **	0.259 **	0.044	0.047	$-0.073$

** Significant at 0.01 level.

. Results show that the correlations of NTR-PC2 and NTR-PC3 are statistically significant; while only PC2 has a very strong link to the NTR with an anti-correlation value of $-0.820$. Note, that the other links to NTR are weak or very weak. Thus, the PC2 could be another potential input used to predict the NTR in our study.

4.3. South China Sea Index

The direct use of PC2 to predict rainfall in northern Thailand is time-consuming since obtaining the most up-to-date PCs requires performing a new EOF analysis once new data are available. To cope with this problem, we use the observed SSHA within the dominant regions seen in the second EOF pattern (as boxed in Figure 7). Region A is in the Gulf of Thailand, covering 115°–120.25° E and 15°–20° N and Region B is east of the Philippines, covering 49°–105° E and 5°–14° N. Using these SSHA information, it is possible to obtain a time series similar to PC2 time series. To do so, we adapt the formulation of the SOI index to propose a new oceanic index as described in Algorithm 1.

Algorithm 1: South China Sea Index Procedure

Define $X_A,X_B$ as the monthly averages of SSHA within regions A and B. Compute the pooled variance, $S_p^2$, based on the idea of [45], over the longtime period (1993–2022) for regions A and B by: $$\begin{array}{cc}\hfill S_p^2& ={\displaystyle \frac{(n_A-1)S_A^2+(n_B-1)S_B^2}{n_A+n_B-2}}\hfill \end{array}$$ (2) where $n_A,n_B$ are numbers of the data in regions A and B and $S_A^2,S_B^2$ are variances within regions A and B. Compute the monthly difference between $X_A$ and $X_B$ defined as $D_{AB}$ by $$\begin{array}{c}\hfill D_{AB}=X_A-X_B.\end{array}$$ (3) Define the South China Sea Index, shorted by SCSI as $$\begin{array}{cc}\hfill \mathrm{SCSI}& ={\displaystyle \frac{D_{AB}-\overline{D_{AB}}}{S_p^2}}\hfill \end{array}$$ (4) where $\overline{D_{AB}}$ is the average of $D_{AB}$.

The comparison between SCSI and PC2 is shown in Figure 8. One can observe that these two time series are in-phase with a very strong correlation value of 0.978 (p-value < 0.01). However, most of the peaks of SCSI are larger in magnitude compared to those of PC2. This means that using the proposed SCSI to study the relationship with NTR could provide similar results when PC2 is used. The advantage of using SCSI instead of PC2 is that we do not need to perform EOF analysis on the updated SSHA data.

4.4. Relationship between NTR and SCSI

To have a better visualization of the relationship between rainfall and SCSI, we standardize the NTR data by shifting its longtime mean (112.1 mm per month) to zero. The relationship between NTR anomaly and SCSI clearly shows a significantly negative correlation, as seen in Figure 9, with an anti-correlation value of $-0.842$. That means when the SCSI is positive (negative), the rainfall anomaly is lower (higher)-than average.

It is worth noting that there are about 7.18% of the total months that SCSI and NTR anomalies are in phase. About 5.4% of negative SCSI values with lower-than-average NTR are found in March (2009), April (2001, 2009, 2012, 2013, 2014), May (1997, 2003, 2005, 2010, 2020, 2021) and October (1993, 1995, 1998, 2002, 2005, 2013, 2020). While positive SCSI values with higher-than-average NTR of about 1.7% occur in April (2011, 2018), May (2002), and October (2011, 2014, 2018). One can notice that most of these in-phase events occur during transition periods in which the SCSI changes from positive (negative) to negative (positive) in the following month. This allows us to use the information of positive (or negative) of SCSI as an indicator to determine whether the (non-transition) months would have less (or more) rainfall in the north of Thailand than the longtime average.

In order to see the efficiency of using SCSI, the seasonal relationships between the NTR anomaly and SCSI are displayed in Figure 10. During the monsoon season (JJAS), all SCSI are negative with higher-than-average NTR in most months except for three months (about 2.58%) in June 1993, 1997 and 2019. In these three months, the assumption fails; i.e., having negative SCSI values with NTR below the average falling within $-0.5$ to $+0$ SD. Typically, there is an average of 204.9 mm per month in July but in these months turns out to have less than 112.1 mm per month. Referring to the history of ENSO events, it is evident that June 1997 and June 2019 correspond to periods reflecting very strong El Niño and weak El Niño events, respectively. As for June 1993, it is possible that there may be affected from the dry spells or other meteorological factors at play.

During the off-monsoon season (NDJFMA), as expected, most SCSI (about 92.5%) are positive with lower-than-average NTR. There are 8 out of 174 months (about 4.59%), showing in-phase between SCSI and NTR anomaly. Considering the in-phase month, one can observe that mostly occurred in April. With 7 out of 29 (24.1%) of April months, NTR are higher-than-average rainfall. Typically, during April, northern Thailand should experience little to no rain, yet it turns out to have more rainfall than average in these seven months which were consistent with strong La Niña events (1999, 2000, 2008), moderate La Niña (2011, 2021) and weak La Niña (2018). It is worth pointing out that only one month in April 2021 with negative SCSI has a significantly higher amount of the NTR than the average (almost $+1$ SD).

For the two-month transition periods (May and October), most of the SCSI in May months (22 out of 29 months or about 75.86%) are negative with higher-than-average NTR, while 6 out of 29 months of May (20.68%) have lower-than-average NTR. These situations are consistent with the onset of monsoon season in those periods with mostly high amounts of rainfall. While SCSI values in October months (blue dots) are randomly distributed with the NTR lying within $\pm 1$ SD from the average. Note, that about half of the October months received lower-than-average NTR. This reflects the transition from the wet season to the dry/cold season in northern Thailand.

In summary, most SCSI values and the NTR anomaly are out-of-phase in most months (92.82%) which gives information on which month have less or more rainfall than average. In the next section, we will predict the NTR using information on NTR-related indices including SCSI (very strong correlation with no lag), Niño1+2 (strong correlation with 4-month leading the NTR), and Niño3 (moderate correlation with 3-month leading the NTR).

4.5. SARIMAX Model for Rainfall

In this section, we investigate the performance of SARIMAX models for predicting the NTR based on information on NTR, Niño1+2, Niño3, and SCSI. We estimate the parameters of the models using a 70/30 data-splitting approach by using data from January 1993 to December 2013 as a training model. The remaining 30% of data over the period of January 2014 to December 2021 are used to validate the model. We first decompose the rainfall data, using a naive decomposition with an additive option, into three components, namely trend, seasonal (with a period of 12 months) and residual values (see Figure 11). Note, alternative decomposition techniques such as variational mode decomposition or empirical mode decomposition can also be used [46]. From the figure, there is no clear evidence of the trend of the rainfall data, but the seasonal pattern is clearly detected. As a result, the choice of using the SARIMAX model to forecast the NTR time series is feasible. Based on the links between the NTR and oceanic indices discussed above, we consider SCSI without lag, the 3- and 4-month earlier information of Niño3 and Niño1+2 as exogenous inputs in six different SARIMAX models. Models 1 to 3 predict NTR using one exogenous input, say SCSI, Niño1+2, and Niño3, respectively. Models 4 and 5 use two inputs (SCSI and Niño1+2, SCSI and Niño3); while Model 6 uses SCSI, Niño1+2, and Niño3 as inputs.

To obtain suitable parameters in each model, a grid search approach has been conducted on 729 different combinations of nonseasonal $(p,d,q)$ and seasonal $(P,D,Q)$ parameters. These parameters have been chosen from the set of {0, 1, 2}. The seasonal parameter of each model is set to $s=12$ for representing yearly patterns. To choose the best model, we adopt the decision based on the AIC that the smaller AIC is, the better the model’s ability to predict rainfall [47]. The model with lower AIC value is noticeably superior than the model with smaller AIC value when the difference of AIC value is more than 10 [48].

Sets of parameters, along with the AIC values for all models, are listed in

Table 3. Lowest AIC values and corresponding seasonal and non-seasonal parameters.

Model	Exogenous Variables	$(\mathit{p},\mathit{d},\mathit{q})$	${(\mathit{P},\mathit{D},\mathit{Q})}_{\mathit{s}}$	AIC
1	SCSI	$(1,0,1)$	${(2,0,2)}_{12}$	2377.958
2	Niño1+2	$(2,0,2)$	${(0,0,2)}_{12}$	2389.556
3	Niño3	$(2,0,2)$	${(0,0,2)}_{12}$	2385.593
4	SCSI, Niño1+2	$(1,0,1)$	${(2,0,0)}_{12}$	2370.196
5	SCSI, Niño3	$(1,0,1)$	${(0,0,2)}_{12}$	2368.705
6	SCSI, Niño1+2, Niño3	$(0,1,2)$	${(1,0,1)}_{12}$	2468.943

. Results show that among SARIMAX with one exogenous input model, Model 1 using only SCSI as input gives the smallest AIC, while Model 2 using only Niño1+2 as an input has the highest AIC value. Comparing all models, Model 5 using a combination of SCSI and Niño3 yields the lowest AIC value (2368.705), while Model 6 using all three features as exogenous inputs yields the largest AIC value (2468.943) compared to the other models. In this study, based on AIC criteria, we choose Model 5 represented by SARIMAX $(1,0,1){(0,0,2)}_{12}$ as a predicting model for the NTR. The estimated coefficients of Model 5 are given in

Table 4. Estimated coefficients of Model 5 and its standard errors and p-values.

Term	Coefficient	Standard Error	p-Value
SCSI	−59.438	5.037	0.000
Niño3	4.027	0.458	0.000
AR(1)	0.868	0.087	0.000
MA(1)	−0.752	0.115	0.000
SMA(1)	0.237	0.073	0.001
SMA(2)	0.331	0.073	0.000

, where all the coefficients are significant with p-value < 0.05. The prediction model for NTR is in the form:

$$\begin{array}{c}\hfill \mathrm{Rain}\left(t\right)=-59.438\left(\mathrm{SCSI}\left(t\right)\right)+4.027\left(\mathrm{Ni}ñ\mathrm{o}3(t-3)\right)+{\displaystyle \frac{(1+0.752B)(1-0.237B^{12}-0.331B^{24})}{1-0.868B}}{\epsilon }_t,\end{array}$$

(5)

where Rain$\left(t\right)$ denotes the value of NTR at time t, SCSI$\left(t\right)$ denotes observations of the SCSI at time t, Niño3$(t-3)$ denotes the 3-month earlier information of Niño3. The estimated values of $-59.438$ and 4.027 are the coefficients of the SCSI and Niño3 indices, respectively. The autoregressive term, AR(1), is estimated to be 0.868. The moving average term, MA(1), is estimated to be $-0.752$ and the coefficients of the second-order seasonal moving averages are 0.237 and 0.331, respectively. $B^s$ denotes the backshift operator such that $B^s{y}_t=y_{t-s}$ and ${\epsilon }_t$ stand for error terms of prediction. Based on the forecast NTR model in (5), when keeping other factors the same, but increasing SCSI by one unit, it causes NTR to reduce by about 59 mm per month, while an increase of Niño3 three months earlier would cause NTR to increase by 4 mm per month. These interpretations are consistent with the previously observed negative correlation of NTR-SCSI and positive correlation of NTR-Niño3.

4.6. Forecasting Rainfall

Using Model 5 for validating the NTR requires 3-month early information on Niño3 and the present value of SCSI. Thus, we can estimate the NTR over the period of April 1993 to January 2014 (training period). Observed NTR and the estimated results of Model 5 are compared in Figure 12. During this training period, Model 5 had an RMSE of 51.167 mm per month with a strong correlation of $R^2=0.732$. NTR estimation from Model 5 can capture the seasonal pattern of NTR but mostly underestimates the peaks of NTR during the monsoon seasons except in years 1998, 2007, 2008 and 2012, when NTR is overestimated. One may notice that there are some unrealistic NTR estimations (below zero) that commonly occur when time series methods are used.

Next, we use Model 5 with its coefficients to validate NTR over the period of January 2014 to December 2021, then we extend the use of Model 5 to predict the NTR for the period of January–December 2022 (forecast period). The validated and forecast NTR are overlaid with a 95% confidence interval. Results are shown in Figure 13. The validation result provides an RMSE of 59.422 mm per month with a strong correlation value of $R^2=0.675$. Note, that the validated RMSE is slightly higher than the training period (51.167 mm per month) as expected. This implies that the Model 5 in Equation (5) is not overfitting. Moreover, the model can replicate the seasonal pattern of the NTR during the validation period but mostly underestimates the observed rainfall except in the years 2019–2020, when the model overestimates the NTR.

5. Conclusions

In this study, we perform a preliminary investigation of the relationship between the NTR and some of the well-known oceanic and atmospheric indices related to SST and sea level pressure that are commonly used as predictors to study climate variability in various regions. Results reveal that the well-known indices with the largest links to the NTR are the 4- and 3-month leading information of Niño1+2 and Niño3, respectively. These two indices have relatively strong correlations, while the others are weak. We further study by doubting that it may have another oceanic variability affecting the rainfall in northern Thailand. With past research, it is well-known that SSHA can be used to track the propagations of Rossby and Kelvin waves and also observe geostrophic currents. These oceanic variabilities are connected to upper ocean heat content and oceanic heat circulation. Therefore, we further investigate the effect of SSHA in the South China Sea, where there is a significant passage of storms affecting Thailand. First, we perform EOF analysis on SSH data in the South China Sea, with temporal covering from January 1993 to December 2022. Results show that the second mode of the PC time series has the highest correlation to the NTR with its anti-correlation value of $-0.820$. The link between SSHA and NTR is stronger than the correlations of the well-known indices. Thus, SSHA variability in the South China Sea has a potential link to the NTR. Similar results from [25] also support our finding that signals of SSHA have a strong effect on the monsoons in India.

However, using PC2 time series to estimate NTR requires EOF analysis once new SSH data becomes available. Instead, we use SSHA within the dominant regions covering the area east of the Philippines and the Gulf of Thailand observed in the second mode of EOF as a new oceanic index called SCSI which yields a time series with a similar pattern as in PC2. The procedure for obtaining SCSI is in Algorithm 1. Connections between the NTR anomaly and SCSI are significantly negatively correlated, with a coefficient of $-0.842$. In most months, 93%, negative (positive) SCSI could characterize a higher (lower)-than-average NTR. For the remaining 7%, the SCSI and NTR anomalies are in-phase, which may be due to the sudden changes in climate.

Lastly, we combine the lag-free SCSI and 4-month leading of the Niño3 index as exogenous inputs for the SARIMAX model to forecast the NTR. A suitable model for predicting the NTR is SARIMAX $(1,0,1){(0,0,2)}_{12}$ model as described in Equation (5). The model has an RMSE of 51.167 mm per month with $R^2=0.732$ in training and RMSE = 59.422 mm per month with $R^2=0.675$ in testing. The coefficients associated with the exogenous variables can provide insights into the impact of these factors on NTR. Specifically, an increase of 1 unit in the lag-free SCSI would yield an instantaneous decrease in rainfall of 59.438 mm per month, while an increase of 1 unit in Niño3 of that month would be associated with an increase of rainfall in the next 3 months by 4.027 mm per month.

It is worth noting that using AIC, RMSE and $R^2$ values tend to overfit data. Thus, the result of the short-term forecasting is preferred to long-term forecasting which may be considered as a limitation of using our research result. In addition, RMSE is sensitive to outliers. The use of the RMSE is based on the sample size and the normal distribution which is the probability of the occurrence of outliers [41]. Thus, the current study should be reanalyzed from time to time so that the model prediction is updated. Note, that rainfall in Thailand is also influenced by moisture carrying from the southwest monsoon in summer passing through the Indian Ocean. Therefore, a similar study based on oceanic information within the Indian Ocean is currently under our ongoing investigation. The combination of SCSI and new information as well as other decomposition techniques may lead to better estimation of Thailand rainfall. Although this study is based only on statistical artificial facts rather than physical results, the model can still be used to predict the NTR using SCSI which is based on SSHA information.

The water management in Thailand heavily relies on the state of ENSO (El Niño/La Niña event) which are interannual oscillation events. The use of radar can provide information on rainfall within 10–30 min in the regions covered by the radar. There is a gap in how much rainfall would have in a particular region during the intraseasonal period. This proposed SCSI and the prediction model could be new and important tools to fill in this gap. The results of the current study will provide information on how severe the intraseasonal events would affect the water system in the northern Thailand area. The prediction can provide information to farmers for planning their cultivation, or the Thai Government’s authorities can use this information for water management in northern Thailand and downstream regions.